a teacher grades students ’ tests by subtracting twice the number of incorrect responses from the number of correct responses . if student a answers each of the 100 questions on her test and receives a score of 76 , how many questions did student a answer correctly ?

Explanation: "let the number of correct responses be x then the number of incorrect responses = 100 - x according to question x - 2 ( 100 - x ) = 76 ( subtracting twice of incorrect from correct ) 3 x = 276 x = 92 answer : a"

subtract(100, divide(subtract(100, 76), const_3))

<gadget id="calculator">100 - 76</gadget>
<output>24</output>
<gadget id="calculator">24 / 3</gadget>
<output>8</output>
<gadget id="calculator">100 - 8</gadget>
<output>92</output>
<result>92</result>


ravi purchased a refrigerator and a mobile phone for rs . 15000 and rs . 8000 respectively . he sold the refrigerator at a loss of 4 percent and the mobile phone at a profit of 11 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 - 4 / 100 ) = 15000 - 600 m = 8000 ( 1 + 11 / 100 ) = 8000 + 880 total sp - total cp = r + m - ( 15000 + 8000 ) = - 600 + 880 = rs . 280 as this is positive , an overall profit of rs . 280 was made . answer : e"

subtract(add(multiply(15000, subtract(const_1, divide(4, const_100))), multiply(8000, add(const_1, divide(11, const_100)))), add(15000, 8000))

<gadget id="calculator">4 / 100</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">1 - (1/25)</gadget>
<output>24/25 = around 0.96</output>
<gadget id="calculator">15_000 * (24/25)</gadget>
<output>14_400</output>
<gadget id="calculator">11 / 100</gadget>
<output>11/100 = around 0.11</output>
<gadget id="calculator">1 + (11/100)</gadget>
<output>111/100 = around 1.11</output>
<gadget id="calculator">8_000 * (111/100)</gadget>
<output>8_880</output>
<gadget id="calculator">14_400 + 8_880</gadget>
<output>23_280</output>
<gadget id="calculator">15_000 + 8_000</gadget>
<output>23_000</output>
<gadget id="calculator">23_280 - 23_000</gadget>
<output>280</output>
<result>280</result>


in a certain candy store , 22 % of the customers are caught sampling the candy and are charged a small fine , but 5 % of the customers who sample the candy are not caught . what is the total percent of all customers who sample candy ?

Explanation: "since 5 % of the customers who sample the candyare notcaught , then 88 % of the customers who sample the candyarecaught : { % of customers who sample candy } * 0.95 = 0.22 ; { % of customers who sample candy } = 0.231 . answer : b ."

divide(22, divide(subtract(const_100, 5), const_100))

<gadget id="calculator">100 - 5</gadget>
<output>95</output>
<gadget id="calculator">95 / 100</gadget>
<output>19/20 = around 0.95</output>
<gadget id="calculator">22 / (19/20)</gadget>
<output>440/19 = around 23.157895</output>
<result>440/19 = around 23.157895</result>


p , q and r have $ 4000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ?

Explanation: "e 1600 let the amount with r be $ r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 4000 - r ) = > 3 r = 8000 - 2 r = > 5 r = 8000 = > r = 1600 ."

divide(multiply(4000, multiply(const_2, const_2)), add(add(multiply(divide(multiply(const_2, const_2), const_3), const_3), multiply(const_1, const_3)), multiply(const_1, const_3)))

<gadget id="calculator">2 * 2</gadget>
<output>4</output>
<gadget id="calculator">4_000 * 4</gadget>
<output>16_000</output>
<gadget id="calculator">4 / 3</gadget>
<output>4/3 = around 1.333333</output>
<gadget id="calculator">(4/3) * 3</gadget>
<output>4</output>
<gadget id="calculator">1 * 3</gadget>
<output>3</output>
<gadget id="calculator">4 + 3</gadget>
<output>7</output>
<gadget id="calculator">7 + 3</gadget>
<output>10</output>
<gadget id="calculator">16_000 / 10</gadget>
<output>1_600</output>
<result>1_600</result>


rahul and sham together can complete a task in 35 days , but rahul alone can complete same work in 60 days . calculate in how many days sham can complete this work ?

Explanation: explanation : as rahul and sham together can finish work in 35 days . 1 days work of rahul and sham is 1 / 35 rahul can alone complete this work in 60 days , so , rahul one day work is 1 / 60 clearly , sham one day work will be = ( rahul and sham one day work ) - ( rahul one day work ) = 1 / 35 - 1 / 60 = 1 / 84 hence sham will complete the given work in 84 days . answer is a

<gadget id="calculator">1 / 35</gadget>
<output>1/35 = around 0.028571</output>
<gadget id="calculator">1 / 60</gadget>
<output>1/60 = around 0.016667</output>
<gadget id="calculator">(1/35) - (1/60)</gadget>
<output>1/84 = around 0.011905</output>
<gadget id="calculator">1 / (1/84)</gadget>
<output>84</output>
<result>84</result>


a train running at the speed of 60 km / hr crosses a pole in 6 sec . what is the length of the train ?

Explanation: "speed = 60 * 5 / 18 = 50 / 3 m / sec length of the train = speed * time = 50 / 3 * 6 = 100 m answer : d"

multiply(divide(multiply(60, const_1000), const_3600), 6)

<gadget id="calculator">60 * 1_000</gadget>
<output>60_000</output>
<gadget id="calculator">60_000 / 3_600</gadget>
<output>50/3 = around 16.666667</output>
<gadget id="calculator">(50/3) * 6</gadget>
<output>100</output>
<result>100</result>


lucy bought a 1 - year , 10000 certificate of deposit that paid interest at an annual rate of 8 percent compunded semiannually . what was the total amount of interest paid on this certificate at maturity ?

Explanation: solution : it says , 8 percent per annum per compounded semi annually . therefore r = 8 / 2 = 4 % . so , p = 10000 r = 4 n = 2 net amount a = 10816 , i = 800 . answer : d

subtract(multiply(10000, power(add(const_1, divide(divide(8, const_100), const_2)), const_2)), 10000)

<gadget id="calculator">8 / 100</gadget>
<output>2/25 = around 0.08</output>
<gadget id="calculator">(2/25) / 2</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">1 + (1/25)</gadget>
<output>26/25 = around 1.04</output>
<gadget id="calculator">(26/25) ** 2</gadget>
<output>676/625 = around 1.0816</output>
<gadget id="calculator">10_000 * (676/625)</gadget>
<output>10_816</output>
<gadget id="calculator">10_816 - 10_000</gadget>
<output>816</output>
<result>816</result>


a bag marked at $ 125 is sold for $ 120 . the rate of discount is ?

Explanation: rate of discount = 5 / 125 * 100 = 4 % answer is e

multiply(divide(subtract(125, 120), 125), const_100)

<gadget id="calculator">125 - 120</gadget>
<output>5</output>
<gadget id="calculator">5 / 125</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">(1/25) * 100</gadget>
<output>4</output>
<result>4</result>


the radius of a cylindrical vessel is 8 cm and height is 3 cm . find the whole surface of the cylinder ?

Explanation: "r = 8 h = 3 2 π r ( h + r ) = 2 * 22 / 7 * 8 ( 11 ) = 553.1 answer : d"

<gadget id="calculator">2 * pi * 8 * (8 + 3)</gadget>
<output>176*pi = around 552.920307</output>
<result>176*pi = around 552.920307</result>


the marks obtained by vijay and amith are in the ratio 6 : 5 and those obtained by amith and abhishek in the ratio of 3 : 2 . the marks obtained by vijay and abhishek are in the ratio of ?

Explanation: "6 : 5 3 : 2 - - - - - - - 18 : 15 : 10 18 : 10 9 : 5 answer : c"

<gadget id="calculator">6 * 3</gadget>
<output>18</output>
<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">18 / 10</gadget>
<output>9/5 = around 1.8</output>
<result>9/5 = around 1.8</result>


right now , the ratio between the ages of sandy and molly is 4 : 3 . after 6 years , sandy ’ s age will be 66 years . what is molly ' s age right now ?

Explanation: "now , sandy is 66 - 6 = 60 molly ' s age is ( 3 / 4 ) * 60 = 45 the answer is d ."

<gadget id="calculator">66 - 6</gadget>
<output>60</output>
<gadget id="calculator">60 / 4</gadget>
<output>15</output>
<gadget id="calculator">15 * 3</gadget>
<output>45</output>
<result>45</result>


Explanation: "explanation : 935421 × 625 = 935421 × 54 = 935421 × ( 10 / 2 ) 4 = ( 935421 × 10000 ) / 16 = 584638125 . answer : option d"

multiply(935421, power(add(const_4, const_1), const_4))

<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">5 ** 4</gadget>
<output>625</output>
<gadget id="calculator">935_421 * 625</gadget>
<output>584_638_125</output>
<result>584_638_125</result>


bert and rebecca were looking at the price of a condominium . the price of the condominium was 100 % more than bert had in savings , and separately , the same price was also 60 % more than rebecca had in savings . what is the ratio of what bert has in savings to what rebecca has in savings .

Explanation: "suppose bert had 100 so price becomes 200 , this 200 = 1.6 times r ' s saving . . so r ' s saving becomes 125 so required ratio is 100 : 125 = 4 : 5 answer : d"

divide(divide(const_100, add(const_100, 100)), divide(const_100, add(const_100, 60)))

<gadget id="calculator">100 + 100</gadget>
<output>200</output>
<gadget id="calculator">100 / 200</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">100 + 60</gadget>
<output>160</output>
<gadget id="calculator">100 / 160</gadget>
<output>5/8 = around 0.625</output>
<gadget id="calculator">(1/2) / (5/8)</gadget>
<output>4/5 = around 0.8</output>
<result>4/5 = around 0.8</result>


a man swims downstream 30 km and upstream 20 km taking 5 hours each time , what is the speed of the man in still water ?

Explanation: "30 - - - 5 ds = 6 ? - - - - 1 20 - - - - 5 us = 4 ? - - - - 1 m = ? m = ( 6 + 4 ) / 2 = 5 answer : d"

divide(add(divide(20, 5), divide(30, 5)), const_2)

<gadget id="calculator">20 / 5</gadget>
<output>4</output>
<gadget id="calculator">30 / 5</gadget>
<output>6</output>
<gadget id="calculator">4 + 6</gadget>
<output>10</output>
<gadget id="calculator">10 / 2</gadget>
<output>5</output>
<result>5</result>


andrew purchased 8 kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg . how much amount did he pay to the shopkeeper ?

Explanation: "cost of 8 kg grapes = 70 × 8 = 560 . cost of 9 kg of mangoes = 55 × 9 = 490 . total cost he has to pay = 560 + 490 = 1055 b"

<gadget id="calculator">8 * 70</gadget>
<output>560</output>
<gadget id="calculator">9 * 55</gadget>
<output>495</output>
<gadget id="calculator">560 + 495</gadget>
<output>1_055</output>
<result>1_055</result>


how many integers v are prime numbers in the range 200 < v < 220 ?

Explanation: my friend , every single odd number greater than can be written either as 4 v + 1 or as 4 v + 3 . if you divide any odd number by 4 , you will get a remainder of either 1 or 3 . that ' s not a rule unique to prime numbers at all . the 6 v + 1 or 6 v - 1 rule is basically every odd number that is not divisible by three , so it narrows the search a little . here ' s how i thought about the problem . first , eliminate all the even numbers and the odd multiples of 5 in that range . that leaves us with : { 201 , 203 , 207 , 209 , 211 , 213 , 217 , 219 } eliminate the four multiples of 3 . notice that 21 is a multiple of 3 , so 210 is also a multiple of 3 . if we add or subtract 3 or 9 , we get more multiples of three . when we eliminate those , we are left with . { 203 , 209 , 211 , 217 } now , notice that a cool thing about this range is that 210 is also a multiple 7 ( again , because 21 is a multiple of 7 ) . this means that 210 - 7 = 203 210 + 7 = 217 those two numbers are also multiples of 7 , so eliminate them from the list . now , we are left with { 209 , 211 } . we ' ve already checked all the prime numbers less than 10 , so we know that neither of these numbers is divisible by anything less than 10 . we have to check 11 now . we know that 22 is a multiple of 11 , so 220 is also a multiple of 11 . this means that 220 - 11 = 209 is also a multiple of 11 . we can eliminate this from the list also . that leaves us with just 211 . there ' s no zero option in the question , so this must be a prime number . answer = ( a )

subtract(divide(subtract(subtract(220, 200), const_12), const_4), const_1)

<gadget id="calculator">220 - 200</gadget>
<output>20</output>
<gadget id="calculator">20 - 12</gadget>
<output>8</output>
<gadget id="calculator">8 / 4</gadget>
<output>2</output>
<gadget id="calculator">2 - 1</gadget>
<output>1</output>
<result>1</result>


if the average of 20 digits is 500 and the average of 14 of them is 390 , calculate the average of the remaining 6 numbers ?

