a lady grows broccoli in her garden that is in the shape of a square . each broccoli takes 1 square foot of area in her garden . this year , she has increased her output by 79 broccoli when compared to last year . the shape of the area used for growing the broccoli has remained a square in both these years . how many broccoli did she produce this year ?

Explanation: explanatory answer the shape of the area used for growing broccoli has remained a square in both the years . let the side of the square area used for growing broccoli this year be x ft . therefore , the area of the ground used for cultivation this year = x 2 sq . ft . let the side of the square area used for growing broccoli last year be y ft . therefore , the area of the ground used for cultivation last year = y 2 sq . ft . as the number of broccoli grown has increased by 79 , the area would have increased by 79 sq ft because each broccoli takes 1 sq ft space . hence , x 2 - y 2 = 79 ( x + y ) ( x - y ) = 79 . 79 is a prime number and hence it will have only two factors . i . e . , 79 and 1 . therefore , 79 can be expressed as product of 2 numbers in only way = 79 * 1 i . e . , ( x + y ) ( x - y ) = 79 * 1 so , ( x + y ) should be 79 and ( x - y ) should be 1 . solving the two equations we get x = 40 and y = 39 . therefore , number of broccoli produced this year = x 2 = 402 = 1600 . alternative approach : use answer choices the area in both the years are squares of two numbers . that rules out choice b , c and d . as 1500,1650 and 1700 are not the square of any number . check choice a : if this year ' s produce is 1600 , last year ' s produce would have been 1600 - 79 = 1521 1521 is the square of 39 . so , 1600 is the answer . choice a

power(divide(add(79, 1), const_2), const_2)

<gadget id="calculator">79 + 1</gadget>
<output>80</output>
<gadget id="calculator">80 / 2</gadget>
<output>40</output>
<gadget id="calculator">40 ** 2</gadget>
<output>1_600</output>
<result>1_600</result>


a train 120 m long is running at 60 kmph . in how much time will it pass a platform 240 m long ?

Explanation: distance travelled = 120 + 240 m = 360 m speed = 60 * 5 / 8 = 50 / 3 m time = 360 * 3 / 50 = 21.6 seconds answer : c .

<gadget id="calculator">120 + 240</gadget>
<output>360</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">60 * (5/18)</gadget>
<output>50/3 = around 16.666667</output>
<gadget id="calculator">360 / (50/3)</gadget>
<output>108/5 = around 21.6</output>
<result>108/5 = around 21.6</result>


a is twice as good a workman as b and together they complete a work in 12 days . in how many days a alone can do the work ?

Explanation: a ’ s one day ’ s work : b ’ s one day ’ s work = 2 : 1 ( a + b ) ’ s one day ’ s work = 1 / 12 b ’ s one day ’ s work = 1 / 12 * 1 / 3 = 1 / 36 b alone can do the work in 36 days answer : e

<gadget id="calculator">1 + 2</gadget>
<output>3</output>
<gadget id="calculator">3 * 12</gadget>
<output>36</output>
<result>36</result>


10 women can complete a work in 5 days and 10 children take 10 days to complete the work . how many days will 5 women and 10 children take to complete the work ?

Explanation: "1 women ' s 1 day work = 1 / 50 1 child ' s 1 day work = 1 / 100 ( 5 women + 10 children ) ' s 1 day work = ( 5 / 50 + 10 / 100 ) = 1 / 5 5 women and 10 children will complete the work in 5 days . b"

inverse(add(divide(5, multiply(10, 5)), divide(10, multiply(10, 10))))

<gadget id="calculator">10 * 5</gadget>
<output>50</output>
<gadget id="calculator">5 / 50</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">10 * 10</gadget>
<output>100</output>
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/10) + (1/10)</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 / (1/5)</gadget>
<output>5</output>
<result>5</result>


if p # q denotes the least common multiple of p and q , then e = ( ( 12 # 16 ) # ( 18 # 24 ) ) = ?

Explanation: there are several ways to find the least common multiple of two numbers . in this case , the most efficient method is to use the greatest common factor : ( a * b ) / ( gcf ab ) = lcm ab the greatest common factor of 12 and 16 is 4 . so , 12 # 16 = 12 * 16 / 4 = 48 . the greatest common factor of 18 and 24 is 6 . so , 18 # 24 = 18 * 24 / 6 = 72 finally , the greatest common factor of 48 and 72 is 24 . so , e = ( ( 12 # 16 ) # ( 18 # 24 ) ) = 48 # 72 = ( 48 * 72 ) / 24 = 2 * 72 = 144 the correct answer is c .

add(divide(subtract(multiply(18, 24), multiply(12, 16)), const_2), 24)

<gadget id="calculator">18 * 24</gadget>
<output>432</output>
<gadget id="calculator">12 * 16</gadget>
<output>192</output>
<gadget id="calculator">432 - 192</gadget>
<output>240</output>
<gadget id="calculator">240 / 2</gadget>
<output>120</output>
<gadget id="calculator">120 + 24</gadget>
<output>144</output>
<result>144</result>


if m is an integer such that ( - 2 ) ^ 2 m = 2 ^ ( 6 - m ) then m = ?

Explanation: ( - 2 ) ^ ( 2 m ) = 4 ^ m and 2 ^ ( 6 - m ) = 4 ^ ( ( 6 - m ) / 2 ) therefore , m = ( 6 - m ) / 2 2 m = 6 - m m = 2 answer b

<gadget id="calculator">2 + 1</gadget>
<output>3</output>
<gadget id="calculator">6 / 3</gadget>
<output>2</output>
<result>2</result>


a train passes a platform in 44 seconds . the same train passes a man standing on the platform in 20 seconds . if the speed of the train is 54 km / hr , the length of the platform is

Explanation: "speed of the train = 54 km / hr = ( 54 × 10 ) / 36 m / s = 15 m / s length of the train = speed × time taken to cross the man = 15 × 20 = 300 m let the length of the platform = l time taken to cross the platform = ( 300 + l ) / 15 = > ( 300 + l ) / 15 = 36 = > 300 + l = 15 × 44 = 660 = > l = 660 - 300 = 360 meter answer is c ."

multiply(multiply(const_0_2778, 54), subtract(44, 20))

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">(5/18) * 54</gadget>
<output>15</output>
<gadget id="calculator">44 - 20</gadget>
<output>24</output>
<gadget id="calculator">15 * 24</gadget>
<output>360</output>
<result>360</result>


exactly 35 % of the reporters for a certain wire service cover local politics in country x . if 30 % of the reporters who cover politics for the wire service do not cover local politics in country x , what percent of the reporters for the wire service do not cover politics ?

Explanation: "you are correct . people who cover local politics are a subset of people who cover politics . 30 % of reporters who cover politics do not cover local politics so 70 % do cover local politics . reporters covering local politics = 70 % of reporters covering politics = 35 % ofall reporters reporters covering politics / all reporters = 35 / 70 = 1 / 2 reporters not covering politics / all reporters = 1 / 2 = 50 % = d"

multiply(subtract(const_1, divide(35, subtract(const_100, 30))), const_100)

<gadget id="calculator">100 - 30</gadget>
<output>70</output>
<gadget id="calculator">35 / 70</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 - (1/2)</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) * 100</gadget>
<output>50</output>
<result>50</result>


if rs . 10 be allowed as true discount on a bill of rs . 110 due at the end of a certain time , then the discount allowed on the same sum due at the end of double the time is :

Explanation: "solution s . i . on rs . ( 110 - 10 ) for a certain time = rs . 10 . s . i . on rs . 100 for double the time = rs . 20 . t . d . on rs . 120 = rs . ( 120 - 100 ) = rs . 20 . t . d . on rs . 110 = rs . ( 20 / 120 x 120 ) = rs . 18.33 . answer d"

multiply(110, divide(subtract(add(10, 110), const_100), add(10, 110)))

<gadget id="calculator">10 + 110</gadget>
<output>120</output>
<gadget id="calculator">120 - 100</gadget>
<output>20</output>
<gadget id="calculator">20 / 120</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">110 * (1/6)</gadget>
<output>55/3 = around 18.333333</output>
<result>55/3 = around 18.333333</result>


a shopkeeper gave an additional 20 per cent concession on the reduced price after giving 30 per cent standard concession on an article . if arun bought that article for 1120 , what was the original price ?

Explanation: original price = 1120 × 100 ⁄ 70 × 100 ⁄ 80 = 2000 answer d

divide(divide(multiply(multiply(1120, const_100), const_100), subtract(const_100, 20)), subtract(const_100, 30))

<gadget id="calculator">1_120 * 100</gadget>
<output>112_000</output>
<gadget id="calculator">112_000 * 100</gadget>
<output>11_200_000</output>
<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">11_200_000 / 80</gadget>
<output>140_000</output>
<gadget id="calculator">100 - 30</gadget>
<output>70</output>
<gadget id="calculator">140_000 / 70</gadget>
<output>2_000</output>
<result>2_000</result>


if x , y , and z are positive integers and 3 x = 4 y = 7 z , then the least possible value of x - y + z is

Explanation: x - y + z = - 3 x / 4 + x + 3 x / 7 = ( - 21 + 28 + 12 ) x / 28 = 19 x / 28 19 is not divisible by 28 ( it ' s a prime # ) , so for least value , x = 28 answer - d

add(subtract(divide(multiply(multiply(3, 4), 7), 3), divide(multiply(multiply(3, 4), 7), 4)), divide(multiply(multiply(3, 4), 7), 7))

<gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">12 * 7</gadget>
<output>84</output>
<gadget id="calculator">84 / 3</gadget>
<output>28</output>
<gadget id="calculator">84 / 4</gadget>
<output>21</output>
<gadget id="calculator">28 - 21</gadget>
<output>7</output>
<gadget id="calculator">84 / 7</gadget>
<output>12</output>
<gadget id="calculator">7 + 12</gadget>
<output>19</output>
<result>19</result>


a man buys an article for $ 100 . and sells it for $ 130 . find the gain percent ?

Explanation: "c . p . = $ 100 s . p . = $ 130 gain = $ 30 gain % = 30 / 100 * 100 = 30 % answer is e"

subtract(divide(130, divide(100, const_100)), const_100)

<gadget id="calculator">100 / 100</gadget>
<output>1</output>
<gadget id="calculator">130 / 1</gadget>
<output>130</output>
<gadget id="calculator">130 - 100</gadget>
<output>30</output>
<result>30</result>


how many cubes of 20 cm edge can be put in a cubical box of 1 m edge .

Explanation: "number of cubes = 100 â ˆ — 100 â ˆ — 100 / 20 â ˆ — 20 â ˆ — 20 = 125 note : 1 m = 100 cm answer : b"

<gadget id="calculator">1 ** 3</gadget>
<output>1</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) ** 3</gadget>
<output>1/125 = around 0.008</output>
<gadget id="calculator">1 / (1/125)</gadget>
<output>125</output>
<result>125</result>


3 houses are available in a new flat . 3 persons apply for the houses . each applies for 1 house without consulting others . the probability that all the 3 apply for the same house is ?

Explanation: one person can select one house out of 3 = \ inline { \ color { black } 3 c _ { 1 } } ways = 3 . hence , three persons can select one house out of 3 in 3 x 3 x 3 = 9 . therefore , probability that all thre apply for the same house is 1 / 9 b

divide(1, multiply(choose(3, 1), choose(3, 1)))

<gadget id="calculator">binomial(3, 1)</gadget>
<output>3</output>
<gadget id="calculator">3 * 3</gadget>
<output>9</output>
<gadget id="calculator">1 / 9</gadget>
<output>1/9 = around 0.111111</output>
<result>1/9 = around 0.111111</result>


if log 10 5 + log 10 ( 5 x + 1 ) = log 10 ( x + 5 ) + 1 , then x is equal to :

Explanation: log 10 5 + log 10 ( 5 x + 1 ) = log 10 ( x + 5 ) + 1 log 10 5 + log 10 ( 5 x + 1 ) = log 10 ( x + 5 ) + log 10 10 log 10 [ 5 ( 5 x + 1 ) ] = log 10 [ 10 ( x + 5 ) ] 5 ( 5 x + 1 ) = 10 ( x + 5 ) 5 x + 1 = 2 x + 10 3 x = 9 = > x = 3 answer c

divide(subtract(10, 1), subtract(5, const_2))

<gadget id="calculator">10 - 1</gadget>
<output>9</output>
<gadget id="calculator">5 - 2</gadget>
<output>3</output>
<gadget id="calculator">9 / 3</gadget>
<output>3</output>
<result>3</result>


the sum of 4 consecutive even numbers is 140 . what would be the smallest number ?

