Question: a soccer team played 160 games and won 65 percent of them . how many games did it win ?

<gadget id="calculator">65 * 160</gadget>
<output>10_400</output>

<gadget id="calculator">10_400 / 100</gadget>
<output>104</output>
<result>104</result>

Choices:
A. 84
B. 94
C. 104
D. 114
E. 124

Explanation: "65 % of 160 = x 0.65 * 160 = x 104 = x answer : c"


Question: a trader sells 80 meters of cloth for rs . 9000 at the profit of rs . 23.5 per metre of cloth . what is the cost price of one metre of cloth ?

<gadget id="calculator">9_000 / 80</gadget>
<output>225/2 = around 112.5</output>

<gadget id="calculator">(225/2) - 23.5</gadget>
<output>89</output>
<result>89</result>

Choices:
A. 22
B. 89
C. 90
D. 78
E. 80

Explanation: "sp of 1 m of cloth = 9000 / 80 = rs . 112.5 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 112.5 - rs . 23.5 = rs . 89 . answer : b"


Question: a farm has chickens , cows and sheep . there are 6 times the number of chickens and cows than sheep . if there are more cows than chickens or sheep , and together , cows and chickens have a total of 100 feet and heads , how many sheep live at the farm ?

<gadget id="calculator">6 - 2</gadget>
<output>4</output>
<result>4</result>

Choices:
A. 5
B. 8
C. 10
D. 4
E. 17

Explanation: chicken - ch cows - c sheep - s ch + c = 6 s c > ch and c > s each cow has 4 legs and 1 head each chicken has 2 legs and 1 head so 5 c + 3 ch = 100 ( sum of legs and head ) there are 2 possible solutions to this equation c = 11 and ch = 9 or c = 14 and ch = 10 since from first equation where ch + c = 6 s the sum of ch and c should be divisbile by 6 . 20 is not so the only possible solution is c = 14 and ch = 10 . so s = 4 answer : d


Question: in a certain city , 60 percent of the registered voters are democrats and the rest are republicans . in a mayoral race , if 75 percent of the registered voters who are democrats and 25 percent of the registered voters who are republicans are expected to vote for candidate a , what percent of the registered voters are expected to vote for candidate a ?

<gadget id="calculator">75 / 100</gadget>
<output>3/4 = around 0.75</output>

<gadget id="calculator">60 * (3/4)</gadget>
<output>45</output>

<gadget id="calculator">100 - 60</gadget>
<output>40</output>

<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">40 * (1/4)</gadget>
<output>10</output>

<gadget id="calculator">45 + 10</gadget>
<output>55</output>
<result>55</result>

Choices:
A. 50 %
B. 53 %
C. 54 %
D. 55 %
E. 57 %

add(multiply(60, divide(75, const_100)), multiply(subtract(const_100, 60), divide(25, const_100)))

Explanation: "say there are total of 100 registered voters in that city . thus 60 are democrats and 40 are republicans . 60 * 0.75 = 45 democrats are expected to vote for candidate a ; 40 * 0.25 = 10 republicans are expected to vote for candidate a . thus total of 45 + 10 = 55 registered voters are expected to vote for candidate a , which is 55 % of the total number of registered voters . answer : d ."


Question: a rower can row 5 km / h in still water . when the river is running at 2 km / h , it takes the rower 1 hour to row to big rock and back . how many kilometers is it to big rock ?

<gadget id="calculator">5 - 2</gadget>
<output>3</output>

<gadget id="calculator">5 + 2</gadget>
<output>7</output>

<gadget id="calculator">7 + 3</gadget>
<output>10</output>

<gadget id="calculator">3 / 10</gadget>
<output>3/10 = around 0.3</output>

<gadget id="calculator">(3/10) * 7</gadget>
<output>21/10 = around 2.1</output>
<result>21/10 = around 2.1</result>

Choices:
A. 1.5
B. 1.8
C. 2.1
D. 2.4
E. 2.7

multiply(divide(subtract(5, 2), add(add(5, 2), subtract(5, 2))), add(5, 2))

Explanation: "let x be the distance to big rock . time = x / 3 + x / 7 = 1 x = 21 / 10 = 2.1 km the answer is c ."


Question: a brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 24 m * 2 m * 0.75 m ?

<gadget id="calculator">24 * 100</gadget>
<output>2_400</output>

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

<gadget id="calculator">2_400 * 200</gadget>
<output>480_000</output>

<gadget id="calculator">0.75 * 100</gadget>
<output>75</output>

<gadget id="calculator">480_000 * 75</gadget>
<output>36_000_000</output>

<gadget id="calculator">36_000_000 / 20</gadget>
<output>1_800_000</output>

<gadget id="calculator">1_800_000 / 10</gadget>
<output>180_000</output>

<gadget id="calculator">180_000 / 7.5</gadget>
<output>24_000</output>
<result>24_000</result>

Choices:
A. 29798
B. 27908
C. 24000
D. 25000
E. 27991

divide(divide(divide(multiply(multiply(multiply(24, const_100), multiply(2, const_100)), multiply(0.75, const_100)), 20), 10), 7.5)

Explanation: "24 * 2 * 0.75 = 20 / 100 * 10 / 100 * 7.5 / 100 * x 24 = 1 / 100 * x = > x = 24000 answer : c"


Question: in a group of ducks and cows , the total number of legs are 28 more than twice the no . of heads . find the total no . of buffaloes .

<gadget id="calculator">28 / 2</gadget>
<output>14</output>
<result>14</result>

Choices:
A. 11
B. 12
C. 14
D. 16
E. 18

Explanation: "let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 28 = > 2 x = 28 = > x = 14 c"


Question: 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 26 per kg , then his gain percent is

<gadget id="calculator">5 + 3</gadget>
<output>8</output>

<gadget id="calculator">26 * 8</gadget>
<output>208</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">208 - 150</gadget>
<output>58</output>

<gadget id="calculator">58 * 100</gadget>
<output>5_800</output>

<gadget id="calculator">5_800 / 150</gadget>
<output>116/3 = around 38.666667</output>
<result>116/3 = around 38.666667</result>

Choices:
A. 12 %
B. 39 %
C. 14 %
D. 15 %
E. 16 %

divide(multiply(subtract(multiply(26, add(5, 3)), add(multiply(5, 18), multiply(3, 20))), const_100), add(multiply(5, 18), multiply(3, 20)))

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 26 ) = rs . 208 . profit = 208 - 150 = 58 so , profit % = ( 58 / 150 ) * 100 = 39 % option b"


Question: joe needs to paint all the airplane hangars at the airport , so he buys 360 gallons of paint to do the job . during the first week , he uses 1 / 4 of all the paint . during the second week , he uses 1 / 4 of the remaining paint . how many gallons of paint has joe used ?

<gadget id="calculator">360 / 4</gadget>
<output>90</output>

<gadget id="calculator">90 * 1</gadget>
<output>90</output>

<gadget id="calculator">360 - 90</gadget>
<output>270</output>

<gadget id="calculator">270 / 4</gadget>
<output>135/2 = around 67.5</output>

<gadget id="calculator">90 + (135/2)</gadget>
<output>315/2 = around 157.5</output>
<result>315/2 = around 157.5</result>

Choices:
A. 18
B. 157
C. 175
D. 216
E. 250

add(multiply(divide(360, 4), 1), divide(subtract(360, multiply(divide(360, 4), 1)), 4))

Explanation: "total paint initially = 360 gallons paint used in the first week = ( 1 / 4 ) * 360 = 90 gallons . remaning paint = 270 gallons paint used in the second week = ( 1 / 4 ) * 270 = 67 gallons total paint used = 157 gallons . option b"


Question: a man has some hens and cows . if the number of heads be 50 and the number of feet equals 160 , then the number of hens will be :

<gadget id="calculator">50 * 4</gadget>
<output>200</output>

<gadget id="calculator">200 - 160</gadget>
<output>40</output>

<gadget id="calculator">40 / 2</gadget>
<output>20</output>
<result>20</result>

Choices:
A. 22
B. 23
C. 24
D. 20
E. 28

divide(subtract(multiply(50, const_4), 160), const_2)

Explanation: "explanation : let the number of hens be x and the number of cows be y . then , x + y = 50 . . . . ( i ) and 2 x + 4 y = 160 x + 2 y = 80 . . . . ( ii ) solving ( i ) and ( ii ) we get : x = 20 , y = 30 the required answer = 20 . answer : d"


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

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

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

Choices:
A. 100 %
B. 120 %
C. 200 %
D. 150 %
E. 180 %

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


Question: how many even multiples of 65 are there between 649 and 1301 ?

<gadget id="calculator">1_301 - 649</gadget>
<output>652</output>

<gadget id="calculator">65 * 2</gadget>
<output>130</output>

<gadget id="calculator">652 / 130</gadget>
<output>326/65 = around 5.015385</output>

<gadget id="calculator">(326/65) + 1</gadget>
<output>391/65 = around 6.015385</output>
<result>391/65 = around 6.015385</result>

Choices:
A. 5
B. 6
C. 9
D. 10
E. 11

add(divide(subtract(1301, 649), multiply(65, const_2)), const_1)

Explanation: "650 = 10 * 65 1300 = 20 * 65 the even multiples are 65 multiplied by 10 , 12 , 14 , 16 , 18 , and 20 for a total of 6 . the answer is b ."


Question: two trains are moving in opposite directions with speed of 70 km / hr and 90 km / hr respectively . their lengths are 1.10 km and 0.9 km respectively . the slower train cross the faster train in - - - seconds

<gadget id="calculator">1.1 + 0.9</gadget>
<output>2</output>

<gadget id="calculator">70 + 90</gadget>
<output>160</output>

<gadget id="calculator">2 / 160</gadget>
<output>1/80 = around 0.0125</output>

<gadget id="calculator">(1/80) * 3_600</gadget>
<output>45</output>
<result>45</result>

Choices:
A. 56
B. 45
C. 47
D. 26
E. 25

Explanation: "explanation : relative speed = 70 + 90 = 160 km / hr ( since both trains are moving in opposite directions ) total distance = 1.1 + . 9 = 2 km time = 2 / 160 hr = 1 / 80 hr = 3600 / 80 seconds = = 45 seconds answer : option b"


Question: in 1998 the profits of company n were 10 percent of revenues . in 1999 , the revenues of company n fell by 20 percent , but profits were 10 percent of revenues . the profits in 1999 were what percent of the profits in 1998 ?

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>

<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>

<gadget id="calculator">(4/5) * (1/10)</gadget>
<output>2/25 = around 0.08</output>

<gadget id="calculator">(2/25) / (1/10)</gadget>
<output>4/5 = around 0.8</output>

<gadget id="calculator">(4/5) * 100</gadget>
<output>80</output>
<result>80</result>

Choices:
A. 80 %
B. 105 %
C. 120 %
D. 124.2 %
E. 138 %

multiply(divide(multiply(subtract(const_1, divide(20, const_100)), divide(10, const_100)), divide(10, const_100)), const_100)

Explanation: "0,08 r = x / 100 * 0.1 r answer a"


Question: if ( 2 to the x ) - ( 2 to the ( x - 2 ) ) = 3 ( 2 to the 5 ) , what is the value of x ?

<gadget id="calculator">5 + 2</gadget>
<output>7</output>
<result>7</result>

Choices:
A. 7
B. 11
C. 13
D. 15
E. 17

Explanation: "( 2 to the power x ) - ( 2 to the power ( x - 2 ) ) = 3 ( 2 to the power 5 ) 2 ^ x - 2 ^ ( x - 2 ) = 3 . 2 ^ 5 hence x = 7 . answer is a"


Question: in an examination , the percentage of students qualified to the students appeared from school ' p ' is 70 % . in school ' q ' , the number of students appeared is 30 % more than the students appeared from school ' p ' and the number of students qualified from school ' q ' is 50 % more than the students qualified from school ' p ' . what is the % of students qualified to the number of students appeared from school ' q ' ?

<gadget id="calculator">50 + 100</gadget>
<output>150</output>

<gadget id="calculator">150 / 100</gadget>
<output>3/2 = around 1.5</output>

<gadget id="calculator">70 / 100</gadget>
<output>7/10 = around 0.7</output>

<gadget id="calculator">(3/2) * (7/10)</gadget>
<output>21/20 = around 1.05</output>

<gadget id="calculator">30 + 100</gadget>
<output>130</output>

<gadget id="calculator">130 / 100</gadget>
<output>13/10 = around 1.3</output>

<gadget id="calculator">(21/20) / (13/10)</gadget>
<output>21/26 = around 0.807692</output>

<gadget id="calculator">(21/26) * 100</gadget>
<output>1_050/13 = around 80.769231</output>
<result>1_050/13 = around 80.769231</result>

Choices:
A. 80.78 %
B. 80.76 %
C. 80.72 %
D. 80.79 %
E. 80.74 %

multiply(divide(multiply(divide(add(50, const_100), const_100), divide(70, const_100)), divide(add(30, const_100), const_100)), const_100)

Explanation: explanation : number of students appeared from school ' p ' = 100 , say number of students qualified from school ' p ' = 70 and number of students appeared from school ' q ' = 130 number of students qualified from school ' q ' = 50 % more than those qualified from school ' p ' . = 70 + 35 = 105 % of students qualified to the number of students appeared from school b = 105 / 130 * 100 = 80.76 % answer : b


Question: there are 4 people of different heights standing in order of increasing height . the difference is 2 inches between the first person and the second person , and also between the second person and the third person . the difference between the third person and the fourth person is 6 inches and the average height is 75 . how tall is the fourth person ?

