the average marks of a class of 12 students is 40 and that of another class of 28 students is 60 . find the average marks of all the students ?

Explanation: "sum of the marks for the class of 12 students = 12 * 40 = 480 sum of the marks for the class of 28 students = 28 * 60 = 1680 sum of the marks for the class of 40 students = 480 + 1680 = 2160 average marks of all the students = 2160 / 40 = 54 answer : e"

divide(add(multiply(12, 40), multiply(28, 60)), add(12, 28))

<gadget id="calculator">12 * 40</gadget>
<output>480</output>
<gadget id="calculator">28 * 60</gadget>
<output>1_680</output>
<gadget id="calculator">480 + 1_680</gadget>
<output>2_160</output>
<gadget id="calculator">12 + 28</gadget>
<output>40</output>
<gadget id="calculator">2_160 / 40</gadget>
<output>54</output>
<result>54</result>


if 10 gallons of grape juice are added to 40 gallons of a mixture , which contains 20 percent grape juice then what percent of the resulting mixture is grape juice ?

Explanation: official solution : if we start with 40 gallons of a mixture that is 10 % grape juice , then we have : 40 × 0.20 = 8 gallons of grape juice . 40 × 0.80 = 32 gallons of other components . if we add 10 gallons of grape juice , we will end up with 18 gallons of grape juice and 32 gallons of other components , and we will have a total of 50 gallons of the mixture . so 18 / 50 of the new mixture is grape juice . now we convert this to a percent : percent grape juice = 18 / 50 = 36 / 100 = 36 % . the correct answer is choice ( d )

multiply(divide(add(multiply(divide(20, const_100), 40), 10), add(40, 10)), const_100)

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 40</gadget>
<output>8</output>
<gadget id="calculator">8 + 10</gadget>
<output>18</output>
<gadget id="calculator">40 + 10</gadget>
<output>50</output>
<gadget id="calculator">18 / 50</gadget>
<output>9/25 = around 0.36</output>
<gadget id="calculator">(9/25) * 100</gadget>
<output>36</output>
<result>36</result>


15 men take 21 days of 8 hrs . each to do a piece of work . how many days of 5 hrs . each would it take for 21 women if 3 women do as much work as 2 men ?

Explanation: "let 1 man does 1 unit / hr of work 15 m in 21 days of 8 hrs will do ( 15 * 21 * 8 ) units 3 w = 2 m 1 w = ( 2 / 3 ) units / hr 21 w with 6 hrs a day will take ( 15 * 21 * 8 ) / ( 21 * 5 * ( 2 / 3 ) ) days = > 36 days answer : e"

divide(multiply(multiply(15, 21), 8), multiply(multiply(21, 5), divide(2, 3)))

<gadget id="calculator">15 * 21</gadget>
<output>315</output>
<gadget id="calculator">315 * 8</gadget>
<output>2_520</output>
<gadget id="calculator">21 * 5</gadget>
<output>105</output>
<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">105 * (2/3)</gadget>
<output>70</output>
<gadget id="calculator">2_520 / 70</gadget>
<output>36</output>
<result>36</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 e 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 e 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>


as a treat for her two crying children , a mother runs to the freezer in which she has 4 cherry ice pops , 3 orange ice pops , and 4 lemon - lime ice pops . if she chooses two at random to bring outside to the children , but realizes as she runs out the door that she can not bring them different flavors without one invariably being jealous of the other and getting even more upset , what is the probability that she has to return to the freezer to make sure that they each receive the same flavor ?

Explanation: probability of not getting the same flavor - > fouvarable - > cherry - orange [ 4 c 1 * 3 c 1 [ or simply 4 * 3 ] or cherry - lemon [ 4 * 4 ] or orange - lemon [ 3 * 4 ] prob = ( 4 * 3 + 4 * 4 + 3 * 4 ) / 9 c 2 = 40 / 3960 = 1 / 99 answer - > a

divide(subtract(4, 3), subtract(const_100, subtract(4, 3)))

<gadget id="calculator">4 - 3</gadget>
<output>1</output>
<gadget id="calculator">100 - 1</gadget>
<output>99</output>
<gadget id="calculator">1 / 99</gadget>
<output>1/99 = around 0.010101</output>
<result>1/99 = around 0.010101</result>


a and b together can complete a work in 12 days . a alone complete it in 20 days . if b does the work only for half a day daily , then in how many days a and b together will complete the work ?

Explanation: b ' s one day work = ( 1 / 12 - 1 / 20 ) = 1 / 30 . now , ( a + b ) ' s one day work = ( 1 / 20 + 1 / 60 ) = 1 / 15 . [ ∵ b work for half day only ] . so , a and b together will complete the work in 15 days . correct answer : ` ` c ' ' .

<gadget id="calculator">12 + 3</gadget>
<output>15</output>
<result>15</result>


in a fuel station the service costs $ 1.65 per car , every liter of fuel costs 0.65 $ . assuming that a company owns 12 cars and that every fuel tank contains 55 liters and they are all empty , how much money total will it cost to fuel all cars ?

Explanation: "total cost = ( 1.65 * 12 ) + ( 0.65 * 12 * 55 ) = 19.8 + 429 = > 448.8 hence answer will be ( d )"

<gadget id="calculator">0.65 * 55</gadget>
<output>35.75</output>
<gadget id="calculator">35.75 * 12</gadget>
<output>429</output>
<result>429</result>


a certain rectangular crate measures 6 feet by 8 feet by 10 feet . a cylindrical gas tank is to be made for shipment in the crate and will stand upright when the crate is placed on one of its six faces . what should the radius of the tank be if it is to be of the largest possible volume ?

Explanation: "ans is ` ` b ' ' . for max volume of cylinder ( pi * r ^ 2 * h ) we need to max out r ^ 2 * h . we do n ' t know what the dimensions of the crate refer to . . therefore for max vol base should be 8 x 10 i . e . of radius 8 / 2 = 4 b"

sqrt(divide(volume_cylinder(divide(8, const_2), 6), multiply(const_pi, 6)))

<gadget id="calculator">8 / 2</gadget>
<output>4</output>
<gadget id="calculator">pi * (4 ** 2) * 6</gadget>
<output>96*pi = around 301.592895</output>
<gadget id="calculator">pi * 6</gadget>
<output>6*pi = around 18.849556</output>
<gadget id="calculator">(96*pi) / (6*pi)</gadget>
<output>16</output>
<gadget id="calculator">16 ** (1/2)</gadget>
<output>4</output>
<result>4</result>


the lenght of a room is 5.5 m and width is 4 m . find the cost of paving the floor by slabs at the rate of rs . 950 per sq . metre .

Explanation: "area of the floor = ( 5.5 ã — 4 ) m 2 = 22 m 2 . cost of paving = rs . ( 950 ã — 22 ) = rs . 20900 answer : option c"

<gadget id="calculator">5.5 * 4</gadget>
<output>22</output>
<gadget id="calculator">950 * 22</gadget>
<output>20_900</output>
<result>20_900</result>


how long does a train 110 m long running at the speed of 72 km / hr takes to cross a bridge 136 m length ?

Explanation: "speed = 72 * 5 / 18 = 20 m / sec total distance covered = 110 + 136 = 246 m . required time = 246 / 20 = 12.3 sec . answer : b"

<gadget id="calculator">110 + 136</gadget>
<output>246</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">72 * (5/18)</gadget>
<output>20</output>
<gadget id="calculator">246 / 20</gadget>
<output>123/10 = around 12.3</output>
<result>123/10 = around 12.3</result>


two mba admissions committees are to be formed randomly from 6 second year mbas with 3 members each . what is the probability that jane will be on the same committee as albert ?

Explanation: total number of ways to choose 3 member committee - 6 c 3 = ( 6 ! / 3 ! 3 ! ) = 20 no . of ways albert n jane are in same committee : - ( 4 c 1 * 2 ) = 8 probability = ( 8 / 20 ) * 100 = 40 % . ans : : d

multiply(divide(multiply(choose(const_4, const_1), const_2), choose(6, 3)), multiply(multiply(const_5, const_5), const_4))

<gadget id="calculator">binomial(4, 1)</gadget>
<output>4</output>
<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">binomial(6, 3)</gadget>
<output>20</output>
<gadget id="calculator">8 / 20</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">5 * 5</gadget>
<output>25</output>
<gadget id="calculator">25 * 4</gadget>
<output>100</output>
<gadget id="calculator">(2/5) * 100</gadget>
<output>40</output>
<result>40</result>


a group of 7 teenagers recently visited the japanese restaurant . the total bill for the meal , including 20 % gratuity , came to $ 840 . on average , how much did the meal of each individual cost before gratuity ?

Explanation: 7 teenagers - so total 7 people the bill $ 840 includes 20 % gratuity . . . so the actual cost of dinner was $ 700 now , the cost per person will be $ 700 / 7 which is $ 10 option d

subtract(subtract(subtract(divide(840, 20), 20), const_10), const_2)

<gadget id="calculator">840 / 20</gadget>
<output>42</output>
<gadget id="calculator">42 - 20</gadget>
<output>22</output>
<gadget id="calculator">22 - 10</gadget>
<output>12</output>
<gadget id="calculator">12 - 2</gadget>
<output>10</output>
<result>10</result>


a particular library has 75 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 65 percent of books that were loaned out are returned and there are 68 books in the special collection at that time , how many books of the special collection were loaned out during that month ?

Explanation: "total = 75 books . 65 % of books that were loaned out are returned - - > 100 % - 65 % = 35 % of books that were loaned out are not returned . now , there are 68 books , thus 76 - 68 = 7 books are not returned . { loaned out } * 0.35 = 7 - - > { loaned out } = 20 . answer : a ."

divide(subtract(75, 68), subtract(const_1, divide(65, const_100)))

<gadget id="calculator">75 - 68</gadget>
<output>7</output>
<gadget id="calculator">65 / 100</gadget>
<output>13/20 = around 0.65</output>
<gadget id="calculator">1 - (13/20)</gadget>
<output>7/20 = around 0.35</output>
<gadget id="calculator">7 / (7/20)</gadget>
<output>20</output>
<result>20</result>


if 7 ^ q is a factor of the product of the integers from 1 to 100 , inclusive , what is the largest value of q ?

Explanation: so the question just means that we have to find all the multiples q of 7 between 1 to 100 so there are 14 multiples of 7 ( 7 - 98 ) but 49 and 98 contain two 7 ' s as factors so we have to add 14 + 2 = 16 e

add(divide(100, 7), divide(divide(100, 7), 7))

<gadget id="calculator">100 / 7</gadget>
<output>100/7 = around 14.285714</output>
<gadget id="calculator">(100/7) / 7</gadget>
<output>100/49 = around 2.040816</output>
<gadget id="calculator">(100/7) + (100/49)</gadget>
<output>800/49 = around 16.326531</output>
<result>800/49 = around 16.326531</result>


susan drove an average speed of 30 miles per hour for the first 60 miles of a tripthen at a average speed of 60 miles / hr for the remaining 30 miles of the trip if she made no stops during the trip what was susan ' s avg speed in miles / hr for the entire trip

Explanation: "avg . speed = total distance / total time total distance = 90 miles total time = 60 / 30 + 30 / 60 = 5 / 2 avg . speed = 36 answer - b"

<gadget id="calculator">60 + 30</gadget>
<output>90</output>
<gadget id="calculator">60 / 30</gadget>
<output>2</output>
<gadget id="calculator">30 / 60</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">2 + (1/2)</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">90 / (5/2)</gadget>
<output>36</output>
<result>36</result>


a 415 m long train is running at 63 km / hr . in how much time will it cross a tunnel 285 m long ?

Explanation: "speed of the train = ( 63 * 5 / 18 ) m / sec = 35 / 2 m / sec . distance travelled = ( speed x time ) time = ( distance travelled / speed ) distance travelled = length of the train + length of the tunnel = 415 + 285 = 700 m time = ( 700 / 35 / 2 ) = 40 sec answer : e"

<gadget id="calculator">415 + 285</gadget>
<output>700</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">63 * (5/18)</gadget>
<output>35/2 = around 17.5</output>
<gadget id="calculator">700 / (35/2)</gadget>
<output>40</output>
<result>40</result>


the bankers discount of a certain sum of money is rs . 288 and the true discount on the same sum for the same time is rs . 240 . the sum due is :

Explanation: "sum = ( b . d * t . d ) / ( b . d - t . d ) ( 288 * 240 ) / 288 - 240 ; 1440 answer : c"

divide(multiply(240, 288), subtract(288, 240))

<gadget id="calculator">240 * 288</gadget>
<output>69_120</output>
<gadget id="calculator">288 - 240</gadget>
<output>48</output>
<gadget id="calculator">69_120 / 48</gadget>
<output>1_440</output>
<result>1_440</result>


a shopkeeper sold an article offering a discount of 4 % and earned a profit of 32 % . what would have been the percentage of profit earned if no discount was offered ?