Explanation: "explanation : total of the 20 digits - 20 * 500 = 10000 total of the 14 digits - 14 * 390 = 5460 total of the remaining 6 digits - 10000 - 5460 = 4540 average of the remaining 6 numbers = 4540 / 6 = 756.7 answer : a"

divide(subtract(multiply(20, 500), multiply(14, 390)), 6)

<gadget id="calculator">20 * 500</gadget>
<output>10_000</output>
<gadget id="calculator">14 * 390</gadget>
<output>5_460</output>
<gadget id="calculator">10_000 - 5_460</gadget>
<output>4_540</output>
<gadget id="calculator">4_540 / 6</gadget>
<output>2_270/3 = around 756.666667</output>
<result>2_270/3 = around 756.666667</result>


two bullet train s 140 m and 180 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time ( in seconds ) which they take to cross each other , is :

Explanation: "relative speed = ( 60 + 40 ) km / hr = 100 x 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = ( 140 + 180 ) m = 320 m . required time = 320 x 9 / 250 = 11.52 sec . answer b"

<gadget id="calculator">140 + 180</gadget>
<output>320</output>
<gadget id="calculator">60 + 40</gadget>
<output>100</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">100 * (5/18)</gadget>
<output>250/9 = around 27.777778</output>
<gadget id="calculator">320 / (250/9)</gadget>
<output>288/25 = around 11.52</output>
<result>288/25 = around 11.52</result>


a producer of tea blends two varieties of tea from two tea gardens one costing rs 18 per kg and another rs 20 per kg in the ratio 5 : 3 . if he sells the blended variety at rs 25 per kg , then his gain percent is

Explanation: "explanation : suppose he bought 5 kg and 3 kg of tea . cost price = rs . ( 5 x 18 + 3 x 20 ) = rs . 150 . selling price = rs . ( 8 x 25 ) = rs . 200 . profit = 200 - 150 = 50 so , profit % = ( 50 / 150 ) * 100 = 33 % option b"

divide(multiply(subtract(multiply(25, add(5, 3)), add(multiply(5, 18), multiply(3, 20))), const_100), add(multiply(5, 18), multiply(3, 20)))

<gadget id="calculator">5 + 3</gadget>
<output>8</output>
<gadget id="calculator">25 * 8</gadget>
<output>200</output>
<gadget id="calculator">5 * 18</gadget>
<output>90</output>
<gadget id="calculator">3 * 20</gadget>
<output>60</output>
<gadget id="calculator">90 + 60</gadget>
<output>150</output>
<gadget id="calculator">200 - 150</gadget>
<output>50</output>
<gadget id="calculator">50 * 100</gadget>
<output>5_000</output>
<gadget id="calculator">5_000 / 150</gadget>
<output>100/3 = around 33.333333</output>
<result>100/3 = around 33.333333</result>


if p / q = 4 / 5 , then the value of 25 / 7 + { ( 2 q - p ) / ( 2 q + p ) } is ?

Explanation: "answer given exp . = 25 / 7 + { ( 2 q - p ) / ( 2 q + p ) } dividing numerator as well as denominator by q , exp = 25 / 7 + { 2 - p / q ) / ( 2 + p / q ) } = 25 / 7 + { ( 2 - 4 / 5 ) / ( 2 + 4 / 5 ) } = 25 / 7 + 6 / 14 = 25 / 7 + 3 / 7 = 28 / 7 = 4 correct option : a"

add(divide(25, 7), divide(subtract(2, divide(4, 5)), add(2, divide(4, 5))))

<gadget id="calculator">25 / 7</gadget>
<output>25/7 = around 3.571429</output>
<gadget id="calculator">4 / 5</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">2 - (4/5)</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">2 + (4/5)</gadget>
<output>14/5 = around 2.8</output>
<gadget id="calculator">(6/5) / (14/5)</gadget>
<output>3/7 = around 0.428571</output>
<gadget id="calculator">(25/7) + (3/7)</gadget>
<output>4</output>
<result>4</result>


a retailer bought a machine at a wholesale price of $ 90 and later on sold it after a 10 % discount of the retail price . if the retailer made a profit equivalent to 20 % of the whole price , what is the retail price r of the machine ?

Explanation: "since the wholesale price was $ 90 and the profit was 20 % of the wholesale price ( [ . 2 ] [ 90 ] = $ 18 ) , the retail price would have to be above $ 108 , but not that much greater than that . let ' s start by testing answer c : $ 120 . . . . if . . . . . retail price r = $ 120 10 % discount off = $ 120 - ( . 1 ) ( 120 ) = 120 - 12 = 108 20 % profit on wholesale price = 90 + ( . 2 ) ( 90 ) = 90 + 18 = 108 these two numbers match , so this must be the answer ! final answer : [ reveal ] spoiler : c"

divide(multiply(add(90, divide(multiply(90, 20), const_100)), const_100), multiply(multiply(const_3, const_3), 10))

<gadget id="calculator">90 * 20</gadget>
<output>1_800</output>
<gadget id="calculator">1_800 / 100</gadget>
<output>18</output>
<gadget id="calculator">90 + 18</gadget>
<output>108</output>
<gadget id="calculator">108 * 100</gadget>
<output>10_800</output>
<gadget id="calculator">3 * 3</gadget>
<output>9</output>
<gadget id="calculator">9 * 10</gadget>
<output>90</output>
<gadget id="calculator">10_800 / 90</gadget>
<output>120</output>
<result>120</result>


bottle r contains 350 capsules and costs $ 6.25 . bottle t contains 130 capsules and costs $ 2.99 . what is the difference between the cost per capsule for bottle r and the cost per capsule for bottle t ?

Explanation: "cost per capsule in r is 6.25 / 350 = 0.0178 cost per capsule in t is 2.99 / 130 = 0.023 the difference is 0.0052 the answer is c"

<gadget id="calculator">2.99 / 130</gadget>
<output>0.023</output>
<gadget id="calculator">6.25 / 350</gadget>
<output>0.017857</output>
<gadget id="calculator">0.023 - 0.017857</gadget>
<output>0.005143</output>
<result>0.005143</result>


the milk level in a rectangular box measuring 58 feet by 25 feet is to be lowered by 6 inches . how many gallons of milk must be removed ? ( 1 cu ft = 7.5 gallons )

Explanation: "6 inches = 1 / 2 feet ( there are 12 inches in a foot . ) , so 58 * 25 * 1 / 2 = 725 feet ^ 3 of milk must be removed , which equals to 725 * 7.5 = 5437.5 gallons . answer : d ."

multiply(multiply(multiply(58, 25), divide(1, const_2)), 7.5)

<gadget id="calculator">58 * 25</gadget>
<output>1_450</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1_450 * (1/2)</gadget>
<output>725</output>
<gadget id="calculator">725 * 7.5</gadget>
<output>5_437.5</output>
<result>5_437.5</result>


a rectangular block 15 cm by 30 cm by 75 cm is cut into an exact number of equal cubes . find the least possible number of cubes ?

Explanation: volume of the block = 15 * 30 * 75 = 33750 cm ^ 3 side of the largest cube = h . c . f of 15 , 30,75 = 15 cm volume of the cube = 15 * 15 * 15 = 3375 cm ^ 3 number of cubes = 33750 / 3375 = 10 answer is d

divide(add(subtract(divide(rectangle_area(const_360, const_1000), const_10), multiply(const_1000, multiply(const_3, const_2))), add(multiply(const_3, const_1000), multiply(75, const_10))), divide(add(subtract(divide(rectangle_area(const_360, const_1000), const_10), multiply(const_1000, multiply(const_3, const_2))), add(multiply(const_3, const_1000), multiply(75, const_10))), const_10))

<gadget id="calculator">360 * 1_000</gadget>
<output>360_000</output>
<gadget id="calculator">360_000 / 10</gadget>
<output>36_000</output>
<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">1_000 * 6</gadget>
<output>6_000</output>
<gadget id="calculator">36_000 - 6_000</gadget>
<output>30_000</output>
<gadget id="calculator">3 * 1_000</gadget>
<output>3_000</output>
<gadget id="calculator">75 * 10</gadget>
<output>750</output>
<gadget id="calculator">3_000 + 750</gadget>
<output>3_750</output>
<gadget id="calculator">30_000 + 3_750</gadget>
<output>33_750</output>
<gadget id="calculator">33_750 / 10</gadget>
<output>3_375</output>
<gadget id="calculator">33_750 / 3_375</gadget>
<output>10</output>
<result>10</result>


after replacing an old member by a new member , it was found that the average age of 5 members of a club is the same as it was 3 years ago . what is the difference between the ages of the replaced and the new member ?

Explanation: explanation : i ) let the ages of the five members at present be a , b , c , d & e years . and the age of the new member be f years . ii ) so the new average of five members ' age = ( a + b + c + d + f ) / 5 - - - - - - - ( 1 ) iii ) their corresponding ages 3 years ago = ( a - 3 ) , ( b - 3 ) , ( c - 3 ) , ( d - 3 ) & ( e - 3 ) years so their average age 3 years ago = ( a + b + c + d + e - 15 ) / 5 = x - - - - - ( 2 ) = = > a + b + c + d + e = 5 x + 15 = = > a + b + c + d = 5 x + 15 - e - - - - - - ( 3 ) iv ) substituting this value of a + b + c + d = 5 x + 15 - e in ( 1 ) above , the new average is : ( 5 x + 15 - e + f ) / 5 equating this to the average age of x years , 3 yrs , ago as in ( 2 ) above , ( 5 x + 15 - e + f ) / 5 = x = = > ( 5 x + 15 - e + f ) = 5 x solving e - f = 15 years . thus the difference of ages between replaced and new member = 15 years . answer : d

<gadget id="calculator">5 * 3</gadget>
<output>15</output>
<result>15</result>


zinc and copper are melted together in the ratio 9 : 11 . what is the weight of melted mixture , if 26.1 kg of zinc has been consumed in it ?

Explanation: "sol . for 9 kg zinc , mixture melted = ( 9 + 11 ) kg . for 26.1 kg zinc , mixture , melted = [ 20 / 9 x 26.1 ] kg = 58 kg . answer a"

<gadget id="calculator">11 / 9</gadget>
<output>11/9 = around 1.222222</output>
<gadget id="calculator">(11/9) * 26.1</gadget>
<output>31.9</output>
<gadget id="calculator">31.9 + 26.1</gadget>
<output>58</output>
<result>58</result>


the ratio of boys to girls is 6 : 4.60 % of the boys and 40 % of girls take lunch in the canteen . what % of class takes lunch ?

Explanation: let total no of students 100 , boy 60 and girl 40 , so lunch taken by boy and girl respectively 60 * 60 / 100 = 36 and 40 * 40 / 100 = 16 so total 52 students takes lunch out of 100 students . . so required % is 52 % answer : b

add(multiply(divide(6, const_10), subtract(const_100, 40)), multiply(divide(const_4, const_10), 40))

<gadget id="calculator">6 / 10</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">100 - 40</gadget>
<output>60</output>
<gadget id="calculator">(3/5) * 60</gadget>
<output>36</output>
<gadget id="calculator">4 / 10</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) * 40</gadget>
<output>16</output>
<gadget id="calculator">36 + 16</gadget>
<output>52</output>
<result>52</result>


a person x started at 3 hours earlier at 40 km / h from a place p , then another person y followed him at 60 km / h . started his journey at 3 o ' clock , afternoon . what is the diference in time when x was 30 km ahead of y and when y was 30 km ahead of x ?

Explanation: explanation : time ( when x was 30 km ahead of y ) = ( 120 - 30 ) / 20 = 4.5 h time ( when y was 30 km ahead of x ) = ( 120 + 30 ) / 20 = 7.5 h thus , required difference in time = 3 h answer : b

subtract(divide(add(multiply(40, 3), 30), divide(40, const_2)), divide(subtract(multiply(40, 3), 30), divide(40, const_2)))

<gadget id="calculator">40 * 3</gadget>
<output>120</output>
<gadget id="calculator">120 + 30</gadget>
<output>150</output>
<gadget id="calculator">40 / 2</gadget>
<output>20</output>
<gadget id="calculator">150 / 20</gadget>
<output>15/2 = around 7.5</output>
<gadget id="calculator">120 - 30</gadget>
<output>90</output>
<gadget id="calculator">90 / 20</gadget>
<output>9/2 = around 4.5</output>
<gadget id="calculator">(15/2) - (9/2)</gadget>
<output>3</output>
<result>3</result>


a room of 5 m 44 cm long and 3 m 74 cm broad is to be paved with squre tiles . find the least number of squre tiles required to cover the floor ?

Explanation: "area of the room = 544 * 374 sq cm size of largest square tile = h . c . f of 544 cm and 374 cm = 34 cm area of 1 tile = 34 * 34 sq cm no . of tiles required = ( 544 * 374 ) / ( 34 * 34 ) = 176 answer : d"

divide(multiply(add(multiply(5, const_100), 44), add(multiply(3, const_100), 74)), power(divide(add(multiply(5, const_100), 44), power(const_2, const_4)), const_2))

<gadget id="calculator">5 * 100</gadget>
<output>500</output>
<gadget id="calculator">500 + 44</gadget>
<output>544</output>
<gadget id="calculator">3 * 100</gadget>
<output>300</output>
<gadget id="calculator">300 + 74</gadget>
<output>374</output>
<gadget id="calculator">544 * 374</gadget>
<output>203_456</output>
<gadget id="calculator">2 ** 4</gadget>
<output>16</output>
<gadget id="calculator">544 / 16</gadget>
<output>34</output>
<gadget id="calculator">34 ** 2</gadget>
<output>1_156</output>
<gadget id="calculator">203_456 / 1_156</gadget>
<output>176</output>
<result>176</result>


if 35 % of a number is 24 less than 50 % of that number , then the number is ?