Explanation: let the four consecutive even numbers be 2 ( x - 2 ) , 2 ( x - 1 ) , 2 x , 2 ( x + 1 ) their sum = 8 x - 4 = 140 = > x = 18 smallest number is : 2 ( x - 2 ) = 32 answer : a

subtract(subtract(subtract(multiply(divide(140, add(4, 4)), const_2), const_1), const_1), const_1)

<gadget id="calculator">4 + 4</gadget>
<output>8</output>
<gadget id="calculator">140 / 8</gadget>
<output>35/2 = around 17.5</output>
<gadget id="calculator">(35/2) * 2</gadget>
<output>35</output>
<gadget id="calculator">35 - 1</gadget>
<output>34</output>
<gadget id="calculator">34 - 1</gadget>
<output>33</output>
<gadget id="calculator">33 - 1</gadget>
<output>32</output>
<result>32</result>


an article is sold at a certain price . by selling it at 2 / 3 of that price one loses 10 % . find the gain percent at original price ?

Explanation: let the original s . p . be $ x then , new s . p . = $ 2 / 3 x loss = 10 % c . p . = 100 / 90 * 2 / 3 x = 20 x / 27 c . p . = 20 x / 27 gain = x - 20 x / 27 = 7 x / 27 gain % = 7 x / 27 * 27 / 20 x * 100 = 35 % answer is c

subtract(divide(subtract(const_100, 10), divide(2, 3)), const_100)

<gadget id="calculator">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">90 / (2/3)</gadget>
<output>135</output>
<gadget id="calculator">135 - 100</gadget>
<output>35</output>
<result>35</result>


in a sports club with 30 members , 17 play badminton and 19 play tennis and 3 do not play either . how many members play both badminton and tennis ?

Explanation: "let x play both badminton and tennis so 17 - x play only badminton and 19 - x play only tennis . 2 play none and there are total 30 students . hence , ( 17 - x ) + ( 19 - x ) + x + 3 = 30 39 - 2 x + x = 30 39 - x = 30 x = 9 so 9 members play both badminton and tennis . c"

<gadget id="calculator">17 + 19</gadget>
<output>36</output>
<gadget id="calculator">36 + 3</gadget>
<output>39</output>
<gadget id="calculator">39 - 30</gadget>
<output>9</output>
<result>9</result>


the local recycling plant had a contract requiring anyone who obtained recycled bottles for storage for them , to bring them back to be recycled again . the plant could make one new bottle from every 7 bottles returned . one week , on monday , they got 343 bottles to recycle . assuming that everybody brought back all the empties , how many could they eventually remake from the 343 ?

Explanation: in 1 st level they will make 343 / 7 = 49 bottles . in 2 nd level they will make 49 / 7 = 7 bottles . in 3 rd level they will make 7 / 7 = 1 bottle . totally they can remake 49 + 7 + 1 = 57 bottles answer : e

<gadget id="calculator">343 / 7</gadget>
<output>49</output>
<gadget id="calculator">49 + 7</gadget>
<output>56</output>
<result>56</result>


the difference between the heights of two trees is 20 cm . 10 years ago , the taller one was thrice as taller as the shorter one . the present height of the taller tree is

Explanation: let their heights of x cm and ( x + 20 ) cm respectively . then , ( x + 20 ) - 10 = 3 ( x - 10 ) ⇔ x + 10 = 3 x - 30 ⇔ 2 x = 40 ∴ present height of taller tree = ( 20 + 10 ) = 30 cm . answer : 30 cm

<gadget id="calculator">20 + 10</gadget>
<output>30</output>
<gadget id="calculator">30 * 10</gadget>
<output>300</output>
<result>300</result>


in an examination , 35 % of total students failed in hindi , 45 % failed in english and 20 % in both . the percentage of these who passed in both the subjects is :

Explanation: "pass percentage = 100 - ( 35 + 45 - 20 ) = 100 - 60 = 40 answer : d"

subtract(const_100, subtract(add(35, 45), 20))

<gadget id="calculator">35 + 45</gadget>
<output>80</output>
<gadget id="calculator">80 - 20</gadget>
<output>60</output>
<gadget id="calculator">100 - 60</gadget>
<output>40</output>
<result>40</result>


8 people went to a restaurant for dinner . 7 of them spent $ 10 each on their meals and the eighth spent $ 7 more than the average expenditure of all 8 people . what was the total amount of money that the 8 people spent ?

Explanation: let t be the total amount of money spent . 7 * 10 + ( t / 8 + 7 ) = t 77 = 7 t / 8 t = ( 8 * 77 ) / 7 = 88 the answer is b .

add(multiply(7, 10), add(divide(add(multiply(7, 10), 7), subtract(8, const_1)), 7))

<gadget id="calculator">7 * 10</gadget>
<output>70</output>
<gadget id="calculator">70 + 7</gadget>
<output>77</output>
<gadget id="calculator">8 - 1</gadget>
<output>7</output>
<gadget id="calculator">77 / 7</gadget>
<output>11</output>
<gadget id="calculator">11 + 7</gadget>
<output>18</output>
<gadget id="calculator">70 + 18</gadget>
<output>88</output>
<result>88</result>


a person crosses a 1080 m long street in 12 minutes . what is his speed in km per hour ?

Explanation: "speed = 1080 / ( 12 x 60 ) m / sec = 1.5 m / sec . converting m / sec to km / hr = 1.5 x ( 18 / 5 ) km / hr = 5.4 km / hr . answer : d"

divide(divide(1080, const_1000), divide(multiply(12, const_60), const_3600))

<gadget id="calculator">1_080 / 1_000</gadget>
<output>27/25 = around 1.08</output>
<gadget id="calculator">12 * 60</gadget>
<output>720</output>
<gadget id="calculator">720 / 3_600</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(27/25) / (1/5)</gadget>
<output>27/5 = around 5.4</output>
<result>27/5 = around 5.4</result>


there were two candidates in an election . winner candidate received 62 % of votes and won the election by 384 votes . find the number of votes casted to the winning candidate ?

Explanation: "w = 62 % l = 38 % 62 % - 38 % = 24 % 24 % - - - - - - - - 384 62 % - - - - - - - - ? = > 992 answer : c"

divide(multiply(divide(384, divide(subtract(62, subtract(const_100, 62)), const_100)), 62), const_100)

<gadget id="calculator">100 - 62</gadget>
<output>38</output>
<gadget id="calculator">62 - 38</gadget>
<output>24</output>
<gadget id="calculator">24 / 100</gadget>
<output>6/25 = around 0.24</output>
<gadget id="calculator">384 / (6/25)</gadget>
<output>1_600</output>
<gadget id="calculator">1_600 * 62</gadget>
<output>99_200</output>
<gadget id="calculator">99_200 / 100</gadget>
<output>992</output>
<result>992</result>


a grocer is storing soap boxes in cartons that measure 25 inches by 42 inches by 60 inches . if the measurement of each soap box is 7 inches by 6 inches by 10 inches , then what is the maximum number of soap boxes that can be placed in each carton ?

Explanation: "however the process of dividing the volume of box by the volume of a soap seems flawed but it does work in this case due to the numbers dimensions of the box = 25 * 42 * 60 dimensions of the soap = 10 * 6 * 7 we get = 5 x 6 x 5 = 150 so the question is why this particular arrangement , in order to maximize number of soaps we need to minimize the space wasted and this is the only config where we dont waste any space so we can expect the maximum number the answer is ( d )"

divide(multiply(multiply(25, 42), 60), multiply(multiply(7, 6), 10))

<gadget id="calculator">25 * 42</gadget>
<output>1_050</output>
<gadget id="calculator">1_050 * 60</gadget>
<output>63_000</output>
<gadget id="calculator">7 * 6</gadget>
<output>42</output>
<gadget id="calculator">42 * 10</gadget>
<output>420</output>
<gadget id="calculator">63_000 / 420</gadget>
<output>150</output>
<result>150</result>


selling an kite for rs . 30 , a shop keeper gains 25 % . during a clearance sale , the shopkeeper allows a discount of 10 % on the marked price . his gain percent during the sale is ?

Explanation: "explanation : marked price = rs . 30 c . p . = 100 / 125 * 30 = rs . 24 sale price = 90 % of rs . 30 = rs . 27 required gain % = 3 / 24 * 100 = 12.5 % . answer : d"

multiply(divide(subtract(multiply(divide(30, const_100), subtract(const_100, 10)), divide(multiply(30, const_100), add(25, const_100))), divide(multiply(30, const_100), add(25, const_100))), const_100)

<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">(3/10) * 90</gadget>
<output>27</output>
<gadget id="calculator">30 * 100</gadget>
<output>3_000</output>
<gadget id="calculator">25 + 100</gadget>
<output>125</output>
<gadget id="calculator">3_000 / 125</gadget>
<output>24</output>
<gadget id="calculator">27 - 24</gadget>
<output>3</output>
<gadget id="calculator">3 / 24</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">(1/8) * 100</gadget>
<output>25/2 = around 12.5</output>
<result>25/2 = around 12.5</result>


in a university the average age in an arts class is 21 and average age in technical class is 18 . what is the age average of university if there are 8 arts classes and 5 technical classes ?

Explanation: average age of university = ( ( 8 x 21 ) + ( 5 x 18 ) ) / 13 = 19.85 answer : b

divide(add(multiply(8, 21), multiply(5, 18)), add(8, 5))

<gadget id="calculator">8 * 21</gadget>
<output>168</output>
<gadget id="calculator">5 * 18</gadget>
<output>90</output>
<gadget id="calculator">168 + 90</gadget>
<output>258</output>
<gadget id="calculator">8 + 5</gadget>
<output>13</output>
<gadget id="calculator">258 / 13</gadget>
<output>258/13 = around 19.846154</output>
<result>258/13 = around 19.846154</result>


a theater box office sold an average ( arithmetic mean ) of 65 tickets per staff member to a particular movie . among the daytime staff , the average number sold per member was 75 , and among the evening staff , the average number sold was 60 . if there are no other employees , what was the ratio of the number of daytime staff members to the number of evening staff members ?

Explanation: "deviation from the mean for the daytime staff = 75 - 65 = 10 . deviation from the mean for the evening staff = 65 - 60 = 5 . thus , the ratio of the number of daytime staff members to the number of evening staff members is 5 : 10 = 1 : 2 . the answer is a ."

divide(subtract(65, 60), subtract(75, 65))

<gadget id="calculator">65 - 60</gadget>
<output>5</output>
<gadget id="calculator">75 - 65</gadget>
<output>10</output>
<gadget id="calculator">5 / 10</gadget>
<output>1/2 = around 0.5</output>
<result>1/2 = around 0.5</result>


in a kilometer race , if abhishek gives bharti a 40 m start , abhishek wins by 19 sec . but if abhishek gives bharti a 30 sec start , bharti wins by 40 m . find the time taken by bharti to run 5,000 m ?

Explanation: explanation : if abhishek takes x seconds and bharti takes y seconds to run 1 km , then : = > y = 150 sec and x = 125 sec = > x + 19 = 960 y / 1000 and = ( 960 x / 1000 ) + 30 = y = > y = 150 sec and x = 125 sec answer = ( 150 / 1000 ) × 500 = 750 sec answer : b

multiply(add(multiply(const_1000, const_4), const_1000), divide(add(multiply(divide(subtract(multiply(30, divide(subtract(const_1000, 40), const_1000)), 19), subtract(const_1, power(divide(subtract(const_1000, 40), const_1000), const_2))), divide(subtract(const_1000, 40), const_1000)), 30), const_1000))

<gadget id="calculator">1_000 * 4</gadget>
<output>4_000</output>
<gadget id="calculator">4_000 + 1_000</gadget>
<output>5_000</output>
<gadget id="calculator">1_000 - 40</gadget>
<output>960</output>
<gadget id="calculator">960 / 1_000</gadget>
<output>24/25 = around 0.96</output>
<gadget id="calculator">30 * (24/25)</gadget>
<output>144/5 = around 28.8</output>
<gadget id="calculator">(144/5) - 19</gadget>
<output>49/5 = around 9.8</output>
<gadget id="calculator">(24/25) ** 2</gadget>
<output>576/625 = around 0.9216</output>
<gadget id="calculator">1 - (576/625)</gadget>
<output>49/625 = around 0.0784</output>
<gadget id="calculator">(49/5) / (49/625)</gadget>
<output>125</output>
<gadget id="calculator">125 * (24/25)</gadget>
<output>120</output>
<gadget id="calculator">120 + 30</gadget>
<output>150</output>
<gadget id="calculator">150 / 1_000</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">5_000 * (3/20)</gadget>
<output>750</output>
<result>750</result>


every disk in a bag is either blue , yellow or green . the ratio of blue disks to yellow disks to green disks in this bag is 3 : 7 : 8 . if the total number of disks in the bag is 144 , how many more green disks than blue disks are in the bag ?