<gadget id="calculator">75 * 4</gadget>
<output>300</output>

<gadget id="calculator">4 + 6</gadget>
<output>10</output>

<gadget id="calculator">6 + 10</gadget>
<output>16</output>

<gadget id="calculator">300 - 16</gadget>
<output>284</output>

<gadget id="calculator">284 / 4</gadget>
<output>71</output>

<gadget id="calculator">71 + 10</gadget>
<output>81</output>
<result>81</result>

Choices:
A. 73
B. 75
C. 77
D. 79
E. 81

add(divide(subtract(multiply(75, 4), add(6, add(4, 6))), 4), add(4, 6))

Explanation: let x be the height of the first person . then the heights are x , x + 2 , x + 4 , and x + 10 . 4 x + 16 = 4 ( 75 ) = 300 x = 71 and the fourth person has a height of 71 + 10 = 81 inches the answer is e .


Question: if the angles of an n sided polygon are in a . p and a > = 20 and d > = 20 then wat is the maximum possible value of n ?

<gadget id="calculator">20 - 3</gadget>
<output>17</output>

<gadget id="calculator">17 ** 2</gadget>
<output>289</output>

<gadget id="calculator">4 * 2</gadget>
<output>8</output>

<gadget id="calculator">10 * 8</gadget>
<output>80</output>

<gadget id="calculator">80 + 100</gadget>
<output>180</output>

<gadget id="calculator">180 / 10</gadget>
<output>18</output>

<gadget id="calculator">18 * 2</gadget>
<output>36</output>

<gadget id="calculator">4 * 36</gadget>
<output>144</output>

<gadget id="calculator">289 - 144</gadget>
<output>145</output>

<gadget id="calculator">145 ** (1/2)</gadget>
<output>sqrt(145) = around 12.041595</output>

<gadget id="calculator">(sqrt(145)) + 17</gadget>
<output>sqrt(145) + 17 = around 29.041595</output>

<gadget id="calculator">(sqrt(145) + 17) / 2</gadget>
<output>sqrt(145)/2 + 17/2 = around 14.520797</output>
<result>sqrt(145)/2 + 17/2 = around 14.520797</result>

Choices:
A. 12
B. 14
C. 21
D. 25
E. cant determine

divide(add(sqrt(subtract(power(subtract(20, const_3), const_2), multiply(const_4, multiply(divide(add(multiply(const_10, multiply(const_4, const_2)), const_100), const_10), const_2)))), subtract(20, const_3)), const_2)

Explanation: sum of interior angles of a polygon = ( n - 2 ) × 180 ° where n = number of sides there will be n angles which are in a . p . therefore , since we need to find maximum value of n , put minimum value for a and d . i . e . , take a = 20 and d = 20 then sum of the angles = n / 2 [ 2 × 20 + ( n − 1 ) 20 ] therefore , 10 n ( n + 1 ) = ( n − 2 ) 180 n = 14.52 since number of sides must be a positive integer , maximum value of n = 14 answer : b


Question: if there are only 2 wheelers and 4 wheelers parked in a school located at the heart of the city , find the number of 4 wheelers parked there if the total number of wheels is 82 ?

<gadget id="calculator">82 - 2</gadget>
<output>80</output>

<gadget id="calculator">80 / 4</gadget>
<output>20</output>
<result>20</result>

Choices:
A. 11
B. 12
C. 13
D. 20
E. 25

Explanation: "four wheeler = 20 * 4 = 80 ( max ) 2 wheel = 1 so no of 4 wheeler = 20 answer : d"


Question: if 50 % of x is 25 less than 25 % of 2500 , then x is ?

<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">2_500 * (1/4)</gadget>
<output>625</output>

<gadget id="calculator">625 - 25</gadget>
<output>600</output>

<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">600 / (1/2)</gadget>
<output>1_200</output>
<result>1_200</result>

Choices:
A. 1880
B. 2160
C. 1200
D. 8400
E. 1210

divide(subtract(multiply(2500, divide(25, const_100)), 25), divide(50, const_100))

Explanation: "50 % of x = x / 2 ; 25 % of 2500 = 25 / 100 * 2500 = 625 given that , x / 2 = 625 - 25 = > x / 2 = 600 = > x = 1200 . answer : c"


Question: a contractor undertakes to built a walls in 50 days . he employs 30 peoples for the same . however after 25 days he finds that only 40 % of the work is complete . how many more man need to be employed to complete the work in time ?

<gadget id="calculator">100 - 40</gadget>
<output>60</output>

<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>

<gadget id="calculator">30 * (3/5)</gadget>
<output>18</output>

<gadget id="calculator">4 / 10</gadget>
<output>2/5 = around 0.4</output>

<gadget id="calculator">18 / (2/5)</gadget>
<output>45</output>
<result>45</result>

Choices:
A. 25
B. 30
C. 45
D. 20
E. none of these

divide(multiply(30, divide(subtract(const_100, 40), const_100)), divide(const_4, const_10))

Explanation: "30 men complete 0.4 work in 25 days . applying the work rule , m 1 × d 1 × w 2 = m 2 × d 2 × w 1 we have , 30 × 25 × 0.6 = m 2 × 25 × 0.4 or m 2 = 30 × 25 × 0.6 / 25 × 0.4 = 45 men answerc"


Question: in an examination , 30 % of total students failed in hindi , 35 % failed in english and 35 % in both . the percentage of these who passed in both the subjects is :

<gadget id="calculator">30 + 35</gadget>
<output>65</output>

<gadget id="calculator">65 - 35</gadget>
<output>30</output>

<gadget id="calculator">100 - 30</gadget>
<output>70</output>
<result>70</result>

Choices:
A. 10 %
B. 20 %
C. 30 %
D. 70 %
E. 50 %

subtract(const_100, subtract(add(30, 35), 35))

Explanation: "pass percentage = 100 - ( 30 + 35 - 35 ) = 100 - 30 = 70 answer : d"


Question: in a shop , the profit is 320 % of the cost . if the cost increases by 25 % but the selling price remains constant , find out approximately what percentage of the selling price is the profit ?

<gadget id="calculator">320 + 100</gadget>
<output>420</output>

<gadget id="calculator">25 + 100</gadget>
<output>125</output>

<gadget id="calculator">420 - 125</gadget>
<output>295</output>

<gadget id="calculator">295 / 420</gadget>
<output>59/84 = around 0.702381</output>

<gadget id="calculator">(59/84) * 100</gadget>
<output>1_475/21 = around 70.238095</output>
<result>1_475/21 = around 70.238095</result>

Choices:
A. 180 %
B. 120 %
C. 90 %
D. 80 %
E. 70 %

multiply(divide(subtract(add(320, const_100), add(25, const_100)), add(320, const_100)), const_100)

Explanation: let the cp = 100 profit = ( 320 / 100 ) × 100 = 320 sp = cp + profit = 100 + 320 = 420 if the cost increases by 25 % , new cp = ( 125 / 100 ) × 100 = 125 selling price is constant , hence new sp = 420 profit = sp – cp = 420 – 125 = 295 required percentage = ( 295 / 420 ) × 100 = 2950 / 42 = 1475 / 21 ≈ 70 answer : e


Question: a person spends 40 % of his salary on food , 25 % on house rent , 15 % on entertainment and 10 % on conveyance . if his savings at the end of the month is rs . 1200 , then his salary per month in rupees is :

<gadget id="calculator">1_200 * 100</gadget>
<output>120_000</output>

<gadget id="calculator">120_000 / 10</gadget>
<output>12_000</output>
<result>12_000</result>

Choices:
A. 12000
B. 6000
C. 8000
D. 10000
E. none of these

Explanation: total expenditure = 40 + 25 + 15 + 10 = 90 % saving = ( 100 - 90 ) = 10 % 10 / 100 × salary = 1200 , salary = 12000 rs . answer : a


Question: the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 12000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is ?

<gadget id="calculator">12_000 - 8_000</gadget>
<output>4_000</output>

<gadget id="calculator">7 * 4_000</gadget>
<output>28_000</output>

<gadget id="calculator">8_000 - 6_000</gadget>
<output>2_000</output>

<gadget id="calculator">28_000 / 2_000</gadget>
<output>14</output>

<gadget id="calculator">7 + 14</gadget>
<output>21</output>
<result>21</result>

Choices:
A. 76
B. 21
C. 26
D. 28
E. 11

Explanation: "explanation : lot the total number of workers be v then , 8 ooov = ( 12000 * 7 ) + 6000 ( v - 7 ) < = > 2000 v = 42000 < = > v = 21 . answer : b"


Question: a student chose a number , multiplied it by 2 , then subtracted 138 from the result and got 108 . what was the number he chose ?

<gadget id="calculator">108 + 138</gadget>
<output>246</output>

<gadget id="calculator">246 / 2</gadget>
<output>123</output>
<result>123</result>

Choices:
A. 123
B. 267
C. 277
D. 267
E. 120

Explanation: "let xx be the number he chose , then 2 â ‹ … x â ˆ ’ 138 = 108 x = 123 answer : a"


Question: express 30 mps in kmph ?

<gadget id="calculator">30 / 1_000</gadget>
<output>3/100 = around 0.03</output>

<gadget id="calculator">(3/100) * 3_600</gadget>
<output>108</output>
<result>108</result>

Choices:
A. 122
B. 108
C. 110
D. 150
E. 100

Explanation: "30 * 18 / 5 = 108 kmph answer : b"


Question: in a group of ducks and cows , the total number of legs are 8 more than twice the no . of heads . find the total no . of buffaloes .

<gadget id="calculator">8 / 2</gadget>
<output>4</output>
<result>4</result>

Choices:
A. 5
B. 4
C. 6
D. 3
E. 2

Explanation: "let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 8 = > 2 x = 8 = > x = 4 b"


Question: if log 8 x + log 8 1 / 6 = 1 / 3 , then the value of x is :

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">8 ** (1/3)</gadget>
<output>2</output>

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

Choices:
A. 12
B. 16
C. 18
D. 24
E. 26

Explanation: "log 8 x + log 8 ( 1 / 6 ) = 1 / 3 = > ( log x / log 8 ) + ( log 1 / 6 / log 8 ) = log ( 81 / 3 ) = log 2 = > log x = log 2 – log 1 / 6 = log ( 2 * 6 / 1 ) = log 12 answer : a"


Question: if the sum of two numbers is 12 and the sum of their squares is 124 , then the product of the numbers is

<gadget id="calculator">12 ** 2</gadget>
<output>144</output>

<gadget id="calculator">144 - 124</gadget>
<output>20</output>

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

Choices:
A. 10
B. 44
C. 80
D. 88
E. 90

divide(subtract(power(12, const_2), 124), const_2)

Explanation: "sol . let the numbers be x and y . then , ( x + y ) = 12 and x 2 + y 2 = 124 . now , 2 xy = ( x + y ) 2 - ( x 2 + y 2 ) = ( 12 ) 2 - 124 = 144 - 124 = 20 xy = 10 . answer a"


Question: the ratio between the sale price and the cost price of an article is 8 : 5 . what is the ratio between the profit and the cost price of that article ?

<gadget id="calculator">8 - 5</gadget>
<output>3</output>

<gadget id="calculator">3 / 5</gadget>
<output>3/5 = around 0.6</output>
<result>3/5 = around 0.6</result>

Choices:
A. 23
B. 1 : 2
C. 2 : 5
D. 3 : 5
E. 25

Explanation: "c . p . = rs . 5 x and s . p . = rs . 8 x . then , gain = rs . 3 x required ratio = 3 x : 5 x = 3 : 5 d"


Question: tim came second in math . when his mother asked him how much he had scored , he answered that he got the sum of the first 9 even numbers . his mother immediately worked out the answer . how much had he scored in math ?

<gadget id="calculator">9 + 1</gadget>
<output>10</output>

<gadget id="calculator">10 * 9</gadget>
<output>90</output>
<result>90</result>

Choices:
A. 80
B. 90
C. 30
D. 70
E. 60

Explanation: "b 90 sum = ( n x n ) + n hence , 9 x 9 = 81 + 9 = 90"


Question: out of 400 students of a school , 325 play football , 175 play cricket and 50 neither play football nor cricket . how many students play both football and cricket ?