Explanation: explanation : let the number be n . then , 50 % of n - 35 % of n = 24 50 / 100 n - 35 / 100 n = 24 n = ( 24 x 100 ) / 15 = 160 . answer c

divide(24, divide(subtract(50, 35), const_100))

<gadget id="calculator">50 - 35</gadget>
<output>15</output>
<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">24 / (3/20)</gadget>
<output>160</output>
<result>160</result>


tom opened a shop investing rs . 3000 . jose joined him 2 months later , investing rs . 4500 . they earned a profit of rs . 5400 after completion of one year . what will be jose ' s share of profit ?

Explanation: "sol = ~ s - so anju ’ s share = [ 5 / 9 ] x 5400 = 3000 a"

multiply(5400, subtract(const_1, divide(multiply(3000, multiply(2, multiply(2, const_3))), add(multiply(4500, subtract(multiply(2, multiply(2, const_3)), 2)), multiply(3000, multiply(2, multiply(2, const_3)))))))

<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">2 * 6</gadget>
<output>12</output>
<gadget id="calculator">3_000 * 12</gadget>
<output>36_000</output>
<gadget id="calculator">12 - 2</gadget>
<output>10</output>
<gadget id="calculator">4_500 * 10</gadget>
<output>45_000</output>
<gadget id="calculator">45_000 + 36_000</gadget>
<output>81_000</output>
<gadget id="calculator">36_000 / 81_000</gadget>
<output>4/9 = around 0.444444</output>
<gadget id="calculator">1 - (4/9)</gadget>
<output>5/9 = around 0.555556</output>
<gadget id="calculator">5_400 * (5/9)</gadget>
<output>3_000</output>
<result>3_000</result>


there are 5 fictions and 6 non - fictions . how many cases are there such that 2 fictions and 2 non - fictions are selected from them ?

Explanation: number of ways of selecting 2 fiction books = 5 c 2 number of ways of selecting 2 non fiction books = 6 c 2 5 c 2 * 6 c 2 = 10 * 15 = 150 answer : c

divide(multiply(multiply(5, const_4), multiply(6, 5)), power(factorial(const_2), const_2))

<gadget id="calculator">5 * 4</gadget>
<output>20</output>
<gadget id="calculator">6 * 5</gadget>
<output>30</output>
<gadget id="calculator">20 * 30</gadget>
<output>600</output>
<gadget id="calculator">factorial(2)</gadget>
<output>2</output>
<gadget id="calculator">2 ** 2</gadget>
<output>4</output>
<gadget id="calculator">600 / 4</gadget>
<output>150</output>
<result>150</result>


the area of a triangle is with base 4 m and height 6 m ?

Explanation: "1 / 2 * 4 * 6 = 12 m 2 answer : e"

<gadget id="calculator">(4 * 6) / 2</gadget>
<output>12</output>
<result>12</result>


if 40 sheep eat 40 bags of grass in 40 days . in how many days one sheep will eat one bag of grass ?

Explanation: explanation : let the required number of days be x . less sheep , more days ( indirect proportion ) less bags , less days ( direct proportion ) sheep 1 : 40 : : 40 : x bags 40 : 1 1 x 40 x x = 40 x 1 x 40 x = 40 . answer : c

divide(divide(multiply(multiply(40, 40), 40), 40), 40)

<gadget id="calculator">40 * 40</gadget>
<output>1_600</output>
<gadget id="calculator">1_600 * 40</gadget>
<output>64_000</output>
<gadget id="calculator">64_000 / 40</gadget>
<output>1_600</output>
<gadget id="calculator">1_600 / 40</gadget>
<output>40</output>
<result>40</result>


increasing the original price of an article by 20 percent and then increasing the new price by 20 percent is equivalent to increasing the original price by

Explanation: "1.2 * 1.2 * x = 1.44 * x the answer is e ."

multiply(const_100, subtract(multiply(add(const_1, divide(20, const_100)), add(const_1, divide(20, const_100))), const_1))

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 + (1/5)</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">(6/5) * (6/5)</gadget>
<output>36/25 = around 1.44</output>
<gadget id="calculator">(36/25) - 1</gadget>
<output>11/25 = around 0.44</output>
<gadget id="calculator">100 * (11/25)</gadget>
<output>44</output>
<result>44</result>


the age of somu is one - third his father ' s . 6 years back he was one - fifth of his father ' s age . what is his persent age ?

Explanation: "explanation : let somu ' s age be x and that of his father be 3 x . so , x - 6 = 3 x - 6 / 5 = x = 12 answer : option d"

divide(subtract(multiply(add(const_4, const_1), 6), 6), subtract(add(const_4, const_1), const_3))

<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">5 * 6</gadget>
<output>30</output>
<gadget id="calculator">30 - 6</gadget>
<output>24</output>
<gadget id="calculator">5 - 3</gadget>
<output>2</output>
<gadget id="calculator">24 / 2</gadget>
<output>12</output>
<result>12</result>


john builds a square with a side of 12 cm from some wire . if from the same wire , he builds a rectangle with a width of 6 cm , what will be the length of the rectangle ?

Explanation: solution : if the side of the square is 12 cm , then its perimetre will be 48 cm . we build the rectangle from the same wire , so it will have the same perimetre . its width is 6 cm , so its length will be ( 48 - 12 ) ÷ 2 = 36 ÷ 2 = 18 cm answer a

divide(subtract(square_perimeter(12), multiply(6, const_2)), const_2)

<gadget id="calculator">4 * 12</gadget>
<output>48</output>
<gadget id="calculator">6 * 2</gadget>
<output>12</output>
<gadget id="calculator">48 - 12</gadget>
<output>36</output>
<gadget id="calculator">36 / 2</gadget>
<output>18</output>
<result>18</result>


a train 560 m long , running with a speed of 63 km / hr will pass a tree in ?

Explanation: "speed = 63 * 5 / 18 = 35 / 2 m / sec time taken = 560 * 2 / 35 = 32 sec answer : option e"

multiply(divide(560, multiply(63, const_1000)), const_3600)

<gadget id="calculator">63 * 1_000</gadget>
<output>63_000</output>
<gadget id="calculator">560 / 63_000</gadget>
<output>2/225 = around 0.008889</output>
<gadget id="calculator">(2/225) * 3_600</gadget>
<output>32</output>
<result>32</result>


the banker â € ™ s gain on a sum due 3 years hence at 12 % per annum is rs . 180 . the banker â € ™ s discount is

Explanation: solution t . d = ( b . g x 100 / r x t ) = rs . ( 180 x 100 / 12 x 3 ) = rs . 500 . b . d = rs ( 500 + 180 ) = rs . 680 . answer d

add(divide(multiply(180, const_100), multiply(3, 12)), 180)

<gadget id="calculator">180 * 100</gadget>
<output>18_000</output>
<gadget id="calculator">3 * 12</gadget>
<output>36</output>
<gadget id="calculator">18_000 / 36</gadget>
<output>500</output>
<gadget id="calculator">500 + 180</gadget>
<output>680</output>
<result>680</result>


12 . what is the dividend . divisor 17 , the quotient is 9 and the remainder is 10 .

Explanation: "d = d * q + r d = 17 * 9 + 10 d = 153 + 10 d = 163 answer d"

<gadget id="calculator">17 * 9</gadget>
<output>153</output>
<gadget id="calculator">153 + 10</gadget>
<output>163</output>
<result>163</result>


a lady builds 8 cm length , 15 cm width , and 5 cm height box using 10 cubic cm cubes . what is the minimum number of cubes required to build the box ?

Explanation: "number of cubes required = volume of box / volume of cube = 8 * 15 * 5 / 10 = 60 cubes answer : b"

divide(multiply(multiply(8, 15), 5), 10)

<gadget id="calculator">8 * 15</gadget>
<output>120</output>
<gadget id="calculator">120 * 5</gadget>
<output>600</output>
<gadget id="calculator">600 / 10</gadget>
<output>60</output>
<result>60</result>


there 3 kinds of books in the library physics , chemistry and biology . ratio of physics to chemistry is 3 to 2 ; ratio of chemistry to biology is 4 to 3 , and the total of the books is more than 3000 . which one of following can be the total w of the book ?

Explanation: "first , you have to find the common ratio for all 3 books . you have : p : c : b 3 : 2 - - > multiply by 2 ( gives you row 3 ) 4 : 6 6 : 4 : 3 hence : p : c : b : t ( total ) w 6 : 4 : 3 : 13 - - - - > this means , the total number must be a multiple of 13 . answer a is correct since 299 is divisible by 13 , hence is 2990 and so is 3003 ( 2990 + 13 ) ."

<gadget id="calculator">3_000 + 3</gadget>
<output>3_003</output>
<result>3_003</result>


the population of a bacteria colony doubles every day . if it was started 8 days ago with 2 bacteria and each bacteria lives for 12 days , how large is the colony today ?

Explanation: "8 days ago - 2 7 days ago - 4 6 days ago - 8 5 days ago - 16 4 days ago - 32 3 days ago - 64 2 days ago - 128 yesterday - 256 today - 512 ans : a"

subtract(power(2, add(8, const_1)), const_1)

<gadget id="calculator">8 + 1</gadget>
<output>9</output>
<gadget id="calculator">2 ** 9</gadget>
<output>512</output>
<gadget id="calculator">512 - 1</gadget>
<output>511</output>
<result>511</result>


how many quarters are equal to 7 dollars ?

Explanation: "7 * 4 = 28 quarters answer : b"

<gadget id="calculator">7 * 4</gadget>
<output>28</output>
<result>28</result>


Explanation: since , percent = 1 / 100 , what = something ( s ) , and is : = . we can write the question as s = 0.1 ( 1 / 100 ) 12,356 . the answer is 12.356 . hence , the correct answer is c .

divide(multiply(0.1, add(add(multiply(multiply(add(const_3, const_2), const_2), multiply(multiply(const_3, const_4), const_100)), multiply(multiply(add(const_3, const_4), add(const_3, const_2)), multiply(add(const_3, const_2), const_2))), add(const_3, const_3))), const_100)

<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">12 * 100</gadget>
<output>1_200</output>
<gadget id="calculator">10 * 1_200</gadget>
<output>12_000</output>
<gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">7 * 5</gadget>
<output>35</output>
<gadget id="calculator">35 * 10</gadget>
<output>350</output>
<gadget id="calculator">12_000 + 350</gadget>
<output>12_350</output>
<gadget id="calculator">3 + 3</gadget>
<output>6</output>
<gadget id="calculator">12_350 + 6</gadget>
<output>12_356</output>
<gadget id="calculator">0.1 * 12_356</gadget>
<output>1_235.6</output>
<gadget id="calculator">1_235.6 / 100</gadget>
<output>12.356</output>
<result>12.356</result>


the difference between the value of a number increased by 25 % and the value of the original number decreased by 30 % is 22 . what is the original number ?

Explanation: "let the original # be x then 1.25 x − 0.7 x = 22 - - > x = 40 answer : a ."

divide(22, subtract(add(const_1, divide(25, const_100)), subtract(const_1, divide(30, const_100))))

<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 + (1/4)</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">1 - (3/10)</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">(5/4) - (7/10)</gadget>
<output>11/20 = around 0.55</output>
<gadget id="calculator">22 / (11/20)</gadget>
<output>40</output>
<result>40</result>


if a - b = 3 and a ^ 2 + b ^ 2 = 33 , find the value of ab .

Explanation: "2 ab = ( a ^ 2 + b ^ 2 ) - ( a - b ) ^ 2 = 33 - 9 = 24 ab = 12 . answer is a ."

multiply(multiply(add(3, divide(subtract(sqrt(33), 3), 2)), divide(subtract(sqrt(33), 3), 2)), 2)


1 : 3 = 1 2 / 3 : x . the value of x is ?

Explanation: x * 1 = 3 * 5 / 3 x = 5 answer : d

divide(add(divide(2, 3), 1), divide(1, 3))

<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(2/3) + 1</gadget>
<output>5/3 = around 1.666667</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(5/3) / (1/3)</gadget>
<output>5</output>
<result>5</result>


how many figures are required to number the pages the pages of a book containing 709 pages ?