Explanation: "let b : y : g = 3 x : 7 x : 8 x . 3 x + 7 x + 8 x = 18 x = 144 - - > x = 8 . g - b = 8 x - 3 x = 5 x = 40 . the answer is e ."

multiply(divide(144, add(add(3, 7), 8)), subtract(8, 3))

<gadget id="calculator">3 + 7</gadget>
<output>10</output>
<gadget id="calculator">10 + 8</gadget>
<output>18</output>
<gadget id="calculator">144 / 18</gadget>
<output>8</output>
<gadget id="calculator">8 - 3</gadget>
<output>5</output>
<gadget id="calculator">8 * 5</gadget>
<output>40</output>
<result>40</result>


if the sum of two numbers is 22 and the sum of their squares is 404 , then the product of the numbers is

Explanation: "according to the given conditions x + y = 22 and x ^ 2 + y ^ 2 = 404 now ( x + y ) ^ 2 = x ^ 2 + y ^ 2 + 2 xy so 22 ^ 2 = 404 + 2 xy so xy = 80 / 2 = 40 answer : a"

divide(subtract(power(22, const_2), 404), const_2)

<gadget id="calculator">22 ** 2</gadget>
<output>484</output>
<gadget id="calculator">484 - 404</gadget>
<output>80</output>
<gadget id="calculator">80 / 2</gadget>
<output>40</output>
<result>40</result>


there are 200 female managers in a certain company . find the total number w of female employees in the company , if 2 / 5 of all the employees are managers and 2 / 5 of all male employees are managers .

Explanation: "{ managers } = { female managers } + { male managers } ; we are told that the total number of managers in the company is 2 / 5 of all the employees , thus { managers } = 2 / 5 ( m + f ) , where m and f are number of female and male employees , respectively . also , we know that 2 / 5 of all male employees are managers : { male managers } = 2 / 5 * mas well as there are total of 200 female managers : { female managers } = 200 ; thus : 2 / 5 ( m + f ) = 200 + 2 / 5 * m - - > f = 500 . answer : c ."

<gadget id="calculator">2 / 5</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">200 / (2/5)</gadget>
<output>500</output>
<result>500</result>


a store reduced the price of all items in the store by 10 % on the first day and by another 10 % on the second day . the price of items on the second day was what percent of the price before the first reduction took place ?

Explanation: "consider price of the all items as $ 100 after a initial reduction of 10 % price becomes = 0.9 * 100 = $ 90 after the final reduction of 10 % price becomes = 0.9 * 90 = $ 81 price of all items on second day is 81 % of price on first day correct answer option c"

multiply(multiply(divide(subtract(const_100, 10), const_100), divide(subtract(const_100, 10), const_100)), const_100)

<gadget id="calculator">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">90 / 100</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">(9/10) * (9/10)</gadget>
<output>81/100 = around 0.81</output>
<gadget id="calculator">(81/100) * 100</gadget>
<output>81</output>
<result>81</result>


on the first of the year , james invested x dollars at proudstar bank in an account that yields 0.5 % in interest every quarter year . at the end of the year , during which he made no additional deposits or withdrawals , he had y dollars in the account . if james had invested the same amount in an account which pays interest on a yearly basis , what must the interest rate be for james to have y dollars at the end of the year ?

Explanation: per quarter , interest = 0.5 % so for a year , interest = 2 % due to quarter cumulation , effective yield ( ytm ) would be slight higher than 2 % answer = 2.04 % = answer : a

<gadget id="calculator">0.5 * 4</gadget>
<output>2</output>
<result>2</result>


the chance of rain on any given day in tel - aviv is 50 % . what is the probability w that it rained in tel - aviv on exactly 4 out of 6 randomly chosen days ?

Explanation: chances of rain on exactly 4 days and not rain on 2 days = ( 1 / 2 ) ^ 4 * ( 1 / 2 ) ^ 2 = 1 / 64 chosing 4 days out of 6 = 6 ! / ( 4 ! * 2 ! ) = 15 chances of rain on exactly 4 days out of 6 days w = 15 / 64 ans a it is .

divide(choose(6, 4), inverse(multiply(power(divide(const_1, const_2), const_4), power(divide(const_1, const_2), const_2))))

<gadget id="calculator">binomial(6, 4)</gadget>
<output>15</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) ** 4</gadget>
<output>1/16 = around 0.0625</output>
<gadget id="calculator">(1/2) ** 2</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/16) * (1/4)</gadget>
<output>1/64 = around 0.015625</output>
<gadget id="calculator">1 / (1/64)</gadget>
<output>64</output>
<gadget id="calculator">15 / 64</gadget>
<output>15/64 = around 0.234375</output>
<result>15/64 = around 0.234375</result>


the sum of two numbers is 77 . 5 times one number is equal to 6 times the other . the bigger of the two numbers is

Explanation: a : b 5 : 6 a + b = 77 5 x + 6 x = 77 x = 7 then two numbers are 35,42 . the bigger number is 42 answer : b

subtract(77, divide(77, add(divide(6, 5), const_1)))

<gadget id="calculator">6 / 5</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">(6/5) + 1</gadget>
<output>11/5 = around 2.2</output>
<gadget id="calculator">77 / (11/5)</gadget>
<output>35</output>
<gadget id="calculator">77 - 35</gadget>
<output>42</output>
<result>42</result>


income and expenditure of a person are in the ratio 7 : 6 . if the income of the person is rs . 14000 , then find his savings ?

Explanation: "let the income and the expenditure of the person be rs . 7 x and rs . 6 x respectively . income , 7 x = 14000 = > x = 2000 savings = income - expenditure = 7 x - 6 x = x so , savings = rs . 2000 . answer : d"

subtract(14000, multiply(divide(6, 7), 14000))

<gadget id="calculator">6 / 7</gadget>
<output>6/7 = around 0.857143</output>
<gadget id="calculator">(6/7) * 14_000</gadget>
<output>12_000</output>
<gadget id="calculator">14_000 - 12_000</gadget>
<output>2_000</output>
<result>2_000</result>


3 people took gmat practice tests in which the minimum and maximum possible scores are 200 and 800 , respectively . they each took a test 3 times , and no one scored below 400 or over 700 . if the individual ranges of the 3 people ' s scores in those 3 practice tests were 40 , 70 and 100 , what is the difference between the maximum and minimum possible ranges of all their scores put together .

Explanation: according to the information in the question the maximum range would be between 400 and 700 ( 300 ) . the minimum range would be the greatest range for any one individual , which is listed in the problem as 100 . so the difference between these would be 300 - 100 or 200 . answer : e

<gadget id="calculator">700 - 400</gadget>
<output>300</output>
<gadget id="calculator">300 - 100</gadget>
<output>200</output>
<result>200</result>


Explanation: let p = 3 , q = 11 then 2 * 3 + 11 = 17 so 2 p + q = 17 . answer : c

<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">6 + 11</gadget>
<output>17</output>
<result>17</result>


what is the probability of rolling a total of 5 with a single roll of two fair 6 - sided dice , each with the distinct numbers 1 through 6 on each side ?

Explanation: totalsample spacefrom two fair six - sided dice is 36 . there are six possible ways to be 5 i . e . ( 1 + 4 ) , ( 2 + 3 ) , ( 3 + 2 ) , ( 4 + 1 ) so , total probability is 4 / 36 or 1 / 9 . answer is e .

<gadget id="calculator">6 * 6</gadget>
<output>36</output>
<gadget id="calculator">4 / 36</gadget>
<output>1/9 = around 0.111111</output>
<result>1/9 = around 0.111111</result>


if the simple interest on a certain sum of money for 6 years is one – fifth of the sum , then the rate of interest per annum is

Explanation: "explanation : let the principal ( p ) be x then , simple interest ( si ) = x / 5 time ( t ) = 6 years rate of interest per annum ( r ) = ( 100 × si ) / pt = ( 100 × ( x / 5 ) / ( x × 6 ) = 20 / 6 = 3.3 % answer : option a"

divide(divide(const_100, add(const_1, const_4)), 6)

<gadget id="calculator">1 + 4</gadget>
<output>5</output>
<gadget id="calculator">100 / 5</gadget>
<output>20</output>
<gadget id="calculator">20 / 6</gadget>
<output>10/3 = around 3.333333</output>
<result>10/3 = around 3.333333</result>


the population of a city is 415600 . it increased by 25 % in the first year and decreased by 30 % in the second year . what is the population of the city at the end of second year ?

Explanation: as per given data , p = 415600 , r 1 = 25 % incresed , r 2 = 30 % decreased population of the city at the end of the second year = p ( 1 + r 1 / 100 ) ( 1 - r 2 / 100 ) = 415600 ( 1 + 25 / 100 ) ( 1 - 30 / 100 ) = 363650 answer : c

multiply(divide(subtract(const_100, 30), const_100), multiply(divide(add(25, const_100), const_100), 415600))

<gadget id="calculator">100 - 30</gadget>
<output>70</output>
<gadget id="calculator">70 / 100</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">25 + 100</gadget>
<output>125</output>
<gadget id="calculator">125 / 100</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">(5/4) * 415_600</gadget>
<output>519_500</output>
<gadget id="calculator">(7/10) * 519_500</gadget>
<output>363_650</output>
<result>363_650</result>


a thief is spotted by a policeman from a distance of 150 meters . when the policeman starts the chase , the thief also starts running . if the speed of the thief be 8 km / hr and that of the policeman 10 km / hr , how far the thief will have run before he is overtaken ?

Explanation: "relative speed of the policeman = ( 10 - 8 ) km / hr = 2 km / hr . time taken by police man to cover ( 150 m / 1000 ) x 1 / 2 hr = 3 / 40 hr . in 3 / 40 hrs , the thief covers a distance of 8 x 3 / 40 km = 3 / 5 km = 600 m answer is d"

divide(multiply(150, 8), subtract(10, 8))

<gadget id="calculator">150 * 8</gadget>
<output>1_200</output>
<gadget id="calculator">10 - 8</gadget>
<output>2</output>
<gadget id="calculator">1_200 / 2</gadget>
<output>600</output>
<result>600</result>


car x began traveling at an average speed of 35 miles per hour . after 72 minutes , car y began traveling at an average speed of 70 miles per hour . when both cars had traveled the same distance , both cars stopped . how many miles did car x travel from the time car y began traveling until both cars stopped ?

Explanation: "car y began travelling after 72 minutes or 1.2 hours . let t be the time for which car y travelled before it stopped . both cars stop when they have travelled the same distance . so , 35 ( t + 1.2 ) = 70 t t = 1.2 distance traveled by car x from the time car y began traveling until both cars stopped is 35 x 1.2 = 42 miles answer : - d"

multiply(35, divide(multiply(divide(72, const_60), 35), subtract(70, 35)))

<gadget id="calculator">72 / 60</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">(6/5) * 35</gadget>
<output>42</output>
<gadget id="calculator">70 - 35</gadget>
<output>35</output>
<gadget id="calculator">42 / 35</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">35 * (6/5)</gadget>
<output>42</output>
<result>42</result>


a fruit juice company earns $ 150 per 100 gallons of apple juice sold , $ 170 per 100 gallons of guava juice sold , $ 130 per 100 gallons of grape juice sold , $ 100 per 100 gallons of orange juice . if the company manages to sell 230 gallons of apple , 210 gallons of guava , 310 gallons of grape , 270 gallons of orange on a particular day . what is the average earning of the company per 100 gallon of the juice sold ?

Explanation: earning of the company from apple = 150 / 100 x 230 = 345 earning of the company from guava = 170 / 100 x 210 = 357 earning of the company from grape = 130 / 100 x 310 = 403 earning of the company from orange = 100 / 100 x 270 = 270 total earning of the company = 345 + 357 + 403 + 270 = 1375 total juice sold = 1020 average earning per 100 gallon of juice sold = ( 1375 / 1020 ) x 100 = $ 134.8 answer : a

add(add(130, const_4), divide(add(const_4, const_4), const_10))

<gadget id="calculator">130 + 4</gadget>
<output>134</output>
<gadget id="calculator">4 + 4</gadget>
<output>8</output>
<gadget id="calculator">8 / 10</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">134 + (4/5)</gadget>
<output>674/5 = around 134.8</output>
<result>674/5 = around 134.8</result>


if a mixture is 1 ⁄ 7 alcohol by volume and 2 ⁄ 7 water by volume , what is the ratio of the volume of alcohol to the volume of water in this mixture ?

Explanation: "should be a sub - 600 level q . . volume = { 1 / 7 } / { 2 / 7 } = 1 / 2 c"

<gadget id="calculator">1 / 7</gadget>
<output>1/7 = around 0.142857</output>
<gadget id="calculator">2 / 7</gadget>
<output>2/7 = around 0.285714</output>
<gadget id="calculator">(1/7) / (2/7)</gadget>
<output>1/2 = around 0.5</output>
<result>1/2 = around 0.5</result>


the average of 10 numbers is 7 . if each number is multiplied by 12 , then the average of new set of numbers is

Explanation: explanation : if each number is multiplied by k , then the new average increases by k times . so new average = 84 answer : d

<gadget id="calculator">7 * 12</gadget>
<output>84</output>
<result>84</result>


a train 500 m long can cross an electric pole in 50 sec and then find the speed of the train ?