Explanation: let c . p . be rs . 100 . then , s . p . = rs . 132 let marked price be rs . x . then , 96 / 100 x = 132 x = 13200 / 96 = rs . 137.5 now , s . p . = rs . 137.5 , c . p . = rs . 100 profit % = 37.5 % . answer : e

subtract(divide(multiply(add(const_100, 32), const_100), subtract(const_100, 4)), const_100)

<gadget id="calculator">100 + 32</gadget>
<output>132</output>
<gadget id="calculator">132 * 100</gadget>
<output>13_200</output>
<gadget id="calculator">100 - 4</gadget>
<output>96</output>
<gadget id="calculator">13_200 / 96</gadget>
<output>275/2 = around 137.5</output>
<gadget id="calculator">(275/2) - 100</gadget>
<output>75/2 = around 37.5</output>
<result>75/2 = around 37.5</result>


the volume of the sphere qq is ( dfrac { 37 } { 64 } % ) less than the volume of sphere pp and the volume of sphere rr is ( dfrac { 19 } { 27 } % ) less than that of sphere qq . by what is the surface areaof sphere rr less than the surfacearea of sphere pp ?

Explanation: let the volume of sphere pp be 64 parts . therefore volume of sphere qq = 64 − 3764 % = 64 − 3764 % of 6464 = 64 − 37 = 27 = 64 − 37 = 27 parts . the volume of rr = 27 − 1927 × 27 = 27 − 1927 × 27 = 27 − 19 = 8 = 27 − 19 = 8 parts . volume ratio : = p : q : r = 64 : 27 : 8 = p : q : r = 64 : 27 : 8 radius ratio : = p : q : r = 4 : 3 : 2 = p : q : r = 4 : 3 : 2 the surface area will be 16 : 9 : 516 : 9 : 5 surface area of rr is less than the surface area of sphere pp 16 k − 4 k = 12 k 16 k − 4 k = 12 k now , = 12 k 16 k × 100 = 12 k 16 k × 100 = 75 % = 75 % thus surface area of sphere rr is less than the surface area of sphere p by 75 % c

subtract(const_100, multiply(multiply(multiply(divide(37, 64), divide(19, 27)), divide(37, 64)), const_100))


what will be the cost of gardening 1 meter boundary around a rectangular plot having perimeter of 340 meters at the rate of rs . 10 per square meter ?

Explanation: explanation : in this question , we are having perimeter . we know perimeter = 2 ( l + b ) , right so , 2 ( l + b ) = 340 as we have to make 1 meter boundary around this , so area of boundary = ( ( l + 2 ) + ( b + 2 ) - lb ) = 2 ( l + b ) + 4 = 340 + 4 = 344 so required cost will be = 344 * 10 = 3440 answer : option b

<gadget id="calculator">340 + 4</gadget>
<output>344</output>
<gadget id="calculator">344 * 10</gadget>
<output>3_440</output>
<result>3_440</result>


a can do a piece of work in 15 days . a does the work for 5 days only and leaves the job . b does the remaining work in 18 days . in how many days b alone can do the work ?

Explanation: "explanation : a ’ s 5 day work = 5 * 1 / 15 = 1 / 3 remaining work = 1 - 1 / 3 = 2 / 3 b completes 2 / 3 work in 6 days b alone can do in x days 2 / 3 * x = 18 x = 27 days answer : option c"

inverse(multiply(inverse(18), subtract(const_1, multiply(5, inverse(15)))))

<gadget id="calculator">1 / 18</gadget>
<output>1/18 = around 0.055556</output>
<gadget id="calculator">1 / 15</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">5 * (1/15)</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 - (1/3)</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(1/18) * (2/3)</gadget>
<output>1/27 = around 0.037037</output>
<gadget id="calculator">1 / (1/27)</gadget>
<output>27</output>
<result>27</result>


the h . c . f . of two numbers is 30 and the other two factors of their l . c . m . are 25 and 24 . the larger of the two numbers is

Explanation: "solution clearly , the numbers are ( 30 x 25 ) and ( 30 x 24 ) . larger number = ( 30 x 25 ) = 750 . answer d"

<gadget id="calculator">30 * 24</gadget>
<output>720</output>
<result>720</result>


arun purchased 30 kg of wheat at the rate of rs . 11.50 per kg and 20 kg of wheat at the rate of 14.25 per kg . he mixed the two and sold the mixture . approximately what price per kg should be sell the mixture to make 15 % profit ?

Explanation: "c . p . of 50 kg wheat = ( 30 * 11.50 + 20 * 14.25 ) = rs . 630 . s . p . of 50 kg wheat = 115 % of rs . 630 = 115 / 100 * 630 = rs . 724.5 s . p . per kg = 724.5 / 50 = 14.49 a"

<gadget id="calculator">30 * 11.5</gadget>
<output>345</output>
<gadget id="calculator">20 * 14.25</gadget>
<output>285</output>
<gadget id="calculator">345 + 285</gadget>
<output>630</output>
<gadget id="calculator">630 / 100</gadget>
<output>63/10 = around 6.3</output>
<gadget id="calculator">(63/10) * 15</gadget>
<output>189/2 = around 94.5</output>
<gadget id="calculator">630 + (189/2)</gadget>
<output>1_449/2 = around 724.5</output>
<gadget id="calculator">30 + 20</gadget>
<output>50</output>
<gadget id="calculator">(1_449/2) / 50</gadget>
<output>1_449/100 = around 14.49</output>
<result>1_449/100 = around 14.49</result>


one pipe can fill a tank four times as fast as another pipe . if together the two pipes can fill the tank in 36 minutes , then the slower pipe alone will be able to fill the tank in :

Explanation: explanation : let time taken by the faster pipe to fill the tank = x minutes . then , time taken by the slower pipe to fill the tank = 4 x minutes . time taken by both pipes together to fill the tank = x x 4 x / x + 4 x = 4 x / 5 4 x / 5 = 36 ⇒ x = 45 time taken by the slower pipe to fill the tank = 4 x = 180 minutes . answer : option a

<gadget id="calculator">1 + 4</gadget>
<output>5</output>
<gadget id="calculator">5 * 36</gadget>
<output>180</output>
<result>180</result>


carl is facing very difficult financial times and can only pay the interest on a $ 10,000 loan he has taken . the bank charges him a quarterly compound rate of 8 % . what is the approximate interest he pays annually ?

Explanation: "an easy way too attempt this is by approximation : for the first quarter , he pays 8 % of 10,000 which is $ 800 . so for the four quarters in the year , he will approximately play 800 * 4 = 3200 over the entire year . because of compound interest it will be more than 3200 . approx . option d is correct . answer : d"

subtract(multiply(multiply(const_100, const_100), power(add(const_1, divide(8, const_100)), const_4)), multiply(const_100, const_100))


a patient is given exactly 750 milliliters of a mixture of two medications daily . medication a contains 40 % pain killer and medication b contains 20 % pain killer . if the patient receives exactly 215 milliliters of pain killer daily , how many milliliters of medication b are in the mixture ?

Explanation: let there be a milliliters of medication a and b milliliters of medication b a + b = 750 - - 1 medication a contains 40 % pain killer and medication b contains 20 % pain killer . ( 40 / 100 ) * a + ( 20 / 100 ) * b = 215 = > ( 2 / 5 ) * a + ( 1 / 5 ) * b = 215 multiplying by 5 , we get 2 a + b = 1075 - - 2 equation 2 - equation 1 , we get a = 325 b = 425 answer d

divide(subtract(multiply(divide(40, const_100), 750), 215), subtract(divide(40, const_100), divide(20, const_100)))

<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) * 750</gadget>
<output>300</output>
<gadget id="calculator">300 - 215</gadget>
<output>85</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(2/5) - (1/5)</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">85 / (1/5)</gadget>
<output>425</output>
<result>425</result>


let s is a set of all natural numbers less than 120 such that hcf of any element in s and 120 is 1 . find the sum of all elements in s ?

Explanation: s is a set of all natural numbers less than 120 such that hcf of any element in s and 120 is 1 . such numbers are , s = { 1 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , 43 , 47 , 53 , 59 , 61 , 67 , 71 , 73 , 79 , 83 , 89 , 97 , 101 , 103 , 107 , 109 , 113 } sum of s = 1584 . answer : a

add(add(multiply(add(1, const_4), const_100), const_1000), add(multiply(multiply(const_2, const_4), const_10), const_4))

<gadget id="calculator">1 + 4</gadget>
<output>5</output>
<gadget id="calculator">5 * 100</gadget>
<output>500</output>
<gadget id="calculator">500 + 1_000</gadget>
<output>1_500</output>
<gadget id="calculator">2 * 4</gadget>
<output>8</output>
<gadget id="calculator">8 * 10</gadget>
<output>80</output>
<gadget id="calculator">80 + 4</gadget>
<output>84</output>
<gadget id="calculator">1_500 + 84</gadget>
<output>1_584</output>
<result>1_584</result>


a swimmer can swim in still water at 4 km / h . if the speed of the water current is 2 km / h , how many hours will the swimmer take to swim against the current for 5 km ?

Explanation: "the swimmer can swim against the current at a speed of 4 - 2 = 2 km / h . the time it will take is 5 / 2 = 2.5 hours . the answer is b ."

<gadget id="calculator">4 - 2</gadget>
<output>2</output>
<gadget id="calculator">5 / 2</gadget>
<output>5/2 = around 2.5</output>
<result>5/2 = around 2.5</result>


if a tire rotates at 400 revolutions per minute when the car is traveling 48 km / h , what is the circumference of the tire ?

Explanation: "400 rev / minute = 400 * 60 rev / 60 minutes = 24,000 rev / hour 24,000 * c = 48,000 m : c is the circumference c = 2 meters correct answer d"

multiply(divide(48, multiply(multiply(multiply(const_2, const_3), const_10), 400)), const_1000)

<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">6 * 10</gadget>
<output>60</output>
<gadget id="calculator">60 * 400</gadget>
<output>24_000</output>
<gadget id="calculator">48 / 24_000</gadget>
<output>1/500 = around 0.002</output>
<gadget id="calculator">(1/500) * 1_000</gadget>
<output>2</output>
<result>2</result>


a snooker tournament charges $ 45.00 for vip seats and $ 20.00 for general admission ( “ regular ” seats ) . on a certain night , a total of 320 tickets were sold , for a total cost of $ 7500 . how many fewer tickets were sold that night for vip seats than for general admission seats ?

Explanation: let no of sits in vip enclosure is x then x * 45 + 20 ( 320 - x ) = 7500 or 25 x = 7500 - 6400 , x = 1100 / 25 = 44 vip = 44 general 320 - 44 = 276 b

subtract(320, divide(subtract(divide(7500, 20), 320), subtract(divide(45, 20), const_1)))

<gadget id="calculator">7_500 / 20</gadget>
<output>375</output>
<gadget id="calculator">375 - 320</gadget>
<output>55</output>
<gadget id="calculator">45 / 20</gadget>
<output>9/4 = around 2.25</output>
<gadget id="calculator">(9/4) - 1</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">55 / (5/4)</gadget>
<output>44</output>
<gadget id="calculator">320 - 44</gadget>
<output>276</output>
<result>276</result>


find the principle on a certain sum of money at 5 % per annum for 3 1 / 5 years if the amount being rs . 1160 ?

Explanation: "explanation : 1160 = p [ 1 + ( 5 * 16 / 5 ) / 100 ] p = 1000 answer : option a"

divide(1160, add(divide(multiply(divide(add(multiply(3, 5), 3), 5), 5), const_100), const_1))

<gadget id="calculator">3 * 5</gadget>
<output>15</output>
<gadget id="calculator">15 + 3</gadget>
<output>18</output>
<gadget id="calculator">18 / 5</gadget>
<output>18/5 = around 3.6</output>
<gadget id="calculator">(18/5) * 5</gadget>
<output>18</output>
<gadget id="calculator">18 / 100</gadget>
<output>9/50 = around 0.18</output>
<gadget id="calculator">(9/50) + 1</gadget>
<output>59/50 = around 1.18</output>
<gadget id="calculator">1_160 / (59/50)</gadget>
<output>58_000/59 = around 983.050847</output>
<result>58_000/59 = around 983.050847</result>


4 balls of different colors are to be placed in 3 different boxes such that any box contains at least 1 ball . what is the maximum number of different ways in which this can be done ?