Explanation: "1 to 9 = 9 * 1 = 9 10 to 99 = 90 * 2 = 180 100 to 709 = 610 * 3 = 1830 - - - - - - - - - - - 2019 answer : b"

add(add(subtract(divide(divide(709, const_10), const_10), const_1), subtract(subtract(divide(709, const_10), const_1), subtract(divide(divide(709, const_10), const_10), const_1))), multiply(subtract(subtract(709, const_1), subtract(divide(709, const_10), const_1)), const_3))

<gadget id="calculator">709 / 10</gadget>
<output>709/10 = around 70.9</output>
<gadget id="calculator">(709/10) / 10</gadget>
<output>709/100 = around 7.09</output>
<gadget id="calculator">(709/100) - 1</gadget>
<output>609/100 = around 6.09</output>
<gadget id="calculator">(709/10) - 1</gadget>
<output>699/10 = around 69.9</output>
<gadget id="calculator">(699/10) - (609/100)</gadget>
<output>6_381/100 = around 63.81</output>
<gadget id="calculator">(609/100) + (6_381/100)</gadget>
<output>699/10 = around 69.9</output>
<gadget id="calculator">709 - 1</gadget>
<output>708</output>
<gadget id="calculator">708 - (699/10)</gadget>
<output>6_381/10 = around 638.1</output>
<gadget id="calculator">(6_381/10) * 3</gadget>
<output>19_143/10 = around 1_914.3</output>
<gadget id="calculator">(699/10) + (19_143/10)</gadget>
<output>9_921/5 = around 1_984.2</output>
<result>9_921/5 = around 1_984.2</result>


a cone of height 9 cm with diameter of its base 18 cm is carved out from a wooden solid sphere of radius 9 cm . the percentage of the wood wasted is :

Explanation: explanation : we will first subtract the cone volume from wood volume to get the wood wasted . then we can calculate its percentage . sphere volume = 4 / 3 π r 3 cone volume = 1 / 3 π r 2 h volume of wood wasted = ( 4 / 3 π ∗ 9 ∗ 9 ∗ 9 ) − ( 1 / 3 π ∗ 9 ∗ 9 ∗ 9 ) = π ∗ 9 ∗ 9 ∗ 9 cm 3 required percentage = π ∗ 9 ∗ 9 ∗ 9 / 4 / 3 π ∗ 9 ∗ 9 ∗ 9 ∗ 100 % = 3 / 4 ∗ 100 % = 75 % option d

multiply(divide(subtract(volume_sphere(9), volume_cone(9, 9)), volume_sphere(9)), const_100)

<gadget id="calculator">4/3 * pi * (9 ** 3)</gadget>
<output>972*pi = around 3_053.628059</output>
<gadget id="calculator">pi * (9 ** 2) * 9 / 3</gadget>
<output>243*pi = around 763.407015</output>
<gadget id="calculator">(972*pi) - (243*pi)</gadget>
<output>729*pi = around 2_290.221044</output>
<gadget id="calculator">(729*pi) / (972*pi)</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(3/4) * 100</gadget>
<output>75</output>
<result>75</result>


of the votes cast on a certain proposal , 66 more were in favor of the proposal than were against it . if the number of votes against the proposal was 40 percent of the total vote , what was the total number of votes cast ? ( each vote cast was either in favor of the proposal or against it . )

Explanation: "let x be the total number of votes cast . 0.6 x = 0.4 x + 66 0.2 x = 66 x = 330 the answer is c ."

divide(66, subtract(subtract(const_1, divide(40, const_100)), divide(40, const_100)))

<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">1 - (2/5)</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(3/5) - (2/5)</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">66 / (1/5)</gadget>
<output>330</output>
<result>330</result>


the average earning of amechanic for the first 4 days of a week is rs . 25 and for the last 4 days is rs . 22 . if heearns rs . 20 on the fourth day , his average earning forthe whole week is ?

Explanation: total earning for the week = sum of earning of first four days + sum of earning of last four days - earning of 4 th day = 4 x 25 + 4 x 22 - 20 = rs . 168 â ˆ ´ average earning = 168 / 7 = rs . 24 b

divide(subtract(add(multiply(4, 25), multiply(4, 22)), 20), add(const_3, const_4))

<gadget id="calculator">4 * 25</gadget>
<output>100</output>
<gadget id="calculator">4 * 22</gadget>
<output>88</output>
<gadget id="calculator">100 + 88</gadget>
<output>188</output>
<gadget id="calculator">188 - 20</gadget>
<output>168</output>
<gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">168 / 7</gadget>
<output>24</output>
<result>24</result>


a sum of money deposited at c . i . amounts to rs . 2420 in 2 years and to rs . 3025 in 3 years . find the rate percent ?

Explanation: "explanation : 2420 - - - 605 100 - - - ? = > 25 % answer : option d"

multiply(divide(subtract(3025, 2420), 2420), const_100)

<gadget id="calculator">3_025 - 2_420</gadget>
<output>605</output>
<gadget id="calculator">605 / 2_420</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 100</gadget>
<output>25</output>
<result>25</result>


9 men working 8 hours per day dig 30 m deep . how many extra men should be put to dig to a depth of 50 m working 6 hours per day ?

Explanation: "( 9 * 8 ) / 30 = ( x * 6 ) / 50 = > x = 20 20 – 9 = 11 answer : d"

subtract(divide(multiply(divide(multiply(9, 8), 30), 50), 6), 9)

<gadget id="calculator">9 * 8</gadget>
<output>72</output>
<gadget id="calculator">72 / 30</gadget>
<output>12/5 = around 2.4</output>
<gadget id="calculator">(12/5) * 50</gadget>
<output>120</output>
<gadget id="calculator">120 / 6</gadget>
<output>20</output>
<gadget id="calculator">20 - 9</gadget>
<output>11</output>
<result>11</result>


a building contractor employs 20 male , 15 female and 5 child workers . to a male worker he pays rs . 25 per day , to a female worker rs . 20 per day and a child worker rs . 8 per day . the average wage per day paid by the contractor is ?

Explanation: explanation : 20 15 5 25 20 8 500 + 300 + 40 = 840 / 40 = 21 b

divide(add(add(multiply(20, 25), multiply(15, 20)), multiply(5, 8)), add(add(20, 15), 5))

<gadget id="calculator">20 * 25</gadget>
<output>500</output>
<gadget id="calculator">15 * 20</gadget>
<output>300</output>
<gadget id="calculator">500 + 300</gadget>
<output>800</output>
<gadget id="calculator">5 * 8</gadget>
<output>40</output>
<gadget id="calculator">800 + 40</gadget>
<output>840</output>
<gadget id="calculator">20 + 15</gadget>
<output>35</output>
<gadget id="calculator">35 + 5</gadget>
<output>40</output>
<gadget id="calculator">840 / 40</gadget>
<output>21</output>
<result>21</result>


Explanation: "x / 2 y = 3 / 2 = > x = 6 y / 2 = 3 y = > ( 7 x + 2 y ) / ( x - 2 y ) = ( ( 7 * ( 3 y ) ) + 2 y ) / ( 3 y - 2 y ) = > 23 y / y = 23 answer : a"

divide(add(multiply(multiply(divide(3, 2), 2), 7), 2), subtract(multiply(divide(3, 2), 2), 2))

<gadget id="calculator">3 / 2</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">(3/2) * 2</gadget>
<output>3</output>
<gadget id="calculator">3 * 7</gadget>
<output>21</output>
<gadget id="calculator">21 + 2</gadget>
<output>23</output>
<gadget id="calculator">3 - 2</gadget>
<output>1</output>
<gadget id="calculator">23 / 1</gadget>
<output>23</output>
<result>23</result>


john left home and drove at the rate of 45 mph for 2 hours . he stopped for lunch then drove for another 3 hours at the rate of 45 mph to reach his destination . how many miles did john drive ?

Explanation: "the total distance d traveled by john is given by d = 45 * 2 + 3 * 45 = 225 miles . answer c"

<gadget id="calculator">45 * 2</gadget>
<output>90</output>
<gadget id="calculator">3 * 45</gadget>
<output>135</output>
<gadget id="calculator">90 + 135</gadget>
<output>225</output>
<result>225</result>


a statue is being carved by a sculptor . the original piece of marble weighed 190 kg . in the first week 25 percent is cut away . in the second week 15 percent of the remainder is cut away . in the third week the statue is completed when 10 percent of the remainder is cut away . what is the weight of the final statue ?

Explanation: "c 109 kg 190 ã — 0.75 ã — 0.85 ã — 0.9 = 109 kg ."

multiply(subtract(const_1, divide(10, const_100)), multiply(subtract(const_1, divide(15, const_100)), multiply(190, subtract(const_1, divide(25, const_100)))))

<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 - (1/10)</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">1 - (3/20)</gadget>
<output>17/20 = around 0.85</output>
<gadget id="calculator">25 / 100</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">190 * (3/4)</gadget>
<output>285/2 = around 142.5</output>
<gadget id="calculator">(17/20) * (285/2)</gadget>
<output>969/8 = around 121.125</output>
<gadget id="calculator">(9/10) * (969/8)</gadget>
<output>8_721/80 = around 109.0125</output>
<result>8_721/80 = around 109.0125</result>


the population of a town increased from 1 , 75,000 to 2 , 97,500 in a decade . the average percent increase of population per year is

Explanation: solution increase in 10 years = ( 297500 - 175000 ) = 122500 increase % = ( 122500 / 175000 ã — 100 ) % = 70 % . required average = ( 70 / 10 ) % = 7 % . answer e

add(multiply(divide(subtract(divide(subtract(subtract(subtract(multiply(multiply(const_10, const_1000), const_10), const_1000), const_1000), multiply(add(const_2, const_3), const_100)), multiply(add(multiply(add(const_3, const_4), const_10), add(const_2, const_3)), const_1000)), const_1), const_10), const_100), const_4)

<gadget id="calculator">10 * 1_000</gadget>
<output>10_000</output>
<gadget id="calculator">10_000 * 10</gadget>
<output>100_000</output>
<gadget id="calculator">100_000 - 1_000</gadget>
<output>99_000</output>
<gadget id="calculator">99_000 - 1_000</gadget>
<output>98_000</output>
<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">5 * 100</gadget>
<output>500</output>
<gadget id="calculator">98_000 - 500</gadget>
<output>97_500</output>
<gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">7 * 10</gadget>
<output>70</output>
<gadget id="calculator">70 + 5</gadget>
<output>75</output>
<gadget id="calculator">75 * 1_000</gadget>
<output>75_000</output>
<gadget id="calculator">97_500 / 75_000</gadget>
<output>13/10 = around 1.3</output>
<gadget id="calculator">(13/10) - 1</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(3/10) / 10</gadget>
<output>3/100 = around 0.03</output>
<gadget id="calculator">(3/100) * 100</gadget>
<output>3</output>
<result>7</result>


in an exam , gibi scored 59 percent , jigi scored 55 percent , mike scored 99 percent and lizzy 67 percent . the maximum score awarded in the exam is 700 . find the average mark scored by all the 4 students ?

Explanation: average mark scored by all the three boys = [ 59 / 100 ( 700 ) + 55 / 100 ( 700 ) + 99 / 100 ( 700 ) + 67 / 100 ( 700 ) ] / 4 ( 413 + 385 + 693 + 469 ) / 4 = 490 answer : b

divide(divide(multiply(add(add(59, 55), add(99, 67)), 700), const_100), 4)

<gadget id="calculator">59 + 55</gadget>
<output>114</output>
<gadget id="calculator">99 + 67</gadget>
<output>166</output>
<gadget id="calculator">114 + 166</gadget>
<output>280</output>
<gadget id="calculator">280 * 700</gadget>
<output>196_000</output>
<gadget id="calculator">196_000 / 100</gadget>
<output>1_960</output>
<gadget id="calculator">1_960 / 4</gadget>
<output>490</output>
<result>490</result>


in how many no . between 10 and 50 exactly two of the digits is 5 ?

Explanation: "it ' s simple can be solved by elimination of answer choices . option b and d are too large , not possible . even ae are large to have correct choice . ans : c"

<gadget id="calculator">50 / 10</gadget>
<output>5</output>
<gadget id="calculator">5 / 5</gadget>
<output>1</output>
<result>1</result>


john and david work at a hospital with 8 other workers . for an internal review , 2 of the 8 workers will be randomly chosen to be interviewed . what is the probability that john and david will both be chosen ?

Explanation: probability that john and david will both be chosen out of 8 workers = ( 2 / 8 ) * ( 1 / 7 ) = 1 / 28 answer d

multiply(2, multiply(divide(const_1, subtract(8, const_1)), divide(const_1, 8)))

<gadget id="calculator">8 - 1</gadget>
<output>7</output>
<gadget id="calculator">1 / 7</gadget>
<output>1/7 = around 0.142857</output>
<gadget id="calculator">1 / 8</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">(1/7) * (1/8)</gadget>
<output>1/56 = around 0.017857</output>
<gadget id="calculator">2 * (1/56)</gadget>
<output>1/28 = around 0.035714</output>
<result>1/28 = around 0.035714</result>


by selling 8 pens for a rupee a woman loses 25 % . how many for a rupee should he sell in order to gain 25 % ?