Explanation: "length = speed * time speed = l / t s = 500 / 50 s = 10 m / sec speed = 10 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 36 kmph answer : e"

divide(divide(500, const_1000), divide(50, const_3600))

<gadget id="calculator">500 / 1_000</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">50 / 3_600</gadget>
<output>1/72 = around 0.013889</output>
<gadget id="calculator">(1/2) / (1/72)</gadget>
<output>36</output>
<result>36</result>


the length of a rectangle is increased by 40 % while its width is halved . what is the % change in area ?

Explanation: the original area is l * w the new area is 1.4 l * 0.5 w = 0.7 * l * w = l * w - 0.3 * l * w the area decreased by 30 % . the answer is b .

multiply(subtract(const_1, multiply(divide(const_1, const_2), add(divide(40, const_100), const_1))), const_100)

<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) + 1</gadget>
<output>7/5 = around 1.4</output>
<gadget id="calculator">(1/2) * (7/5)</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">1 - (7/10)</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(3/10) * 100</gadget>
<output>30</output>
<result>30</result>


if 5 x = 3 y and xy ≠ 0 , what is the ratio of 1 / 5 * x to 1 / 6 * y ?

Explanation: "5 x = 3 y = > x / y = 3 / 5 1 / 5 * x to 1 / 6 * y = x / y * 6 / 5 = ( 3 / 5 ) * ( 6 / 5 ) = 18 / 25 ans : c"

multiply(divide(divide(1, 5), divide(1, 6)), divide(3, 5))

<gadget id="calculator">1 / 5</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(1/5) / (1/6)</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">3 / 5</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(6/5) * (3/5)</gadget>
<output>18/25 = around 0.72</output>
<result>18/25 = around 0.72</result>


for every integer n ≥ 3 , the function g ( n ) is defined as the product of all the odd integers from 1 to n , inclusive . what is the value of g ( 101 ) – g ( 99 ) ?

Explanation: "g ( 101 ) = 1 * 3 * 5 * 7 * 9 * . . . * 99 * 101 g ( 99 ) = 1 * 3 * 5 * 7 * 9 * . . . * 99 g ( 101 ) - g ( 99 ) = 1 * 3 * 5 * 7 * 9 * . . . * 99 * 101 - 1 * 3 * 5 * 7 * 9 * . . . * 99 = 1 * 3 * 5 * 7 * 9 * . . . * 99 * ( 101 - 1 ) = 1 * 3 * 5 * 7 * 9 * . . . * 99 * 100 hence : d"

<gadget id="calculator">101 - 1</gadget>
<output>100</output>
<result>100</result>


two trains of equal length are running on parallel lines in the same directions at 46 km / hr . and 36 km / hr . the faster trains pass the slower train in 72 seconds . the length of each train is :

Explanation: "explanation : the relative speed of train is 46 - 36 = 10 km / hr = ( 10 x 5 ) / 18 = 25 / 9 m / s 10 × 518 = 259 m / s in 72 secs the total distance traveled is 72 x 25 / 9 = 200 m . therefore the length of each train is = 200 / 2 = 100 m . answer d"

divide(multiply(divide(multiply(subtract(46, 36), const_1000), const_3600), 72), const_2)

<gadget id="calculator">46 - 36</gadget>
<output>10</output>
<gadget id="calculator">10 * 1_000</gadget>
<output>10_000</output>
<gadget id="calculator">10_000 / 3_600</gadget>
<output>25/9 = around 2.777778</output>
<gadget id="calculator">(25/9) * 72</gadget>
<output>200</output>
<gadget id="calculator">200 / 2</gadget>
<output>100</output>
<result>100</result>


a vendor bought toffees at 6 for a rupee . how many for a rupee must he sell to gain 30 % ?

Explanation: c . p . of 6 toffees = re . 1 s . p . of 6 toffees = 180 % of re . 1 = rs . 9 / 5 for rs . 9 / 5 , toffees sold = 6 . for re . 1 , toffees sold = 9 x 5 / 6 = 15 / 2 . answer e

multiply(6, add(const_1, divide(30, const_100)))

<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">1 + (3/10)</gadget>
<output>13/10 = around 1.3</output>
<gadget id="calculator">6 * (13/10)</gadget>
<output>39/5 = around 7.8</output>
<result>39/5 = around 7.8</result>


how many seconds will a train 140 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph ?

Explanation: "d = 140 + 150 = 290 s = 36 * 5 / 18 = 10 mps t = 290 / 10 = 29 sec b"

<gadget id="calculator">150 + 140</gadget>
<output>290</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">36 * (5/18)</gadget>
<output>10</output>
<gadget id="calculator">290 / 10</gadget>
<output>29</output>
<result>29</result>


sophia finished 2323 of a book . she calculated that she finished 90 more pages than she has yet to read . how long is her book ?

Explanation: let x be the total number of pages in the book , then she finished 23 ⋅ x pages . then she has x − 23 ⋅ x = 13 ⋅ xpages left . 23 ⋅ x − 13 ⋅ x = 90 13 ⋅ x = 90 x = 270 so the book is 270 pages long . correct answer is d ) 270

divide(90, subtract(divide(const_2, const_3), subtract(const_1, divide(const_2, const_3))))

<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">1 - (2/3)</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(2/3) - (1/3)</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">90 / (1/3)</gadget>
<output>270</output>
<result>270</result>


on her annual road trip to visit her family in seal beach , california , traci stopped to rest after she traveled 1 ⁄ 3 of the total distance and again after she traveled 1 ⁄ 4 of the distance remaining between her first stop and her destination . she then drove the remaining 300 miles and arrived safely at her destination . what was the total distance , in miles , from traci ’ s starting point to seal beach ?

Explanation: let d = total distance traci traveled 1 / 3 = d / 3 i . e . remaining distance = 2 d / 3 she traveled 1 / 4 th of 2 d / 3 = d / 6 thus : d = ( d / 3 ) + ( d / 6 ) + 300 d = 600 answer : a

<gadget id="calculator">300 * 2</gadget>
<output>600</output>
<result>600</result>


the marks obtained by vijay and amith are in the ratio 4 : 5 and those obtained by amith and abhishek in the ratio of 3 : 4 . the marks obtained by vijay and abhishek are in the ratio of ?

Explanation: "4 : 5 3 : 4 - - - - - - - 12 : 15 : 20 12 : 20 - - - - - - > 6 : 10 3 : 5 answer : b"

<gadget id="calculator">4 * 3</gadget>
<output>12</output>
<gadget id="calculator">5 * 4</gadget>
<output>20</output>
<gadget id="calculator">12 / 20</gadget>
<output>3/5 = around 0.6</output>
<result>3/5 = around 0.6</result>


the length of a room is 5.5 m and width is 3.75 m . find the cost of paying the floor by slabs at the rate of rs . 1200 per sq . metre .

Explanation: "solution area of the floor = ( 5.5 x 3.75 ) m ² = 20.635 m ² cost of paying = rs . ( 1200 x 20.625 ) = rs . 24,750 . answer b"

<gadget id="calculator">5.5 * 3.75</gadget>
<output>20.625</output>
<gadget id="calculator">1_200 * 20.625</gadget>
<output>24_750</output>
<result>24_750</result>


how many zeroes are there at the end of the number n , if n = 70 ! + 140 ! ?

Explanation: "the number of zeroes at the end of 70 ! will be less than the number of zeroes at the end of 140 ! hence it is sufficient to calculate the number of zeroes at the end of 70 ! the number of zeroes = [ 70 / 5 ] + [ 70 / 25 ] + [ 70 / 125 ] = 14 + 2 + 0 = 16 the answer is c ."

add(divide(70, add(const_4, const_1)), const_2)

<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">70 / 5</gadget>
<output>14</output>
<gadget id="calculator">14 + 2</gadget>
<output>16</output>
<result>16</result>


if 15 percent of the students at a certain school went to a camping trip and took more than $ 100 , and 75 percent of the students who went to the camping trip did not take more than $ 100 , what percentage of the students at the school went to the camping trip ?

Explanation: "let x be the number of students in the school . 0.15 x students went to the trip and took more than 100 $ . they compose ( 100 - 75 ) = 25 % of all students who went to the trip . therefore the toal of 0.15 x / 0.25 = 0.6 x students went to the camping which is 60 % . the answer is e"

divide(15, divide(subtract(100, 75), 100))

<gadget id="calculator">100 - 75</gadget>
<output>25</output>
<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">15 / (1/4)</gadget>
<output>60</output>
<result>60</result>


an object thrown directly upward is at a height of h feet after t seconds , where h = - 14 ( t - 3 ) ^ 2 + 150 . at what height , in feet , is the object 2 seconds after it reaches its maximum height ?

Explanation: "we see that h will be a maximum h = 150 when t - 3 = 0 , that is when t = 3 . at t = 5 , h = - 14 ( 5 - 3 ) ^ 2 + 150 = - 14 ( 4 ) + 150 = 94 the answer is c ."

add(multiply(negate(14), power(subtract(add(3, 2), 3), 2)), 150)

<gadget id="calculator">-14</gadget>
<output>-14</output>
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">5 - 3</gadget>
<output>2</output>
<gadget id="calculator">2 ** 2</gadget>
<output>4</output>
<gadget id="calculator">(-14) * 4</gadget>
<output>-56</output>
<gadget id="calculator">(-56) + 150</gadget>
<output>94</output>
<result>94</result>


how many cones of radius 4 m , height 2 m can be formed from a cylinder of 12 m radius , 10 m height :

Explanation: ( cylinder volume ) / ( cone volume ) ( π r ( power 2 ) h ) / ( 1 / 3 π r ( power 2 ) h ) = ( π × 12 × 12 × 10 ) / ( 1 / 3 π × 4 × 4 × 2 ) = 135 answer is a .

divide(volume_cylinder(12, 10), volume_cone(4, 2))

<gadget id="calculator">pi * (12 ** 2) * 10</gadget>
<output>1440*pi = around 4_523.893421</output>
<gadget id="calculator">pi * (4 ** 2) * 2 / 3</gadget>
<output>32*pi/3 = around 33.510322</output>
<gadget id="calculator">(1440*pi) / (32*pi/3)</gadget>
<output>135</output>
<result>135</result>


70 is increased by 50 % . find the final number .

Explanation: "final number = initial number + 50 % ( original number ) = 70 + 50 % ( 70 ) = 70 + 35 = 105 . answer c"

add(70, multiply(70, divide(50, const_100)))

<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">70 * (1/2)</gadget>
<output>35</output>
<gadget id="calculator">70 + 35</gadget>
<output>105</output>
<result>105</result>


in a group of 8 semifinalists , all but 2 will advance to the final round . if in the final round only the top 3 will be awarded medals , then how many groups of medal winners are possible ?

Explanation: 1 ) is it important here that how many go into finals . . . no . . . . what is important is how many get medals . . 3 finally these 3 can be any of the 8 - 8 c 3 = 8 ! 5 ! 3 ! = 8 ∗ 7 ∗ 63 ∗ 2 = 568 c 3 = 8 ! 5 ! 3 ! = 8 ∗ 7 ∗ 63 ∗ 2 = 56 2 ) is order important . . . no we are looking for groups only . . ans 56 answer : b

divide(multiply(divide(factorial(8), multiply(factorial(subtract(8, 2)), 2)), divide(factorial(subtract(8, 2)), multiply(factorial(3), factorial(3)))), const_10)

<gadget id="calculator">factorial(8)</gadget>
<output>40_320</output>
<gadget id="calculator">8 - 2</gadget>
<output>6</output>
<gadget id="calculator">factorial(6)</gadget>
<output>720</output>
<gadget id="calculator">720 * 2</gadget>
<output>1_440</output>
<gadget id="calculator">40_320 / 1_440</gadget>
<output>28</output>
<gadget id="calculator">factorial(3)</gadget>
<output>6</output>
<gadget id="calculator">6 * 6</gadget>
<output>36</output>
<gadget id="calculator">720 / 36</gadget>
<output>20</output>
<gadget id="calculator">28 * 20</gadget>
<output>560</output>
<gadget id="calculator">560 / 10</gadget>
<output>56</output>
<result>56</result>


martha has the unique talent of being able to guess other people ’ s height and weight . for every 6 people that martha meets , she consistently guesses the people ’ s correct height 5 times , and for every 8 people that she meets , she consistently guesses the people ’ s correct weight 6 times . if martha meets 3 people and her success rate remains constant , what is the probability that martha correctly guesses a person ’ s weight and height at least once ?