Explanation: since the balls are all of different colors , let ' s permute them and then decide how many balls we put in each box . for example , arrange in a row the balls , then decide : two balls go into the first box , next two in the second box , and the last ball goes to the third box . since in each box there must be at least one ball , we have the possibilities of ( 2 , 2,1 ) , ( 2 , 1,2 ) , ( 1 , 2,2 ) or ( 3 , 1,1 ) , ( 1 , 3,1 ) , ( 1 , 1,3 ) balls in the three boxes . for the 2 , 2,1 type arrangements , we have [ 6 ! / ( 2 ! 2 ! 1 ! ) ] * 3 = 100 possibilities . inside a box , it does n ' t matter the order of the balls . for the 3 , 1,1 type arrangements , we have [ 6 ! / ( 3 ! 1 ! 1 ! ) ] * 3 = 80 possibilities . total of 100 + 80 = 180 possibilities . answer e .

add(multiply(multiply(multiply(4, 3), const_2), multiply(3, const_2)), multiply(multiply(3, const_2), multiply(3, const_2)))

<gadget id="calculator">4 * 3</gadget>
<output>12</output>
<gadget id="calculator">12 * 2</gadget>
<output>24</output>
<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">24 * 6</gadget>
<output>144</output>
<gadget id="calculator">6 * 6</gadget>
<output>36</output>
<gadget id="calculator">144 + 36</gadget>
<output>180</output>
<result>180</result>


the length of the bridge , which a train 140 metres long and travelling at 45 km / hr can cross in 30 seconds , is ?

Explanation: "speed = [ 45 x 5 / 18 ] m / sec = [ 25 / 2 ] m / sec time = 30 sec let the length of bridge be x metres . then , ( 140 + x ) / 30 = 25 / 2 = > 2 ( 140 + x ) = 750 = > x = 235 m . answer : c"

subtract(multiply(divide(multiply(45, speed(const_1000, const_1)), speed(const_3600, const_1)), 30), 140)

<gadget id="calculator">1_000 / 1</gadget>
<output>1_000</output>
<gadget id="calculator">45 * 1_000</gadget>
<output>45_000</output>
<gadget id="calculator">3_600 / 1</gadget>
<output>3_600</output>
<gadget id="calculator">45_000 / 3_600</gadget>
<output>25/2 = around 12.5</output>
<gadget id="calculator">(25/2) * 30</gadget>
<output>375</output>
<gadget id="calculator">375 - 140</gadget>
<output>235</output>
<result>235</result>


the average height of 35 boys in a class was calculated as 185 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ?

Explanation: "calculated average height of 35 boys = 185 cm . wrong total height of 35 boys = 180 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 166 cm . correct total height of 35 boys = 185 cm - ( 166 cm - 106 cm ) / 35 = 185 cm - 60 / 35 cm = 185 cm - 1.71 cm = 183.29 cm . answer : b"

floor(divide(add(subtract(multiply(35, 185), 166), 106), 35))

<gadget id="calculator">35 * 185</gadget>
<output>6_475</output>
<gadget id="calculator">6_475 - 166</gadget>
<output>6_309</output>
<gadget id="calculator">6_309 + 106</gadget>
<output>6_415</output>
<gadget id="calculator">6_415 / 35</gadget>
<output>1_283/7 = around 183.285714</output>
<gadget id="calculator">floor(1_283/7)</gadget>
<output>183</output>
<result>183</result>


Explanation: a number ending in a 0 is divisible by 2 . a number ending in 2 zeroes is divisible by 4 . a number ending in 3 zeroes is divisible by 8 . a number ending in 4 zeroes in divisible by 16 . given the obscene number , you should immediately be convinced that you will need to focus on a very small part of it . 65,985 , 241,545 , 898,754 , 582,556 , 898,522 , 454,889 = 65,985 , 241,545 , 898,754 , 582,556 , 898,522 , 450,000 + 4,889 the first number is divisible by 16 . you just have to find the remainder when you divide 5287 by 16 . that will be the remainder when you divide the original number by 16 . 4889 / 16 gives remainder 9 . answer ( e )

add(multiply(const_4, const_2), reminder(add(add(multiply(subtract(const_10, const_1), const_100), multiply(multiply(add(const_3, const_2), const_100), const_10)), multiply(add(const_12, add(const_3, const_2)), add(const_3, const_2))), 16))

<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">10 - 1</gadget>
<output>9</output>
<gadget id="calculator">9 * 100</gadget>
<output>900</output>
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">5 * 100</gadget>
<output>500</output>
<gadget id="calculator">500 * 10</gadget>
<output>5_000</output>
<gadget id="calculator">900 + 5_000</gadget>
<output>5_900</output>
<gadget id="calculator">12 + 5</gadget>
<output>17</output>
<gadget id="calculator">17 * 5</gadget>
<output>85</output>
<gadget id="calculator">5_900 + 85</gadget>
<output>5_985</output>
<gadget id="calculator">5_985 % 16</gadget>
<output>1</output>
<gadget id="calculator">8 + 1</gadget>
<output>9</output>
<result>9</result>


you enter a weight loss challenge game and manage to lose 12 % of your body weight . for the final weigh in you are forced to wear clothes that add 2 % to your weight . what percentage of weight loss is measured at the final weigh in ?

Explanation: "( 100 % - 12 % ) * ( 100 % + 2 % ) = 0.88 * 1.02 = 10.24 % the weigh in records your weight loss at 10.24 % ! the answer is a"

multiply(subtract(const_1, multiply(subtract(const_1, divide(12, const_100)), add(const_1, divide(2, const_100)))), const_100)

<gadget id="calculator">12 / 100</gadget>
<output>3/25 = around 0.12</output>
<gadget id="calculator">1 - (3/25)</gadget>
<output>22/25 = around 0.88</output>
<gadget id="calculator">2 / 100</gadget>
<output>1/50 = around 0.02</output>
<gadget id="calculator">1 + (1/50)</gadget>
<output>51/50 = around 1.02</output>
<gadget id="calculator">(22/25) * (51/50)</gadget>
<output>561/625 = around 0.8976</output>
<gadget id="calculator">1 - (561/625)</gadget>
<output>64/625 = around 0.1024</output>
<gadget id="calculator">(64/625) * 100</gadget>
<output>256/25 = around 10.24</output>
<result>256/25 = around 10.24</result>


if 20 men can build a water fountain 56 metres long in 14 days , what length of a similar water fountain can be built by 35 men in 3 days ?

Explanation: "explanation : let the required length be x metres more men , more length built ( direct proportion ) less days , less length built ( direct proportion ) men 20 : 35 days 14 : 3 : : 56 : x therefore ( 20 x 14 x x ) = ( 35 x 3 x 56 ) x = ( 35 x 3 x 56 ) / 280 = 49 hence , the required length is 21 m . answer : a"

multiply(divide(56, multiply(20, 14)), multiply(35, 3))

<gadget id="calculator">20 * 14</gadget>
<output>280</output>
<gadget id="calculator">56 / 280</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">35 * 3</gadget>
<output>105</output>
<gadget id="calculator">(1/5) * 105</gadget>
<output>21</output>
<result>21</result>


if 4 ( p ' s capital ) = 6 ( q ' s capital ) = 10 ( r ' s capital ) , then out of the total profit of rs 4650 , r will receive

Explanation: "explanation : let p ' s capital = p , q ' s capital = q and r ' s capital = r then 4 p = 6 q = 10 r = > 2 p = 3 q = 5 r = > q = 2 p / 3 r = 2 p / 5 p : q : r = p : 2 p / 3 : 2 p / 5 = 15 : 10 : 6 r ' s share = 4650 * ( 6 / 31 ) = 150 * 6 = 900 . answer : option d"

multiply(4650, divide(6, add(add(add(10, add(4, const_1)), 10), 6)))

<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">10 + 5</gadget>
<output>15</output>
<gadget id="calculator">15 + 10</gadget>
<output>25</output>
<gadget id="calculator">25 + 6</gadget>
<output>31</output>
<gadget id="calculator">6 / 31</gadget>
<output>6/31 = around 0.193548</output>
<gadget id="calculator">4_650 * (6/31)</gadget>
<output>900</output>
<result>900</result>


the average age of 15 students of a class is 15 years . out of these , the average age of 8 students is 14 years and that of the other 6 students is 16 years , the age of the 15 th student is

Explanation: "explanation : age of the 15 th student = [ 15 * 15 - ( 14 * 8 + 16 * 6 ) ] = 17 years . answer : a"

subtract(multiply(15, 15), add(multiply(8, 14), multiply(6, 16)))

<gadget id="calculator">15 * 15</gadget>
<output>225</output>
<gadget id="calculator">8 * 14</gadget>
<output>112</output>
<gadget id="calculator">6 * 16</gadget>
<output>96</output>
<gadget id="calculator">112 + 96</gadget>
<output>208</output>
<gadget id="calculator">225 - 208</gadget>
<output>17</output>
<result>17</result>


a committee is reviewing a total of 40 x black - and - white films and 10 y color films for a festival . if the committee selects y / x % of the black - and - white films and all of the color films , what fraction of the selected films are in color ?

Explanation: "say x = y = 10 . in this case we would have : 40 x = 400 black - and - white films ; 10 y = 100 color films . y / x % = 10 / 10 % = 1 % of the black - and - white films , so 4 black - and - white films and all 100 color films , thus total of 104 films were selected . color films thus compose 100 / 104 = 50 / 52 of the selected films . answer : a"

divide(10, add(divide(40, const_100), 10))

<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) + 10</gadget>
<output>52/5 = around 10.4</output>
<gadget id="calculator">10 / (52/5)</gadget>
<output>25/26 = around 0.961538</output>
<result>25/26 = around 0.961538</result>


if the cost price of 24 chocolates is equal to the selling price of 16 chocolates , the gain percent is :

Explanation: "explanation : solution : let c . p . of each chocolate be re . 1 . then , c . p . of 16 chocolates = rs . 16 ; s . p . of 16 chocolates = rs . 24 . . ' . gain % = 8 * 100 / 16 = 50 % answer : c"

divide(const_100, divide(16, subtract(24, 16)))

<gadget id="calculator">24 - 16</gadget>
<output>8</output>
<gadget id="calculator">16 / 8</gadget>
<output>2</output>
<gadget id="calculator">100 / 2</gadget>
<output>50</output>
<result>50</result>


a fort had provision of food for 150 men for 45 days . after 10 days , 25 men left the fort . find out the number of days for which the remaining food will last .

Explanation: explanation : given that fort had provision of food for 150 men for 45 days hence , after 10 days , the remaining food is sufficient for 150 men for 35 days remaining men after 10 days = 150 - 25 = 125 assume that after 10 days , the remaining food is sufficient for 125 men for x days more men , less days ( indirect proportion ) ( men ) 150 : 125 : : x : 35 ⇒ 150 × 35 = 125 x ⇒ 6 × 35 = 5 x ⇒ x = 6 × 7 = 42 i . e . , the remaining food is sufficient for 125 men for 42 days answer : option b

divide(multiply(150, add(25, 10)), subtract(150, 25))

<gadget id="calculator">25 + 10</gadget>
<output>35</output>
<gadget id="calculator">150 * 35</gadget>
<output>5_250</output>
<gadget id="calculator">150 - 25</gadget>
<output>125</output>
<gadget id="calculator">5_250 / 125</gadget>
<output>42</output>
<result>42</result>


the h . c . f of two numbers is 23 and the other two factors of their l . c . m are 14 and 15 . the larger of the two numbers is :

Explanation: "clearly , the numbers are ( 23 * 14 ) and ( 23 * 15 ) . larger number = ( 23 * 15 ) = 345 . answer : c"

<gadget id="calculator">23 * 15</gadget>
<output>345</output>
<result>345</result>


during a given week a programmer spends 1 / 4 of his time preparing flow chart , 3 / 8 of his time coding and the rest of the time in debugging the programs . if he works 48 hours during the week , how many hours did he spend debugging the program .

Explanation: programmer takes 1 / 4 * 48 = 12 hrs a week to make flowchrt same way . . . . . 18 hrs a week for codin . . . so . . . . for debugging = 48 - ( 12 + 18 ) = 18 hrs answer : c

<gadget id="calculator">48 * 3</gadget>
<output>144</output>
<gadget id="calculator">144 / 8</gadget>
<output>18</output>
<result>18</result>


there is enough provisions for 600 men in an army camp for 25 days . if there were 250 men less , how long will the provision last ?

Explanation: "exp : we have , m 1 d 1 = m 2 d 2 600 * 25 = 250 * d 2 d 2 = 600 * 25 / 250 = 60 days . answer : d"

<gadget id="calculator">600 * 25</gadget>
<output>15_000</output>
<gadget id="calculator">15_000 / 250</gadget>
<output>60</output>
<result>60</result>


in what time will a train 200 m long cross an electric pole , it its speed be 144 km / hr ?

Explanation: "speed = 144 * 5 / 18 = 40 m / sec time taken = 200 / 40 = 5 sec . answer : e"

<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">200 / 40</gadget>
<output>5</output>
<result>5</result>


in a group of 100 cars , 49 cars do not have air conditioning . if at least 51 cars have racing stripes , what is the greatest number of cars that could have air conditioning but not racing stripes ?