Explanation: "d 75 % - - - 8 125 % - - - ? 75 / 125 * 8 = 5"

inverse(add(divide(divide(const_100, subtract(const_100, 25)), 8), divide(multiply(divide(divide(const_100, subtract(const_100, 25)), 8), 25), const_100)))

<gadget id="calculator">100 - 25</gadget>
<output>75</output>
<gadget id="calculator">100 / 75</gadget>
<output>4/3 = around 1.333333</output>
<gadget id="calculator">(4/3) / 8</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(1/6) * 25</gadget>
<output>25/6 = around 4.166667</output>
<gadget id="calculator">(25/6) / 100</gadget>
<output>1/24 = around 0.041667</output>
<gadget id="calculator">(1/6) + (1/24)</gadget>
<output>5/24 = around 0.208333</output>
<gadget id="calculator">1 / (5/24)</gadget>
<output>24/5 = around 4.8</output>
<result>24/5 = around 4.8</result>


3.20 can be expressed in terms of percentage as

Explanation: explanation : while calculation in terms of percentage we need to multiply by 100 , so 3.20 * 100 = 320 answer : option c

<gadget id="calculator">3.2 * 100</gadget>
<output>320</output>
<result>320</result>


a person was asked to subtract 25 % of a number from the original but he subtracted 25 from the number . his answer was 25 more than correct one . what was the original number ?

Explanation: 25 + 25 = 50 25 % - - - - - - 50 100 % - - - - - ? = > 200 answer : d

divide(add(25, 25), subtract(const_1, subtract(const_1, divide(25, const_100))))

<gadget id="calculator">25 + 25</gadget>
<output>50</output>
<gadget id="calculator">25 / 100</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 - (3/4)</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">50 / (1/4)</gadget>
<output>200</output>
<result>200</result>


if x : y is 1 : 5 and y : z is 5 : 7 then x : z is equal to

Explanation: the two ratios given are having the same number 5 for y in both the ratios . hence - x : y = 1 : 5 y : z = 5 : 7 = > x : z = 1 : 7 answer d

<gadget id="calculator">1 / 7</gadget>
<output>1/7 = around 0.142857</output>
<result>1/7 = around 0.142857</result>


maxwell leaves his home and walks toward brad ' s house at the same time that brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 72 kilometers , maxwell ' s walking speed is 6 km / h , and brad ' s running speed is 12 km / h . what is the distance traveled by maxwell when they meet in the middle ?

Explanation: "consider max starts from point a and brad starts from point b and move towards each other . assume they shall meet at point o after time ' t ' . the question asks us to find oa . from the question stem we can make out : - distance oa = 50 km - distance ob = > 6 xt = 72 - 12 xt ( i . e distance = speed x time ) = > 18 t = 72 hence t = 4 oa = 6 x 4 = 24 km answer : b"

<gadget id="calculator">6 + 12</gadget>
<output>18</output>
<gadget id="calculator">72 / 18</gadget>
<output>4</output>
<gadget id="calculator">6 * 4</gadget>
<output>24</output>
<result>24</result>


carolyn bought 17 gumballs , lew bought 12 gumballs , and carey bought x gumballs . the average ( arithmetic mean ) number of gumballs the 3 bought is between 19 and 25 , inclusive . what is the difference between the greatest number and the smallest number of gumballs carey could have bought ?

Explanation: smallest gumballs = ( 19 - 17 ) + ( 19 - 12 ) + 19 = 28 largest gumballs = ( 25 - 17 ) + ( 25 - 12 ) + 25 = 46 difference = 46 - 28 = 18 a

subtract(subtract(multiply(25, 3), add(17, 12)), subtract(multiply(19, 3), add(17, 12)))

<gadget id="calculator">25 * 3</gadget>
<output>75</output>
<gadget id="calculator">17 + 12</gadget>
<output>29</output>
<gadget id="calculator">75 - 29</gadget>
<output>46</output>
<gadget id="calculator">19 * 3</gadget>
<output>57</output>
<gadget id="calculator">57 - 29</gadget>
<output>28</output>
<gadget id="calculator">46 - 28</gadget>
<output>18</output>
<result>18</result>


a train 250 m long passed a pole in 10 sec . how long will it take to pass a platform 1250 m long ?

Explanation: speed = 250 / 10 = 25 m / sec . required time = ( 250 + 1250 ) / 25 = 60 sec answer : a

<gadget id="calculator">250 + 1_250</gadget>
<output>1_500</output>
<gadget id="calculator">250 / 10</gadget>
<output>25</output>
<gadget id="calculator">1_500 / 25</gadget>
<output>60</output>
<result>60</result>


one ball will drop from a certain height . the height it will reach after rebounding from the floor is 50 percent of the previous height . the total travel is 225 cm when it touches the floor on third time . what is the value of the original height ?

Explanation: "when ball comes down , then i have indicated the distance covered in green when ball goes up , then i have indicated the distance covered in red distance travelled uptil the ball touches the floor 3 rd time : h + 0.5 h + 0.5 h + 0.5 * 0.5 h + 0.5 * 0.5 h h + 2 * 0.5 * h + 2 * 0.25 * h = h ( 1 + 2 * 0.5 + 2 * 0.25 ) = h ( 1 + 1 + 0.5 ) = 225 2.5 h = 225 h = 90 . b is the answer ."

divide(225, add(const_2, divide(50, const_100)))

<gadget id="calculator">50 / 100</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">225 / (5/2)</gadget>
<output>90</output>
<result>90</result>


a man fell in a 30 meter deep well , in one day he climbs 4 meters up and slips 3 meters down . how many days would it take for him to come out of the well ?

Explanation: d i will take 27 days to come out of that well for that man , he climbs 4 meter every day and slips 3 meter down that means he climbs 1 meter in total each day , so like this on 26 th day he would have climbed 26 meter and on 27 th day he will climb 4 meeter again so total 30 meter he will climb in 27 days .

<gadget id="calculator">30 - 3</gadget>
<output>27</output>
<result>27</result>


if a mixture is 2 ⁄ 7 alcohol by volume and 3 ⁄ 7 water by volume , what is the ratio of the volume of alcohol to the volume of water in this mixture ?

Explanation: should be a sub - 600 level q . . volume = { 2 / 7 } / { 3 / 7 } = 2 / 3 c

<gadget id="calculator">2 / 7</gadget>
<output>2/7 = around 0.285714</output>
<gadget id="calculator">3 / 7</gadget>
<output>3/7 = around 0.428571</output>
<gadget id="calculator">(2/7) / (3/7)</gadget>
<output>2/3 = around 0.666667</output>
<result>2/3 = around 0.666667</result>


20 percent of country y ' s yearly exports come from fruit exports . one - sixth of all fruit exports from country y are orange exports . if country y generates $ 4.25 million from its orange exports , how much money does it generate from its yearly total of exports ?

Explanation: 2 / 10 * 1 / 6 * ( total ) = 4.25 1 / 30 * ( total ) = 4.25 ( total ) = 4.25 * 30 = 127.5 answer : d .

divide(multiply(divide(4.25, divide(const_1, multiply(const_2, const_3))), const_100), 20)

<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">4.25 / (1/6)</gadget>
<output>25.5</output>
<gadget id="calculator">25.5 * 100</gadget>
<output>2_550</output>
<gadget id="calculator">2_550 / 20</gadget>
<output>255/2 = around 127.5</output>
<result>255/2 = around 127.5</result>


what is the value of n if the sum of the consecutive odd intergers w from 1 to n equals 169 ?

Explanation: "before you tackle this question you must first understand that the question is comprised of two key parts , 1 st is finding out how manytermsis in that sequence and 2 nd whatactual number valuethat term is . in an arithmetic progression , in this case consecutive odd integers 1 , 3 , 5 , . . . . , there are two set of rules . rule # 1 ( arithmetic sequence ) : xn = a + d ( n - 1 ) identifies what the actual # in the sequence would be . each number in the sequence has a term such as 1 ( is the first term ) , 3 ( is the second term ) and so on . so if i were to ask you to find out what the 10 th term is of that sequence you would use that formula to find that value . a = 1 ( first term ) d = 2 ( the common difference ) remember in the sequence 1 , 3 , 5 , 7 the common difference is always 2 * on a side note we use n - 1 because we do n ' t have d in the first term , therefore if we were solving for the first term we would get 0 as n - 1 and 0 times d would give us 0 , leaving only the first term . this works regardless what your first term is in any sequence . but remember the question askswhat is thevalueof n if the sum of the consecutive odd integers from 1 to n equals 169 ? which means we first need a consecutive sequence that sums up to 169 and than find what the value of the n is , in this case it would be the last number in that sequence . in order to find that we first need to knowhow many terms ( how many of the n there is ) in order to be able to plug n in this formula given we know what the sum is . for that to happen we need to use rule # 2 . rule # 2 ( summing an arithmetic series ) : 169 = n / 2 ( 2 a + ( n - 1 ) d ) . given the question gives us what the sum is ( 169 in this case ) we would simply use this formula to solve for n . once we solve for n ( 13 in this case ) we can simply plug n into the first formula ( rule 1 ) and find the value . it feels very confusing and difficult at first , but once you identify the steps all you need to do is plug and play . we have the sum ( 169 ) of a sequence , the number of terms in that sequence is ( unknown ) . rule # 2 tells us how many numbers there are in that sequence and rule # 1 gives us what that last term is ."

add(subtract(multiply(sqrt(169), const_2), multiply(const_2, 1)), 1)

<gadget id="calculator">169 ** (1/2)</gadget>
<output>13</output>
<gadget id="calculator">13 * 2</gadget>
<output>26</output>
<gadget id="calculator">2 * 1</gadget>
<output>2</output>
<gadget id="calculator">26 - 2</gadget>
<output>24</output>
<gadget id="calculator">24 + 1</gadget>
<output>25</output>
<result>25</result>


indu gave bindu rs . 7500 on compound interest for 2 years at 4 % per annum . how much loss would indu has suffered had she given it to bindu for 2 years at 4 % per annum simple interest ?

Explanation: "7500 = d ( 100 / 4 ) 2 d = 12 answer : e"

subtract(subtract(multiply(7500, power(add(const_1, divide(4, const_100)), 2)), 7500), multiply(multiply(7500, divide(4, const_100)), 2))

<gadget id="calculator">4 / 100</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">1 + (1/25)</gadget>
<output>26/25 = around 1.04</output>
<gadget id="calculator">(26/25) ** 2</gadget>
<output>676/625 = around 1.0816</output>
<gadget id="calculator">7_500 * (676/625)</gadget>
<output>8_112</output>
<gadget id="calculator">8_112 - 7_500</gadget>
<output>612</output>
<gadget id="calculator">7_500 * (1/25)</gadget>
<output>300</output>
<gadget id="calculator">300 * 2</gadget>
<output>600</output>
<gadget id="calculator">612 - 600</gadget>
<output>12</output>
<result>12</result>


Explanation: "according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 7899665 - 12 * 3 * 2 = 7899665 - 8 = 7899657 correct answer d"

subtract(7899665, multiply(multiply(12, 3), 2))

<gadget id="calculator">12 * 3</gadget>
<output>36</output>
<gadget id="calculator">36 * 2</gadget>
<output>72</output>
<gadget id="calculator">7_899_665 - 72</gadget>
<output>7_899_593</output>
<result>7_899_593</result>


a can do a half of certain work in 70 days and b one third of the same in 35 days . they together will do the whole work in ?

Explanation: a = 140 days b = 105 days 1 / 140 + 1 / 105 = 7 / 420 = 1 / 60 = > 60 days answer : d

add(inverse(multiply(70, const_2)), inverse(multiply(35, const_3)))

<gadget id="calculator">70 * 2</gadget>
<output>140</output>
<gadget id="calculator">1 / 140</gadget>
<output>1/140 = around 0.007143</output>
<gadget id="calculator">35 * 3</gadget>
<output>105</output>
<gadget id="calculator">1 / 105</gadget>
<output>1/105 = around 0.009524</output>
<gadget id="calculator">(1/140) + (1/105)</gadget>
<output>1/60 = around 0.016667</output>
<result>1/60 = around 0.016667</result>


Explanation: "the expression 9 / ( 1 + 4 / x ) = 1 should have been equal to something . if 9 / ( 1 + 4 / x ) = 1 = 1 = > 9 x / ( x + 4 ) = 1 = > 9 x = x + 4 = > 8 x = 4 = > x = 1 / 2 correct option : b"

<gadget id="calculator">9 - 1</gadget>
<output>8</output>
<gadget id="calculator">4 / 8</gadget>
<output>1/2 = around 0.5</output>
<result>1/2 = around 0.5</result>


an automobile parts supplier charges $ 25 per package of gaskets . when a customer orders more than 10 packages of gaskets , the supplier charges 4 / 5 the price for each package in excess of 10 . during a certain week , the supplier sold 60 packages of gaskets . if 15 percent of the gaskets went to company x , 15 percent to company y , and the rest to company z , what was the total amount , in dollars , that the parts supplier received in payment for the gaskets ?