Explanation: probability that she guesses the height correctly p ( h ) = 5 / 6 probability that she guesses the weight correctlyp ( w ) = 6 / 8 probability that she guesses both weight and height correctly ( p ( h ) * p ( w ) ) = 5 / 6 * 6 / 8 = 30 / 48 now the q asks about the probability of this happening atleast once . we calculate it by finding the probability of not being able to guess in any of the three occasions . probability of not being able to guess any no . of times = 1 - 30 / 48 = 18 / 48 = 3 / 8 for all three occasions p ( a ) = 3 / 8 * 3 / 8 * 3 / 8 = 27 / 512 probability of the event happening atleast once = 1 - p ( a ) = 1 - 27 / 512 = 485 / 512 ans should be c

subtract(const_1, power(subtract(const_1, multiply(divide(5, 6), divide(6, 8))), const_3))

<gadget id="calculator">5 / 6</gadget>
<output>5/6 = around 0.833333</output>
<gadget id="calculator">6 / 8</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(5/6) * (3/4)</gadget>
<output>5/8 = around 0.625</output>
<gadget id="calculator">1 - (5/8)</gadget>
<output>3/8 = around 0.375</output>
<gadget id="calculator">(3/8) ** 3</gadget>
<output>27/512 = around 0.052734</output>
<gadget id="calculator">1 - (27/512)</gadget>
<output>485/512 = around 0.947266</output>
<result>485/512 = around 0.947266</result>


the ratio of the number of red cars in a certain parking lot to the number of black cars is 3 to 8 . if there are 90 black cars in the lot , how many red cars are there in the lot ?

Explanation: b is correct r / b = 3 / 8 and b = 90 r = 90 * 3 / 8 = 33

<gadget id="calculator">3 / 8</gadget>
<output>3/8 = around 0.375</output>
<gadget id="calculator">(3/8) * 90</gadget>
<output>135/4 = around 33.75</output>
<gadget id="calculator">floor(135/4)</gadget>
<output>33</output>
<result>33</result>


a bowl was filled with 10 ounces of water , and 0.004 ounce of the water evaporated each day during a 50 - day period . what percent of the original amount of water evaporated during this period ?

Explanation: "total amount of water evaporated each day during a 50 - day period = . 004 * 50 = . 004 * 100 / 2 = . 4 / 2 = . 2 percent of the original amount of water evaporated during this period = ( . 2 / 10 ) * 100 % = 2 % answer d"

multiply(divide(multiply(50, 0.004), 10), const_100)

<gadget id="calculator">50 * 0.004</gadget>
<output>0.2</output>
<gadget id="calculator">0.2 / 10</gadget>
<output>0.02</output>
<gadget id="calculator">0.02 * 100</gadget>
<output>2</output>
<result>2</result>


of the families in city x in 1994 , 35 percent owned a personal computer . the number of families in city x owning a computer in 1998 was 20 percent greater than it was in 1994 , and the total number of families in city x was 4 percent greater in 1998 than it was in 1994 . what percent of the families in city x owned a personal computer in 1998 ?

Explanation: "say a 100 families existed in 1994 then the number of families owning a computer in 1994 - 40 number of families owning computer in 1998 = 35 * 120 / 100 = 42 number of families in 1998 = 104 the percentage = 42 / 104 * 100 = 40.38 % . option : d"

multiply(const_100, divide(divide(multiply(add(20, const_100), 35), const_100), add(const_100, 4)))

<gadget id="calculator">20 + 100</gadget>
<output>120</output>
<gadget id="calculator">120 * 35</gadget>
<output>4_200</output>
<gadget id="calculator">4_200 / 100</gadget>
<output>42</output>
<gadget id="calculator">100 + 4</gadget>
<output>104</output>
<gadget id="calculator">42 / 104</gadget>
<output>21/52 = around 0.403846</output>
<gadget id="calculator">100 * (21/52)</gadget>
<output>525/13 = around 40.384615</output>
<result>525/13 = around 40.384615</result>


the surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 12 cm each . the radius of the sphere is

Explanation: "solution 4 π r 2 = 2 π 6 x 12 ⇒ r 2 = ( 6 x 12 / 2 ) ⇒ 36 ⇒ r = 6 cm . answer c"

sqrt(divide(multiply(multiply(const_pi, multiply(12, divide(12, const_2))), const_2), multiply(const_pi, const_4)))

<gadget id="calculator">12 / 2</gadget>
<output>6</output>
<gadget id="calculator">12 * 6</gadget>
<output>72</output>
<gadget id="calculator">pi * 72</gadget>
<output>72*pi = around 226.194671</output>
<gadget id="calculator">(72*pi) * 2</gadget>
<output>144*pi = around 452.389342</output>
<gadget id="calculator">pi * 4</gadget>
<output>4*pi = around 12.566371</output>
<gadget id="calculator">(144*pi) / (4*pi)</gadget>
<output>36</output>
<gadget id="calculator">36 ** (1/2)</gadget>
<output>6</output>
<result>6</result>


the area of a parallelogram is 72 sq m and its base is 12 m . then the length of the height is ?

Explanation: b * h = 72 . h * 12 = 72 = > h = 6 m . answer : ( a )

<gadget id="calculator">72 / 2</gadget>
<output>36</output>
<gadget id="calculator">36 ** (1/2)</gadget>
<output>6</output>
<result>6</result>


a set of pictures of butterflies contains 10 pictures . jim bought 3 of the pictures . if 2 pictures are to be picked out from the 10 pictures , what is the probability that both pictures are not those that were already bought by jim ?

Explanation: probability of first pick not one of the jim ' s picture is = 7 / 10 ( except for 3 which jim purchased ) probability of second pick not one of the jim ' s picture is = 6 / 9 total = 7 / 10 ∗ 6 / 9 = 7 / 15 answer is d option d

divide(divide(divide(factorial(subtract(10, 3)), factorial(subtract(subtract(10, 3), 2))), factorial(2)), divide(divide(factorial(10), factorial(subtract(10, 2))), factorial(2)))

<gadget id="calculator">10 - 3</gadget>
<output>7</output>
<gadget id="calculator">factorial(7)</gadget>
<output>5_040</output>
<gadget id="calculator">7 - 2</gadget>
<output>5</output>
<gadget id="calculator">factorial(5)</gadget>
<output>120</output>
<gadget id="calculator">5_040 / 120</gadget>
<output>42</output>
<gadget id="calculator">factorial(2)</gadget>
<output>2</output>
<gadget id="calculator">42 / 2</gadget>
<output>21</output>
<gadget id="calculator">factorial(10)</gadget>
<output>3_628_800</output>
<gadget id="calculator">10 - 2</gadget>
<output>8</output>
<gadget id="calculator">factorial(8)</gadget>
<output>40_320</output>
<gadget id="calculator">3_628_800 / 40_320</gadget>
<output>90</output>
<gadget id="calculator">90 / 2</gadget>
<output>45</output>
<gadget id="calculator">21 / 45</gadget>
<output>7/15 = around 0.466667</output>
<result>7/15 = around 0.466667</result>


maths , physics and chemistry books are stored on a library shelf that can accommodate 25 books . currently , 20 % of the shelf spots remain empty . there are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books . among all the books , 12 books are soft cover and the remaining are hard - cover . if there are a total of 7 hard - cover books among the maths and physics books . what is the probability q , that a book selected at random is either a hard cover book or a chemistry book ?

Explanation: first phase of this problem requires you to determine how many mathematics and chemistry books are even on the shelf . to do so , you have the equations : m + p + c = 20 ( since 4 / 5 of the 25 spots are full of books ) m = 2 p p = 4 + c from that , you can use substitution to get everything down to one variable . c = p - 4 m = 2 p p = p then ( p - 4 ) + 2 p + p = 20 , so 4 p = 24 and p = 6 . that means that there are 12 math , 6 physics , and 2 chemistry books on the shelf . with those numbers , you also know that there are 8 total hardcovers , 1 of which is chemistry . so if your goal is to get either a hardcover or a chemistry , there are 9 ways towin - either one of the 7 hardcovers that are n ' t chemistry or the two chemistry books . so out of the 20 total , q = 9 provide the desired outcome , making the answer e .

subtract(add(divide(const_2, add(add(const_2, add(const_2, 4)), 12)), divide(add(const_2, add(const_2, 4)), add(add(const_2, add(const_2, 4)), 12))), multiply(divide(const_2, add(add(const_2, add(const_2, 4)), 12)), divide(add(const_2, add(const_2, 4)), add(add(const_2, add(const_2, 4)), 12))))

<gadget id="calculator">2 + 4</gadget>
<output>6</output>
<gadget id="calculator">2 + 6</gadget>
<output>8</output>
<gadget id="calculator">8 + 12</gadget>
<output>20</output>
<gadget id="calculator">2 / 20</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">8 / 20</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(1/10) + (2/5)</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/10) * (2/5)</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">(1/2) - (1/25)</gadget>
<output>23/50 = around 0.46</output>
<result>23/50 = around 0.46</result>


a man started driving at a constant speed , from the site of a blast , the moment he heard the blast . he heard a second blast after a time of 30 mins and 15 seconds . if the second blast occurred exactly 30 mins after the first , how many meters was he from the site when he heard the second blast ? ( speed of sound = 330 m / s )

Explanation: "the distance the sound traveled to the man is 15 * 330 = 4950 meters the answer is d ."

<gadget id="calculator">330 * 15</gadget>
<output>4_950</output>
<result>4_950</result>


eddy and freddy start simultaneously from city a and they travel to city b and city c respectively . eddy takes 3 hours and freddy takes 4 hours to complete the journey . if the distance between city a and city b is 510 kms and city a and city c is 300 kms . what is the ratio of their average speed of travel ? ( eddy : freddy )

Explanation: distance traveled by eddy = 510 km time taken by eddy = 3 hours average speed of eddy = 510 / 3 = 170 km / hour distance traveled by freddy = 300 km time taken by freddy = 4 hours average speed of freddy = 300 / 4 = 75 km / hour ratio of average speed of eddy to freddy = 170 / 75 = 34 / 15 answer e

<gadget id="calculator">510 / 3</gadget>
<output>170</output>
<gadget id="calculator">300 / 4</gadget>
<output>75</output>
<gadget id="calculator">170 / 75</gadget>
<output>34/15 = around 2.266667</output>
<result>34/15 = around 2.266667</result>


two brothers ram and ravi appeared for an exam . the probability of selection of ram is 4 / 7 and that of ravi is 1 / 5 . find the probability that both of them are selected .

Explanation: let a be the event that ram is selected and b is the event that ravi is selected . p ( a ) = 4 / 7 p ( b ) = 1 / 5 let c be the event that both are selected . p ( c ) = p ( a ) x p ( b ) as a and b are independent events : = 4 / 7 x 1 / 5 = 4 / 35 answer : a

<gadget id="calculator">4 / 7</gadget>
<output>4/7 = around 0.571429</output>
<gadget id="calculator">1 / 5</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(4/7) * (1/5)</gadget>
<output>4/35 = around 0.114286</output>
<result>4/35 = around 0.114286</result>


120 kg of an alloy a is mixed with 180 kg of alloy b . if alloy a has lead and tin in the ratio 2 : 3 and alloy b has tin and copper in the ratio 3 : 5 , then the amount of tin in the new alloy is ?

Explanation: "quantity of tin in 120 kg of a = 120 * 3 / 5 = 72 kg quantity of tin in 180 kg of b = 180 * 3 / 8 = 67.5 kg quantity of tin in the new alloy = 72 + 67.5 = 139.5 kg answer is c"

add(multiply(divide(120, add(2, 3)), 3), multiply(divide(180, add(3, 5)), 3))

<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">120 / 5</gadget>
<output>24</output>
<gadget id="calculator">24 * 3</gadget>
<output>72</output>
<gadget id="calculator">3 + 5</gadget>
<output>8</output>
<gadget id="calculator">180 / 8</gadget>
<output>45/2 = around 22.5</output>
<gadget id="calculator">(45/2) * 3</gadget>
<output>135/2 = around 67.5</output>
<gadget id="calculator">72 + (135/2)</gadget>
<output>279/2 = around 139.5</output>
<result>279/2 = around 139.5</result>


how many seconds will a train 120 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph ?

Explanation: "d = 120 + 150 = 270 s = 36 * 5 / 18 = 10 mps t = 270 / 10 = 27 sec"

<gadget id="calculator">150 + 120</gadget>
<output>270</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">36 * (5/18)</gadget>
<output>10</output>
<gadget id="calculator">270 / 10</gadget>
<output>27</output>
<result>27</result>


3 / 4 of a number is 19 less than the original number . the number is ?

Explanation: answer let the original number be n . so from question n - 3 n / 4 = 19 ⇒ 4 n - 3 n = 76 ∴ n = 76 option : c

<gadget id="calculator">19 * 4</gadget>
<output>76</output>
<result>76</result>


the cost price of 40 articles is the same as the selling price of x articles . if the profit is 25 % , what is x ?

Explanation: "let the cost price = y the cost price of 40 articles = 40 y the selling price of x articles = 1.25 y * x 1.25 y * x = 40 y x = 40 / 1.25 = 32 the answer is d ."

divide(multiply(40, const_4), add(const_4, const_1))

<gadget id="calculator">40 * 4</gadget>
<output>160</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">160 / 5</gadget>
<output>32</output>
<result>32</result>


a man can row 6 kmph in still water . when the river is running at 3 kmph , it takes him 1 hour to row to a place and black . what is the total distance traveled by the man ?