Explanation: lets assume ac = 51 ( includesonly ac carsandcars with ac and racing stripes ) lets assume rs ( racing stripes ) > = 51 ( includescars with ac and racing stripesandonly racing stripes ) . now since we want to maximize ( only ac ) we have to see to it thatcars with ac and racing stripesis minimal ( assume 0 ) but since rs > = 51 . . we have to assign atleast 2 tocars with ac and racing stripes . hence ac = 51 - 2 = 49 . the answer is a

<gadget id="calculator">100 - 51</gadget>
<output>49</output>
<result>49</result>


last year a certain bond price with a face value of 5000 yielded 10 % of its face value in interest . if that interest was approx 6.5 of the bond ' s selling price approx what was the bond ' s selling price ?

Explanation: "interest = 0.08 * 5000 = 0.065 * selling price - - > selling price = 0.1 * 5000 / 0.065 - - > selling price = ~ 7692 answer : a ."

divide(multiply(5000, divide(10, const_100)), divide(6.5, const_100))

<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">5_000 * (1/10)</gadget>
<output>500</output>
<gadget id="calculator">6.5 / 100</gadget>
<output>0.065</output>
<gadget id="calculator">500 / 0.065</gadget>
<output>7_692.307692</output>
<result>7_692.307692</result>


the number of people who purchased book a is twice the number of people who purchased book b . the number of people who purchased both books a and b is 500 , which is twice the number of people who purchased only book b . what is the number of people c who purchased only book a ?

Explanation: "this is best solved using overlapping sets or a venn diagram . we know that a = 2 b , and that 500 people purchased both a and b . further , those purchasing both was double those purchasing b only . this gives us 250 people purchasing b only . with the 500 that pruchased both , we have a total of 750 that purchased b and this is 1 / 2 of those that purchased a . so , 1500 purchased a . less the 500 that purchased both , c = 1000 purchased a only . ( this is much simpler to solve using the venn diagram ) . correct answer is d . 1000"

subtract(multiply(add(500, divide(500, const_2)), const_2), 500)

<gadget id="calculator">500 / 2</gadget>
<output>250</output>
<gadget id="calculator">500 + 250</gadget>
<output>750</output>
<gadget id="calculator">750 * 2</gadget>
<output>1_500</output>
<gadget id="calculator">1_500 - 500</gadget>
<output>1_000</output>
<result>1_000</result>


in township k , 1 / 5 of the housing units are equiped with cable tv . if 1 / 10 of the housing units , including 1 / 6 of those that are equiped with cable tv , are equipped with videocassette recorders , what fraction of the housing units have neither cable tv nor videocassette recorders ?

Explanation: "1 / 5 - - cable tv ( this includes some data from video cassette recorder ) 1 / 10 - - video cassette recorder including 1 / 6 ( equiped with cable tv ) i . e . 1 / 6 ( 1 / 5 ) = 1 / 30 therefore only video cassette recorder = 1 / 10 - 1 / 30 = 1 / 15 total = 1 / 5 + 1 / 15 + neither cable tv nor videocassette recorders 1 = 4 / 15 + neither cable tv nor videocassette recorders therefore neither cable tv nor videocassette recorders = 1 - 4 / 15 = 11 / 15 hence b ."

divide(add(10, 5), multiply(10, const_2))

<gadget id="calculator">10 + 5</gadget>
<output>15</output>
<gadget id="calculator">10 * 2</gadget>
<output>20</output>
<gadget id="calculator">15 / 20</gadget>
<output>3/4 = around 0.75</output>
<result>3/4 = around 0.75</result>


walking at 3 / 4 of her normal speed , a worker is 8 minutes later than usual in reaching her office . the usual time ( in minutes ) taken by her to cover the distance between her home and her office is

Explanation: "let v be her normal speed and let t be her normal time . d = ( 3 / 4 ) v * ( t + 8 ) since the distance is the same we can equate this to a regular day which is d = v * t v * t = ( 3 / 4 ) v * ( t + 8 ) t / 4 = 6 t = 24 the answer is b ."

<gadget id="calculator">3 * 8</gadget>
<output>24</output>
<result>24</result>


the total age of a and b is 14 years more than the total age of b and c . c is how many years younger than a ?

Explanation: "( a + b ) - ( b + c ) = 14 a - c = 14 . c is younger than a by 14 years . answer : a"

<gadget id="calculator">14 * 1</gadget>
<output>14</output>
<result>14</result>


in a party every person shakes hands with every other person . if there were a total of 171 handshakes in the party then what is the number of persons present in the party ?

Explanation: explanation : let the number of persons be n â ˆ ´ total handshakes = nc 2 = 171 n ( n - 1 ) / 2 = 171 â ˆ ´ n = 19 answer : option e

divide(add(sqrt(add(multiply(multiply(171, const_2), const_4), const_1)), const_1), const_2)

<gadget id="calculator">171 * 2</gadget>
<output>342</output>
<gadget id="calculator">342 * 4</gadget>
<output>1_368</output>
<gadget id="calculator">1_368 + 1</gadget>
<output>1_369</output>
<gadget id="calculator">1_369 ** (1/2)</gadget>
<output>37</output>
<gadget id="calculator">37 + 1</gadget>
<output>38</output>
<gadget id="calculator">38 / 2</gadget>
<output>19</output>
<result>19</result>


a man performs 3 / 5 of the total journey by rail , 17 / 20 by bus and the remaining 6.5 km on foot . his total journey is

Explanation: explanation : let the journey be x km then , 3 x / 5 + 7 x / 20 + 6.5 = x 12 x + 7 x + 130 = 20 x x = 130 km answer : option d

<gadget id="calculator">20 * 6.5</gadget>
<output>130</output>
<result>130</result>


two trains of length 100 meters and 200 meters are 450 meters apart . they are moving towards each other on parallel tracks , at speeds of 90 km / h and 72 km / h . after how many seconds will the trains meet ?

Explanation: "the speeds are 90000 / 3600 = 25 m / s and 72000 / 3600 = 20 m / s the relative speed is 45 m / s . time = 450 / 45 = 10 seconds the answer is c ."

<gadget id="calculator">90 + 72</gadget>
<output>162</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">162 * (5/18)</gadget>
<output>45</output>
<gadget id="calculator">450 / 45</gadget>
<output>10</output>
<result>10</result>


a train is 360 meter long is running at a speed of 52 km / hour . in what time will it pass a bridge of 140 meter length .

Explanation: "explanation : speed = 52 km / hr = 52 * ( 5 / 18 ) m / sec = 130 / 9 m / sec total distance = 360 + 140 = 500 meter time = distance / speed = 500 / 130 / 9 = 34.62 seconds answer : b"

divide(add(360, 140), divide(multiply(52, const_1000), const_3600))

<gadget id="calculator">360 + 140</gadget>
<output>500</output>
<gadget id="calculator">52 * 1_000</gadget>
<output>52_000</output>
<gadget id="calculator">52_000 / 3_600</gadget>
<output>130/9 = around 14.444444</output>
<gadget id="calculator">500 / (130/9)</gadget>
<output>450/13 = around 34.615385</output>
<result>450/13 = around 34.615385</result>


a straight line in the xy - plane has a slope of 2 and a y - intercept of 2 . on this line , what is the x - coordinate of the point whose y - coordinate is 540 ?

Explanation: "slope of 2 and a y - intercept of 2 y - coordinate is 540 y = 2 x + 2 538 = 2 x x = 269 answer : d . 269"

<gadget id="calculator">540 - 2</gadget>
<output>538</output>
<gadget id="calculator">538 / 2</gadget>
<output>269</output>
<result>269</result>


in what ratio must rice of rs . 16 per kg be mixed with rice of rs . 24 per kg so that cost of mixture is rs . 18 per kg ?

Explanation: "( 18 - 24 ) / ( 16 - 18 ) = 6 / 2 = 3 : 1 answer : c"

divide(divide(subtract(18, 24), subtract(16, 24)), subtract(const_1, divide(subtract(18, 24), subtract(16, 24))))

<gadget id="calculator">18 - 24</gadget>
<output>-6</output>
<gadget id="calculator">16 - 24</gadget>
<output>-8</output>
<gadget id="calculator">(-6) / (-8)</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">(3/4) / (1/4)</gadget>
<output>3</output>
<result>3</result>


in a class of 25 students in an examination in maths 3 students scored 95 marks each , 3 get zero each and the average of the rest was 45 . what is the average of the whole class ?

Explanation: "explanation : total marks obtained by a class of 25 students = 3 * 95 + 3 * 0 + 19 * 45 = 1140 average marks of whole class = 1140 / 25 = 45.6 answer : option b"

divide(add(multiply(45, subtract(25, add(3, 3))), multiply(95, 3)), 25)

<gadget id="calculator">3 + 3</gadget>
<output>6</output>
<gadget id="calculator">25 - 6</gadget>
<output>19</output>
<gadget id="calculator">45 * 19</gadget>
<output>855</output>
<gadget id="calculator">95 * 3</gadget>
<output>285</output>
<gadget id="calculator">855 + 285</gadget>
<output>1_140</output>
<gadget id="calculator">1_140 / 25</gadget>
<output>228/5 = around 45.6</output>
<result>228/5 = around 45.6</result>


ravi purchased a refrigerator and a mobile phone for rs . 15000 and rs . 8000 respectively . he sold the refrigerator at a loss of 3 percent and the mobile phone at a profit of 10 percent . overall he make a .

Explanation: "let the sp of the refrigerator and the mobile phone be rs . r and rs . m respectively . r = 15000 ( 1 - 3 / 100 ) = 15000 - 450 m = 8000 ( 1 + 10 / 100 ) = 8000 + 800 total sp - total cp = r + m - ( 15000 + 8000 ) = - 450 + 800 = rs . 350 as this is positive , an overall profit of rs . 350 was made . answer : b"

subtract(add(multiply(15000, subtract(const_1, divide(3, const_100))), multiply(8000, add(const_1, divide(10, const_100)))), add(15000, 8000))

<gadget id="calculator">3 / 100</gadget>
<output>3/100 = around 0.03</output>
<gadget id="calculator">1 - (3/100)</gadget>
<output>97/100 = around 0.97</output>
<gadget id="calculator">15_000 * (97/100)</gadget>
<output>14_550</output>
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 + (1/10)</gadget>
<output>11/10 = around 1.1</output>
<gadget id="calculator">8_000 * (11/10)</gadget>
<output>8_800</output>
<gadget id="calculator">14_550 + 8_800</gadget>
<output>23_350</output>
<gadget id="calculator">15_000 + 8_000</gadget>
<output>23_000</output>
<gadget id="calculator">23_350 - 23_000</gadget>
<output>350</output>
<result>350</result>


a man , a woman and a boy can together complete a piece of work in 3 days . if a woman alone can do it in 6 days and a boy alone in 18 days , how long will a man take to complete the work ?

Explanation: "explanation : ( 1 man + 1 woman + 1 boy ) ’ s 1 day ’ s work = 1 / 3 1 wo man ’ s 1 day work = 1 / 6 1 boy ’ s 1 day ’ s work = 1 / 18 man alone can finish the work in 9 days . answer : option d"

<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 / 18</gadget>
<output>1/18 = around 0.055556</output>
<gadget id="calculator">(1/6) + (1/18)</gadget>
<output>2/9 = around 0.222222</output>
<gadget id="calculator">(1/3) - (2/9)</gadget>
<output>1/9 = around 0.111111</output>
<gadget id="calculator">1 / (1/9)</gadget>
<output>9</output>
<result>9</result>


a train running at the speed of 70 km / hr crosses a pole in 9 sec . what is the length of the train ?

Explanation: "speed = 70 * 5 / 18 = 175 / 9 m / sec length of the train = speed * time = 175 / 9 * 9 = 175 m answer : d"

multiply(divide(multiply(70, const_1000), const_3600), 9)

<gadget id="calculator">70 * 1_000</gadget>
<output>70_000</output>
<gadget id="calculator">70_000 / 3_600</gadget>
<output>175/9 = around 19.444444</output>
<gadget id="calculator">(175/9) * 9</gadget>
<output>175</output>
<result>175</result>


on my sister ' s birthday , she was 126 cm in height , having grown 5 % since the year before . how tall was she the previous year ?

Explanation: let the previous year ' s height be x . 1.05 x = 126 x = 120 the answer is b .

subtract(126, divide(multiply(126, 5), const_100))

<gadget id="calculator">126 * 5</gadget>
<output>630</output>
<gadget id="calculator">630 / 100</gadget>
<output>63/10 = around 6.3</output>
<gadget id="calculator">126 - (63/10)</gadget>
<output>1_197/10 = around 119.7</output>
<result>1_197/10 = around 119.7</result>


for a certain art exhibit , a museum sold admission tickets to a group of 50 people every 5 minutes from 9 : 00 in the morning to 5 : 55 in the afternoon , inclusive . the price of a regular admission ticket was $ 10 and the price of a student ticket was $ 6 . if on one day 3 times as many regular admission tickets were sold as student tickets , what was the total revenue from ticket sales that day ?