<gadget id="calculator">175 + 325</gadget>
<output>500</output>

<gadget id="calculator">400 - 50</gadget>
<output>350</output>

<gadget id="calculator">500 - 350</gadget>
<output>150</output>
<result>150</result>

Choices:
A. 120
B. 150
C. 100
D. 180
E. 220

Explanation: "n ( a ) = 325 , n ( b ) = 175 , n ( aub ) = 400 - 50 = 350 . required number = n ( anb ) = n ( a ) + n ( b ) - n ( aub ) = 325 + 175 - 350 = 150 . answer is b"


Question: 50 men shake hands with each other . maximum no of handshakes without cyclic handshakes .

<gadget id="calculator">50 - 1</gadget>
<output>49</output>

<gadget id="calculator">50 / 2</gadget>
<output>25</output>

<gadget id="calculator">49 * 25</gadget>
<output>1_225</output>
<result>1_225</result>

Choices:
A. 190
B. 200
C. 1225
D. 220
E. 230

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

Explanation: total no . of handshakes = 49 + 48 + 47 + . . . + 3 + 2 + 1 = 19 * ( 19 + 1 ) / 2 = 1225 or , if there are n persons then no . of shakehands = nc 2 = 50 c 2 = 1225 answer : c


Question: if the population of a certain country increases at the rate of one person every 15 seconds , by how many persons does the population increase in 10 minutes ?

<gadget id="calculator">60 / 15</gadget>
<output>4</output>

<gadget id="calculator">4 * 10</gadget>
<output>40</output>
<result>40</result>

Choices:
A. 40
B. 100
C. 150
D. 240
E. 300

Explanation: "since the population increases at the rate of 1 person every 15 seconds , it increases by 4 people every 60 seconds , that is , by 4 people every minute . thus , in 10 minutes the population increases by 10 x 4 = 40 people . answer . a ."


Question: if p ( a ) = 3 / 5 and p ( b ) = 2 / 5 , find p ( a n b ) if a and b are independent events .

<gadget id="calculator">3 / 5</gadget>
<output>3/5 = around 0.6</output>

<gadget id="calculator">2 / 5</gadget>
<output>2/5 = around 0.4</output>

<gadget id="calculator">(3/5) * (2/5)</gadget>
<output>6/25 = around 0.24</output>
<result>6/25 = around 0.24</result>

Choices:
A. 6 / 25
B. 3 / 25
C. 8 / 25
D. 2 / 13
E. 3 / 17

Explanation: "p ( a n b ) = p ( a ) . p ( b ) p ( a n b ) = 3 / 5 . 2 / 5 p ( a n b ) = 6 / 25 . a"


Question: if a certain coin is flipped , the probability that the coin will land heads is 1 / 2 . if the coin is flipped 5 times , what is the probability that it will land heads up on the first 3 flips and not on the last 2 flips ?

<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">(1/2) ** 5</gadget>
<output>1/32 = around 0.03125</output>
<result>1/32 = around 0.03125</result>

Choices:
A. 3 / 5
B. 1 / 2
C. 1 / 5
D. 1 / 8
E. 1 / 32

Explanation: "on the first three flips , you must get heads . whats the probability of getting heads ? its 1 / 2 so for the first three flips , your probability is ( 1 / 2 ) ^ 3 = 1 / 8 now for the last two , you want to get tails only . whats the prob of getting tails ? well , its the same as prob of getting a heads , namely , 1 / 2 for the last two flips , your probability is ( 1 / 2 ) ^ 2 = 1 / 4 so your overall probability for the event in question is 1 / 8 * 1 / 4 = 1 / 32 answer : e"


Question: if x < y < z and y - x > 5 , where x is an even integer and y and z are odd integers , what is the least possible value q of z - x ?

<gadget id="calculator">5 + 2</gadget>
<output>7</output>

<gadget id="calculator">7 + 2</gadget>
<output>9</output>
<result>9</result>

Choices:
A. 6
B. 7
C. 8
D. 9
E. 10

Explanation: "x < y < z to find the least possible value for z - x ; we need to find the values for z and x that can be closest to each other . if x is some even number , then what could be minimum possible odd z . if x is some even number y - x > 5 ; y > x + 5 ; minimum value for y = x + 5 + 2 = x + 7 [ note : x + 5 is as even + odd = odd and nearest odd greater than x + 5 is x + 5 + 2 ] minimum value for z = y + 2 = x + 7 + 2 = x + 9 [ note : z = y + 2 because both z and y are odd . difference between two odd numbers is 2 ] q = z - x = x + 9 - x = 9 ans : d"


Question: a piece of work can finish by a certain number of men in 100 days . if however , there were 10 men less , it would take 10 days more for the work to be finished . how many men were there originally ?

<gadget id="calculator">100 + 10</gadget>
<output>110</output>

<gadget id="calculator">110 / 10</gadget>
<output>11</output>

<gadget id="calculator">11 * 10</gadget>
<output>110</output>

<gadget id="calculator">11 - 10</gadget>
<output>1</output>

<gadget id="calculator">110 / 1</gadget>
<output>110</output>
<result>110</result>

Choices:
A. 75
B. 82
C. 100
D. 110
E. 120

divide(multiply(divide(add(100, 10), 10), 10), subtract(divide(add(100, 10), 10), 10))

Explanation: originally let there be x men . less men , more days ( indirect ) : . ( x - 10 ) : x : : 100 : 110 or x - 10 / x = 100 / 110 or 11 x - 110 = 10 x or x = 110 so , originally there were 110 men . answer : d


Question: how many seconds will a train 150 meters long take to cross a bridge 200 meters long if the speed of the train is 54 kmph ?

<gadget id="calculator">200 + 150</gadget>
<output>350</output>

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>

<gadget id="calculator">54 * (5/18)</gadget>
<output>15</output>

<gadget id="calculator">350 / 15</gadget>
<output>70/3 = around 23.333333</output>
<result>70/3 = around 23.333333</result>

Choices:
A. 17 sec
B. 21 sec
C. 23.3 sec
D. 27.5 sec
E. 29 sec

Explanation: d = 150 + 200 = 350 s = 54 * 5 / 18 = 15 mps t = 350 / 15 = 23.3 sec c ) 23.3 sec


Question: an error 6 % in excess is made while measuring the side of a square . what is the percentage of error in the calculated area of the square ?

<gadget id="calculator">100 + 6</gadget>
<output>106</output>

<gadget id="calculator">106 ** 2</gadget>
<output>11_236</output>

<gadget id="calculator">100 ** 2</gadget>
<output>10_000</output>

<gadget id="calculator">11_236 - 10_000</gadget>
<output>1_236</output>

<gadget id="calculator">1_236 * 100</gadget>
<output>123_600</output>

<gadget id="calculator">123_600 / 10_000</gadget>
<output>309/25 = around 12.36</output>
<result>309/25 = around 12.36</result>

Choices:
A. 14.05 %
B. 14.02 %
C. 14 %
D. 13 %
E. 12.36 %

divide(multiply(subtract(square_area(add(const_100, 6)), square_area(const_100)), const_100), square_area(const_100))

Explanation: "percentage error in calculated area = ( 6 + 6 + ( 6 ã — 6 ) / 100 ) % = 12.36 % answer : e"


Question: liz drove from point a to point b at 40 km / h . on her way back she drove at 50 km / h and therefore her way back lasted one hour less . what is the distance ( in km ) between a and b ?

<gadget id="calculator">50 - 40</gadget>
<output>10</output>

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

<gadget id="calculator">5 * 40</gadget>
<output>200</output>
<result>200</result>

Choices:
A. 150
B. 200
C. 450
D. 500
E. 600

multiply(divide(50, subtract(50, 40)), 40)

Explanation: distance is same s 1 t 1 = s 2 t 2 40 t = 50 ( t - 1 ) t = 5 distance = speed * time 40 * 5 = 200 answer : b


Question: the ratio of a to b is 4 to 5 , where a and b are positive . if x equals a increased by 75 percent of a , and m equals b decreased by 60 percent of b , what is the value of m / x ?

<gadget id="calculator">100 - 60</gadget>
<output>40</output>

<gadget id="calculator">100 + 75</gadget>
<output>175</output>

<gadget id="calculator">40 / 175</gadget>
<output>8/35 = around 0.228571</output>

<gadget id="calculator">5 / 4</gadget>
<output>5/4 = around 1.25</output>

<gadget id="calculator">(8/35) * (5/4)</gadget>
<output>2/7 = around 0.285714</output>
<result>2/7 = around 0.285714</result>

Choices:
A. 2 / 5
B. 3 / 4
C. 4 / 5
D. 5 / 4
E. 2 / 7

multiply(divide(subtract(const_100, 60), add(const_100, 75)), divide(5, 4))

Explanation: "a / b = 4 / 5 m / x = ( 2 / 5 ) * 5 / ( 7 / 4 ) * 4 = 2 / 7 the answer is e ."


Question: in a certain apartment building , there are one - bedroom and two - bedroom apartments . the rental prices of the apartment depend on a number of factors , but on average , two - bedroom apartments have higher rental prices than do one - bedroom apartments . let m be the average rental price for all apartments in the building . if m is $ 700 higher than the average rental price for all one - bedroom apartments , and if the average rental price for all two - bedroom apartments is $ 2,100 higher that m , then what percentage of apartments in the building are two - bedroom apartments ?

<gadget id="calculator">700 * 100</gadget>
<output>70_000</output>

<gadget id="calculator">2 * 1_000</gadget>
<output>2_000</output>

<gadget id="calculator">2_000 + 100</gadget>
<output>2_100</output>

<gadget id="calculator">2_100 + 700</gadget>
<output>2_800</output>

<gadget id="calculator">70_000 / 2_800</gadget>
<output>25</output>
<result>25</result>

Choices:
A. 25 %
B. 15 %
C. 20 %
D. 40 %
E. 45 %

divide(multiply(700, const_100), add(add(multiply(const_2, const_1000), const_100), 700))

Explanation: ratio of 2 bedroom apartment : 1 bedroom apartment = 700 : 2100 - - - - - > 1 : 3 let total number of apartments be x no . of 2 bedroom apartment = ( 1 / 4 ) * x percentage of apartments in the building are two - bedroom apartments - - - - > ( 1 / 4 ) * 100 - - - > 25 % answer : a


Question: the pilot of a small aircraft with a 40 - gallon fuel tank wants to fly to cleveland , which is 480 miles away . the pilot recognizes that the current engine , which can fly only 8 miles per gallon , will not get him there . by how many miles per gallon must the aircraft ’ s fuel efficiency be improved to make the flight to cleveland possible ?

<gadget id="calculator">480 / 40</gadget>
<output>12</output>

<gadget id="calculator">12 - 8</gadget>
<output>4</output>
<result>4</result>

Choices:
A. 2
B. 4
C. 12
D. 40
E. 160

Explanation: "actual miles / gallon is = 480 / 4 = 12 miles / gallon . current engine miles / gallon is 8 miles / gallon . additional 4 miles / gallon is required to match the actual mileage . answer : b"


Question: a square is drawn inside a right - angled triangle with the two perpendicular sides as 12 cm and 8 cm . what is the side of the largest possible square that can be drawn ?

<gadget id="calculator">12 * 8</gadget>
<output>96</output>

<gadget id="calculator">96 / 2</gadget>
<output>48</output>

<gadget id="calculator">48 / 10</gadget>
<output>24/5 = around 4.8</output>
<result>24/5 = around 4.8</result>

Choices:
A. 4.8 cm
B. 4.4 cm
C. 4.9 cm
D. 5.0 cm
E. 5.2 cm

divide(divide(multiply(12, 8), const_2), const_10)

Explanation: area of triangle is 1 / 2 * 12 * 8 = 48 side of square = x the entire triangle split into two right angled triangle and one square with dimensions as follows i ) square with side x ii ) right angled triangle with perpendicular sides x and 12 - x iii ) right angled triangle with perpendicular sides 8 - x and x sum of area of all three = 48 = x 2 + 1 / 2 * x * ( 12 - x ) + 1 / 2 * x * ( 8 - x ) = 48 = x = 4.8 cm answer : a


Question: the membership of a committee consists of 3 english teachers , 4 mathematics teachers , and 2 social studies teachers . if 2 committee members are to be selected at random to write the committee ’ s report , what is the probability that the two members selected will both be social teachers ?