Explanation: "m = 6 s = 3 ds = 9 us = 3 x / 9 + x / 3 = 1 x = 2.25 d = 2.25 * 2 = 4.5 answer : b"

multiply(divide(multiply(add(6, 3), subtract(6, 3)), add(add(6, 3), subtract(6, 3))), const_2)

<gadget id="calculator">6 + 3</gadget>
<output>9</output>
<gadget id="calculator">6 - 3</gadget>
<output>3</output>
<gadget id="calculator">9 * 3</gadget>
<output>27</output>
<gadget id="calculator">9 + 3</gadget>
<output>12</output>
<gadget id="calculator">27 / 12</gadget>
<output>9/4 = around 2.25</output>
<gadget id="calculator">(9/4) * 2</gadget>
<output>9/2 = around 4.5</output>
<result>9/2 = around 4.5</result>


the interest on a certain deposit at 4.5 % p . a . is rs . 202.50 in one year . how much will the additional interest in one year be on the same deposit at 5 % p . a ?

Explanation: "solution s . i = rs . 202.50 , r = 4.5 % , t = 1 year principal = rs ( 100 * 202.50 / 4.5 * 1 ) = rs . 4500 now p = rs . 4500 , r = 5 % , t = 1 year s . i = ( 4500 * 5 * 1 / 100 ) = rs . 225 different in interest = rs . ( 225 - 202.50 ) = rs . 22.50 answer b"

subtract(divide(multiply(divide(202.50, divide(4.5, const_100)), 5), const_100), 202.50)

<gadget id="calculator">4.5 / 100</gadget>
<output>0.045</output>
<gadget id="calculator">202.5 / 0.045</gadget>
<output>4_500</output>
<gadget id="calculator">4_500 * 5</gadget>
<output>22_500</output>
<gadget id="calculator">22_500 / 100</gadget>
<output>225</output>
<gadget id="calculator">225 - 202.5</gadget>
<output>22.5</output>
<result>22.5</result>


Explanation: "dove straight into calculation but quickly realized that the sum of two negatives is a negative so there is only one option . - 0.852 answer a"

divide(subtract(negate(multiply(1.9, 0.6)), multiply(2.6, 1.2)), 5.0)

<gadget id="calculator">1.9 * 0.6</gadget>
<output>1.14</output>
<gadget id="calculator">-1.14</gadget>
<output>-1.14</output>
<gadget id="calculator">2.6 * 1.2</gadget>
<output>3.12</output>
<gadget id="calculator">(-1.14) - 3.12</gadget>
<output>-4.26</output>
<gadget id="calculator">(-4.26) / 5</gadget>
<output>-0.852</output>
<result>-0.852</result>


if the wheel is 12 cm then the number of revolutions to cover a distance of 1056 cm is ?

Explanation: "2 * 22 / 7 * 12 * x = 1056 = > x = 14 answer : c"

divide(1056, multiply(multiply(const_2, divide(add(add(multiply(const_3, const_100), multiply(const_1, const_10)), const_4), const_100)), 12))

<gadget id="calculator">3 * 100</gadget>
<output>300</output>
<gadget id="calculator">1 * 10</gadget>
<output>10</output>
<gadget id="calculator">300 + 10</gadget>
<output>310</output>
<gadget id="calculator">310 + 4</gadget>
<output>314</output>
<gadget id="calculator">314 / 100</gadget>
<output>157/50 = around 3.14</output>
<gadget id="calculator">2 * (157/50)</gadget>
<output>157/25 = around 6.28</output>
<gadget id="calculator">(157/25) * 12</gadget>
<output>1_884/25 = around 75.36</output>
<gadget id="calculator">1_056 / (1_884/25)</gadget>
<output>2_200/157 = around 14.012739</output>
<result>2_200/157 = around 14.012739</result>


if the length and breadth of a rectangular room are each increased by 1 m , then the area of floor is increased by 21 sq . m . if the length is creased by 1 m and breadth is decreased by 1 m , then the area is decreased by 5 sq . m . the perimeter of the floor is :

Explanation: let length = x meters and breadth = y meters . then , ( x + 1 ) ( y + 1 ) - xy = 21 x + y = 20 ã ¢ â ‚ ¬ â ¦ ã ¢ â ‚ ¬ â ¦ ã ¢ â ‚ ¬ â ¦ ã ¢ â ‚ ¬ â ¦ ã ¢ â ‚ ¬ â ¦ ã ¢ â ‚ ¬ â ¦ 1 and , xy - [ ( x + 1 ) ( y - 1 ) ] = 5 x - y = 6 ã ¢ â ‚ ¬ â ¦ ã ¢ â ‚ ¬ â ¦ ã ¢ â ‚ ¬ â ¦ ã ¢ â ‚ ¬ â ¦ ã ¢ â ‚ ¬ â ¦ ã ¢ â ‚ ¬ â ¦ . . 2 solving ( i ) and ( ii ) , we get : x = 13 and y = 7 so , length = 13 m and breadth = 7 m . perimeter = [ 2 ( 13 + 7 ) ] m = 40 m . answer : c

rectangle_perimeter(divide(subtract(21, 5), const_2), subtract(subtract(21, 1), divide(subtract(21, 5), const_2)))

<gadget id="calculator">21 - 5</gadget>
<output>16</output>
<gadget id="calculator">16 / 2</gadget>
<output>8</output>
<gadget id="calculator">21 - 1</gadget>
<output>20</output>
<gadget id="calculator">20 - 8</gadget>
<output>12</output>
<gadget id="calculator">2 * (8 + 12)</gadget>
<output>40</output>
<result>40</result>


a car is 15 minutes late by running at a speed of 4 / 5 th of its actual speed . the actual time taken by the car to cover that distance is :

Explanation: explanation : new speed = 4 / 5 th of its actual speed new time = 5 / 4 th of its actual time = > 5 / 4 t - t = 15 / 60 = 1 / 4 = > 1 / 4 t = 1 / 4 = > t = 1 hour answer : b

<gadget id="calculator">5 - 4</gadget>
<output>1</output>
<result>1</result>


the average runs scored by a batsman in 20 matches is 40 . in the next 10 matches the batsman scored an average of 30 runs . find his average in all the 30 matches ?

Explanation: "total score of the batsman in 20 matches = 800 . total score of the batsman in the next 10 matches = 300 . total score of the batsman in the 30 matches = 1100 . average score of the batsman = 1100 / 30 = 36.67 . answer : b"

divide(add(multiply(40, 20), multiply(30, 10)), add(20, 10))

<gadget id="calculator">40 * 20</gadget>
<output>800</output>
<gadget id="calculator">30 * 10</gadget>
<output>300</output>
<gadget id="calculator">800 + 300</gadget>
<output>1_100</output>
<gadget id="calculator">20 + 10</gadget>
<output>30</output>
<gadget id="calculator">1_100 / 30</gadget>
<output>110/3 = around 36.666667</output>
<result>110/3 = around 36.666667</result>


the maitre ' d at an expensive manhattan restaurant has noticed that 60 % of the couples order dessert and coffee . however , 20 % of the couples who order dessert do n ' t order coffee . what is the probability t that the next couple the maitre ' d seats will not order dessert ?

Explanation: "could you use a venn diagram and just go with the number 100 . 60 people order dessert and coffee . . . which is the union of d and c . t = 2 / 10 of d are n ' t in d u c = so 8 / 10 of d are in duc which means = 60 = 8 / 10 d . so d in total = 75 , and 15 d ' s are n ' t in d union c . which means 25 people are in c only + neither . b 25 %"

multiply(subtract(const_1, divide(divide(60, multiply(multiply(const_2, const_5), multiply(const_2, const_5))), subtract(const_1, divide(20, multiply(multiply(const_2, const_5), multiply(const_2, const_5)))))), multiply(multiply(const_2, const_5), multiply(const_2, const_5)))

<gadget id="calculator">2 * 5</gadget>
<output>10</output>
<gadget id="calculator">10 * 10</gadget>
<output>100</output>
<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(3/5) / (4/5)</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">1 - (3/4)</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 100</gadget>
<output>25</output>
<result>25</result>


anne bought doughnuts for a class breakfast party . she bought 6 chocolate doughnuts , 8 coconut doughnuts , and 8 jam - filled doughnuts . how many doughnuts did anne buy in all ?

Explanation: "add the numbers of doughnuts . 6 + 8 + 8 = 22 . answer is a ."

<gadget id="calculator">6 + 8</gadget>
<output>14</output>
<gadget id="calculator">14 + 8</gadget>
<output>22</output>
<result>22</result>


i sold a book at a profit of 10 % . had i sold it for $ 110 more , 15 % would have been gained . find the cost price ?

Explanation: 115 % of cost - 110 % of cost = $ 110 5 % of cost = $ 110 cost = 110 * 100 / 5 = $ 2200 answer is b

divide(multiply(divide(multiply(110, 10), subtract(15, 10)), const_100), 10)

<gadget id="calculator">110 * 10</gadget>
<output>1_100</output>
<gadget id="calculator">15 - 10</gadget>
<output>5</output>
<gadget id="calculator">1_100 / 5</gadget>
<output>220</output>
<gadget id="calculator">220 * 100</gadget>
<output>22_000</output>
<gadget id="calculator">22_000 / 10</gadget>
<output>2_200</output>
<result>2_200</result>


90 % of the population of a village is 36000 . the total population of the village is ?

Explanation: "x * ( 90 / 100 ) = 36000 x = 400 * 100 x = 40000 answer : e"

<gadget id="calculator">100 / 90</gadget>
<output>10/9 = around 1.111111</output>
<gadget id="calculator">(10/9) * 36_000</gadget>
<output>40_000</output>
<result>40_000</result>


Explanation: "dove straight into calculation ( ( - 1.9 ) ( 0.6 ) – ( 2.6 ) ( 1.2 ) ) / 2.0 = - 2.13 answer b"

divide(subtract(negate(multiply(1.9, 0.6)), multiply(2.6, 1.2)), 2.0)

<gadget id="calculator">1.9 * 0.6</gadget>
<output>1.14</output>
<gadget id="calculator">-1.14</gadget>
<output>-1.14</output>
<gadget id="calculator">2.6 * 1.2</gadget>
<output>3.12</output>
<gadget id="calculator">(-1.14) - 3.12</gadget>
<output>-4.26</output>
<gadget id="calculator">(-4.26) / 2</gadget>
<output>-2.13</output>
<result>-2.13</result>


the probability that a number selected at random from the first 50 natural numbers is a composite number is

Explanation: the number of exhaustive events = ⁵ ⁰ c ₁ = 50 . we have 15 primes from 1 to 50 . number of favourable cases are 34 . required probability = 34 / 50 = 17 / 25 . nswer : b

divide(multiply(subtract(multiply(const_6, const_3), const_1), const_2), 50)

<gadget id="calculator">6 * 3</gadget>
<output>18</output>
<gadget id="calculator">18 - 1</gadget>
<output>17</output>
<gadget id="calculator">17 * 2</gadget>
<output>34</output>
<gadget id="calculator">34 / 50</gadget>
<output>17/25 = around 0.68</output>
<result>17/25 = around 0.68</result>


a retailer buys 80 pens at the market price of 36 pens from a wholesaler , if he sells these pens giving a discount of 1 % , what is the profit % ?

Explanation: "let the market price of each pen be $ 1 then , cost price of 80 pens = $ 36 selling price of 80 pens = 99 % of $ 80 = $ 79.20 profit % = ( ( 43.20 * 100 ) / 36 ) % = 120 % answer e ) 120"

multiply(const_100, divide(subtract(subtract(1, divide(1, const_100)), divide(36, 80)), divide(36, 80)))

<gadget id="calculator">1 / 100</gadget>
<output>1/100 = around 0.01</output>
<gadget id="calculator">1 - (1/100)</gadget>
<output>99/100 = around 0.99</output>
<gadget id="calculator">36 / 80</gadget>
<output>9/20 = around 0.45</output>
<gadget id="calculator">(99/100) - (9/20)</gadget>
<output>27/50 = around 0.54</output>
<gadget id="calculator">(27/50) / (9/20)</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">100 * (6/5)</gadget>
<output>120</output>
<result>120</result>


if there are only 2 wheelers and 4 wheelers parked in a school located at the heart of the city , find the number of 4 wheelers parked there if the total number of wheels is 66 ?

Explanation: "four wheeler = 16 * 4 = 64 ( max ) 2 wheel = 1 so no of 4 wheeler = 16 answer : d"

<gadget id="calculator">66 - 2</gadget>
<output>64</output>
<gadget id="calculator">64 / 4</gadget>
<output>16</output>
<result>16</result>


a train running at the speed of 27 km / hr crosses a post in 20 seconds . what is the length of the train ?