Explanation: "from 9 : 00 in the morning to 5 : 55 in the afternoon , inclusive there are 9 * 12 = 108 five - minute intervals , thus total of 108 * 50 tickets were sold . say x student and 3 x regular tickets were sold , then x + 3 x = 108 * 50 - - > x = 27 * 50 and 3 x = 3 * ( 27 * 50 ) = 27 * 150 . therefore , the total revenue from ticket sales that day was 27 * 50 * 6 + 27 * 150 * 10 = $ 48,600 . answer : e ."

add(multiply(multiply(divide(multiply(multiply(add(subtract(add(const_12, 5), 9), const_1), const_12), 50), add(3, const_1)), 3), 10), multiply(divide(multiply(multiply(add(subtract(add(const_12, 5), 9), const_1), const_12), 50), add(3, const_1)), 6))

<gadget id="calculator">12 + 5</gadget>
<output>17</output>
<gadget id="calculator">17 - 9</gadget>
<output>8</output>
<gadget id="calculator">8 + 1</gadget>
<output>9</output>
<gadget id="calculator">9 * 12</gadget>
<output>108</output>
<gadget id="calculator">108 * 50</gadget>
<output>5_400</output>
<gadget id="calculator">3 + 1</gadget>
<output>4</output>
<gadget id="calculator">5_400 / 4</gadget>
<output>1_350</output>
<gadget id="calculator">1_350 * 3</gadget>
<output>4_050</output>
<gadget id="calculator">4_050 * 10</gadget>
<output>40_500</output>
<gadget id="calculator">1_350 * 6</gadget>
<output>8_100</output>
<gadget id="calculator">40_500 + 8_100</gadget>
<output>48_600</output>
<result>48_600</result>


sum of 3 numbers 264 , if the first number be twice then second and third number be one third of the first , then the second number is

Explanation: explanation : let the second number is x , then first is 2 x , and third is 1 / 3 ( 2 x ) = > 2 x + x + 2 x / 3 = 264 < = > 11 x / 3 = 264 = > x = 72 answer : option c

divide(264, add(add(const_2, const_1), divide(const_2, const_3)))

<gadget id="calculator">2 + 1</gadget>
<output>3</output>
<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">3 + (2/3)</gadget>
<output>11/3 = around 3.666667</output>
<gadget id="calculator">264 / (11/3)</gadget>
<output>72</output>
<result>72</result>


a train moves with a speed of 216 kmph . its speed in metres per second is

Explanation: solution speed = 216 kmph = ( 216 x 5 / 18 ) m / sec = 60 m / sec . answer e

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">216 * (5/18)</gadget>
<output>60</output>
<result>60</result>


find the least number must be subtracted from 105829 so that remaining no . is divisible by 21 ?

Explanation: "on dividing 105829 by 21 we get the remainder 10 , so 10 should be subtracted answer is b"

subtract(105829, multiply(floor(divide(105829, 21)), 21))

<gadget id="calculator">105_829 / 21</gadget>
<output>105_829/21 = around 5_039.47619</output>
<gadget id="calculator">floor(105_829/21)</gadget>
<output>5_039</output>
<gadget id="calculator">5_039 * 21</gadget>
<output>105_819</output>
<gadget id="calculator">105_829 - 105_819</gadget>
<output>10</output>
<result>10</result>


the average age of 50 students in a class is 14 years . if the age of teacher is also included , the average becomes 15 years , find the age of the teacher .

Explanation: "explanation : if teacher ' s age is 14 years , there is no change in the average . but teacher has contributed 1 year to all the students along with maintaining his age at 15 . age of teacher = average age of all + total increase in age = 15 + ( 1 x 50 ) = 65 years answer : b"

subtract(add(add(multiply(50, 14), 15), 50), multiply(50, 14))

<gadget id="calculator">50 * 14</gadget>
<output>700</output>
<gadget id="calculator">700 + 15</gadget>
<output>715</output>
<gadget id="calculator">715 + 50</gadget>
<output>765</output>
<gadget id="calculator">765 - 700</gadget>
<output>65</output>
<result>65</result>


the total cost of a vacation was divided among 3 people . if the total cost of the vacation had been divided equally among 4 people , the cost per person would have been $ 60 less . what was the total cost cost of the vacation ?

Explanation: "c for cost . p price per person . c = 3 * p c = 4 * p - 240 substituting the value of p from the first equation onto the second we get p = 240 . plugging in the value of p in the first equation , we get c = 720 . which leads us to answer choice d"

multiply(multiply(4, 3), divide(60, subtract(4, 3)))

<gadget id="calculator">4 * 3</gadget>
<output>12</output>
<gadget id="calculator">4 - 3</gadget>
<output>1</output>
<gadget id="calculator">60 / 1</gadget>
<output>60</output>
<gadget id="calculator">12 * 60</gadget>
<output>720</output>
<result>720</result>


twice the larger of two numbers is 3 more than 5 times the smaller , and the sum of 4 times the larger and 3 times the smaller is 71 . what are the numbers ?

Explanation: the larger number : x the smaller number : y twice the larger : 2 x three more than five times the smaller : 5 y + 3 relationship between ( ` ` is ' ' ) : 2 x = 5 y + 3 four times the larger : 4 x three times the smaller : 3 y relationship between ( ` ` sum of ' ' ) : 4 x + 3 y = 71 now i have two equations in two variables : 2 x = 5 y + 3 4 x + 3 y = 71 i will solve , say , the first equation for x : x = ( 5 / 2 ) y + ( 3 / 2 ) then i ' ll plug the right - hand side of this into the second equation in place of the ` ` x ' ' : 4 [ ( 5 / 2 ) y + ( 3 / 2 ) ] + 3 y = 71 10 y + 6 + 3 y = 71 13 y + 6 = 71 13 y = 65 y = 65 / 13 = 5 now that i have the value for y , i can solve for x : x = ( 5 / 2 ) y + ( 3 / 2 ) x = ( 5 / 2 ) ( 5 ) + ( 3 / 2 ) x = ( 25 / 2 ) + ( 3 / 2 ) x = 28 / 2 = 14 answer : e

divide(add(add(multiply(5, 5), 3), const_1), const_2)

<gadget id="calculator">5 * 5</gadget>
<output>25</output>
<gadget id="calculator">25 + 3</gadget>
<output>28</output>
<gadget id="calculator">28 + 1</gadget>
<output>29</output>
<gadget id="calculator">29 / 2</gadget>
<output>29/2 = around 14.5</output>
<result>29/2 = around 14.5</result>


if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer w that must divide n is ?

Explanation: "q : if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer w that must divide n is : a 6 , b 12 , c 24 , d 36 , e 48 n ^ 2 is divisible by 72 , but it must also be greater than 72 . if n is an integer , then n ^ 2 must be a perfect square . the factorization of 72 is ( 8 ) ( 9 ) , so if it is multiplied by 2 , it will be ( 2 ) ( 8 ) ( 9 ) = ( 16 ) ( 9 ) = 144 , a perfect square . so n ^ 2 must be at least 144 or a multiple of 144 , which means that n must be 12 or a multiple of 12 . b"

<gadget id="calculator">72 / 2</gadget>
<output>36</output>
<gadget id="calculator">36 ** (1/2)</gadget>
<output>6</output>
<gadget id="calculator">6 * 2</gadget>
<output>12</output>
<result>12</result>


800 men have provisions for 20 days . if 200 more men join them , for how many days will the provisions last now ?

Explanation: "800 * 20 = 1200 * x x = 16 . answer : c"

<gadget id="calculator">20 * 800</gadget>
<output>16_000</output>
<gadget id="calculator">800 + 200</gadget>
<output>1_000</output>
<gadget id="calculator">16_000 / 1_000</gadget>
<output>16</output>
<result>16</result>


the list price of an article is rs . 70 . a customer pays rs . 59.22 for it . he was given two successive discounts , one of them being 10 % . the other discount is ?

Explanation: "option e explanation : 70 * ( 90 / 100 ) * ( ( 100 - x ) / 100 ) = 59.22 x = 6 %"

multiply(divide(subtract(subtract(70, multiply(70, divide(10, const_100))), 59.22), subtract(70, multiply(70, divide(10, const_100)))), const_100)

<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">70 * (1/10)</gadget>
<output>7</output>
<gadget id="calculator">70 - 7</gadget>
<output>63</output>
<gadget id="calculator">63 - 59.22</gadget>
<output>3.78</output>
<gadget id="calculator">3.78 / 63</gadget>
<output>0.06</output>
<gadget id="calculator">0.06 * 100</gadget>
<output>6</output>
<result>6</result>


a train crosses a platform of 200 m in 15 sec , same train crosses another platform of length 300 m in 20 sec . then find the length of the train ?

Explanation: "length of the train be ‘ x ’ x + 200 / 15 = x + 300 / 20 4 x + 800 = 3 x + 900 x = 100 m answer : a"

subtract(multiply(300, divide(15, divide(15, const_3))), multiply(200, divide(20, divide(15, const_3))))

<gadget id="calculator">15 / 3</gadget>
<output>5</output>
<gadget id="calculator">15 / 5</gadget>
<output>3</output>
<gadget id="calculator">300 * 3</gadget>
<output>900</output>
<gadget id="calculator">20 / 5</gadget>
<output>4</output>
<gadget id="calculator">200 * 4</gadget>
<output>800</output>
<gadget id="calculator">900 - 800</gadget>
<output>100</output>
<result>100</result>


one man can do a piece of work in 10 days . one boys join him & he complete the work in 6 days . if he gets 50 rs for his work then what will be the share of the boy .

Explanation: 1 day work of man = 1 / 10 , if boy ' s 1 day work = 1 / x , then ( 1 / 10 ) + ( 1 / x ) = 1 / 6 , x = 15 ratio of work of man & boy = 1 / 10 : 1 / 15 = 3 : 2 so out of 50 rs . boy ' s share = 2 * 50 / ( 3 + 2 ) = 20 answer : b

<gadget id="calculator">10 / 4</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">50 / (5/2)</gadget>
<output>20</output>
<result>20</result>


Explanation: according to order of operations , 10 ? 2 ? 5 ( division and multiplication ) is done first from left to right 10 / 2 = 5 * 2 = 10 hence 10111 - 10 * 2 * 5 = 10111 - 10 = 10101 correct answer a

subtract(10111, multiply(multiply(10, 2), 5))

<gadget id="calculator">10 * 2</gadget>
<output>20</output>
<gadget id="calculator">20 * 5</gadget>
<output>100</output>
<gadget id="calculator">10_111 - 100</gadget>
<output>10_011</output>
<result>10_011</result>


seed mixture x is 40 percent ryegrass and 60 percent bluegrass by weight ; seed mixture y is 25 percent ryegrass and 75 percent fescue . if a mixture of x and y contains 35 percent ryegrass , what percent of the weight of this mixture is x ?

Explanation: "- - - - - - - - - - - - - - - - > ryegrass x - - - - - - - - - - - - - - > 40 % y - - - - - - - - - - - - - - > 25 % m ( mixture ) - - - - > 35 % 0.4 x + ( m - x ) 0.25 = 0.35 m 0.15 x = 0.10 m x = 0.6666 m x = 66.66 % of m e"

divide(subtract(35, 25), subtract(divide(40, const_100), divide(25, const_100)))

<gadget id="calculator">35 - 25</gadget>
<output>10</output>
<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(2/5) - (1/4)</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">10 / (3/20)</gadget>
<output>200/3 = around 66.666667</output>
<result>200/3 = around 66.666667</result>


a rectangular garden is to be twice as long as it is wide . if 150 yards of fencing , including the gate , will completely enclose the garden , what will be the length of the garden , in yards ?

Explanation: alternate approach backsolving ( using answer options to reach the correct answer ) can work wonders here if one is fast in calculations . given perimeter is 150 so , 2 ( l + b ) = 150 or , l + b = 75 now use the answer options ( given length ; breath will be half the length ) ( a ) 40 l = 40 ; b = 20 l + b = 60 ( b ) 50 l = 50 ; b = 25 l + b = 75 ( c ) 60 l = 60 ; b = 30 l + b = 90 ( d ) 70 l = 70 ; b = 35 l + b = 105 ( e ) 80 l = 80 ; b = 40 l + b = 120 thus you see no , need of any calculations , u can reach the correct option only by checking options ; correct answer will be ( b )

multiply(divide(150, multiply(add(const_2, const_1), const_2)), const_2)

<gadget id="calculator">2 + 1</gadget>
<output>3</output>
<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">150 / 6</gadget>
<output>25</output>
<gadget id="calculator">25 * 2</gadget>
<output>50</output>
<result>50</result>


a jar of 364 marbles is divided equally among a group of marble - players today . if 2 people joined the group in the future , each person would receive 1 marble less . how many people are there in the group today ?