<gadget id="calculator">3 + 4</gadget>
<output>7</output>

<gadget id="calculator">7 + 2</gadget>
<output>9</output>

<gadget id="calculator">3 / 9</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">9 - 1</gadget>
<output>8</output>

<gadget id="calculator">2 / 8</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">(1/3) * (1/4)</gadget>
<output>1/12 = around 0.083333</output>
<result>1/12 = around 0.083333</result>

Choices:
A. 2 / 3
B. 1 / 12
C. 2 / 9
D. 1 / 2
E. 1 / 24

multiply(divide(3, add(add(3, 4), 2)), divide(2, subtract(add(add(3, 4), 2), const_1)))

Explanation: "probability of first member an english teacher = 3 / 9 probability of second member an english teacher = 2 / 8 probability of both being english teacher = 3 / 9 x 2 / 8 = 1 / 12 ( b )"


Question: in a 160 meters race a beats b by 56 m or 7 seconds . a ' s time over the course is :

<gadget id="calculator">7 / 56</gadget>
<output>1/8 = around 0.125</output>

<gadget id="calculator">(1/8) * 160</gadget>
<output>20</output>

<gadget id="calculator">20 - 7</gadget>
<output>13</output>
<result>13</result>

Choices:
A. 22 seconds
B. 12 seconds
C. 13 seconds
D. 18 seconds
E. 28 seconds

subtract(multiply(divide(7, 56), 160), 7)

Explanation: b runs 56 m in 7 sec . = > b runs 160 m in 7 / 56 * 160 = 20 seconds since a beats b by 7 seconds , a runs 160 m in ( 20 - 7 ) = 13 seconds hence , a ' s time over the course = 13 seconds answer : c


Question: by how much is 70 % of 120 greater than 35 % of 200 .

<gadget id="calculator">70 / 100</gadget>
<output>7/10 = around 0.7</output>

<gadget id="calculator">120 * (7/10)</gadget>
<output>84</output>

<gadget id="calculator">35 / 100</gadget>
<output>7/20 = around 0.35</output>

<gadget id="calculator">(7/20) * 200</gadget>
<output>70</output>

<gadget id="calculator">84 - 70</gadget>
<output>14</output>
<result>14</result>

Choices:
A. 15
B. 14
C. 13
D. 16
E. 17

subtract(multiply(120, divide(70, const_100)), multiply(divide(35, const_100), 200))

Explanation: ( 70 / 100 ) * 120 â € “ ( 35 / 100 ) * 200 84 - 70 = 14 answer : b


Question: in 10 years , a will be twice as old 5 as b was 10 years ago . if a is now 5 years older than b , the present age of b is

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

<gadget id="calculator">5 + 10</gadget>
<output>15</output>

<gadget id="calculator">20 + 15</gadget>
<output>35</output>
<result>35</result>

Choices:
A. 35
B. 37
C. 39
D. 41
E. 42

Explanation: "explanation : let b ' s age = x years . then , as age = ( x + 5 ) years . ( x + 5 + 10 ) = 2 ( x — 10 ) hence x = 35 . present age of b = 35 years answer : option a"


Question: if 2 + 7 = 57 ; 3 + 6 = 63 ; 5 + 9 = 206 then 5 + 8 = ?

<gadget id="calculator">5 ** 3</gadget>
<output>125</output>

<gadget id="calculator">8 ** 2</gadget>
<output>64</output>

<gadget id="calculator">125 + 64</gadget>
<output>189</output>
<result>189</result>

Choices:
A. 185
B. 186
C. 177
D. 168
E. 189

Explanation: "2 ^ 3 + 7 ^ 2 = 57 3 ^ 3 + 6 ^ 2 = 63 5 ^ 3 + 9 ^ 2 = 206 and 5 ^ 3 + 8 ^ 2 = 189 answer : e"


Question: if a man lost 7 % by selling oranges at the rate of 21 a rupee at how many a rupee must he sell them to gain 42 % ?

<gadget id="calculator">100 - 7</gadget>
<output>93</output>

<gadget id="calculator">93 * 21</gadget>
<output>1_953</output>

<gadget id="calculator">100 + 42</gadget>
<output>142</output>

<gadget id="calculator">1_953 / 142</gadget>
<output>1_953/142 = around 13.753521</output>
<result>1_953/142 = around 13.753521</result>

Choices:
A. 12.75
B. 11.75
C. 8.75
D. 15.75
E. 13.75

divide(multiply(subtract(const_100, 7), 21), add(const_100, 42))

Explanation: "93 % - - - - 21 142 % - - - - ? 93 / 142 * 21 = 13.75 answer : e"


Question: a cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.4 m and its walls are 5 cm thick . the thickness of the bottom is :

<gadget id="calculator">3.3 * 2.6</gadget>
<output>8.58</output>

<gadget id="calculator">8.58 * 1.4</gadget>
<output>12.012</output>

<gadget id="calculator">8_000 / 1_000</gadget>
<output>8</output>

<gadget id="calculator">12.012 - 8</gadget>
<output>4.012</output>
<result>4.012</result>

Choices:
A. 90 cm
B. 4 dm
C. 1 m
D. 1.1 cm
E. none of these

subtract(multiply(multiply(3.3, 2.6), 1.4), divide(8000, const_1000))

Explanation: "explanation : let the thickness of the bottom be x cm . then , [ ( 330 - 10 ) × ( 260 - 10 ) × ( 140 - x ) ] = 8000 × 1000 = > 320 × 250 × ( 140 - x ) = 8000 × 1000 = > ( 140 - x ) = 8000 × 1000 / 320 = 100 = > x = 40 cm = 4 dm . answer : b"


Question: a can do a piece of work in 15 days . a does the work for 5 days only and leaves the job . b does the remaining work in 16 days . in how many days b alone can do the work ?

<gadget id="calculator">1 / 16</gadget>
<output>1/16 = around 0.0625</output>

<gadget id="calculator">1 / 15</gadget>
<output>1/15 = around 0.066667</output>

<gadget id="calculator">5 * (1/15)</gadget>
<output>1/3 = around 0.333333</output>

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

<gadget id="calculator">(1/16) * (2/3)</gadget>
<output>1/24 = around 0.041667</output>

<gadget id="calculator">1 / (1/24)</gadget>
<output>24</output>
<result>24</result>

Choices:
A. 5 days
B. 7 days
C. 12 days
D. 24 days
E. 10 days

inverse(multiply(inverse(16), subtract(const_1, multiply(5, inverse(15)))))

Explanation: "explanation : a ’ s 5 day work = 5 * 1 / 15 = 1 / 3 remaining work = 1 - 1 / 3 = 2 / 3 b completes 2 / 3 work in 6 days b alone can do in x days 2 / 3 * x = 16 x = 24 days answer : option d"


Question: a train is 360 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length .

<gadget id="calculator">360 + 140</gadget>
<output>500</output>

<gadget id="calculator">45 * 1_000</gadget>
<output>45_000</output>

<gadget id="calculator">45_000 / 3_600</gadget>
<output>25/2 = around 12.5</output>

<gadget id="calculator">500 / (25/2)</gadget>
<output>40</output>
<result>40</result>

Choices:
A. 20 seconds
B. 27 seconds
C. 30 seconds
D. 40 seconds
E. 50 seconds

divide(add(360, 140), divide(multiply(45, const_1000), const_3600))

Explanation: "speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 360 + 140 = 500 meter time = distance / speed = 500 ∗ 2 / 25 = 40 seconds answer : d"


Question: if a 2 - b 2 = 9 and a * b = 4 , find a 4 + b 4 .

<gadget id="calculator">9 ** 2</gadget>
<output>81</output>

<gadget id="calculator">4 ** 2</gadget>
<output>16</output>

<gadget id="calculator">16 * 2</gadget>
<output>32</output>

<gadget id="calculator">81 + 32</gadget>
<output>113</output>
<result>113</result>

Choices:
A. 32
B. 90
C. 113
D. 92
E. 81

add(power(9, 2), multiply(power(4, 2), 2))

Explanation: "a 2 - b 2 = 9 : given a 4 + b 4 - 2 a 2 b 2 = 92 : square both sides and expand . a * b = 4 : given a 2 b 2 = 42 : square both sides . a 4 + b 4 - 2 ( 16 ) = 81 : substitute a 4 + b 4 = 113 correct answer c"


Question: a chemist mixes one liter of pure water with x liters of a 50 % salt solution , and the resulting mixture is a 15 % salt solution . what is the value of x ?

<gadget id="calculator">50 - 15</gadget>
<output>35</output>

<gadget id="calculator">15 / 35</gadget>
<output>3/7 = around 0.428571</output>
<result>3/7 = around 0.428571</result>

Choices:
A. 1 / 4
B. 1 / 3
C. 1 / 2
D. 1
E. 3 / 7

Explanation: "concentration of salt in pure solution = 0 concentration of salt in salt solution = 50 % concentration of salt in the mixed solution = 15 % the pure solution and the salt solution is mixed in the ratio of - - > ( 50 - 15 ) / ( 15 - 0 ) = 7 / 3 1 / x = 7 / 3 x = 3 / 7 answer : e"


Question: the cyclist going at a constant rate of 18 miles per hour is passed by a motor - cyclist traveling in the same direction along the same path at 48 miles per hour . the motor - cyclist stops to wait for the cyclist 15 minutes after passing cyclist , while the cyclist continues to travel at constant rate , how many minutes must the motor - cyclist wait until the cyclist catches up ?

<gadget id="calculator">48 / 4</gadget>
<output>12</output>

<gadget id="calculator">18 / 4</gadget>
<output>9/2 = around 4.5</output>

<gadget id="calculator">12 - (9/2)</gadget>
<output>15/2 = around 7.5</output>

<gadget id="calculator">(15/2) * 60</gadget>
<output>450</output>

<gadget id="calculator">450 / 18</gadget>
<output>25</output>
<result>25</result>

Choices:
A. 25
B. 30
C. 35
D. 40
E. 45

divide(multiply(subtract(divide(48, const_4), divide(18, const_4)), const_60), 18)

Explanation: for the 15 minutes the motor - cyclist continues to overtake the cyclist , she is going at 30 miles per hour faster than the cyclist . once the motor - cyclist stops , the cyclist is going at 18 miles per hour while the motor - cyclist is at rest so the amount of time the cyclist will take to cover the distance between them is going to be in the ratio of the relative speeds . 30 / 18 * 15 or 25 minutes answer is ( a )


Question: a number is doubled and 9 is added . if the resultant is trebled , it becomes 81 . what is that number ?

<gadget id="calculator">3 * 9</gadget>
<output>27</output>

<gadget id="calculator">81 - 27</gadget>
<output>54</output>

<gadget id="calculator">3 * 2</gadget>
<output>6</output>

<gadget id="calculator">54 / 6</gadget>
<output>9</output>
<result>9</result>

Choices:
A. 3.5
B. 6
C. 8
D. 7
E. 9

divide(subtract(81, multiply(const_3, 9)), multiply(const_3, const_2))

Explanation: "let the number be x . then , 3 ( 2 x + 9 ) = 81 2 x = 18 = > x = 9 answer : e"


Question: in a renowned city , the average birth rate is 9 people every two seconds and the death rate is 3 people every two seconds . estimate the size of the population net increase that occurs in one day .

<gadget id="calculator">9 - 3</gadget>
<output>6</output>

<gadget id="calculator">6 * 3_600</gadget>
<output>21_600</output>

<gadget id="calculator">21_600 * 12</gadget>
<output>259_200</output>
<result>259_200</result>

Choices:
A. 32,300
B. 172,800
C. 468,830
D. 338,200
E. 259,200

multiply(multiply(subtract(9, 3), const_3600), const_12)

Explanation: "every 2 seconds , 6 persons are added ( 9 - 3 ) . every second 3 persons are added . in a day 24 hrs = 24 * 60 minutes = 24 * 60 * 60 = 86400 seconds . 86400 * 3 = 259200 option e"


Question: the squared value of the diagonal of a rectangle is ( 64 + b 2 ) sq cm , where b is less than 8 cm . what is the breadth of that rectangle ?

<gadget id="calculator">64 ** (1/2)</gadget>
<output>8</output>

<gadget id="calculator">8 - 2</gadget>
<output>6</output>
<result>6</result>

Choices:
A. 6 cm
B. 10 cm
C. 8 cm
D. data inadequate
E. none of these

Explanation: diagonal 2 = 64 + b 2 or , 10 ( 2 ) = 64 + 6 ( 2 ) answer a


Question: the cost price of 60 articles is the same as the selling price of x articles . if the profit is 20 % , what is x ?

<gadget id="calculator">60 * 4</gadget>
<output>240</output>

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

<gadget id="calculator">240 / 5</gadget>
<output>48</output>
<result>48</result>

Choices:
A. 42
B. 45
C. 48
D. 50
E. 54

divide(multiply(60, const_4), add(const_4, const_1))

Explanation: "let the cost price = y the cost price of 60 articles = 60 y the selling price of x articles = 1.20 y * x 1.20 y * x = 60 y x = 60 / 1.2 = 50 the answer is d ."