Explanation: $ 25 per packet of gasket in case a customer orders less than 10 in case a customer orders > 10 price per gasket = 25 * 4 / 5 = 20 a certain week the supplier sold 60 gasket 1 . he sold 15 % of the gaskets to x = 9 gaskets = 25 * 9 = 225 2 . he sold 15 % of the gaskets to y = 9 gaskets = 25 * 9 = 225 3 . he sold remaining 70 % to z = 42 gaskets = 25 * 10 = 250 + 20 * 32 = 890 thus , total money earned 225 + 225 + 890 = 1340 answer is a

add(add(multiply(multiply(25, divide(4, 5)), subtract(subtract(subtract(60, multiply(60, divide(15, const_100))), multiply(60, divide(15, const_100))), 10)), multiply(25, 10)), add(multiply(25, multiply(60, divide(15, const_100))), multiply(25, multiply(60, divide(15, const_100)))))

<gadget id="calculator">4 / 5</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">25 * (4/5)</gadget>
<output>20</output>
<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">60 * (3/20)</gadget>
<output>9</output>
<gadget id="calculator">60 - 9</gadget>
<output>51</output>
<gadget id="calculator">51 - 9</gadget>
<output>42</output>
<gadget id="calculator">42 - 10</gadget>
<output>32</output>
<gadget id="calculator">20 * 32</gadget>
<output>640</output>
<gadget id="calculator">25 * 10</gadget>
<output>250</output>
<gadget id="calculator">640 + 250</gadget>
<output>890</output>
<gadget id="calculator">25 * 9</gadget>
<output>225</output>
<gadget id="calculator">225 + 225</gadget>
<output>450</output>
<gadget id="calculator">890 + 450</gadget>
<output>1_340</output>
<result>1_340</result>


suresh started a business , investing rs . 18000 . after 3 months and 4 months respectively , rohan and sudhir joined him with capitals of 12000 and 9000 . at the end of the year the total profit was rs . 3982 . what is the difference between rohan ’ s and sudhir ’ s share in the profit ?

Explanation: "suresh : rohan : sudhir ratio of their investments = 18000 × 12 : 12000 × 9 : 9000 × 8 = 6 : 3 : 2 the difference between rohan ’ s and sudhir ’ s share = 1 share : . i . e . = rs . 3982 × 1 / 11 = rs . 362 . a )"

multiply(subtract(multiply(12000, divide(subtract(multiply(3, 4), 3), multiply(3, 4))), multiply(9000, divide(subtract(multiply(3, 4), 4), multiply(3, 4)))), divide(3982, add(add(18000, multiply(12000, divide(subtract(multiply(3, 4), 3), multiply(3, 4)))), multiply(9000, divide(subtract(multiply(3, 4), 4), multiply(3, 4))))))

<gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">12 - 3</gadget>
<output>9</output>
<gadget id="calculator">9 / 12</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">12_000 * (3/4)</gadget>
<output>9_000</output>
<gadget id="calculator">12 - 4</gadget>
<output>8</output>
<gadget id="calculator">8 / 12</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">9_000 * (2/3)</gadget>
<output>6_000</output>
<gadget id="calculator">9_000 - 6_000</gadget>
<output>3_000</output>
<gadget id="calculator">18_000 + 9_000</gadget>
<output>27_000</output>
<gadget id="calculator">27_000 + 6_000</gadget>
<output>33_000</output>
<gadget id="calculator">3_982 / 33_000</gadget>
<output>181/1_500 = around 0.120667</output>
<gadget id="calculator">3_000 * (181/1_500)</gadget>
<output>362</output>
<result>362</result>


a salesman sold twice as much pears in the afternoon than in the morning . if he sold $ 360 kilograms of pears that day , how many kilograms did he sell in the morning and how many in the afternoon ?

Explanation: "let x be the number of kilograms he sold in the morning . then in the afternoon he sold 2 x kilograms . so , the total is x + 2 x = 3 x . this must be equal to 360 . 3 x = 360 x = 3603 x = 120 therefore , the salesman sold 120 kg in the morning and 2 ⋅ 120 = 240 kg in the afternoon . so answer is c ."

<gadget id="calculator">360 / 3</gadget>
<output>120</output>
<gadget id="calculator">120 * 2</gadget>
<output>240</output>
<result>240</result>


the average of the marks of 25 students in a class is 70 . if the marks of each student are doubled , find the new average ?

Explanation: "sum of the marks for the 25 students = 25 * 70 = 1750 . the marks of each student are doubled , the sum also will be doubled . the new sum = 1750 * 2 = 3500 . so , the new average = 3500 / 25 = 140 . answer : a"

<gadget id="calculator">70 * 2</gadget>
<output>140</output>
<result>140</result>


a train after traveling for 50 km meets with an accident and then proceeds at 3 / 4 of its former speed and arrives at its destination 35 minutes late . had the accident occurred 24 km farther , it would have reached the destination only 25 minutes late . what is the speed w of the train .

Explanation: "let y be the balance distance to be covered and x be the former speed . a train after traveling for 50 km meets with an accident and then proceeds at 3 / 4 of its former speed and arrives at its destination 35 minutes late so , y / ( 3 x / 4 ) - y / x = 35 / 60 4 y / 3 x - y / x = 7 / 12 y / x ( 4 / 3 - 1 ) = 7 / 12 y / x * 1 / 3 = 7 / 12 y / x = 7 / 4 4 y - 7 x = 0 . . . . . . . . 1 had the accident occurred 24 km farther , it would have reached the destination only 25 minutes late so , ( y - 24 ) / ( 3 x / 4 ) - ( y - 24 ) / x = 25 / 60 4 ( y - 24 ) / 3 x - ( y - 24 ) / x = 5 / 12 ( y - 24 ) / x ( 4 / 3 - 1 ) = 5 / 12 ( y - 24 ) / x * 1 / 3 = 5 / 12 ( y - 24 ) * 12 = 3 x * 5 ( y - 24 ) * 4 = 5 x 4 y - 5 x = 96 . . . . . . . 2 eq 2 - eq 1 2 x = 96 x = 48 = w ans = c"

multiply(subtract(divide(multiply(24, 4), 3), 24), divide(add(subtract(35, 25), 50), subtract(35, 25)))

<gadget id="calculator">24 * 4</gadget>
<output>96</output>
<gadget id="calculator">96 / 3</gadget>
<output>32</output>
<gadget id="calculator">32 - 24</gadget>
<output>8</output>
<gadget id="calculator">35 - 25</gadget>
<output>10</output>
<gadget id="calculator">10 + 50</gadget>
<output>60</output>
<gadget id="calculator">60 / 10</gadget>
<output>6</output>
<gadget id="calculator">8 * 6</gadget>
<output>48</output>
<result>48</result>


amit and ananthu can do a work in 10 days and 20 days respectively . amit started the work and left after 2 days . ananthu took over and completed the work . in how many days was the total work completed ?

Explanation: amit ’ s one day ’ s work = 1 / 10 amit ’ s 2 day ’ s work = 1 / 10 * 2 = 1 / 5 work left = 1 - 1 / 5 = 4 / 5 ananthu ’ s one day ’ s work = 1 / 20 ananthu can do work in = 4 / 5 * 20 = 16 days so total days = 16 + 2 = 18 days answer : a

add(divide(subtract(const_1, multiply(inverse(10), const_2)), inverse(20)), const_2)

<gadget id="calculator">1 / 10</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/10) * 2</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">1 / 20</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(4/5) / (1/20)</gadget>
<output>16</output>
<gadget id="calculator">16 + 2</gadget>
<output>18</output>
<result>18</result>


cheese , bologna , and peanut butter sandwiches were made for a picnic in a ratio of 1 to 7 to 8 . if a total of 80 sandwiches were made , how many bologna sandwiches were made ?

Explanation: for deciding such task we should calculate all parts 1 + 7 + 8 = 16 parts and we should calculate how many sandwiches holds 1 part : 80 / 16 = 5 sandwiches in one part for bologna we have 7 parts so : 7 * 5 = 35 answer is c

multiply(divide(80, add(add(1, 7), 8)), 7)

<gadget id="calculator">1 + 7</gadget>
<output>8</output>
<gadget id="calculator">8 + 8</gadget>
<output>16</output>
<gadget id="calculator">80 / 16</gadget>
<output>5</output>
<gadget id="calculator">5 * 7</gadget>
<output>35</output>
<result>35</result>


for the past n days , the average ( arithmetic mean ) daily production at a company was 50 units . if today ' s production of 110 units raises the average to 55 units per day , what is the value of n ?

Explanation: "the daily production was raised by 5 units for n days , which has a weighting of 5 n . 5 n = 110 - 55 = 55 n = 11 the answer is b ."

subtract(divide(subtract(110, 50), subtract(55, 50)), const_1)

<gadget id="calculator">110 - 50</gadget>
<output>60</output>
<gadget id="calculator">55 - 50</gadget>
<output>5</output>
<gadget id="calculator">60 / 5</gadget>
<output>12</output>
<gadget id="calculator">12 - 1</gadget>
<output>11</output>
<result>11</result>


a train is 360 meter long is running at a speed of 50 km / hour . in what time will it pass a bridge of 140 meter length ?

Explanation: "speed = 50 km / hr = 50 * ( 5 / 18 ) m / sec = 125 / 9 m / sec total distance = 360 + 140 = 500 meter time = distance / speed = 500 * ( 9 / 125 ) = 36 seconds answer : c"

divide(add(360, 140), divide(multiply(50, const_1000), const_3600))

<gadget id="calculator">360 + 140</gadget>
<output>500</output>
<gadget id="calculator">50 * 1_000</gadget>
<output>50_000</output>
<gadget id="calculator">50_000 / 3_600</gadget>
<output>125/9 = around 13.888889</output>
<gadget id="calculator">500 / (125/9)</gadget>
<output>36</output>
<result>36</result>


the cash difference between the selling prices of an book at a profit of 12 % and 20 % is $ 3 . the ratio of the two selling prices is :

Explanation: "let c . p . of the book be $ x . then , required ratio = 112 % of x / 120 % of x = 112 / 120 = 14 / 15 = 14 : 15 e"

divide(add(const_100, 12), add(const_100, 20))

<gadget id="calculator">100 + 12</gadget>
<output>112</output>
<gadget id="calculator">100 + 20</gadget>
<output>120</output>
<gadget id="calculator">112 / 120</gadget>
<output>14/15 = around 0.933333</output>
<result>14/15 = around 0.933333</result>


mixture contains alcohol and water in the ratio 4 : 3 . if 5 liters of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture .

Explanation: "let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 20 x = 4 ( 3 x + 5 ) 8 x = 20 x = 2.5 quantity of alcohol = ( 4 x 2.5 ) litres = 10 litres . answer : a"

multiply(divide(multiply(4, 5), subtract(multiply(5, 4), multiply(3, 4))), 4)

<gadget id="calculator">4 * 5</gadget>
<output>20</output>
<gadget id="calculator">5 * 4</gadget>
<output>20</output>
<gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">20 - 12</gadget>
<output>8</output>
<gadget id="calculator">20 / 8</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">(5/2) * 4</gadget>
<output>10</output>
<result>10</result>


two pipes a and b can fill a tank in 36 hours and 46 hours respectively . if both the pipes are opened simultaneously , how much time will be taken to fill the tank ?

Explanation: "a fill in one hour = 1 / 36 b fill in one hour = 1 / 46 both fill in one hour = 1 / 36 + 1 / 46 = 82 / 1656 time taken by both pipes = 1656 / 82 = 20.195 hrs answer : a"

divide(const_1, add(divide(const_1, 36), divide(const_1, 46)))

<gadget id="calculator">1 / 36</gadget>
<output>1/36 = around 0.027778</output>
<gadget id="calculator">1 / 46</gadget>
<output>1/46 = around 0.021739</output>
<gadget id="calculator">(1/36) + (1/46)</gadget>
<output>41/828 = around 0.049517</output>
<gadget id="calculator">1 / (41/828)</gadget>
<output>828/41 = around 20.195122</output>
<result>828/41 = around 20.195122</result>


a grocer has a sale of rs . 5435 , rs . 5927 , rs . 5855 , rs . 6230 and rs . 5562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 5500 ?

Explanation: "total sale for 5 months = rs . ( 5435 + 5927 + 5855 + 6230 + 5562 ) = rs . 29009 . required sale = rs . [ ( 5500 x 6 ) - 29009 ] = rs . ( 33000 - 29009 ) = rs . 3991 answer : option c"

<gadget id="calculator">5 + 1</gadget>
<output>6</output>
<gadget id="calculator">6 * 5_500</gadget>
<output>33_000</output>
<gadget id="calculator">5_435 + 5_927</gadget>
<output>11_362</output>
<gadget id="calculator">11_362 + 5_855</gadget>
<output>17_217</output>
<gadget id="calculator">17_217 + 6_230</gadget>
<output>23_447</output>
<gadget id="calculator">23_447 + 5_562</gadget>
<output>29_009</output>
<gadget id="calculator">33_000 - 29_009</gadget>
<output>3_991</output>
<result>3_991</result>


find the result of equation of the ellipse whose foci are at ( 0 , - 5 ) and ( 0 , 5 ) and the length of its major axis is 14 .