Explanation: "364 = 26 * 14 = 28 * 13 there are 26 people in the group today . the answer is d ."

divide(subtract(sqrt(add(multiply(multiply(364, 2), const_4), power(2, 2))), 2), 2)

<gadget id="calculator">364 * 2</gadget>
<output>728</output>
<gadget id="calculator">728 * 4</gadget>
<output>2_912</output>
<gadget id="calculator">2 ** 2</gadget>
<output>4</output>
<gadget id="calculator">2_912 + 4</gadget>
<output>2_916</output>
<gadget id="calculator">2_916 ** (1/2)</gadget>
<output>54</output>
<gadget id="calculator">54 - 2</gadget>
<output>52</output>
<gadget id="calculator">52 / 2</gadget>
<output>26</output>
<result>26</result>


peter invested a certain sum of money in a simple interest bond whose value grew to $ 300 at the end of 3 years and to $ 400 at the end of another 5 years . what was the rate of interest in which he invested his sum ?

Explanation: "now after a time of 3 years the principal p amounts to $ 300 and after a time of 8 years ( question says after another 5 years so 3 + 5 ) p becomes $ 400 . formulating the above data amount ( a 1 ) at end of 3 years a 1 = p ( 1 + 3 r / 100 ) = 300 amount ( a 2 ) at end of 8 years a 2 = p ( 1 + 8 r / 100 ) = 400 dividing a 2 by a 1 we get ( 1 + 8 r / 100 ) / ( 1 + 3 r / 100 ) = 4 / 3 after cross multiplication we are left with 12 r = 100 which gives r = 8.33 % answer : e"

multiply(divide(divide(subtract(400, 300), 5), subtract(300, multiply(divide(subtract(400, 300), 5), 3))), const_100)

<gadget id="calculator">400 - 300</gadget>
<output>100</output>
<gadget id="calculator">100 / 5</gadget>
<output>20</output>
<gadget id="calculator">20 * 3</gadget>
<output>60</output>
<gadget id="calculator">300 - 60</gadget>
<output>240</output>
<gadget id="calculator">20 / 240</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">(1/12) * 100</gadget>
<output>25/3 = around 8.333333</output>
<result>25/3 = around 8.333333</result>


at what rate percent on simple interest will rs . 750 amount to rs . 900 in 5 years ?

Explanation: "150 = ( 750 * 5 * r ) / 100 r = 4 % . answer : c"

multiply(divide(divide(subtract(900, 750), 750), 5), const_100)

<gadget id="calculator">900 - 750</gadget>
<output>150</output>
<gadget id="calculator">150 / 750</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) / 5</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">(1/25) * 100</gadget>
<output>4</output>
<result>4</result>


a person borrows rs . 5000 for 2 years at 4 % p . a . simple interest . he immediately lends it to another person at 6 p . a for 2 years . find his gain in the transaction per year .

Explanation: "gain in 2 years = [ ( 5000 * 6 * 2 ) / 100 ] - [ ( 5000 * 4 * 2 ) / 100 ] 600 - 400 = 200 gain in 1 year = ( 200 / 2 ) = 100 rs answer : a"

divide(subtract(divide(multiply(multiply(5000, 6), 2), const_100), divide(multiply(multiply(5000, 4), 2), const_100)), 2)

<gadget id="calculator">5_000 * 6</gadget>
<output>30_000</output>
<gadget id="calculator">30_000 * 2</gadget>
<output>60_000</output>
<gadget id="calculator">60_000 / 100</gadget>
<output>600</output>
<gadget id="calculator">5_000 * 4</gadget>
<output>20_000</output>
<gadget id="calculator">20_000 * 2</gadget>
<output>40_000</output>
<gadget id="calculator">40_000 / 100</gadget>
<output>400</output>
<gadget id="calculator">600 - 400</gadget>
<output>200</output>
<gadget id="calculator">200 / 2</gadget>
<output>100</output>
<result>100</result>


if 1 / 5 th of a number decreased by 5 is 5 , then the number is

Explanation: explanation : let the number be a , then a / 5 − 5 = 5 ⇒ a / 5 = 10 ⇒ a = 50 correct option : b

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


earl can stuff advertising circulars into envelopes at the rate of 36 envelopes per minutes and ellen requires a minutes and half to stuff the same number of envelops . working together , how long will it take earl and ellen to stuff 240 envelopes

Explanation: "earl takes 1 min . for 36 envelopes . ellen takes 3 / 2 mins for the same . so ellen can stuff ( ( 36 ) / ( 3 / 2 ) ) in 1 min . i . e . , 24 envlpes a min . so both of them when work together can stuff 36 + 24 = 60 envelopes in 1 min . for 240 envelopes they will take 240 / 60 mins . i . e . , 4 mins . answer : e"

divide(240, add(36, divide(36, divide(const_3, const_2))))

<gadget id="calculator">3 / 2</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">36 / (3/2)</gadget>
<output>24</output>
<gadget id="calculator">36 + 24</gadget>
<output>60</output>
<gadget id="calculator">240 / 60</gadget>
<output>4</output>
<result>4</result>


if ( x + 3 ) ^ 2 / ( 2 x + 15 ) = 3 , then the difference between the two possible values of x is :

Explanation: ( x + 3 ) ^ 2 / ( 2 x + 15 ) = 3 ( x + 3 ) ^ 2 = 3 ( 2 x + 15 ) x ^ 2 + 6 x + 9 = 6 x + 45 x ^ 2 - 36 = 0 ( x - 6 ) ( x + 6 ) = 0 x = 6 or x = - 6 the answer is c .

multiply(sqrt(subtract(multiply(15, 3), multiply(const_3, 3))), const_2)

<gadget id="calculator">15 * 3</gadget>
<output>45</output>
<gadget id="calculator">3 * 3</gadget>
<output>9</output>
<gadget id="calculator">45 - 9</gadget>
<output>36</output>
<gadget id="calculator">36 ** (1/2)</gadget>
<output>6</output>
<gadget id="calculator">6 * 2</gadget>
<output>12</output>
<result>12</result>


what is the measure of the angle y made by the diagonals of the any adjacent sides of a cube .

Explanation: "c . . 60 degrees all the diagonals are equal . if we take 3 touching sides and connect their diagonals , we form an equilateral triangle . therefore , each angle would be 60 . c"

<gadget id="calculator">180 / 3</gadget>
<output>60</output>
<result>60</result>


a placed 3 sheets with two carbons to get two extra copies of the original . then he decided to get more carbon copies and folded the paper in such a way that the upper half of the sheets were on top of the lower half . then he typed . how many carbon copies did he get ?

Explanation: explanation : since the number of carbons is 2 , only two copies can be obtained . answer : b

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


the average age of applicants for a new job is 30 , with a standard deviation of 8 . the hiring manager is only willing to accept applicants whose age is within one standard deviation of the average age . assuming that all applicants ' ages are integers and that the endpoints of the range are included , what is the maximum number of different ages of the applicants ?

Explanation: "minimum age = average - 1 standard deviation = 30 - 8 = 22 maximum age = average + 1 standard deviation = 30 + 8 = 38 maximum number of different ages of the applicants = 38 - 22 + 1 = 17 answer c"

add(subtract(add(30, 8), subtract(30, 8)), const_1)

<gadget id="calculator">30 + 8</gadget>
<output>38</output>
<gadget id="calculator">30 - 8</gadget>
<output>22</output>
<gadget id="calculator">38 - 22</gadget>
<output>16</output>
<gadget id="calculator">16 + 1</gadget>
<output>17</output>
<result>17</result>


hcf and lcm two numbers are 16 and 396 respectively . if one of the numbers is 36 , then the other number is ?

Explanation: "16 * 396 = 36 * x x = 176 answer : d"

<gadget id="calculator">16 * 396</gadget>
<output>6_336</output>
<gadget id="calculator">6_336 / 36</gadget>
<output>176</output>
<result>176</result>


a 10000 liter tank , half - full of water is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes . at the same time , the tank is losing water from two drains at a rate of 1 kiloliter every 4 minutes and every 6 minutes . how many minutes does it take to fill the tank completely ?

Explanation: "in : we have : 1,000 / 2 min = 500 litres per minute out : we have : 1,000 / 4 + 1,000 / 6 then do : in - out to figure out the net inflow per minute ( you get 83.3 ) . then divide the total number of litres you need ( 5,000 by that net inflow to get the minutes ) - 60 min . answer e ."

divide(multiply(add(add(6, 4), 2), divide(10000, 2)), const_1000)

<gadget id="calculator">6 + 4</gadget>
<output>10</output>
<gadget id="calculator">10 + 2</gadget>
<output>12</output>
<gadget id="calculator">10_000 / 2</gadget>
<output>5_000</output>
<gadget id="calculator">12 * 5_000</gadget>
<output>60_000</output>
<gadget id="calculator">60_000 / 1_000</gadget>
<output>60</output>
<result>60</result>


in a village of 2,700 people , 900 people are over 70 years old and 1200 people are female . it is known that 60 percent of the females are younger than 70 years old . if no one in the village is 70 years old , what is the probability that a person chosen at random is either a male or younger than 70 years old ?

Explanation: "the number of people younger than 70 years old is 2700 - 900 = 1800 the number of females older than 70 years old is 0.4 * 1200 = 480 the number of males older than 70 years old is 900 - 480 = 420 the number of people who are either male or younger than 70 is 1800 + 420 = 2220 . p ( a person is younger than 70 or male ) = 2220 / 2700 = 37 / 45 the answer is d ."

divide(subtract(multiply(const_26, divide(multiply(const_5, const_5), const_0_25)), multiply(1200, subtract(const_1, divide(60, divide(multiply(const_5, const_5), const_0_25))))), multiply(const_26, divide(multiply(const_5, const_5), const_0_25)))

<gadget id="calculator">5 * 5</gadget>
<output>25</output>
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">25 / (1/4)</gadget>
<output>100</output>
<gadget id="calculator">26 * 100</gadget>
<output>2_600</output>
<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">1 - (3/5)</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">1_200 * (2/5)</gadget>
<output>480</output>
<gadget id="calculator">2_600 - 480</gadget>
<output>2_120</output>
<gadget id="calculator">2_120 / 2_600</gadget>
<output>53/65 = around 0.815385</output>
<result>53/65 = around 0.815385</result>


the cost of 8 dozen pencil and 2 dozen note book is 520 rupee . if cost of 3 pencil and 4 note book is 60 rupee , then sum of the cost of 1 pencil and 1 note book will be ( in rupee )

Explanation: let cost of pencil = rs x cost of notebook = rs y cost of 8 dozen pencils are 96 x cost of 2 dozen pencils are 24 y cost of 3 pencils are 3 x cost of 4 notebooks are 4 y equations are 96 x + 24 y = 520 - - - - - 1 3 x + 4 y = 60 - - - - - 2 multiplying 6 with equation ( 2 ) and then subtracting eqn ( 1 ) - eqn ( 2 ) , we get 96 x + 24 y = 520 18 x + 24 y = 360 after solving the equations , we get x = 2.05 y = 13.46 cost of 1 pencil and 1 notebook is 2.05 + 13.46 = rs 15.51 answer : b

add(divide(subtract(520, multiply(60, add(const_3, const_3))), subtract(multiply(8, const_12), multiply(3, add(const_3, const_3)))), divide(subtract(60, multiply(divide(subtract(520, multiply(60, add(const_3, const_3))), subtract(multiply(8, const_12), multiply(3, add(const_3, const_3)))), 3)), 4))

<gadget id="calculator">3 + 3</gadget>
<output>6</output>
<gadget id="calculator">60 * 6</gadget>
<output>360</output>
<gadget id="calculator">520 - 360</gadget>
<output>160</output>
<gadget id="calculator">8 * 12</gadget>
<output>96</output>
<gadget id="calculator">3 * 6</gadget>
<output>18</output>
<gadget id="calculator">96 - 18</gadget>
<output>78</output>
<gadget id="calculator">160 / 78</gadget>
<output>80/39 = around 2.051282</output>
<gadget id="calculator">(80/39) * 3</gadget>
<output>80/13 = around 6.153846</output>
<gadget id="calculator">60 - (80/13)</gadget>
<output>700/13 = around 53.846154</output>
<gadget id="calculator">(700/13) / 4</gadget>
<output>175/13 = around 13.461538</output>
<gadget id="calculator">(80/39) + (175/13)</gadget>
<output>605/39 = around 15.512821</output>
<result>605/39 = around 15.512821</result>


8 years ago , p was half of q ' s age . if the ratio of their present ages is 3 : 4 what will be the total of their present ages ?