Question: on a certain transatlantic crossing , 40 percent of a ship ’ s passengers held round - trip tickets and also took their cars abroad the ship . if 20 percent of the passengers with round - trip tickets did not take their cars abroad the ship , what percent of the ship ’ s passengers held round - trip tickets ?

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>

<gadget id="calculator">40 / (4/5)</gadget>
<output>50</output>
<result>50</result>

Choices:
A. 20 %
B. 40 %
C. 50 %
D. 60 %
E. 80 %

divide(40, subtract(const_1, divide(20, const_100)))

Explanation: "let t be the total number of passengers . let x be the number of people with round trip tickets . 0.4 t had round trip tickets and took their cars . 0.8 x had round trip tickets and took their cars . 0.8 x = 0.4 t x = 0.5 t the answer is c ."


Question: in a certain game , a large container is filled with red , yellow , green , and blue beads worth , respectively , 7 , 5 , 3 , and 2 points each . a number of beads are then removed from the container . if the product of the point values of the removed beads is 30 , 870000 , how many red beads were removed ?

<gadget id="calculator">3 * 1</gadget>
<output>3</output>

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

Choices:
A. 1
B. 2
C. 3
D. 4
E. 5

Explanation: 30 , 870,000 = 2 ^ 4 * 5 ^ 4 * 3087 = 2 ^ 4 * 3 * 5 ^ 4 * 1029 = 2 ^ 4 * 3 ^ 2 * 5 ^ 4 * 343 = 2 ^ 4 * 3 ^ 2 * 5 ^ 4 * 7 ^ 3 the answer is c .


Question: # 88 a necklace is made by stringing q no individual beads together in the repeating pattern red bead , green bead , white bead , blue bead , and yellow bead . if the necklace design begins with a red bead and ends with a white bead , then q could equal

<gadget id="calculator">88 / 88</gadget>
<output>1</output>

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

<gadget id="calculator">2 + 3</gadget>
<output>5</output>

<gadget id="calculator">3 + 5</gadget>
<output>8</output>

<gadget id="calculator">8 + 5</gadget>
<output>13</output>

<gadget id="calculator">13 + 5</gadget>
<output>18</output>

<gadget id="calculator">18 + 5</gadget>
<output>23</output>

<gadget id="calculator">23 + 5</gadget>
<output>28</output>
<result>28</result>

Choices:
A. 16
B. 28
C. 41
D. 54
E. 65

add(add(add(add(add(add(divide(88, 88), const_2), add(const_2, const_3)), add(const_2, const_3)), add(const_2, const_3)), add(const_2, const_3)), add(const_2, const_3))

Explanation: you can just write out the pattern and count : rgwbyrgwbyrgwby . . . but to save time a good test taker will just look for a pattern . min # is 3 , because w is the third one . then every 5 beads another white comes , so it must be 3 + 5 + 5 + 5 . . and so on . . . 3 + 5 = 8 3 + 5 + 5 = 13 3 + 5 + 5 + 5 = 18 3 + 5 + 5 + 5 + 5 = 23 so you see it ends in either 8 or 3 . pick an answer that ends in either 8 or 3 . only one answer does , b .


Question: a distributor sells a product through an online store , which take a commission of 20 % of the price set by the distributor . the distributor obtains the product from a producer at the price of $ 16 per item . what is the price that the buyer observers online if the distributor wants to maintain a 20 % profit on the cost of the item ?

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">(1/5) * 16</gadget>
<output>16/5 = around 3.2</output>

<gadget id="calculator">(16/5) + 16</gadget>
<output>96/5 = around 19.2</output>

<gadget id="calculator">100 - 20</gadget>
<output>80</output>

<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>

<gadget id="calculator">(96/5) / (4/5)</gadget>
<output>24</output>
<result>24</result>

Choices:
A. $ 20
B. $ 21
C. $ 22
D. $ 23
E. $ 24

divide(add(multiply(divide(20, const_100), 16), 16), divide(subtract(const_100, 20), const_100))

Explanation: let x be the price that buyers see online . the distributor wants to receive 1.2 ( original price ) which should be 80 % of x . 1.2 ( 16 ) = 0.8 x x = 1.2 ( 16 ) / 0.8 = 1.5 ( 16 ) = $ 24 the answer is e .


Question: rohan spends 40 % of his salary on food , 20 % on house rent , 10 % on entertainment and 10 % on conveyance . if his savings at the end of a month are rs . 3000 . then his monthly salary is

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

<gadget id="calculator">3_000 * 5</gadget>
<output>15_000</output>
<result>15_000</result>

Choices:
A. rs . 15000
B. rs . 12000
C. rs . 9000
D. rs . 6000
E. rs . 3000

Explanation: "sol . saving = [ 100 - ( 40 + 20 + 10 + 10 ] % = 20 % . let the monthly salary be rs . x . then , 20 % of x = 3000 â ‡ ” 20 / 100 x = 3000 â ‡ ” x = 3000 ã — 5 = 15000 . answer a"


Question: last year a certain bond price with a face value of 5000 yielded 9 % of its face value in interest . if that interest was approx 6.5 of the bond ' s selling price approx what was the bond ' s selling price ?

<gadget id="calculator">9 / 100</gadget>
<output>9/100 = around 0.09</output>

<gadget id="calculator">5_000 * (9/100)</gadget>
<output>450</output>

<gadget id="calculator">6.5 / 100</gadget>
<output>0.065</output>

<gadget id="calculator">450 / 0.065</gadget>
<output>6_923.076923</output>
<result>6_923.076923</result>

Choices:
A. 4063
B. 5325
C. 5351
D. 6000
E. 6923

divide(multiply(5000, divide(9, const_100)), divide(6.5, const_100))

Explanation: "interest = 0.09 * 5000 = 0.065 * selling price - - > selling price = 0.09 * 5000 / 0.065 - - > selling price = ~ 6,923 answer : e ."


Question: a train of 40 carriages , each of 60 meters length , when an engine also of 60 meters length is running at a speed of 60 kmph . in what time will the train cross a bridge 1.5 km long ?

<gadget id="calculator">40 + 1</gadget>
<output>41</output>

<gadget id="calculator">41 * 60</gadget>
<output>2_460</output>

<gadget id="calculator">2_460 / 1_000</gadget>
<output>123/50 = around 2.46</output>

<gadget id="calculator">(123/50) + 1.5</gadget>
<output>3.96</output>
<result>3.96</result>

Choices:
A. 6
B. 3
C. 4
D. 3.9
E. 3.6

add(divide(multiply(add(40, const_1), 60), const_1000), 1.5)

Explanation: d = 40 * 60 + 1500 = 3900 m t = 3900 / 60 * 18 / 5 = 234 sec = 3.9 mins answer : d


Question: ( 0.15 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.15 ) ( power 2 ) + 0.015 + ( 0.1 ) ( power 2 ) is :

<gadget id="calculator">0.15 ** 3</gadget>
<output>0.003375</output>

<gadget id="calculator">0.1 ** 3</gadget>
<output>0.001</output>

<gadget id="calculator">0.003375 - 0.001</gadget>
<output>0.002375</output>

<gadget id="calculator">0.15 ** 2</gadget>
<output>0.0225</output>

<gadget id="calculator">0.0225 + 0.015</gadget>
<output>0.0375</output>

<gadget id="calculator">0.1 ** 2</gadget>
<output>0.01</output>

<gadget id="calculator">0.0375 + 0.01</gadget>
<output>0.0475</output>

<gadget id="calculator">0.002375 / 0.0475</gadget>
<output>0.05</output>
<result>0.05</result>

Choices:
A. 0.68
B. 0.08
C. 0.05
D. 0.06
E. none of them

Explanation: "given expression = ( 0.15 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.15 ) ( power 2 ) + ( 0.15 x 0.1 ) + ( 0.1 ) ( power 2 ) = a ( power 3 ) - b ( power 3 ) / a ( power 2 ) + ab + b ( power 2 ) = ( a - b ) = ( 0.15 - 0.1 ) = 0.05 answer is c ."


Question: a retailer sells 7 shirts . the first 2 he sells for $ 38 and $ 42 . if the retailer wishes to sell the 7 shirts for an overall average price of over $ 50 , what must be the minimum average price of the remaining 5 shirts ?

<gadget id="calculator">7 * 50</gadget>
<output>350</output>

<gadget id="calculator">38 + 42</gadget>
<output>80</output>

<gadget id="calculator">350 - 80</gadget>
<output>270</output>

<gadget id="calculator">7 - 2</gadget>
<output>5</output>

<gadget id="calculator">270 / 5</gadget>
<output>54</output>
<result>54</result>

Choices:
A. $ 54.00
B. $ 57.00
C. $ 58.00
D. $ 60.50
E. $ 63.00

divide(subtract(multiply(7, 50), add(38, 42)), subtract(7, 2))

Explanation: first 2 shirts are sold for $ 38 and $ 42 = $ 80 . to get average price of $ 50 , total sale should be 7 * $ 50 = $ 350 so remaining 5 shirts to be sold for $ 350 - $ 80 = $ 270 answer should be 270 / 5 = $ 54.00 that is a


Question: a person crosses a 500 m long street in 4 minutes . what is his speed in km per hour ?

<gadget id="calculator">500 / 1_000</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">4 * 60</gadget>
<output>240</output>

<gadget id="calculator">240 / 3_600</gadget>
<output>1/15 = around 0.066667</output>

<gadget id="calculator">(1/2) / (1/15)</gadget>
<output>15/2 = around 7.5</output>
<result>15/2 = around 7.5</result>

Choices:
A. 7.5
B. 2.6
C. 3.9
D. 8.2
E. 2.7

divide(divide(500, const_1000), divide(multiply(4, const_60), const_3600))

Explanation: "distance = 500 meter time = 4 minutes = 4 x 60 seconds = 240 seconds speed = distance / time = 500 / 240 = 2.08 m / s = 2.08 ã — 18 / 5 km / hr = 7.5 km / hr answer : a"


Question: if a 10 percent deposit that has been paid toward the purchase of a certain product is $ 160 , how much more remains to be paid ?

<gadget id="calculator">100 / 10</gadget>
<output>10</output>

<gadget id="calculator">160 * 10</gadget>
<output>1_600</output>

<gadget id="calculator">1_600 - 160</gadget>
<output>1_440</output>
<result>1_440</result>

Choices:
A. $ 880
B. $ 990
C. $ 1,000
D. $ 1,100
E. $ 1,440

subtract(multiply(160, divide(const_100, 10)), 160)

Explanation: "10 / 100 p = 160 > > p = 160 * 100 / 10 = 1600 1600 - 160 = 1440 answer : e"


Question: if the perimeter of a rectangular garden is 600 m , its length when its breadth is 100 m is ?

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

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

Choices:
A. 227
B. 247
C. 200
D. 277
E. 121

Explanation: "2 ( l + 100 ) = 600 = > l = 200 m answer : c"


Question: you need to pick any number from ' 1 , 3 , 5 , 7 , 9 , 11 , 13 and 15 ' to make below equation true . ( ) + ( ) + ( ) = 30 can you solve it ?

<gadget id="calculator">factorial(3)</gadget>
<output>6</output>

<gadget id="calculator">11 + 6</gadget>
<output>17</output>

<gadget id="calculator">17 + 13</gadget>
<output>30</output>
<result>30</result>

Choices:
A. 29
B. 30
C. 31
D. 32
E. 33

Explanation: solution : 3 ! + 15 + 9 = 30 explanation : 3 ! = 3 * 2 * 1 = 6 6 + 15 + 9 = 30 answer b


Question: ram and shyam start a two - length swimming race at the same moment but from opposite ends of the pool . they swim in lanes at uniform speeds , but hardy is faster than andy . they 1 st pass at a point 18.5 m from the deep end and having completed one length each 1 is allowed to rest on the edge for exactly 45 sec . after setting off on the return length , the swimmers pass for the 2 nd time just 10.5 m from the shallow end . how long is the pool ?

<gadget id="calculator">18.5 * 2</gadget>
<output>37</output>

<gadget id="calculator">37 + 18.5</gadget>
<output>55.5</output>

<gadget id="calculator">55.5 - 10.5</gadget>
<output>45</output>
<result>45</result>

Choices:
A. 65
B. 60
C. 55
D. 50
E. 45

subtract(add(multiply(18.5, const_2), 18.5), 10.5)

Explanation: let x = length of pool at first meeting , combined distance = x at second meeting , combined distance = 3 x if andy swims 18.5 m of x , then he will swim 3 * 18.5 = 55.5 m of 3 x andy ' s total distance to second meeting = x + 10.5 m x + 10.5 = 55.5 m x = 45 m e


Question: what least number must besubtracted from 427398 so that remaining no . is divisible by 15 ?