Explanation: from the coordinates of the foci , c = 5 and the major axis is the y axis . from the length of the major axis , we obtain a = 7 . also b 2 = a 2 - c 2 = 24 . the equation of the ellipse is given by x 2 / 24 + y 2 / 49 = 1 correct answer is e ) 1

<gadget id="calculator">5 + 5</gadget>
<output>10</output>
<gadget id="calculator">10 + 4</gadget>
<output>14</output>
<gadget id="calculator">14 / 14</gadget>
<output>1</output>
<result>1</result>


if 12 machine can finish a job in 40 days , then how many more machines would be needed to finish the job in one - fourth less time ?

Explanation: you might think of this in a management context - we can use the principle of ' person - hours ' to solve any problem where we have identical workers . so , using simpler numbers , suppose you know that 6 identical employees , working simultaneously , would finish a job in 5 hours . then that job requires 6 * 5 = 30 total hours of person - work . if instead you wanted the job done in 3 hours , you ' d assign 30 / 3 = 10 employees to do the job , because you want to get a total of 30 hours of work from the employees . we can solve this problem identically . if 12 machines ( identical ones , i assume ) work simultaneously for 40 days , they will do a total of 12 * 40 machine - days of work . so the job requires 12 * 40 days of machine work in total . we instead want the job done in 1 / 4 less time , so in 30 days . so we ' ll need 12 * 40 / 30 = 16 machines , or 4 additional machines . a

subtract(divide(multiply(12, 40), multiply(divide(const_3, const_4), 40)), 12)

<gadget id="calculator">12 * 40</gadget>
<output>480</output>
<gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(3/4) * 40</gadget>
<output>30</output>
<gadget id="calculator">480 / 30</gadget>
<output>16</output>
<gadget id="calculator">16 - 12</gadget>
<output>4</output>
<result>4</result>


following an increase in prices , the price of a candy box was 20 pounds and the price of a can of soda was 6 pounds . if the price of a candy box was raised by 25 % , and the price of a can of soda was raised by 50 % . what was the price of a box of candy plus a can of soda before prices were raised ?

Explanation: "price of candy before price increase = 20 / 1.25 = 16 price of soda before price increase = 6 / 1.5 = 4 total price = 16 + 4 = 20 b is the answer"

add(divide(multiply(20, const_100), add(const_100, 25)), divide(multiply(6, const_100), add(const_100, 50)))

<gadget id="calculator">20 * 100</gadget>
<output>2_000</output>
<gadget id="calculator">100 + 25</gadget>
<output>125</output>
<gadget id="calculator">2_000 / 125</gadget>
<output>16</output>
<gadget id="calculator">6 * 100</gadget>
<output>600</output>
<gadget id="calculator">100 + 50</gadget>
<output>150</output>
<gadget id="calculator">600 / 150</gadget>
<output>4</output>
<gadget id="calculator">16 + 4</gadget>
<output>20</output>
<result>20</result>


a rectangular farm has to be fenced one long side , one short side and the diagonal . if the cost of fencing is rs . 14 per meter . the area of farm is 1200 m 2 and the short side is 30 m long . how much would the job cost ?

Explanation: "explanation : l * 30 = 1200 è l = 40 40 + 30 + 50 = 120 120 * 14 = 1680 answer : option b"

<gadget id="calculator">1_200 / 30</gadget>
<output>40</output>
<gadget id="calculator">30 + 40</gadget>
<output>70</output>
<gadget id="calculator">30 ** 2</gadget>
<output>900</output>
<gadget id="calculator">40 ** 2</gadget>
<output>1_600</output>
<gadget id="calculator">900 + 1_600</gadget>
<output>2_500</output>
<gadget id="calculator">2_500 ** (1/2)</gadget>
<output>50</output>
<gadget id="calculator">70 + 50</gadget>
<output>120</output>
<gadget id="calculator">120 * 14</gadget>
<output>1_680</output>
<result>1_680</result>


. a car covers a distance of 810 km in 5 hours . find its speed ?

Explanation: "810 / 5 = 162 kmph answer : c"

<gadget id="calculator">810 / 5</gadget>
<output>162</output>
<result>162</result>


the compounded ratio of ( 2 : 3 ) , ( 6 : 11 ) and ( 11 : 2 ) is

Explanation: answer : b ) 2 : 1

multiply(multiply(divide(2, 3), divide(6, 11)), divide(11, 2))

<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">6 / 11</gadget>
<output>6/11 = around 0.545455</output>
<gadget id="calculator">(2/3) * (6/11)</gadget>
<output>4/11 = around 0.363636</output>
<gadget id="calculator">11 / 2</gadget>
<output>11/2 = around 5.5</output>
<gadget id="calculator">(4/11) * (11/2)</gadget>
<output>2</output>
<result>2</result>


in a photography exhibition , some photographs were taken by octavia the photographer , and some photographs were framed by jack the framer . jack had framed 24 photographs taken by octavia , and 12 photographs taken by other photographers . if 36 of the photographs in the exhibition were taken by octavia , how many photographs were either framed by jack or taken by octavia ?

Explanation: the number of photographs either framed by jack or taken by octavia = { jack } + { octavia } - { overlap } = 36 + 36 - 24 = 48 ( { overlap } is green box ) . answer : b

<gadget id="calculator">24 + 12</gadget>
<output>36</output>
<gadget id="calculator">36 - 24</gadget>
<output>12</output>
<gadget id="calculator">36 + 12</gadget>
<output>48</output>
<result>48</result>


what is value of ( p + q ) / ( p - q ) if p / q = 7 ?

Explanation: explanation : ( p + q ) / ( p - q ) = ( p / q + 1 ) / ( p / q - 1 ) = ( 7 + 1 ) / ( 7 - 1 ) = 4 / 3 . answer : c

divide(add(7, const_1), subtract(7, const_1))

<gadget id="calculator">7 + 1</gadget>
<output>8</output>
<gadget id="calculator">7 - 1</gadget>
<output>6</output>
<gadget id="calculator">8 / 6</gadget>
<output>4/3 = around 1.333333</output>
<result>4/3 = around 1.333333</result>


find the area of a cuboid of length 8 cm , breadth 6 cm . and height 9 cm .

Explanation: "area of a cuboid = lxbxh = 8 cm x 6 cm x 9 cm = 432 cm cube answer : d"

<gadget id="calculator">8 * 6</gadget>
<output>48</output>
<gadget id="calculator">48 * 9</gadget>
<output>432</output>
<result>432</result>


a windmill is taking advantage of strong air currents in order to produce electrical energy . on a typical day the wind speed is around 20 mph and in that speed the windmill produces 400 kw / h ( kilowatts per hour ) . on a stormy day a windmill produces 20 % more energy . how much kw / h can 3 windmills produce in two hours on a stormy day ?

Explanation: normal day = 400 kw / h stormy day = 400 * 1.2 = 480 kw / h 3 windmills for 2 hours on stormy day 480 * 3 * 2 = 2880 answer : a

multiply(multiply(add(400, divide(multiply(400, 20), const_100)), 3), const_2)

<gadget id="calculator">400 * 20</gadget>
<output>8_000</output>
<gadget id="calculator">8_000 / 100</gadget>
<output>80</output>
<gadget id="calculator">400 + 80</gadget>
<output>480</output>
<gadget id="calculator">480 * 3</gadget>
<output>1_440</output>
<gadget id="calculator">1_440 * 2</gadget>
<output>2_880</output>
<result>2_880</result>


ramesh purchased a refrigerator for rs . 12500 after getting a discount of 20 % on the labelled price . he spent rs . 125 on transport and rs . 250 on installation . at what price should it be sold so that the profit earned would be 18 % if no discount was offered ?

Explanation: "price at which the tv set is bought = rs . 12,500 discount offered = 20 % marked price = 12500 * 100 / 80 = rs . 15625 the total amount spent on transport and installation = 125 + 250 = rs . 375 \ total price of tv set = 15625 + 375 = rs . 16000 the price at whichthe tv should be sold to get a profit of 18 % if no discount was offered = 16000 * 118 / 100 = rs . 18880 . answer : e"

divide(multiply(add(const_100, 18), add(divide(multiply(12500, const_100), subtract(const_100, 20)), add(125, 250))), const_100)

<gadget id="calculator">100 + 18</gadget>
<output>118</output>
<gadget id="calculator">12_500 * 100</gadget>
<output>1_250_000</output>
<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">1_250_000 / 80</gadget>
<output>15_625</output>
<gadget id="calculator">125 + 250</gadget>
<output>375</output>
<gadget id="calculator">15_625 + 375</gadget>
<output>16_000</output>
<gadget id="calculator">118 * 16_000</gadget>
<output>1_888_000</output>
<gadget id="calculator">1_888_000 / 100</gadget>
<output>18_880</output>
<result>18_880</result>


a hall is 15 meters long and 15 meters wide . if the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls , what is the volume of the hall ( in cubic meters ) ?

Explanation: "2 hl + 2 hw = 2 lw h = lw / ( l + w ) volume = lwh = ( lw ) ^ 2 / ( l + w ) = 1687.5 the answer is d ."

volume_rectangular_prism(15, 15, divide(multiply(rectangle_area(15, 15), const_2), rectangle_perimeter(15, 15)))

<gadget id="calculator">15 * 15</gadget>
<output>225</output>
<gadget id="calculator">225 * 2</gadget>
<output>450</output>
<gadget id="calculator">2 * (15 + 15)</gadget>
<output>60</output>
<gadget id="calculator">450 / 60</gadget>
<output>15/2 = around 7.5</output>
<gadget id="calculator">15 * 15 * (15/2)</gadget>
<output>3_375/2 = around 1_687.5</output>
<result>3_375/2 = around 1_687.5</result>


what is the total surface area in square meters of a rectangular solid whose length is 9 meters , width is 8 meters , and depth is 5 meters ?

Explanation: "surface area of a cuboid = 2 ( lb + bh + lh ) = 2 ( 9 * 8 + 8 * 5 + 9 * 5 ) = 2 ( 72 + 40 + 45 ) = 2 * 157 = 314 m 2 answer : e"

<gadget id="calculator">2 * (8 * 9 + 9 * 5 + 8 * 5)</gadget>
<output>314</output>
<result>314</result>


a car traveling at a certain constant speed takes 4 seconds longer to travel 1 km than it would take to travel 1 km at 80 km / hour . at what speed , in km / hr , is the car traveling ?

Explanation: "time to cover 1 kilometer at 80 kilometers per hour is 1 / 80 hours = 3,600 / 80 seconds = 45 seconds ; time to cover 1 kilometer at regular speed is 45 + 4 = 49 seconds = 49 / 3,600 hours = 1 / 74 hours ; so , we get that to cover 1 kilometer 1 / 74 hours is needed - - > regular speed 74 kilometers per hour ( rate is a reciprocal of time or rate = distance / time ) . answer : c"

divide(1, divide(add(multiply(const_3600, divide(1, 80)), 4), const_3600))

<gadget id="calculator">1 / 80</gadget>
<output>1/80 = around 0.0125</output>
<gadget id="calculator">3_600 * (1/80)</gadget>
<output>45</output>
<gadget id="calculator">45 + 4</gadget>
<output>49</output>
<gadget id="calculator">49 / 3_600</gadget>
<output>49/3_600 = around 0.013611</output>
<gadget id="calculator">1 / (49/3_600)</gadget>
<output>3_600/49 = around 73.469388</output>
<result>3_600/49 = around 73.469388</result>


a , b and c invested rs . 6300 , rs . 4200 and rs . 10500 respectively , in a partnership business . find the share of a in profit of rs . 12500 after a year ?

Explanation: 6300 : 4200 : 10500 3 : 2 : 5 3 / 10 * 12100 = 3750 . answer : d

<gadget id="calculator">6_300 + 4_200</gadget>
<output>10_500</output>
<gadget id="calculator">10_500 + 10_500</gadget>
<output>21_000</output>
<gadget id="calculator">6_300 / 21_000</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(3/10) * 12_500</gadget>
<output>3_750</output>
<result>3_750</result>


a student needs 30 % of the marks on a test to pass the test . if the student gets 80 marks and fails the test by 100 marks , find the maximum marks set for the test .

Explanation: "30 % = 180 marks 1 % = 6 marks 100 % = 600 marks the answer is b ."

divide(add(80, 100), divide(30, const_100))

<gadget id="calculator">80 + 100</gadget>
<output>180</output>
<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">180 / (3/10)</gadget>
<output>600</output>
<result>600</result>


to asphalt 1 km road , 30 men spent 12 days working 8 hours per day . how many days , 20 men will spend to asphalt a road of 2 km working 8 hours a day ?