Explanation: "speed = ( 27 x 5 / 18 ) = 7.5 m / sec . length of the train = ( speed x time ) . length of the train = 7.5 x 20 m = 150 m . answer : b"

multiply(divide(multiply(27, const_1000), const_3600), 20)

<gadget id="calculator">27 * 1_000</gadget>
<output>27_000</output>
<gadget id="calculator">27_000 / 3_600</gadget>
<output>15/2 = around 7.5</output>
<gadget id="calculator">(15/2) * 20</gadget>
<output>150</output>
<result>150</result>


what is the rate percent when the simple interest on rs . 800 amount to rs . 128 in 4 years ?

Explanation: "128 = ( 800 * 4 * r ) / 100 r = 4 % answer : c"

divide(multiply(const_100, 128), multiply(800, 4))

<gadget id="calculator">100 * 128</gadget>
<output>12_800</output>
<gadget id="calculator">800 * 4</gadget>
<output>3_200</output>
<gadget id="calculator">12_800 / 3_200</gadget>
<output>4</output>
<result>4</result>


an error 1 % in excess is made while measuring the side of a square . the percentage of error in the calculated area of the square is :

Explanation: "explanation : 100 cm is read as 101 cm . a 1 = ( 100 × 100 ) cm 2 = 10000 and a 2 = ( 101 × 101 ) cm 2 = 10609 ( a 2 - a 1 ) = 10201 - 10000 = 201 = > 201 / 10000 * 100 = 2.01 answer : a"

divide(multiply(subtract(square_area(add(const_100, 1)), square_area(const_100)), const_100), square_area(const_100))

<gadget id="calculator">100 + 1</gadget>
<output>101</output>
<gadget id="calculator">101 ** 2</gadget>
<output>10_201</output>
<gadget id="calculator">100 ** 2</gadget>
<output>10_000</output>
<gadget id="calculator">10_201 - 10_000</gadget>
<output>201</output>
<gadget id="calculator">201 * 100</gadget>
<output>20_100</output>
<gadget id="calculator">20_100 / 10_000</gadget>
<output>201/100 = around 2.01</output>
<result>201/100 = around 2.01</result>


the average mark of the students of a class in a particular exam is 80 . if 5 students whose average mark in that exam is 60 are excluded , the average mark of the remaining will be 90 . find the number of students who wrote the exam .

Explanation: "let the number of students who wrote the exam be x . total marks of students = 80 x . total marks of ( x - 5 ) students = 90 ( x - 5 ) 80 x - ( 5 * 60 ) = 90 ( x - 5 ) 150 = 10 x = > x = 15 . answer : c"

divide(subtract(multiply(90, 5), multiply(5, 60)), subtract(90, 80))

<gadget id="calculator">90 * 5</gadget>
<output>450</output>
<gadget id="calculator">5 * 60</gadget>
<output>300</output>
<gadget id="calculator">450 - 300</gadget>
<output>150</output>
<gadget id="calculator">90 - 80</gadget>
<output>10</output>
<gadget id="calculator">150 / 10</gadget>
<output>15</output>
<result>15</result>


ann and bob drive separately to a meeting . ann ' s average driving speed is greater than bob ' s avergae driving speed by one - third of bob ' s average driving speed , and ann drives twice as many miles as bob . what is the ratio w of the number of hours ann spends driving to the meeting to the number of hours bob spends driving to the meeting ?

Explanation: "say the rate of bob is 3 mph and he covers 6 miles then he needs 6 / 3 = 2 hours to do that . now , in this case the rate of ann would be 3 + 3 * 1 / 3 = 4 mph and the distance she covers would be 6 * 2 = 12 miles , so she needs 12 / 4 = 3 hours for that . the ratio w of ann ' s time to bob ' s time is 3 : 2 . answer : b ."

divide(const_2, add(const_1, divide(const_1, const_3)))

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 + (1/3)</gadget>
<output>4/3 = around 1.333333</output>
<gadget id="calculator">2 / (4/3)</gadget>
<output>3/2 = around 1.5</output>
<result>3/2 = around 1.5</result>


Explanation: "72515 x 9999 = 72515 x ( 10000 - 1 ) = 72515 x 10000 - 72515 x 1 = 725150000 - 72515 = 725077485 d"

<gadget id="calculator">9_999 - 4</gadget>
<output>9_995</output>
<gadget id="calculator">9_995 * 72_515</gadget>
<output>724_787_425</output>
<result>724_787_425</result>


a can give b 50 meters start and c 200 meters start in a kilometer race . how much start can b give c in a kilometer race ?

Explanation: "a runs 1000 m while b runs 950 m and c runs 800 m . the number of meters that c runs when b runs 1000 m , = ( 1000 * 800 ) / 950 = 842.10 m . b can give c = 1000 - 842.10 = 157.89 m . answer : a"

subtract(multiply(const_100, const_10), divide(multiply(multiply(const_100, const_10), subtract(multiply(const_100, const_10), 200)), subtract(multiply(const_100, const_10), 50)))

<gadget id="calculator">100 * 10</gadget>
<output>1_000</output>
<gadget id="calculator">1_000 - 200</gadget>
<output>800</output>
<gadget id="calculator">1_000 * 800</gadget>
<output>800_000</output>
<gadget id="calculator">1_000 - 50</gadget>
<output>950</output>
<gadget id="calculator">800_000 / 950</gadget>
<output>16_000/19 = around 842.105263</output>
<gadget id="calculator">1_000 - (16_000/19)</gadget>
<output>3_000/19 = around 157.894737</output>
<result>3_000/19 = around 157.894737</result>


the present population of a town is 1240 . population increase rate is 4 % p . a . find the population of town after 1 years ?

Explanation: "p = 1240 r = 4 % required population of town = p * ( 1 + r / 100 ) ^ t = 1240 * ( 1 + 4 / 100 ) = 1240 * ( 26 / 25 ) = 1290 ( approximately ) answer is e"

add(1240, divide(multiply(1240, 4), const_100))

<gadget id="calculator">1_240 * 4</gadget>
<output>4_960</output>
<gadget id="calculator">4_960 / 100</gadget>
<output>248/5 = around 49.6</output>
<gadget id="calculator">1_240 + (248/5)</gadget>
<output>6_448/5 = around 1_289.6</output>
<result>6_448/5 = around 1_289.6</result>


sandy bought 65 books for $ 1080 from one shop and 55 books for $ 840 from another shop . what is the average price that sandy paid per book ?

Explanation: "average price per book = ( 1080 + 840 ) / ( 65 + 55 ) = 1920 / 120 = $ 16 the answer is b ."

<gadget id="calculator">1_080 + 840</gadget>
<output>1_920</output>
<gadget id="calculator">65 + 55</gadget>
<output>120</output>
<gadget id="calculator">1_920 / 120</gadget>
<output>16</output>
<result>16</result>


a merchant marks goods up by 80 % and then offers a discount on the marked price . the profit that the merchant makes after offering the discount is 35 % . what % discount did the merchant offer ?

Explanation: "let p be the original price of the goods and let x be the rate after the markup . ( 1.8 p ) * x = 1.35 p x = 1.35 / 1.8 = 0.75 which is a discount of 25 % . the answer is b ."

multiply(divide(subtract(subtract(add(const_1, divide(80, const_100)), const_1), divide(35, const_100)), add(const_1, divide(80, const_100))), const_100)

<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">1 + (4/5)</gadget>
<output>9/5 = around 1.8</output>
<gadget id="calculator">(9/5) - 1</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">35 / 100</gadget>
<output>7/20 = around 0.35</output>
<gadget id="calculator">(4/5) - (7/20)</gadget>
<output>9/20 = around 0.45</output>
<gadget id="calculator">(9/20) / (9/5)</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 100</gadget>
<output>25</output>
<result>25</result>


the average height of 20 students in a class was calculated as 175 cm . it has later found that the height of one of the students in the class was incorrectly written as 151 cm whereas the actual height was 136 cm . what was the actual average height of the students in the class ?

Explanation: the total height was 15 cm too much . the average height should be reduced by 15 cm / 20 = 0.75 cm the answer is b .

divide(subtract(multiply(20, 175), subtract(151, 136)), 20)

<gadget id="calculator">20 * 175</gadget>
<output>3_500</output>
<gadget id="calculator">151 - 136</gadget>
<output>15</output>
<gadget id="calculator">3_500 - 15</gadget>
<output>3_485</output>
<gadget id="calculator">3_485 / 20</gadget>
<output>697/4 = around 174.25</output>
<result>697/4 = around 174.25</result>


the cost price of a radio is rs . 3300 and it was sold for rs . 1230 , find the loss % ?

Explanation: "3300 - - - - 2070 100 - - - - ? = > 62.7 % answer : a"

multiply(divide(subtract(3300, 1230), 3300), const_100)

<gadget id="calculator">3_300 - 1_230</gadget>
<output>2_070</output>
<gadget id="calculator">2_070 / 3_300</gadget>
<output>69/110 = around 0.627273</output>
<gadget id="calculator">(69/110) * 100</gadget>
<output>690/11 = around 62.727273</output>
<result>690/11 = around 62.727273</result>


at what rate percent per annum will the simple interest on a sum of money be 3 / 5 of the amount in 10 years ?

Explanation: "let sum = x . then , s . i . = 2 x / 5 , time = 10 years . rate = ( 100 * 3 x ) / ( x * 5 * 10 ) = 6 % answer : a"

divide(multiply(divide(3, 5), const_100), 10)

<gadget id="calculator">3 / 5</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(3/5) * 100</gadget>
<output>60</output>
<gadget id="calculator">60 / 10</gadget>
<output>6</output>
<result>6</result>


working simultaneously and independently at an identical constant rate , 5 machines of a certain type can produce a total of x units of product p in 4 days . how many of these machines , working simultaneously and independently at this constant rate , can produce a total of 2 x units of product p in 2 days ?

Explanation: "the rate of 5 machines is rate = job / time = x / 4 units per day - - > the rate of 1 machine 1 / 5 * ( x / 4 ) = x / 20 units per day ; now , again as { time } * { combined rate } = { job done } then 2 * ( m * x / 20 ) = 2 x - - > m = 20 . answer : e ."

<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">4 / 2</gadget>
<output>2</output>
<gadget id="calculator">10 * 2</gadget>
<output>20</output>
<result>20</result>


heinz produces tomato puree by boiling tomato juice . the tomato puree has only 20 % water while the tomato juice has 90 % water . how many litres of tomato puree will be obtained from 20 litres of tomato juice ?

Explanation: "tomato juice has 90 % water and 10 % tomato tomato puree has 20 % water and 80 % tomato so 20 liter of tomato juice has 20 * 90 / 100 = 18 liters of water and 2 liters of tomato . as tomato puree has 80 % content of tomato , so 2 liters of tomato from 20 liter juice corresponds to 80 % so tomato purees that can be obtained = 100 * 2 / 80 = 2.5 answer : c"

divide(multiply(divide(subtract(const_100, 90), const_100), 20), divide(subtract(const_100, 20), const_100))

<gadget id="calculator">100 - 90</gadget>
<output>10</output>
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/10) * 20</gadget>
<output>2</output>
<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">2 / (4/5)</gadget>
<output>5/2 = around 2.5</output>
<result>5/2 = around 2.5</result>


a seller of used cars has 12 cars to sell and each of his clients selected 4 cars that he liked most . if each car was selected exactly thrice , how many clients visited the garage ?

Explanation: "ifno caris selected more than once then the number of clients = 12 / 4 = 3 but since every car is being selected three times so no . of clients must be thrice as well = 3 * 3 = 9 answer : option a"

<gadget id="calculator">12 / 4</gadget>
<output>3</output>
<gadget id="calculator">3 * 3</gadget>
<output>9</output>
<result>9</result>


set a contains all the even numbers between 2 and 50 inclusive . set b contains all the even numbers between 62 and 110 inclusive . what is the difference between the sum of elements of set b and the sum of the elements of set a ?

Explanation: "each term in set b is 60 more than the corresponding term in set a . the difference of the sums = 25 * 60 = 1500 . the answer is a ."

multiply(subtract(62, 2), add(divide(subtract(50, 2), const_2), const_1))

<gadget id="calculator">62 - 2</gadget>
<output>60</output>
<gadget id="calculator">50 - 2</gadget>
<output>48</output>
<gadget id="calculator">48 / 2</gadget>
<output>24</output>
<gadget id="calculator">24 + 1</gadget>
<output>25</output>
<gadget id="calculator">60 * 25</gadget>
<output>1_500</output>
<result>1_500</result>


the cost price of 20 articles is the same as the selling price of x articles . if the profit is 25 % , then the value of x is :

Explanation: "explanation : let the cost price of 1 article be z . so , the cost price of 20 article = 20 z - - - - - - - - - - - - - - - - - - - - - - - - - ( 1 ) selling price of 20 articles = 20 z + 25 % of 20 z = 25 z = > selling price of 1 article = 25 z / 20 = ( 5 / 4 ) * z = > selling price of x articles = ( 5 / 4 ) * z * x - - - - - - - - - - - - - - - - - - - - - - - - - ( 2 ) given that selling price ( s . p . ) of x articles = cost price ( c . p . ) of 20 articles = > ( 5 / 4 ) * z * x = 20 z = > x = 16 answer : b"

divide(multiply(20, const_4), add(const_4, const_1))

<gadget id="calculator">20 * 4</gadget>
<output>80</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">80 / 5</gadget>
<output>16</output>
<result>16</result>


the ratio of male to female in a class is 2 : 3 . the career preference of the students in the class are to be represented in a circle graph . if the area of the graph allocated to each career preference is to be proportional to the number of students who have that career preference , how many degrees of the circle should be used to represent a career that is preferred by one fourth of the males and 3 / 4 th of the females in the class ?