Choices:
A. 725117481
B. 343564689
C. 454564690
D. 759900434
E. 656590009

subtract(subtract(subtract(multiply(multiply(multiply(427398, const_100), const_10), const_2), 427398), multiply(427398, const_100)), multiply(multiply(multiply(const_100, const_100), const_100), const_100))

Explanation: on dividing 427398 by 15 we get the remainder 3 , so 3 should be subtracted answer : option a


Question: in covering a distance of 48 km , abhay takes 2 hours more than sameer . if abhay doubles his speed , then he would take 1 hour less than sameer . abhay ' s speed is :

<gadget id="calculator">48 / 2</gadget>
<output>24</output>

<gadget id="calculator">48 - 24</gadget>
<output>24</output>

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

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

Choices:
A. 5 kmph
B. 6 kmph
C. 6.25 kmph
D. 7.5 kmph
E. 8 kmph

divide(subtract(48, divide(48, 2)), add(1, 2))

Explanation: "let abhay ' s speed be x km / hr . then , 48 / x - 48 / 2 x = 3 6 x = 48 x = 8 km / hr . answer : option e"


Question: the speed of a bus increases by 2 kmph after every one hour . if the distance travelled in the first one hour was 35 km , what was the total distance travelled in 12 hours ?

<gadget id="calculator">12 / 2</gadget>
<output>6</output>

<gadget id="calculator">12 - 1</gadget>
<output>11</output>

<gadget id="calculator">11 * 2</gadget>
<output>22</output>

<gadget id="calculator">2 * 35</gadget>
<output>70</output>

<gadget id="calculator">22 + 70</gadget>
<output>92</output>

<gadget id="calculator">6 * 92</gadget>
<output>552</output>
<result>552</result>

Choices:
A. 550
B. 500
C. 552
D. 560
E. 580

multiply(divide(12, 2), add(multiply(subtract(12, const_1), 2), multiply(2, 35)))

Explanation: dist 1 st hr = 35 km speed of bus by 2 kmph 2 nd hr = 37 km 3 rd hr = 39 km tot = 35 + 37 + 39 + . . . . ( 12 terms ) 12 / 2 ( 2 * 35 + ( 12 - 1 ) 2 ] = 6 * 92 = 552 answer c


Question: harkamal purchased 8 kg of grapes at the rate of 90 per kg and 9 kg of mangoes at the rate of 55 per kg . how much amount did he pay to the shopkeeper ?

<gadget id="calculator">8 * 90</gadget>
<output>720</output>

<gadget id="calculator">9 * 55</gadget>
<output>495</output>

<gadget id="calculator">720 + 495</gadget>
<output>1_215</output>
<result>1_215</result>

Choices:
A. 1055
B. 1215
C. 1065
D. 1070
E. 1080

Explanation: "cost of 8 kg grapes = 90 × 8 = 720 . cost of 9 kg of mangoes = 55 × 9 = 495 . total cost he has to pay = 720 + 495 = 1215 . b )"


Question: the sum of the fourth and twelfth term of an arithmetic progression is 20 . what is the sum of the first 16 terms of the arithmetic progression ?

<gadget id="calculator">20 * 16</gadget>
<output>320</output>

<gadget id="calculator">320 / 2</gadget>
<output>160</output>
<result>160</result>

Choices:
A. 300
B. 120
C. 150
D. 160
E. 270

Explanation: "n th term of a . p . is given by a + ( n - 1 ) d 4 th term = a + 3 d 12 th term = a + 11 d given a + 3 d + a + 11 d = 20 - - > 2 a + 14 d = 20 - - > a + 7 d = 10 sum of n term of a . p = n / 2 [ 2 a + ( n - 1 ) d ] subsitiuing n = 16 . . . we get 15 / 2 [ 2 a + 14 d ] = 16 [ a + 7 d ] = 16 * 10 = 160 . . . answer is d . . ."


Question: there are 3 red shoes & 7 green shoes . if two of red shoes are drawn what is the probability of getting red shoes

<gadget id="calculator">binomial(3, 2)</gadget>
<output>3</output>

<gadget id="calculator">3 + 7</gadget>
<output>10</output>

<gadget id="calculator">binomial(10, 2)</gadget>
<output>45</output>

<gadget id="calculator">3 / 45</gadget>
<output>1/15 = around 0.066667</output>
<result>1/15 = around 0.066667</result>

Choices:
A. 1 / 13
B. 1 / 14
C. 1 / 12
D. 1 / 15
E. 1 / 16

divide(choose(3, const_2), choose(add(3, 7), const_2))

Explanation: "taking 2 red shoe the probablity is 3 c 2 from 10 shoes probablity of taking 2 red shoe is 3 c 2 / 10 c 2 = 1 / 15 answer : d"


Question: it will take 16 days for mary to complete a certain task alone . she worked for 8 days before she was joined by her sister . both of them completed the remaining task in 2 and half days . if her sister had joined her when she started the task , how many days would it have taken ?

<gadget id="calculator">1 / 8</gadget>
<output>1/8 = around 0.125</output>

<gadget id="calculator">1 / 16</gadget>
<output>1/16 = around 0.0625</output>

<gadget id="calculator">(1/8) / (1/16)</gadget>
<output>2</output>

<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<result>5</result>

Choices:
A. 6
B. 8
C. 2
D. 5
E. 4

add(divide(divide(const_1, 8), divide(const_1, 16)), const_3)

Explanation: explanation : mary and her sister complete half work in 2.5 days = > they can complete whole work in 5 days answer : option d


Question: on dividing 73 by a number , the quotient is 9 and the remainder is 1 . find the divisor ?

<gadget id="calculator">73 / 9</gadget>
<output>73/9 = around 8.111111</output>

<gadget id="calculator">floor(73/9)</gadget>
<output>8</output>
<result>8</result>

Choices:
A. 8
B. 15
C. 16
D. 17
E. 18

Explanation: "d = ( d - r ) / q = ( 73 - 1 ) / 9 = 72 / 9 = 8 a )"


Question: shruti purchased several number of 3 articles p , q and r in the proportion 3 : 2 : 3 . if the unit costs of the articles p , q and r are 200 , rs . 90 and rs . 60 respectively , how many articles of q must have been purchased in the total purchases of rs . 4800 ?

<gadget id="calculator">3 * 200</gadget>
<output>600</output>

<gadget id="calculator">2 * 90</gadget>
<output>180</output>

<gadget id="calculator">600 + 180</gadget>
<output>780</output>

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

<gadget id="calculator">780 + 180</gadget>
<output>960</output>

<gadget id="calculator">4_800 / 960</gadget>
<output>5</output>

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

Choices:
A. 8
B. 10
C. 12
D. 14
E. 16

multiply(divide(4800, add(add(multiply(3, 200), multiply(2, 90)), multiply(3, 60))), 2)

Explanation: explanation : let the number of articles of types p , q and r be 3 a , 2 a and 3 a respectively . thus , we get , ( 200 x 3 a ) + ( 90 x 2 a ) + ( 60 x 3 a ) = 4800 960 a = 4800 a = 5 hence , the number of articles of type “ q ” = 2 x 5 = 10 answer b


Question: a boy multiplied 987 by a certain number and obtained 559981 as his answer . if in the answer both 9 are wrong and the other digits are correct , then the correct answer would be :

Choices:
A. 553681
B. 555181
C. 555681
D. 556581
E. 556881

multiply(subtract(subtract(divide(559981, 987), const_4), const_0_33), 987)

Explanation: 987 = 3 x 7 x 47 so , the required number must be divisible by each one of 3 , 7 , 47 553681 - > ( sum of digits = 28 , not divisible by 3 ) 555181 - > ( sum of digits = 25 , not divisible by 3 ) 555681 is divisible by 3 , 7 , 47 answer c


Question: the least number which when increased by 5 each divisible by each one of 24 , 32 , 36 and 54 is :

<gadget id="calculator">lcm(24, 32)</gadget>
<output>96</output>

<gadget id="calculator">lcm(96, 36)</gadget>
<output>288</output>

<gadget id="calculator">lcm(288, 54)</gadget>
<output>864</output>

<gadget id="calculator">864 - 5</gadget>
<output>859</output>
<result>859</result>

Choices:
A. 427
B. 859
C. 869
D. 4320
E. none of these

Explanation: solution required number = ( l . c . m . of 24 , 32 , 36 , 54 ) - 5 = 864 - 5 = 859 . answer b


Question: a certain company reported that the revenue on sales increased 40 % from 2000 to 2003 , and increased 80 % from 2000 to 2005 . what was the approximate percent increase in revenue for this store from 2003 to 2005 ?

<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>

<gadget id="calculator">1 + (4/5)</gadget>
<output>9/5 = around 1.8</output>

<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>

<gadget id="calculator">1 + (2/5)</gadget>
<output>7/5 = around 1.4</output>

<gadget id="calculator">(9/5) - (7/5)</gadget>
<output>2/5 = around 0.4</output>

<gadget id="calculator">(2/5) / (7/5)</gadget>
<output>2/7 = around 0.285714</output>

<gadget id="calculator">(2/7) * 100</gadget>
<output>200/7 = around 28.571429</output>
<result>200/7 = around 28.571429</result>

Choices:
A. 50 %
B. 40 %
C. 35 %
D. 32 %
E. 29 %

multiply(divide(subtract(add(const_1, divide(80, const_100)), add(const_1, divide(40, const_100))), add(const_1, divide(40, const_100))), const_100)

Explanation: "assume the revenue in 2000 to be 100 . then in 2003 it would be 140 and and in 2005 180 , so from 2003 to 2005 it increased by ( 180 - 140 ) / 140 = 40 / 140 = 2 / 7 = ~ 29 % . answer : e ."


Question: if the ratio of the sum of the first 6 terms of a g . p . to the sum of the first 3 terms of the g . p . is 65 , what is the common ratio of the g . p ?

<gadget id="calculator">65 - 1</gadget>
<output>64</output>

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">64 ** (1/3)</gadget>
<output>4</output>
<result>4</result>

Choices:
A. 4
B. 1 / 4
C. 2
D. 9
E. 1 / 9

power(subtract(65, const_1), divide(const_1, const_3))

Explanation: 65 = ( a 1 + a 2 + a 3 + a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) factorize the same terms 65 = 1 + ( a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) write every term with respect to r a 1 = a 1 a 2 = a 1 * r ^ 1 a 3 = a 1 * r ^ 2 . . . . . . . . . 65 = 1 + ( a 1 ( r ^ 3 + r ^ 4 + r ^ 5 ) ) / ( a 1 ( 1 + r ^ 1 + r ^ 2 ) ) 64 = ( r ^ 3 ( 1 + r ^ 1 + r ^ 2 ) ) / ( ( 1 + r ^ 1 + r ^ 2 ) ) 64 = r ^ 3 r = 4 a


Question: when jessica withdrew $ 200 from her bank account , her account balance decreased by 2 / 5 . if she deposits an amount equal to 1 / 3 of the remaining balance , what will be the final balance in her bank account ?

<gadget id="calculator">3 / 5</gadget>
<output>3/5 = around 0.6</output>

<gadget id="calculator">1 - (3/5)</gadget>
<output>2/5 = around 0.4</output>

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

<gadget id="calculator">500 - 200</gadget>
<output>300</output>

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>

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

<gadget id="calculator">300 * (4/3)</gadget>
<output>400</output>
<result>400</result>

Choices:
A. 300
B. 375
C. 400
D. 500
E. 575

multiply(subtract(divide(200, subtract(1, divide(const_3, 5))), 200), add(1, divide(1, 3)))

Explanation: "as per the question 200 = 2 a / 5 thus - a which is the total amount = 500 the amount thus left = 300 she then deposited 1 / 3 of 300 = 100 total amount in her account = 400 answer c"


Question: a man traveled a total distance of 1200 km . he traveled one - third of the whole trip by plane and the distance traveled by train is two - thirds of the distance traveled by bus . if he traveled by train , plane and bus , how many kilometers did he travel by bus ?

<gadget id="calculator">1_200 * 2</gadget>
<output>2_400</output>

<gadget id="calculator">2_400 / 3</gadget>
<output>800</output>

<gadget id="calculator">800 * 3</gadget>
<output>2_400</output>

<gadget id="calculator">2 + 3</gadget>
<output>5</output>

<gadget id="calculator">2_400 / 5</gadget>
<output>480</output>
<result>480</result>

Choices:
A. 400
B. 440
C. 480
D. 520
E. 560

divide(multiply(divide(multiply(1200, const_2), const_3), const_3), add(const_2, const_3))

Explanation: total distance traveled = 1200 km . distance traveled by plane = 400 km . distance traveled by bus = x distance traveled by train = 2 x / 3 x + 2 x / 3 + 400 = 1200 5 x / 3 = 800 x = 480 km the answer is c .