Explanation: let present age of p and q be 3 x 3 x and 4 x 4 x respectively . eight years ago , p was half of q ' s age â ‡ ’ ( 3 x â ˆ ’ 8 ) = 1 / 2 ( 4 x â ˆ ’ 8 ) â ‡ ’ 6 x â ˆ ’ 16 = 4 x â ˆ ’ 8 â ‡ ’ 2 x = 8 â ‡ ’ x = 4 total of their present ages = 3 x + 4 x = 7 x = 7 ã — 4 = 28 c

<gadget id="calculator">4 + 3</gadget>
<output>7</output>
<gadget id="calculator">8 / 2</gadget>
<output>4</output>
<gadget id="calculator">7 * 4</gadget>
<output>28</output>
<result>28</result>


selling an kite for rs . 30 , a shop keeper gains 15 % . 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 / 115 * 30 = rs . 26.08 sale price = 90 % of rs . 30 = rs . 27 required gain % = 0.92 / 26.08 * 100 = 3.5 % . answer : a"

multiply(divide(subtract(multiply(divide(30, const_100), subtract(const_100, 10)), divide(multiply(30, const_100), add(15, const_100))), divide(multiply(30, const_100), add(15, 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">15 + 100</gadget>
<output>115</output>
<gadget id="calculator">3_000 / 115</gadget>
<output>600/23 = around 26.086957</output>
<gadget id="calculator">27 - (600/23)</gadget>
<output>21/23 = around 0.913043</output>
<gadget id="calculator">(21/23) / (600/23)</gadget>
<output>7/200 = around 0.035</output>
<gadget id="calculator">(7/200) * 100</gadget>
<output>7/2 = around 3.5</output>
<result>7/2 = around 3.5</result>


john makes $ 40 a week from his job . he earns a raise and now makes $ 80 a week . what is the % increase ?

Explanation: increase = ( 40 / 40 ) * 100 = ( 1 ) * 100 = 100 % . e

multiply(divide(subtract(80, 40), 40), const_100)

<gadget id="calculator">80 - 40</gadget>
<output>40</output>
<gadget id="calculator">40 / 40</gadget>
<output>1</output>
<gadget id="calculator">1 * 100</gadget>
<output>100</output>
<result>100</result>


the average of 6 no . ' s is 4.60 . the average of 2 of them is 3.4 , while the average of the other 2 is 3.8 . what is the average of the remaining 2 no ' s ?

Explanation: "sum of the remaining two numbers = ( 4.6 * 6 ) - [ ( 3.4 * 2 ) + ( 3.8 * 2 ) ] = 27.60 - ( 6.8 + 7.6 ) = 27.60 - 14.40 = 13.20 . required average = ( 13.2 / 2 ) = 6.6 . answer : b"

divide(subtract(multiply(6, 4.60), add(multiply(2, 3.4), multiply(2, 3.8))), 2)

<gadget id="calculator">6 * 4.6</gadget>
<output>27.6</output>
<gadget id="calculator">2 * 3.4</gadget>
<output>6.8</output>
<gadget id="calculator">2 * 3.8</gadget>
<output>7.6</output>
<gadget id="calculator">6.8 + 7.6</gadget>
<output>14.4</output>
<gadget id="calculator">27.6 - 14.4</gadget>
<output>13.2</output>
<gadget id="calculator">13.2 / 2</gadget>
<output>6.6</output>
<result>6.6</result>


what least number must be subtracted from 13294 so that the remainder is exactly divisible by 97 ?

Explanation: "sol . on dividing 13924 by 97 , we get remainder = 5 . ∴ required number to be subtracted = 5 . answer b"

subtract(13294, multiply(floor(divide(13294, 97)), 97))

<gadget id="calculator">13_294 / 97</gadget>
<output>13_294/97 = around 137.051546</output>
<gadget id="calculator">floor(13_294/97)</gadget>
<output>137</output>
<gadget id="calculator">137 * 97</gadget>
<output>13_289</output>
<gadget id="calculator">13_294 - 13_289</gadget>
<output>5</output>
<result>5</result>


amar takes as much time in running 18 meters as a car takes in covering 12 meters . what will be the distance covered by amar during the time the car covers 1.6 km ?

Explanation: "b 2400 m distance covered by amar = 18 / 1.2 ( 1.6 km ) = 3 / 8 ( 1600 ) = 2400 m answer is b"

divide(multiply(18, multiply(1.6, const_1000)), 12)

<gadget id="calculator">1.6 * 1_000</gadget>
<output>1_600</output>
<gadget id="calculator">18 * 1_600</gadget>
<output>28_800</output>
<gadget id="calculator">28_800 / 12</gadget>
<output>2_400</output>
<result>2_400</result>


with both valves open , the pool will be filled with water in 48 minutes . the first valve alone would fill the pool in 2 hours . if the second valve emits 50 cubic meters of water more than the first every minute , then what is the capacity w of the pool ?

Explanation: "d . 12000 cubic meters . if both hte valves fill the pool in 48 minutes and valve 1 only fills in 120 minutes then valve 2 alone will fill the pool in ( 48 * 120 ) / ( 120 - 48 ) = 80 minutes . now , if valve 1 admits x cubic meter of water per minute then the capacity of pool will be 120 x and also 80 ( x + 50 ) . or , 120 x = 80 ( x + 50 ) . or x = 100 . hence , the capacity of pool = 120 x = 12000 cubic meters ."

multiply(50, multiply(const_60, multiply(divide(48, const_60), add(const_4, const_1))))

<gadget id="calculator">48 / 60</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">(4/5) * 5</gadget>
<output>4</output>
<gadget id="calculator">60 * 4</gadget>
<output>240</output>
<gadget id="calculator">50 * 240</gadget>
<output>12_000</output>
<result>12_000</result>


the average speed of a car is 1 4 / 5 times the avg speed of a bike . a tractor covers 575 km in 23 hrs . how much distance will the car cover in 4 hrs if the speed of the bike is twice speed of the tractor ?

Explanation: "sol . average speed of a tractor = 25 km / h the speed of a bus in an hour = 25 × 2 = 50 km the speed of a car in an hour = 9 / 5 * 50 = 90 km so , the distance covered by car in 4 h is 90 × 4 = 360 km ans . ( c )"

multiply(multiply(add(1, divide(4, 5)), multiply(const_2, divide(575, 23))), 4)

<gadget id="calculator">4 / 5</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">575 / 23</gadget>
<output>25</output>
<gadget id="calculator">2 * 25</gadget>
<output>50</output>
<gadget id="calculator">(9/5) * 50</gadget>
<output>90</output>
<gadget id="calculator">90 * 4</gadget>
<output>360</output>
<result>360</result>


a man bought an article and sold it at a gain of 5 % . if he had bought it at 5 % less and sold it for re 5 less , he would have made a profit of 10 % . the c . p . of the article was

Explanation: "explanation : let original cost price is x its selling price = ( 105 / 100 ) * x = 21 x / 20 new cost price = ( 95 / 100 ) * x = 19 x / 20 new selling price = ( 110 / 100 ) * ( 19 x / 20 ) = 209 x / 200 [ ( 21 x / 20 ) - ( 209 x / 200 ) ] = 1 = > x = 1000 answer : e ) rs 1000"

multiply(multiply(multiply(5, const_4.0), 10), 5)

<gadget id="calculator">5 * 4</gadget>
<output>20</output>
<gadget id="calculator">20 * 10</gadget>
<output>200</output>
<gadget id="calculator">200 * 5</gadget>
<output>1_000</output>
<result>1_000</result>


the difference between a number and its 3 - fourth is 100 . what is 25 % of that number ?

Explanation: explanation : solution : let the number be x . then , x - 3 / 4 x = 100 = > x / 4 = 100 = > x = 400 . 25 % of x = 25 % of 400 = 25 / 100 * 400 = 100 . answer : b

multiply(divide(100, subtract(const_1, divide(3, const_4))), divide(25, 100))

<gadget id="calculator">3 / 4</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">100 / (1/4)</gadget>
<output>400</output>
<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">400 * (1/4)</gadget>
<output>100</output>
<result>100</result>


i chose a number and divide it by 4 . then i subtracted 175 from the result and got 10 . what was the number i chose ?

Explanation: "let x be the number i chose , then x / 4 − 175 = 10 x / 4 = 185 x = 740 answer is b ."

<gadget id="calculator">175 + 10</gadget>
<output>185</output>
<gadget id="calculator">185 * 4</gadget>
<output>740</output>
<result>740</result>


ramu bought an old car for rs . 42000 . he spent rs . 15000 on repairs and sold it for rs . 64900 . what is his profit percent ?

Explanation: "total cp = rs . 42000 + rs . 15000 = rs . 57000 and sp = rs . 64900 profit ( % ) = ( 64900 - 57000 ) / 57000 * 100 = 13.8 % answer : a"

<gadget id="calculator">42_000 + 15_000</gadget>
<output>57_000</output>
<gadget id="calculator">64_900 - 57_000</gadget>
<output>7_900</output>
<gadget id="calculator">7_900 / 57_000</gadget>
<output>79/570 = around 0.138596</output>
<gadget id="calculator">(79/570) * 100</gadget>
<output>790/57 = around 13.859649</output>
<result>790/57 = around 13.859649</result>


how many 3 digit numbers n are divisible by 78 or 91 ?

Explanation: the answer will be 19 . explanation : 78 = 2 * 3 * 13 now multiples of 78 , 156 . . . . 780 , now 1000 - 780 = 220 only two more muktiples of 78 can exists . so total number of 3 digit multiples of 78 are 9 + 2 = 11 91 = 13 * 7 - - total number of three digit multiples - - 9 no remember we have a common multiples as well n - - 13 * 7 * 6 = 91 * 6 = 546 so total number of multiples - - 11 + 9 - 1 = 19 . hence answer is 19 . b

add(subtract(91, 78), multiply(3, const_2))

<gadget id="calculator">91 - 78</gadget>
<output>13</output>
<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">13 + 6</gadget>
<output>19</output>
<result>19</result>


the length and breadth of a rectangle is increased by 3 % and 6 % respectively . what is the increase in the area ?

Explanation: "100 * 100 = 10000 103 * 106 = 10918 - - - - - - - - - - - 918 10000 - - - - - - - 918 100 - - - - - - - - - - 9.18 ans a"

divide(multiply(subtract(rectangle_area(add(3, const_100), add(6, const_100)), rectangle_area(const_100, const_100)), const_100), rectangle_area(const_100, const_100))

<gadget id="calculator">3 + 100</gadget>
<output>103</output>
<gadget id="calculator">6 + 100</gadget>
<output>106</output>
<gadget id="calculator">103 * 106</gadget>
<output>10_918</output>
<gadget id="calculator">100 * 100</gadget>
<output>10_000</output>
<gadget id="calculator">10_918 - 10_000</gadget>
<output>918</output>
<gadget id="calculator">918 * 100</gadget>
<output>91_800</output>
<gadget id="calculator">91_800 / 10_000</gadget>
<output>459/50 = around 9.18</output>
<result>459/50 = around 9.18</result>


a sells a bicycle to b and makes a profit of 60 % . b sells the same bicycle to c at a profit of 25 % . 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 60 % profit so sp = 160 b sells at 25 % profit = 160 x ( 1 + 25 / 100 ) = 200 cp sp 100 - - - 200 x - - - 225 cp = 225 x 100 / 200 = 112.5 answer : e"

divide(divide(225, divide(add(const_100, 25), const_100)), divide(add(60, const_100), const_100))

<gadget id="calculator">100 + 25</gadget>
<output>125</output>
<gadget id="calculator">125 / 100</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">225 / (5/4)</gadget>
<output>180</output>
<gadget id="calculator">60 + 100</gadget>
<output>160</output>
<gadget id="calculator">160 / 100</gadget>
<output>8/5 = around 1.6</output>
<gadget id="calculator">180 / (8/5)</gadget>
<output>225/2 = around 112.5</output>
<result>225/2 = around 112.5</result>


if x is 50 percent greater than 88 , then x =

Explanation: "x = 88 * 1.5 = 132 so the answer is b ."

add(88, multiply(divide(50, const_100), 88))

<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) * 88</gadget>
<output>44</output>
<gadget id="calculator">88 + 44</gadget>
<output>132</output>
<result>132</result>


if x represents the product of the first 15 positive integers , then x is not a multiple of :

Explanation: a ) 99 = 9 * 11 b ) 84 = 4 * 7 * 3 c ) 72 = 9 * 11 d ) 65 = 5 * 13 e ) 57 = 19 * 3 since 19 is not there in first 15 positive numbers it is the only possibility d )

<gadget id="calculator">15 + 4</gadget>
<output>19</output>
<gadget id="calculator">19 * 3</gadget>
<output>57</output>
<result>57</result>


a can complete a project in 20 days and b can complete the same project in 40 days . if a and b start working on the project together and a quits 10 days before the project is completed , in how many days will the project be completed ?