Explanation: let the common ratio be x . . so m = 2 x and f = 3 x and total = 5 x 1 / 4 of m = 2 x / 4 and 3 / 4 of f = 9 / 4 x . . total preferring that carrer = x / 2 + 9 x / 4 = 11 x / 4 now 5 x = 360 , so x = 360 / 5 = 72 . . so 72 * 11 / 4 = 198 ans 198 b

add(divide(multiply(multiply(divide(const_360, add(2, 3)), 3), 3), 4), divide(multiply(divide(const_360, add(2, 3)), 2), const_4))

<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">360 / 5</gadget>
<output>72</output>
<gadget id="calculator">72 * 3</gadget>
<output>216</output>
<gadget id="calculator">216 * 3</gadget>
<output>648</output>
<gadget id="calculator">648 / 4</gadget>
<output>162</output>
<gadget id="calculator">72 * 2</gadget>
<output>144</output>
<gadget id="calculator">144 / 4</gadget>
<output>36</output>
<gadget id="calculator">162 + 36</gadget>
<output>198</output>
<result>198</result>


at what price must an article costing rs . 47.50 be marked in order that after deducting 20 % from the list price . it may be sold at a profit of 25 % on the cost price ?

Explanation: cp = 47.50 sp = 47.50 * ( 125 / 100 ) = 59.375 mp * ( 80 / 100 ) = 59.375 mp = 74.2 answer : d

divide(multiply(add(47.5, divide(multiply(47.5, 25), const_100)), const_100), subtract(const_100, 20))

<gadget id="calculator">47.5 * 25</gadget>
<output>1_187.5</output>
<gadget id="calculator">1_187.5 / 100</gadget>
<output>11.875</output>
<gadget id="calculator">47.5 + 11.875</gadget>
<output>59.375</output>
<gadget id="calculator">59.375 * 100</gadget>
<output>5_937.5</output>
<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">5_937.5 / 80</gadget>
<output>74.21875</output>
<result>74.21875</result>


a mail handler needs 3 hours to sort the mail . his assistant takes 6 hours to sort the mail . how many hours will it take for both of them working together to sort the mail ?

Explanation: work hrs = ab / ( a + b ) = 18 / 9 = 2 answer is b

inverse(add(divide(const_1, 3), divide(const_1, 6)))

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(1/3) + (1/6)</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 / (1/2)</gadget>
<output>2</output>
<result>2</result>


a bag contains 7 black and 8 white balls . if two balls are drawn simultaneously , what is the probability that both are of the same color is ?

Explanation: drawing two balls of same color from seven black balls can be done in ⁷ c ₂ ways . similarly from eight white balls two can be drawn in ⁸ c ₂ ways . p = ⁷ c ₂ / ¹ ⁵ c ₂ + ⁸ c ₂ / ¹ ⁵ c ₂ = 7 / 15 answer is e

divide(add(divide(divide(factorial(8), factorial(subtract(8, const_2))), factorial(const_2)), divide(divide(factorial(7), factorial(subtract(7, const_2))), factorial(const_2))), divide(divide(factorial(add(7, 8)), factorial(subtract(add(7, 8), const_2))), factorial(const_2)))

<gadget id="calculator">factorial(8)</gadget>
<output>40_320</output>
<gadget id="calculator">8 - 2</gadget>
<output>6</output>
<gadget id="calculator">factorial(6)</gadget>
<output>720</output>
<gadget id="calculator">40_320 / 720</gadget>
<output>56</output>
<gadget id="calculator">factorial(2)</gadget>
<output>2</output>
<gadget id="calculator">56 / 2</gadget>
<output>28</output>
<gadget id="calculator">factorial(7)</gadget>
<output>5_040</output>
<gadget id="calculator">7 - 2</gadget>
<output>5</output>
<gadget id="calculator">factorial(5)</gadget>
<output>120</output>
<gadget id="calculator">5_040 / 120</gadget>
<output>42</output>
<gadget id="calculator">42 / 2</gadget>
<output>21</output>
<gadget id="calculator">28 + 21</gadget>
<output>49</output>
<gadget id="calculator">7 + 8</gadget>
<output>15</output>
<gadget id="calculator">factorial(15)</gadget>
<output>1_307_674_368_000</output>
<gadget id="calculator">15 - 2</gadget>
<output>13</output>
<gadget id="calculator">factorial(13)</gadget>
<output>6_227_020_800</output>
<gadget id="calculator">1_307_674_368_000 / 6_227_020_800</gadget>
<output>210</output>
<gadget id="calculator">210 / 2</gadget>
<output>105</output>
<gadget id="calculator">49 / 105</gadget>
<output>7/15 = around 0.466667</output>
<result>7/15 = around 0.466667</result>


if it is assumed that 60 percent of those who receive a questionnaire by mail will respond and 240 responses are needed , what is the minimum number of questionnaires that should be mailed ?

Explanation: "let x be the minimum number of questionnaires to be mailed . 0.6 x = 240 x = 400 the answer is a ."

<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">240 / (3/5)</gadget>
<output>400</output>
<result>400</result>


a does half as much work as b in 3 - fourth of the time . if together they take 18 days to complete the work , how much time shall b take to do it ?

Explanation: explanation : let ‘ x ’ be the number of days taken by b alone to finish the whole work then , a alone will finish the whole work in 3 x / 4 × 2 days = 3 x / 2 days . then , working together , 3 x / 2 × x / 3 x / 2 + x = 18 days 3 x × x / 5 x = 18 3 x / 5 = 18 therefore , the number of days taken by b = x = 18 × 5 / 3 = 30 days . answer : option a

divide(multiply(18, add(3, const_2)), 3)

<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">18 * 5</gadget>
<output>90</output>
<gadget id="calculator">90 / 3</gadget>
<output>30</output>
<result>30</result>


a certain sum of money is divided among a , b and c so that for each rs . a has , b has 65 paisa and c 40 paisa . if c ' s share is rs . 56 , find the sum of money ?

Explanation: "a : b : c = 100 : 65 : 40 = 20 : 13 : 8 8 - - - - 56 41 - - - - ? = > rs . 287 answer : b"

multiply(divide(56, 40), add(add(const_100, 65), 40))

<gadget id="calculator">56 / 40</gadget>
<output>7/5 = around 1.4</output>
<gadget id="calculator">100 + 65</gadget>
<output>165</output>
<gadget id="calculator">165 + 40</gadget>
<output>205</output>
<gadget id="calculator">(7/5) * 205</gadget>
<output>287</output>
<result>287</result>


in what time will a train 80 m long cross an electric pole , it its speed be 144 km / hr ?

Explanation: "speed = 144 * 5 / 18 = 40 m / sec time taken = 80 / 40 = 2.0 sec . answer : a"

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">144 * (5/18)</gadget>
<output>40</output>
<gadget id="calculator">80 / 40</gadget>
<output>2</output>
<result>2</result>


john purchased 1375 large bottles at $ 1.75 per bottle and 690 small bottles at $ 1.35 per bottle . what was the approximate average price paid per bottle ?

Explanation: "( 1375 * 1.75 + 690 * 1.35 ) / ( 1375 + 690 ) = ~ 1.62 option ( a )"

<gadget id="calculator">1_375 * 1.75</gadget>
<output>2_406.25</output>
<gadget id="calculator">690 * 1.35</gadget>
<output>931.5</output>
<gadget id="calculator">2_406.25 + 931.5</gadget>
<output>3_337.75</output>
<gadget id="calculator">1_375 + 690</gadget>
<output>2_065</output>
<gadget id="calculator">3_337.75 / 2_065</gadget>
<output>1.616344</output>
<result>1.616344</result>


an investor deposited $ 5,000 to open a new savings account that earned 8 percent annual interest , compounded quarterly . if there were no other transactions in the account , what was the amount of money in the account 6 months after the account was opened ?

Explanation: "the amount in the account after 6 months is 1.02 * 1.02 ( $ 5,000 ) = $ 5202 the answer is c ."

multiply(multiply(multiply(add(const_2, const_3), const_100), multiply(add(const_2, const_3), const_2)), power(add(divide(divide(8, const_4), const_100), const_1), const_2))

<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">5 * 100</gadget>
<output>500</output>
<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">500 * 10</gadget>
<output>5_000</output>
<gadget id="calculator">8 / 4</gadget>
<output>2</output>
<gadget id="calculator">2 / 100</gadget>
<output>1/50 = around 0.02</output>
<gadget id="calculator">(1/50) + 1</gadget>
<output>51/50 = around 1.02</output>
<gadget id="calculator">(51/50) ** 2</gadget>
<output>2_601/2_500 = around 1.0404</output>
<gadget id="calculator">5_000 * (2_601/2_500)</gadget>
<output>5_202</output>
<result>5_202</result>


a pet store holds cats and dogs . if the difference between the number of cats and the number of dogs is 11 . what could be the ratio of cats to dogs in the pet store ?

Explanation: say theratioof cats to dogs is a / b . then thenumberof cats would be ax and thenumberof dogs bx , for some positive integer x . we are told that ax - bx = 11 - - > x ( a - b ) = 11 . since 11 is a prime number it could be broken into the product of two positive multiples only in one way : x ( a - b ) = 1 * 11 . the above implies that either x = 1 and ( a - b ) = 11 or x = 11 and ( a - b ) = 1 . therefore the correct answer should have the difference between numerator and denominator equal to 1 or 11 . for the original question only option which fits is e , 4 : 5 . cats = 11 * 4 = 44 and dogs = 11 * 5 = 55 . answer : d .

divide(multiply(11, const_4), add(multiply(11, const_4), 11))

<gadget id="calculator">11 * 4</gadget>
<output>44</output>
<gadget id="calculator">44 + 11</gadget>
<output>55</output>
<gadget id="calculator">44 / 55</gadget>
<output>4/5 = around 0.8</output>
<result>4/5 = around 0.8</result>


john makes $ 60 a week from his job . he earns a raise and now makes $ 90 a week . what is the % increase ?

Explanation: "increase = ( 30 / 60 ) * 100 = ( 3 / 6 ) * 100 = 50 % . b"

multiply(divide(subtract(90, 60), 60), const_100)

<gadget id="calculator">90 - 60</gadget>
<output>30</output>
<gadget id="calculator">30 / 60</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) * 100</gadget>
<output>50</output>
<result>50</result>


x can finish a work in 21 days . y can finish the same work in 15 days . yworked for 10 days and left the job . how many days does x alone need to finish the remaining work ?

Explanation: "work done by x in 1 day = 1 / 21 work done by y in 1 day = 1 / 15 work done by y in 10 days = 10 / 15 = 2 / 3 remaining work = 1 – 2 / 3 = 1 / 3 number of days in which x can finish the remaining work = ( 1 / 3 ) / ( 1 / 21 ) = 7 c"

divide(subtract(const_1, multiply(10, divide(const_1, 15))), divide(const_1, 21))

<gadget id="calculator">1 / 15</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">10 * (1/15)</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">1 - (2/3)</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 / 21</gadget>
<output>1/21 = around 0.047619</output>
<gadget id="calculator">(1/3) / (1/21)</gadget>
<output>7</output>
<result>7</result>


a sells a bicycle to b and makes a profit of 25 % . b sells the same bicycle to c at a profit of 50 % . if the final s . p . of the bicycle was rs . 225 , find out the cost price of the bicycle for a .

Explanation: explanation : let cp be 100 a sells at 25 % profit so sp = 125 b sells at 50 % profit = 125 x ( 1 + 50 / 100 ) = 187.5 cp - - - sp 100 - - - 187.5 x - - - 225 cp = 225 x 100 / 187.5 = 120 answer : e

divide(divide(225, divide(add(const_100, 50), const_100)), divide(add(25, const_100), const_100))

<gadget id="calculator">100 + 50</gadget>
<output>150</output>
<gadget id="calculator">150 / 100</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">225 / (3/2)</gadget>
<output>150</output>
<gadget id="calculator">25 + 100</gadget>
<output>125</output>
<gadget id="calculator">125 / 100</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">150 / (5/4)</gadget>
<output>120</output>
<result>120</result>