Question: in town x , 64 percent of the population are employed , and 40 percent of the population are employed males . what percent of the employed people in town x are females ?

<gadget id="calculator">64 - 40</gadget>
<output>24</output>

<gadget id="calculator">24 / 64</gadget>
<output>3/8 = around 0.375</output>

<gadget id="calculator">(3/8) * 100</gadget>
<output>75/2 = around 37.5</output>
<result>75/2 = around 37.5</result>

Choices:
A. 38 %
B. 25 %
C. 32 %
D. 40 %
E. 52 %

multiply(divide(subtract(64, 40), 64), const_100)

Explanation: "we are asked to find the percentage of females in employed people . total employed people 64 % , out of which 40 are employed males , hence 24 % are employed females . ( employed females ) / ( total employed people ) = 24 / 64 = 38 % answer : a ."


Question: a sells a cricket bat to b at a profit of 20 % . b sells it to c at a profit of 25 % . if c pays $ 237 for it , the cost price of the cricket bat for a is :

<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">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">(6/5) * (5/4)</gadget>
<output>3/2 = around 1.5</output>

<gadget id="calculator">237 / (3/2)</gadget>
<output>158</output>
<result>158</result>

Choices:
A. 150
B. 120
C. 158
D. 160
E. 210

divide(237, multiply(add(const_1, divide(20, const_100)), add(const_1, divide(25, const_100))))

Explanation: "125 % of 120 % of a = 237 125 / 100 * 120 / 100 * a = 237 a = 237 * 2 / 3 = 158 . answer c"


Question: how many numbers between 100 and 756 are divisible by 2 , 3 , and 7 together ?

<gadget id="calculator">2 * 3</gadget>
<output>6</output>

<gadget id="calculator">6 * 7</gadget>
<output>42</output>

<gadget id="calculator">756 / 42</gadget>
<output>18</output>

<gadget id="calculator">100 / 42</gadget>
<output>50/21 = around 2.380952</output>

<gadget id="calculator">18 - (50/21)</gadget>
<output>328/21 = around 15.619048</output>
<result>328/21 = around 15.619048</result>

Choices:
A. 112
B. 77
C. 267
D. 16
E. 99

subtract(divide(756, multiply(multiply(2, 3), 7)), divide(100, multiply(multiply(2, 3), 7)))

Explanation: "explanation : as the division is by 2 , 3 , 7 together , the numbers are to be divisible by : 2 * 3 * 7 = 42 the limits are 100 and 756 the first number divisible is 42 * 3 = 126 to find out the last number divisible by 42 within 756 : 756 / 42 = 18 hence , 42 * 16 = 756 is the last number divisible by 42 within 756 hence , total numbers divisible by 2 , 3 , 7 together are ( 18 â € “ 2 ) = 16 answer : d"


Question: if the sides of a cube are in the ratio 9 : 5 . what is the ratio of their diagonals ?

<gadget id="calculator">9 / 5</gadget>
<output>9/5 = around 1.8</output>
<result>9/5 = around 1.8</result>

Choices:
A. 9 : 5
B. 16 : 9
C. 4 :
D. 3 : 4
E. 3 : 8

Explanation: "explanation : diagonal of a cube = a √ 3 where a is side a 1 : a 2 = 9 : 5 d 1 : d 2 = 9 : 5 where √ 3 cancelled both side answer : a"


Question: a and b together do a work in 20 days . b and c together in 15 days and c and a in 12 days . so a , b and c together finish same work in how many days ?

<gadget id="calculator">1 / 12</gadget>
<output>1/12 = around 0.083333</output>

<gadget id="calculator">1 / 20</gadget>
<output>1/20 = around 0.05</output>

<gadget id="calculator">1 / 15</gadget>
<output>1/15 = around 0.066667</output>

<gadget id="calculator">(1/20) + (1/15)</gadget>
<output>7/60 = around 0.116667</output>

<gadget id="calculator">(1/12) + (7/60)</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">(1/5) / 2</gadget>
<output>1/10 = around 0.1</output>

<gadget id="calculator">1 / (1/10)</gadget>
<output>10</output>
<result>10</result>

Choices:
A. 12
B. 15
C. 8
D. 10
E. 11

inverse(divide(add(inverse(12), add(inverse(20), inverse(15))), const_2))

Explanation: ( a + b ) work in 1 day = 1 / 20 , ( b + c ) work in 1 days = 1 / 15 . , ( c + a ) work in 1 days = 1 / 12 ( 1 ) adding = 2 [ a + b + c ] in 1 day work = [ 1 / 20 + 1 / 15 + 1 / 12 ] = 1 / 5 ( a + b + c ) work in 1 day = 1 / 10 so , all three together finish work in 10 days answer d


Question: if a train , travelling at a speed of 180 kmph , crosses a pole in 6 sec , then the length of train is ?

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>

<gadget id="calculator">180 * (5/18)</gadget>
<output>50</output>

<gadget id="calculator">50 * 6</gadget>
<output>300</output>
<result>300</result>

Choices:
A. 300
B. 125
C. 288
D. 266
E. 121

Explanation: d = 180 * 5 / 18 * 6 = 300 m answer : a


Question: a dealer purchases 15 articles for rs . 25 and sells 12 articles for rs . 36 . find the profit percentage ?

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

<gadget id="calculator">36 * 5</gadget>
<output>180</output>

<gadget id="calculator">25 * 4</gadget>
<output>100</output>

<gadget id="calculator">180 - 100</gadget>
<output>80</output>
<result>80</result>

Choices:
A. 80 %
B. 50 %
C. 59 %
D. 40 %
E. 53 %

subtract(multiply(36, add(const_4, const_1)), multiply(25, const_4))

Explanation: "l . c . m of 15 and 12 = 60 cp of 60 articles = rs . 100 ( 25 * 4 ) sp of 60 articles = rs . 180 ( 36 * 5 ) profit percentage = ( 180 - 100 ) / 100 * 100 = 80 % answer : a"


Question: a can do a piece of work 60 days . b can do work in 90 days . in how many days they will complete the work together ?

<gadget id="calculator">1 / 60</gadget>
<output>1/60 = around 0.016667</output>

<gadget id="calculator">1 / 90</gadget>
<output>1/90 = around 0.011111</output>

<gadget id="calculator">(1/60) + (1/90)</gadget>
<output>1/36 = around 0.027778</output>

<gadget id="calculator">1 / (1/36)</gadget>
<output>36</output>
<result>36</result>

Choices:
A. 36 days
B. 32 days
C. 19 days
D. 17 days
E. 18 days

divide(const_1, add(divide(const_1, 60), divide(const_1, 90)))

Explanation: lcm = 180 , ratio = 60 : 90 = 2 : 3 no of days = 180 / ( 2 + 3 ) = 180 / 5 = 36 days answer : a


Question: what least number should be added to 1536 , so that the sum is completely divisible by 21 ?

<gadget id="calculator">1_536 % 21</gadget>
<output>3</output>

<gadget id="calculator">21 - 3</gadget>
<output>18</output>
<result>18</result>

Choices:
A. 16
B. 17
C. 18
D. 19
E. 20

Explanation: "1536 ÷ 21 = 73 reminder - 3 3 + 18 = 21 hence 18 should be added to 1536 so that the sum will be divisible by 21 answer : c"


Question: gary drove from point a to point b at 60 km / h . on his way back he took a train travelling at 110 km / h and therefore his trip back lasted 5 hours less . what is the distance ( in km ) between a and b ?

<gadget id="calculator">110 * 5</gadget>
<output>550</output>

<gadget id="calculator">110 - 60</gadget>
<output>50</output>

<gadget id="calculator">550 / 50</gadget>
<output>11</output>

<gadget id="calculator">60 * 11</gadget>
<output>660</output>
<result>660</result>

Choices:
A. 600 .
B. 630 .
C. 660 .
D. 690 .
E. 720 .

multiply(60, divide(multiply(110, 5), subtract(110, 60)))

Explanation: distance = speed * time d 1 = s 1 t 1 d 2 = s 2 t 2 the distance from point a to point b is the same for each trip so , d 1 = d 2 and t 2 = t 1 - 5 thus , s 1 t 1 = s 2 t 2 60 t 1 = s 2 ( t 1 - 5 ) t 1 = 11 60 * 11 = 660 answer : c


Question: when n is divided by 19 , the remainder is 7 . find thee difference between previous remainder and the remainder when 18 n is divided by 9 ?

<gadget id="calculator">18 % 9</gadget>
<output>0</output>

<gadget id="calculator">7 - 0</gadget>
<output>7</output>
<result>7</result>

Choices:
A. 7
B. 5
C. 0
D. 3
E. 9

Explanation: let n = 7 ( leaves a remainder of 7 when divided by 19 ) 18 n = 18 ( 7 ) = 126 , which leaves a remainder of 0 when divided by 9 . difference = 7 - 0 = 7 . answer a


Question: solution p is 20 percent lemonade and 80 percent carbonated water by volume ; solution q is 45 percent lemonade and 55 percent carbonated water by volume . if a mixture of pq contains 75 percent carbonated water , what percent of the volume of the mixture is p ?

<gadget id="calculator">75 / 100</gadget>
<output>3/4 = around 0.75</output>

<gadget id="calculator">55 / 100</gadget>
<output>11/20 = around 0.55</output>

<gadget id="calculator">(3/4) - (11/20)</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>

<gadget id="calculator">(4/5) - (3/4)</gadget>
<output>1/20 = around 0.05</output>

<gadget id="calculator">(1/5) + (1/20)</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">(1/5) / (1/4)</gadget>
<output>4/5 = around 0.8</output>

<gadget id="calculator">(4/5) * 100</gadget>
<output>80</output>
<result>80</result>

Choices:
A. 40 %
B. 50 %
C. 60 %
D. 80 %
E. 90 %

multiply(divide(subtract(divide(75, const_100), divide(55, const_100)), add(subtract(divide(75, const_100), divide(55, const_100)), subtract(divide(80, const_100), divide(75, const_100)))), const_100)

Explanation: "75 % is 5 % - points below 80 % and 20 % - points above 55 % . so the ratio of solution p to solution q is 4 : 1 . mixture p is 4 / 5 = 80 % of the volume of mixture pq . the answer is d ."


Question: the jogging track in a sports complex is 1000 meters in circumference . deepak and his wife start from the same point and walk in opposite directions at 20 km / hr and 15 km / hr respectively . they will meet for the first time in ?

<gadget id="calculator">20 + 15</gadget>
<output>35</output>
<result>35</result>

Choices:
A. 50 min
B. 40 min
C. 35 min
D. 25 min
E. 20 min

Explanation: "clearly , the two will meet when they are 1000 m apart to be 20 + 15 = 35 km apart , they take 1 hour to be 1000 m apart , they take 35 * 1000 / 1000 = 35 min . answer is c"


Question: the average weight of a class of 24 students is 35 kg . if the weight of the teacher be included , the average rises by 400 g . the weight of the teacher is :

<gadget id="calculator">400 / 1_000</gadget>
<output>2/5 = around 0.4</output>

<gadget id="calculator">35 + (2/5)</gadget>
<output>177/5 = around 35.4</output>

<gadget id="calculator">24 + 1</gadget>
<output>25</output>

<gadget id="calculator">(177/5) * 25</gadget>
<output>885</output>

<gadget id="calculator">24 * 35</gadget>
<output>840</output>

<gadget id="calculator">885 - 840</gadget>
<output>45</output>
<result>45</result>

Choices:
A. 45
B. 46
C. 47
D. 48
E. 49

subtract(multiply(add(35, divide(400, const_1000)), add(24, const_1)), multiply(24, 35))

Explanation: weight of the teacher = ( 35.4 x 25 - 35 x 24 ) kg = 45 kg . answer : a


Question: the contents of a certain box consist of 14 apples and 24 oranges . how many oranges must be removed from the box so that 70 percent of the pieces of fruit in the box will be apples ?

<gadget id="calculator">14 + 24</gadget>
<output>38</output>

<gadget id="calculator">70 / 100</gadget>
<output>7/10 = around 0.7</output>

<gadget id="calculator">14 / (7/10)</gadget>
<output>20</output>

<gadget id="calculator">38 - 20</gadget>
<output>18</output>
<result>18</result>

Choices:
A. 18
B. 6
C. 14
D. 17
E. 20

subtract(add(14, 24), divide(14, divide(70, const_100)))

Explanation: "the objective here is that 70 % of the fruit in the box should be apples . now , there are 14 apples at start and there is no talk of removing any apples , so number of apples should remain 14 and they should constitute 70 % of total fruit , so total fruit = 14 / 0.7 = 20 so we should have 20 - 14 = 6 oranges . right now , there are 24 oranges , so to get to 6 oranges , we should remove 24 - 6 = 18 oranges . answer a"


Question: mary ' s income is 60 percent more than tim ' s income , and tim ' s income is 40 percent less than juan ' s income . what percent of juan ' s income is mary ' s income ?