Explanation: "man - hours required to asphalt 1 km road = 30 * 12 * 8 = 2880 man - hours required to asphalt 2 km road = 2880 * 2 = 5760 man - hours available per day = 20 * 8 = 160 therefore number of days = 5760 / 240 = 36 days ans = b"

divide(multiply(multiply(multiply(30, 12), 8), 2), multiply(20, 8))

<gadget id="calculator">30 * 12</gadget>
<output>360</output>
<gadget id="calculator">360 * 8</gadget>
<output>2_880</output>
<gadget id="calculator">2_880 * 2</gadget>
<output>5_760</output>
<gadget id="calculator">20 * 8</gadget>
<output>160</output>
<gadget id="calculator">5_760 / 160</gadget>
<output>36</output>
<result>36</result>


if x and j are integers and 2 x – j = 11 , then 4 x + j can not be

Explanation: 2 x - j = 11 . . . . j = 2 x - 11 4 x + j = 4 x + 2 x - 11 = 6 x - 11 6 x - 11 = - 5 . . . x = 1 6 x - 11 = 1 . . . x = 2 6 x - 11 = 13 . . . x = 4 6 x - 11 = 17 . . x is not integer 6 x - 11 = 551 . . x is not integer i think the choice e is 55 not 551 . otherwise both de can not be solution = d

subtract(multiply(11, 2), subtract(11, add(4, 2)))

<gadget id="calculator">11 * 2</gadget>
<output>22</output>
<gadget id="calculator">4 + 2</gadget>
<output>6</output>
<gadget id="calculator">11 - 6</gadget>
<output>5</output>
<gadget id="calculator">22 - 5</gadget>
<output>17</output>
<result>17</result>


an investment yields an interest payment of $ 228 each month . if the simple annual interest rate is 9 % , what is the amount of the investment ?

Explanation: "let the principal amount = p simple annual interest = 9 % simple monthly interest = ( 9 / 12 ) = ( 3 / 4 ) % ( 3 / 4 ) * ( p / 100 ) = 228 = > p = ( 228 * 4 * 10 ^ 2 ) / 3 = 76 * 4 * 10 ^ 2 = 304 * 10 ^ 2 answer b"

multiply(divide(228, divide(9, multiply(const_3, const_4))), const_100)

<gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">9 / 12</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">228 / (3/4)</gadget>
<output>304</output>
<gadget id="calculator">304 * 100</gadget>
<output>30_400</output>
<result>30_400</result>


joe ’ s average ( arithmetic mean ) test score across 4 equally weighted tests was 45 . he was allowed to drop his lowest score . after doing so , his average test score improved to 50 . what is the lowest test score that was dropped ?

Explanation: "the arithmetic mean of 4 equally weighted tests was 45 . so what we can assume is that we have 4 test scores , each 45 . he dropped his lowest score and the avg went to 50 . this means that the lowest score was not 45 and other three scores had given the lowest score 5 each to make it up to 45 too . when the lowest score was removed , the other 3 scores got their 5 back . so the lowest score was 3 * 5 = 15 less than 45 . so the lowest score = 45 - 15 = 30 answer ( b )"

subtract(multiply(45, 4), multiply(50, const_3))

<gadget id="calculator">45 * 4</gadget>
<output>180</output>
<gadget id="calculator">50 * 3</gadget>
<output>150</output>
<gadget id="calculator">180 - 150</gadget>
<output>30</output>
<result>30</result>


if y > 0 , ( 4 y ) / 20 + ( 3 y ) / 10 is what percent of y ?

Explanation: "can be reduced to 2 y / 10 + 3 y / 10 = y / 2 = 50 % answer b"

multiply(const_100, add(divide(4, 20), divide(3, 10)))

<gadget id="calculator">4 / 20</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">3 / 10</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(1/5) + (3/10)</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">100 * (1/2)</gadget>
<output>50</output>
<result>50</result>


in how many years rs 100 will produce the same interest at 5 % as rs . 600 produce in 4 years at 10 %

Explanation: "explanation : clue : firstly we need to calculate the si with prinical 600 , time 4 years and rate 10 % , it will be rs . 240 then we can get the time as time = ( 100 * 240 ) / ( 100 * 5 ) = 48 option e"

divide(multiply(divide(multiply(600, 10), const_100), 4), multiply(divide(5, const_100), 100))

<gadget id="calculator">600 * 10</gadget>
<output>6_000</output>
<gadget id="calculator">6_000 / 100</gadget>
<output>60</output>
<gadget id="calculator">60 * 4</gadget>
<output>240</output>
<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/20) * 100</gadget>
<output>5</output>
<gadget id="calculator">240 / 5</gadget>
<output>48</output>
<result>48</result>


in the number 10,0 ab , a and b represent the tens and units digits , respectively . if 11,0 ab is divisible by 55 , what is the greatest possible value of b × a ?

Explanation: you should notice that 55 * 2 = 110 so 11,000 is divisible by 55 : 55 * 200 = 11,000 ( or you can notice that 11,000 is obviously divisible by both 5 and 11 so by 55 ) - - > b * a = 0 * 0 = 0 . next number divisible by 55 is 11,000 + 55 = 11,055 : b * a = 5 * 5 = 15 ( next number wo n ' t have 110 as the first 3 digits so we have only two options 0 and 25 ) . answer : e . ! please post ps questions in the ps subforum : gmat - problem - solving - ps - 140 / please post ds questions in the ds subforum : gmat - data - sufficiency - ds - 141 / no posting of ps / ds questions is allowed in the mainmath forum . d

subtract(multiply(reminder(reminder(multiply(add(divide(add(power(const_100, const_2), const_1000), 55), const_1), 55), const_100), const_10), divide(subtract(reminder(multiply(add(divide(add(power(const_100, const_2), const_1000), 55), const_1), 55), const_100), reminder(reminder(multiply(add(divide(add(power(const_100, const_2), const_1000), 55), const_1), 55), const_100), const_10)), const_10)), const_10)

<gadget id="calculator">100 ** 2</gadget>
<output>10_000</output>
<gadget id="calculator">10_000 + 1_000</gadget>
<output>11_000</output>
<gadget id="calculator">11_000 / 55</gadget>
<output>200</output>
<gadget id="calculator">200 + 1</gadget>
<output>201</output>
<gadget id="calculator">201 * 55</gadget>
<output>11_055</output>
<gadget id="calculator">11_055 % 100</gadget>
<output>55</output>
<gadget id="calculator">55 % 10</gadget>
<output>5</output>
<gadget id="calculator">55 - 5</gadget>
<output>50</output>
<gadget id="calculator">50 / 10</gadget>
<output>5</output>
<gadget id="calculator">5 * 5</gadget>
<output>25</output>
<gadget id="calculator">25 - 10</gadget>
<output>15</output>
<result>15</result>


if mn ≠ 0 and 25 percent of n equals 37 1 / 2 percent of m , what is the value of 12 n / m ?

Explanation: given : 25 percent of n equals 37 ( 1 / 2 ) percent of m = > ( 25 / 100 ) * n = ( 75 / 200 ) * m = > 2 n = 3 m . 12 n / m = 6 * 2 n / m = 6 * 3 m / m = 18 . hence a .

add(divide(multiply(multiply(divide(37, const_100), const_100), const_10), multiply(divide(25, const_100), const_100)), const_3)

<gadget id="calculator">37 / 100</gadget>
<output>37/100 = around 0.37</output>
<gadget id="calculator">(37/100) * 100</gadget>
<output>37</output>
<gadget id="calculator">37 * 10</gadget>
<output>370</output>
<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 100</gadget>
<output>25</output>
<gadget id="calculator">370 / 25</gadget>
<output>74/5 = around 14.8</output>
<gadget id="calculator">(74/5) + 3</gadget>
<output>89/5 = around 17.8</output>
<result>89/5 = around 17.8</result>


if the cost price of 18 articles is equal to the selling price of 16 articles , what is the percentage of profit or loss that the merchant makes ?

Explanation: "explanation : let cost price of 1 article be re . 1 . therefore , cost price of 18 articles = rs . 18 . selling price of 16 articles = rs . 18 therefore , selling price of 18 articles is : - = > 18 / 16 ã — 18 = > 20.25 . therefore , profit = selling price - cost price . = > 20.25 â ˆ ’ 18 = 2.25 . hence , the percentage of profit = profit x 100 / c . p . = > 2.25 / 18 ã — 100 . = > 12.5 % profit . answer : b"

multiply(const_100, divide(subtract(const_100, divide(multiply(const_100, 16), 18)), divide(multiply(const_100, 16), 18)))

<gadget id="calculator">100 * 16</gadget>
<output>1_600</output>
<gadget id="calculator">1_600 / 18</gadget>
<output>800/9 = around 88.888889</output>
<gadget id="calculator">100 - (800/9)</gadget>
<output>100/9 = around 11.111111</output>
<gadget id="calculator">(100/9) / (800/9)</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">100 * (1/8)</gadget>
<output>25/2 = around 12.5</output>
<result>25/2 = around 12.5</result>


if the length of an edge of cube p is thrice the length of an edge of cube q , what is the ratio of the volume of cube q to the volume of cube p ?

Explanation: the length of cube q = 1 ; the length of cube p = 3 ; the ratio of the volume of cube q to the volume of cube p = 1 ^ 3 / 3 ^ 3 = 1 / 27 answer : d

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(1/3) ** 3</gadget>
<output>1/27 = around 0.037037</output>
<result>1/27 = around 0.037037</result>


si on a certain sum of money for 3 yrs at 8 percent / annum is 1 / 2 the ci on rs . 4000 for 2 yrs at 10 percent / annum . the sum placed on si is ?

Explanation: c . i . = rs . 4000 x 1 + 10 2 - 4000 100 = rs . 4000 x 11 x 11 - 4000 10 10 = rs . 840 . sum = rs . 420 x 100 = rs . 1750 . 3 x 8 c

divide(multiply(divide(subtract(multiply(4000, power(add(1, divide(10, const_100)), const_2)), 4000), const_2), const_100), multiply(3, 8))

<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">(11/10) ** 2</gadget>
<output>121/100 = around 1.21</output>
<gadget id="calculator">4_000 * (121/100)</gadget>
<output>4_840</output>
<gadget id="calculator">4_840 - 4_000</gadget>
<output>840</output>
<gadget id="calculator">840 / 2</gadget>
<output>420</output>
<gadget id="calculator">420 * 100</gadget>
<output>42_000</output>
<gadget id="calculator">3 * 8</gadget>
<output>24</output>
<gadget id="calculator">42_000 / 24</gadget>
<output>1_750</output>
<result>1_750</result>


what is the sum of the first 23 natural numbers ( starting from 1 ) ?

Explanation: the sum of n natural numbers = n * ( n + 1 ) / 2 = 23 * 24 / 2 = 276 the answer is c .

multiply(divide(23, const_2), add(subtract(23, 1), const_2))

<gadget id="calculator">23 / 2</gadget>
<output>23/2 = around 11.5</output>
<gadget id="calculator">23 - 1</gadget>
<output>22</output>
<gadget id="calculator">22 + 2</gadget>
<output>24</output>
<gadget id="calculator">(23/2) * 24</gadget>
<output>276</output>
<result>276</result>


in a garden , 26 trees are planted at equal distances along a yard 700 metres long , one tree being at each end of the yard . what is the distance between two consecutive trees ?

Explanation: "26 trees have 25 gaps between them . length of each gap = 700 / 25 = 28 i . e . , distance between two consecutive trees = 28 answer is b ."

<gadget id="calculator">26 - 1</gadget>
<output>25</output>
<gadget id="calculator">700 / 25</gadget>
<output>28</output>
<result>28</result>


what will be the percentage increase in the area of the cube ' s surface if each of the cube ' s edges grows by 20 % ?

Explanation: "the question is very easy . my logic is the following : a surface = 6 * a ^ 2 after 20 % increase a surface = 6 * ( ( 1.2 a ) ^ 2 ) = 6 * 1.44 * a ^ 2 the increase in the surface area = ( 6 * 1.44 * a ^ 2 - 6 * a ^ 2 ) / 6 * a ^ 2 = ( 6 * a ^ 2 ( 1.44 - 1 ) ) / ( 6 * a ^ 2 ) = 1.44 - 1 = 0.44 = 44 % answer : b"

multiply(subtract(power(add(const_1, divide(20, const_100)), const_2), const_1), const_100)

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 + (1/5)</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">(6/5) ** 2</gadget>
<output>36/25 = around 1.44</output>
<gadget id="calculator">(36/25) - 1</gadget>
<output>11/25 = around 0.44</output>
<gadget id="calculator">(11/25) * 100</gadget>
<output>44</output>
<result>44</result>


a semicircular shaped window has diameter of 63 cm . its perimeter equals

Explanation: explanation : perimeter of window = { \ color { blue } \ pi } r + 2 r = [ { ( 22 / 7 ) * ( 63 / 2 ) } + 63 ] = 99 + 63 = 162 cm answer : a ) 162

add(divide(circumface(divide(63, const_2)), const_2), 63)

<gadget id="calculator">63 / 2</gadget>
<output>63/2 = around 31.5</output>
<gadget id="calculator">2 * pi * (63/2)</gadget>
<output>63*pi = around 197.920337</output>
<gadget id="calculator">(63*pi) / 2</gadget>
<output>63*pi/2 = around 98.960169</output>
<gadget id="calculator">(63*pi/2) + 63</gadget>
<output>63 + 63*pi/2 = around 161.960169</output>
<result>63 + 63*pi/2 = around 161.960169</result>