Explanation: "let x = the number of days taken to complete the project . the amount of work done by a is ( x - 10 ) * ( 1 / 20 ) . the amount of work done by b is ( x ) * ( 1 / 40 ) . ( 1 / 20 ) * ( x - 10 ) + ( 1 / 40 ) * ( x ) = 1 ( x / 20 ) + ( x / 40 ) - ( 10 / 20 ) = 1 3 x / 40 = 3 / 2 x = 20 therefore , the answer is b : 20 ."

add(divide(subtract(const_1, multiply(divide(const_1, 40), 10)), add(divide(const_1, 20), divide(const_1, 40))), 10)

<gadget id="calculator">1 / 40</gadget>
<output>1/40 = around 0.025</output>
<gadget id="calculator">(1/40) * 10</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 - (1/4)</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">1 / 20</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/20) + (1/40)</gadget>
<output>3/40 = around 0.075</output>
<gadget id="calculator">(3/4) / (3/40)</gadget>
<output>10</output>
<gadget id="calculator">10 + 10</gadget>
<output>20</output>
<result>20</result>


a can finish a work in 12 days and b can do same work in half the time taken by a . then working together , what part of same work they can finish in a day ?

Explanation: "explanation : please note in this question , we need to answer part of work for a day rather than complete work . it was worth mentioning here because many do mistake at this point in hurry to solve the question so lets solve now , a ' s 1 day work = 1 / 12 b ' s 1 day work = 1 / 6 [ because b take half the time than a ] ( a + b ) ' s one day work = ( 1 / 12 + 1 / 6 ) = 1 / 4 so in one day 1 / 4 work will be done answer : a"

add(divide(const_1, 12), multiply(divide(const_1, 12), const_2))

<gadget id="calculator">1 / 12</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">(1/12) * 2</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(1/12) + (1/6)</gadget>
<output>1/4 = around 0.25</output>
<result>1/4 = around 0.25</result>


the sum of all the digits of the integers from 18 to 21 inclusive is 24 ( 1 + 8 + 1 + 9 + 2 + 0 + 2 + 1 = 24 ) . what is the sum e of all the digits of the integers from 0 to 99 inclusive ?

Explanation: we want the sum of the digits from 0 to 99 , so i approximated : 0 - 9 - > 45 - > ( 9 + 0 ) * 10 / 2 40 - 49 - > 85 ( 13 + 4 ) * 10 / 2 90 - 99 - > 135 ( 18 + 9 ) * 10 / 2 we can see at a glance that theweightgoes up as the numbers go up ( meaning the difference between 85 and 45 is 40 , while 135 - 85 is 50 , this means that the second part of this sequence carries more weight for our result ) , so we know that the final answer has to be more than 850 ( 85 * 10 ) but close to it , and that ' s just e = 900 : the answer is c .

multiply(divide(multiply(9, add(9, const_1)), const_2), multiply(const_2, const_10))

<gadget id="calculator">9 + 1</gadget>
<output>10</output>
<gadget id="calculator">9 * 10</gadget>
<output>90</output>
<gadget id="calculator">90 / 2</gadget>
<output>45</output>
<gadget id="calculator">2 * 10</gadget>
<output>20</output>
<gadget id="calculator">45 * 20</gadget>
<output>900</output>
<result>900</result>


subtracting 3 % of a from a is equivalent to multiplying a by how much ?

Explanation: "answer let a - 3 % of a = ab . ⇒ ( 97 x a ) / 100 = ab ∴ b = 0.97 correct option : a"

<gadget id="calculator">100 - 3</gadget>
<output>97</output>
<gadget id="calculator">97 / 100</gadget>
<output>97/100 = around 0.97</output>
<result>97/100 = around 0.97</result>


sachin is older than rahul by 7 years . if the ratio of their ages is 11 : 9 , find the age of sachin

Explanation: explanation : if rahul age is x , then sachin age is x + 7 , so , 9 x + 63 = 11 x 2 x = 63 x = 31.5 so sachin age is 31.5 + 7 = 38.5 answer : c ) 38.5

divide(multiply(11, 7), subtract(11, 9))

<gadget id="calculator">11 * 7</gadget>
<output>77</output>
<gadget id="calculator">11 - 9</gadget>
<output>2</output>
<gadget id="calculator">77 / 2</gadget>
<output>77/2 = around 38.5</output>
<result>77/2 = around 38.5</result>


Explanation: "when a certain number x is divided by 61 , the remainder is 24 . what is the remainder when x is divided by 5 ? putting a value say x = 24 we get remainder as 24 when divided by 61 . when 24 divided by 5 we get 4 as remainder . c is the answer ."

<gadget id="calculator">24 % 5</gadget>
<output>4</output>
<result>4</result>


Explanation: "2 x + 1 = - 19 x = - 10 e"

<gadget id="calculator">19 + 1</gadget>
<output>20</output>
<gadget id="calculator">-20</gadget>
<output>-20</output>
<gadget id="calculator">(-20) / 2</gadget>
<output>-10</output>
<result>-10</result>


a train 150 m long can cross an electric pole in 3 sec and then find the speed of the train ?

Explanation: "length = speed * time speed = l / t s = 150 / 3 s = 50 m / sec speed = 50 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 180 kmph answer : a"

divide(divide(150, const_1000), divide(3, const_3600))

<gadget id="calculator">150 / 1_000</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">3 / 3_600</gadget>
<output>1/1_200 = around 0.000833</output>
<gadget id="calculator">(3/20) / (1/1_200)</gadget>
<output>180</output>
<result>180</result>


approximately how many revolutions will be made by a car tire with a 10 - inch diameter if the car travels 1 ⁄ 2 mile ?

Explanation: "diameter of car tire = 10 inches radius of car tire = 5 inches = 5 * 2.54 cm = 12.7 cm circumference of the car tire = 2 * pi * 12.7 = 2 * 3.14 * 12.7 = 79.76 cm distance traveled by car = . 5 mile = . 5 * 1.6 km = . 8 km = 800 m = 8 * 10 ^ 4 cm number of revolutions = distance traveled / circumference of tire = 8 * 10 ^ 4 / 79.76 = 1003 since the answer choices are far apart we should use estimation in this question . ideally , in the gmat the conversion between units would be provided . answer c"

divide(divide(1, 2), divide(multiply(add(divide(add(divide(add(divide(add(divide(multiply(const_3, 2), const_10), 1), const_10), const_4), const_10), 1), const_10), const_3), 10), multiply(add(add(multiply(add(multiply(add(multiply(multiply(const_3, 2), const_10), const_3), const_10), const_3), const_10), const_3), 2), const_10)))

<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">6 / 10</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(3/5) + 1</gadget>
<output>8/5 = around 1.6</output>
<gadget id="calculator">(8/5) / 10</gadget>
<output>4/25 = around 0.16</output>
<gadget id="calculator">(4/25) + 4</gadget>
<output>104/25 = around 4.16</output>
<gadget id="calculator">(104/25) / 10</gadget>
<output>52/125 = around 0.416</output>
<gadget id="calculator">(52/125) + 1</gadget>
<output>177/125 = around 1.416</output>
<gadget id="calculator">(177/125) / 10</gadget>
<output>177/1_250 = around 0.1416</output>
<gadget id="calculator">(177/1_250) + 3</gadget>
<output>3_927/1_250 = around 3.1416</output>
<gadget id="calculator">(3_927/1_250) * 10</gadget>
<output>3_927/125 = around 31.416</output>
<gadget id="calculator">6 * 10</gadget>
<output>60</output>
<gadget id="calculator">60 + 3</gadget>
<output>63</output>
<gadget id="calculator">63 * 10</gadget>
<output>630</output>
<gadget id="calculator">630 + 3</gadget>
<output>633</output>
<gadget id="calculator">633 * 10</gadget>
<output>6_330</output>
<gadget id="calculator">6_330 + 3</gadget>
<output>6_333</output>
<gadget id="calculator">6_333 + 2</gadget>
<output>6_335</output>
<gadget id="calculator">6_335 * 10</gadget>
<output>63_350</output>
<gadget id="calculator">(3_927/125) / 63_350</gadget>
<output>561/1_131_250 = around 0.000496</output>
<gadget id="calculator">(1/2) / (561/1_131_250)</gadget>
<output>565_625/561 = around 1_008.244207</output>
<result>565_625/561 = around 1_008.244207</result>


calculate the share of z , if rs . 3720 is divided among x , y and z in the ratio 7 : 8 : 11 ?

Explanation: 7 + 8 + 11 = 26 3720 / 26 = 143.1 so z ' s share = 11 * 143.1 answer : c


the area of a triangle is with base 18 m and height 6 m ?

Explanation: "1 / 2 * 18 * 6 = 54 m 2 answer : d"

<gadget id="calculator">(18 * 6) / 2</gadget>
<output>54</output>
<result>54</result>


if a population of women in a town is 50 % of men . what is the population of men as a % of population of women ?

Explanation: "we ' re told that the number of women in a town is equal to 50 % of the number of men in that town . if . . . . men = 10 women = 5 we ' re asked for the number of men , as a percentage of the number of women . m / w = 10 / 5 = 2 = 200 % answer is a"

<gadget id="calculator">100 / 50</gadget>
<output>2</output>
<gadget id="calculator">2 * 100</gadget>
<output>200</output>
<result>200</result>


225 mtrs long yard , 26 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between 2 consecutive trees ?

Explanation: 26 trees have 25 gaps between them , required distance ( 225 / 25 ) = 10 a

add(divide(225, subtract(26, const_1)), const_1)

<gadget id="calculator">26 - 1</gadget>
<output>25</output>
<gadget id="calculator">225 / 25</gadget>
<output>9</output>
<gadget id="calculator">9 + 1</gadget>
<output>10</output>
<result>10</result>


in a circuit board factory , all circuit boards that pass a verification process are certified . every board that fails the verification process is indeed faulty , but 1 / 8 of those that pass are also faulty . approximately how many faulty circuit boards exist in a group of 3,200 circuit boards where 64 fail inspection ?

Explanation: total of 3,200 boards . all that fail verification are indeed faulty . so the 64 are indeed faulty . 1 / 8 those that pass are also faulty . from the 3,200 we know 64 fail . so 3,136 must pass . of these 1 / 8 are faulty . 3,136 divided by 8 gives you 392 . what one must do now is to add to the 392 which were not detected the actually detected faulty ones , namely the 64 . total faulty : 456 . answer : c

add(64, divide(subtract(multiply(multiply(add(divide(const_60, const_10), const_0_25), 8), 64), 64), 8))

<gadget id="calculator">60 / 10</gadget>
<output>6</output>
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">6 + (1/4)</gadget>
<output>25/4 = around 6.25</output>
<gadget id="calculator">(25/4) * 8</gadget>
<output>50</output>
<gadget id="calculator">50 * 64</gadget>
<output>3_200</output>
<gadget id="calculator">3_200 - 64</gadget>
<output>3_136</output>
<gadget id="calculator">3_136 / 8</gadget>
<output>392</output>
<gadget id="calculator">64 + 392</gadget>
<output>456</output>
<result>456</result>


the rate of spin of a certain gyroscope doubled every 15 seconds from the moment a particular stopwatch started . if after a minute and a half the gyroscope reached a speed of 400 meters per second , what was the speed , in meters per second , when the stopwatch was started ?

Explanation: "let x be the original speed when the stopwatch was started . in 90 seconds , the speed doubled 6 times . 2 ^ 6 * x = 400 x = ( 2 ^ 4 * 25 ) / 2 ^ 6 = 25 / 4 the answer is b ."

divide(divide(400, power(const_2, subtract(divide(add(divide(const_60, const_2), const_60), 15), const_1))), const_2)

<gadget id="calculator">60 / 2</gadget>
<output>30</output>
<gadget id="calculator">30 + 60</gadget>
<output>90</output>
<gadget id="calculator">90 / 15</gadget>
<output>6</output>
<gadget id="calculator">6 - 1</gadget>
<output>5</output>
<gadget id="calculator">2 ** 5</gadget>
<output>32</output>
<gadget id="calculator">400 / 32</gadget>
<output>25/2 = around 12.5</output>
<gadget id="calculator">(25/2) / 2</gadget>
<output>25/4 = around 6.25</output>
<result>25/4 = around 6.25</result>


the area of a parallelogram is 288 sq m and its altitude is twice the corresponding base . then the length of the base is ?

Explanation: "2 x * x = 288 = > x = 12 answer : a"

<gadget id="calculator">288 / 2</gadget>
<output>144</output>
<gadget id="calculator">144 ** (1/2)</gadget>
<output>12</output>
<result>12</result>