<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">60 / 100</gadget>
<output>3/5 = around 0.6</output>

<gadget id="calculator">1 + (3/5)</gadget>
<output>8/5 = around 1.6</output>

<gadget id="calculator">(3/5) * (8/5)</gadget>
<output>24/25 = around 0.96</output>

<gadget id="calculator">(24/25) * 100</gadget>
<output>96</output>
<result>96</result>

Choices:
A. 124 %
B. 120 %
C. 96 %
D. 80 %
E. 64 %

multiply(multiply(subtract(const_1, divide(40, const_100)), add(const_1, divide(60, const_100))), const_100)

Explanation: "juan ' s income = 100 ( assume ) ; tim ' s income = 60 ( 40 percent less than juan ' s income ) ; mary ' s income = 96 ( 60 percent more than tim ' s income ) . thus , mary ' s income ( 96 ) is 96 % of juan ' s income ( 100 ) . answer : c"


Question: a and b are two circles . the radius of a is four times as large as the diameter of b . what is the ratio between the areas of the circles ?

<gadget id="calculator">1 ** 2</gadget>
<output>1</output>

<gadget id="calculator">2 * 4</gadget>
<output>8</output>

<gadget id="calculator">8 ** 2</gadget>
<output>64</output>

<gadget id="calculator">1 / 64</gadget>
<output>1/64 = around 0.015625</output>
<result>1/64 = around 0.015625</result>

Choices:
A. 1 : 8 .
B. 1 : 2 .
C. 1 : 24 .
D. 1 : 64 .
E. 1 : 6 .

divide(power(const_1, const_2), power(multiply(const_2, const_4), const_2))

Explanation: given : the radius of a is 4 times as large as the diameter of b . = > r ( a ) = 4 * d ( b ) = 4 * 2 * r ( b ) = 8 r ( b ) . the radius are in ratio of 1 : 8 thus the area will be in the ratio of square of radius . 1 : 64 . hence d .


Question: a can run 192 metre in 28 seconds and b in 32 seconds . by what distance a beat b ?

<gadget id="calculator">192 / 32</gadget>
<output>6</output>

<gadget id="calculator">6 * 28</gadget>
<output>168</output>

<gadget id="calculator">192 - 168</gadget>
<output>24</output>
<result>24</result>

Choices:
A. 38 metre
B. 28 metre
C. 24 metre
D. 15 metre
E. 28 metre

subtract(192, multiply(divide(192, 32), 28))

Explanation: "clearly , a beats b by 4 seconds now find out how much b will run in these 4 seconds speed of b = distance / time taken by b = 192 / 32 = 6 m / s distance covered by b in 4 seconds = speed ã — time = 6 ã — 4 = 24 metre i . e . , a beat b by 24 metre answer is c"


Question: a girl scout was selling boxes of cookies . in a month , she sold both boxes of chocolate chip cookies ( $ 1.25 each ) and boxes of plain cookies ( $ 0.75 each ) . altogether , she sold 1,585 boxes for a combined value of $ 1 , 585.75 . how many boxes of plain cookies did she sell ?

<gadget id="calculator">1_000 + 585.75</gadget>
<output>1_585.75</output>

<gadget id="calculator">1_585.75 / 2</gadget>
<output>792.875</output>
<result>792.875</result>

Choices:
A. 0
B. 233
C. 500
D. 695
E. 791

Explanation: "let # plain cookies sold be x then # chocolate cookies = ( total cookies - x ) equating for x ( 0.75 ) * x + ( 1.25 ) * ( 1585 - x ) = 1585.75 = > x = 791 e"


Question: a straight line in the xy - plane has a slope of 2 and a y - intercept of 2 . on this line , what is the x - coordinate of the point whose y - coordinate is 550 ?

<gadget id="calculator">550 - 2</gadget>
<output>548</output>

<gadget id="calculator">548 / 2</gadget>
<output>274</output>
<result>274</result>

Choices:
A. 249
B. 498
C. 676
D. 823
E. 274

Explanation: "slope of 2 and a y - intercept of 2 y - coordinate is 550 y = 2 x + 2 548 = 2 x x = 274 answer : e . 274"


Question: if xy = 4 , x / y = 16 , for positive numbers x and y , y = ?

<gadget id="calculator">4 / 16</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">(1/4) ** (1/2)</gadget>
<output>1/2 = around 0.5</output>
<result>1/2 = around 0.5</result>

Choices:
A. 1 / 2
B. 2
C. 1 / 3
D. 3
E. 1 / 6

Explanation: "very easy question . 2 variables and 2 easy equations . xy = 4 - - - > x = 4 / y - ( i ) x / y = 16 - - - > replacing ( i ) here - - - > 4 / ( y ^ 2 ) = 16 - - - > y ^ 2 = 4 / 16 = 1 / 4 - - - > y = 1 / 2 or - 1 / 2 the question states that x and y are positive integers . therefore , y = 1 / 2 is the answer . answer a ."


Question: if a boat is rowed downstream for 24 km in 4 hours and upstream for 48 km in 24 hours , what is the speed of the boat and the river ?

<gadget id="calculator">48 / 24</gadget>
<output>2</output>

<gadget id="calculator">24 / 4</gadget>
<output>6</output>

<gadget id="calculator">2 + 6</gadget>
<output>8</output>

<gadget id="calculator">8 / 2</gadget>
<output>4</output>
<result>4</result>

Choices:
A. 4 , 3
B. 4 , 4
C. 3 , 3
D. 4 , 5
E. 4 , 2

divide(add(divide(48, 24), divide(24, 4)), const_2)

Explanation: "explanation : if x : speed of boats man in still water y : speed of the river downstream speed ( ds ) = x + y upstream speed ( us ) = x â € “ y x = ( ds + us ) / 2 y = ( ds â € “ us ) / 2 in the above problem ds = 6 ; us = 2 x = ( 6 + 2 ) / 2 = 8 / 2 = 4 km / hr y = ( 6 - 2 ) / 2 = 4 / 2 = 2 km / hr answer : e"


Question: the average ( arithmetic mean ) of all scores on a certain algebra test was 90 . if the average of the 8 male students ’ grades was 86 , and the average of the female students ’ grades was 92 , how many female students took the test ?

<gadget id="calculator">90 * 8</gadget>
<output>720</output>

<gadget id="calculator">86 * 8</gadget>
<output>688</output>

<gadget id="calculator">720 - 688</gadget>
<output>32</output>

<gadget id="calculator">92 - 90</gadget>
<output>2</output>

<gadget id="calculator">32 / 2</gadget>
<output>16</output>
<result>16</result>

Choices:
A. 8
B. 9
C. 10
D. 11
E. 16

divide(subtract(multiply(90, 8), multiply(86, 8)), subtract(92, 90))

Explanation: "total marks of male = m total marks of female = f number of males = 8 number of females = f given : ( m + f ) / ( 8 + f ) = 90 - - - - - - - - - - - - - 1 also given , m / 8 = 86 thus m = 688 - - - - - - - - 2 also , f / f = 92 thus f = 92 f - - - - - - - - - 3 put 2 and 3 in 1 : we get ( 688 + 92 f ) / ( 8 + f ) = 90 solving this we get f = 16 ans : e"


Question: a cycle is bought for rs . 800 and sold for rs . 1080 , find the gain percent ?

<gadget id="calculator">1_080 - 800</gadget>
<output>280</output>

<gadget id="calculator">280 / 800</gadget>
<output>7/20 = around 0.35</output>

<gadget id="calculator">(7/20) * 100</gadget>
<output>35</output>
<result>35</result>

Choices:
A. 22
B. 20
C. 35
D. 88
E. 11

multiply(divide(subtract(1080, 800), 800), const_100)

Explanation: "800 - - - - 180 100 - - - - ? = > 35 % answer : c"


Question: a train running at the speed of 60 km / hr crosses a pole in 6 seconds . find the length of the train .

<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>

Choices:
A. 150
B. 278
C. 100
D. 776
E. 191

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

Explanation: ": speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 6 = 100 meter answer : c"


Question: laura took out a charge account at the general store and agreed to pay 8 % simple annual interest . if she charges $ 35 on her account in january , how much will she owe a year later , assuming she does not make any additional charges or payments ?

<gadget id="calculator">8 / 100</gadget>
<output>2/25 = around 0.08</output>

<gadget id="calculator">(2/25) * 35</gadget>
<output>14/5 = around 2.8</output>

<gadget id="calculator">(14/5) + 35</gadget>
<output>189/5 = around 37.8</output>
<result>189/5 = around 37.8</result>

Choices:
A. $ 2.10
B. $ 37.10
C. $ 37.16
D. $ 37.8
E. $ 38.80

add(multiply(divide(8, const_100), 35), 35)

Explanation: "principal that is amount taken by laura at year beginning = 35 $ rate of interest = 8 % interest = ( 8 / 100 ) * 35 = 2.8 $ total amount that laura owes a year later = 35 + 2.8 = 37.8 $ answer d"


Question: a man purchased 3 blankets @ rs . 100 each , 4 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 150 . find the unknown rate of two blankets ?

<gadget id="calculator">10 * 150</gadget>
<output>1_500</output>

<gadget id="calculator">3 * 100</gadget>
<output>300</output>

<gadget id="calculator">4 * 150</gadget>
<output>600</output>

<gadget id="calculator">300 + 600</gadget>
<output>900</output>

<gadget id="calculator">1_500 - 900</gadget>
<output>600</output>
<result>600</result>

Choices:
A. 600
B. 350
C. 450
D. 470
E. 500

subtract(multiply(const_10, 150), add(multiply(3, 100), multiply(4, 150)))

Explanation: explanation : 10 * 150 = 1500 3 * 100 + 4 * 150 = 900 1500 – 900 = 600 a


Question: rates for having a manuscript typed at a certain typing service are $ 6 per page for the first time a page is typed and $ 4 per page each time a page is revised . if a certain manuscript has 100 pages , of which 40 were revised only once , 10 were revised twice , and the rest required no revisions , what was the total cost of having the manuscript typed ?

<gadget id="calculator">100 * 6</gadget>
<output>600</output>

<gadget id="calculator">40 * 4</gadget>
<output>160</output>

<gadget id="calculator">600 + 160</gadget>
<output>760</output>

<gadget id="calculator">10 * 4</gadget>
<output>40</output>

<gadget id="calculator">40 * 2</gadget>
<output>80</output>

<gadget id="calculator">760 + 80</gadget>
<output>840</output>
<result>840</result>

Choices:
A. $ 850
B. $ 840
C. $ 860
D. $ 870
E. $ 880

add(add(multiply(100, 6), multiply(40, 4)), multiply(multiply(10, 4), const_2))

Explanation: "50 pages typed 1 x 40 pages typed 2 x ( original + one revision ) 10 pages typed 3 x ( original + two revisions ) 50 ( 6 ) + 40 ( 6 + 4 ) + 10 ( 6 + 4 + 4 ) = 300 + 400 + 140 = 840 answer - b"


Question: a gambler has won 40 % of his 30 poker games for the week so far . if , all of a sudden , his luck changes and he begins winning 70 % of the time , how many more games must he play to end up winning 60 % of all his games for the week ?

<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>

<gadget id="calculator">30 * (3/5)</gadget>
<output>18</output>

<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>

<gadget id="calculator">30 * (2/5)</gadget>
<output>12</output>

<gadget id="calculator">18 - 12</gadget>
<output>6</output>

<gadget id="calculator">70 / 100</gadget>
<output>7/10 = around 0.7</output>

<gadget id="calculator">(7/10) - (3/5)</gadget>
<output>1/10 = around 0.1</output>

<gadget id="calculator">6 / (1/10)</gadget>
<output>60</output>
<result>60</result>

Choices:
A. 36
B. 42
C. 48
D. 54
E. 60

divide(subtract(multiply(30, divide(60, const_100)), multiply(30, divide(40, const_100))), subtract(divide(70, const_100), divide(60, const_100)))

Explanation: let x be the number of additional games the gambler needs to play . 0.4 ( 30 ) + 0.7 x = 0.6 ( x + 30 ) 0.1 x = 6 x = 60 the answer is e .


Question: a is 30 % more efficient than b . how much time they will working together take to complete a job which a alone could have done in 23 days ?

<gadget id="calculator">1 / 23</gadget>
<output>1/23 = around 0.043478</output>

<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>

<gadget id="calculator">(3/10) + 1</gadget>
<output>13/10 = around 1.3</output>

<gadget id="calculator">(13/10) * 23</gadget>
<output>299/10 = around 29.9</output>

<gadget id="calculator">1 / (299/10)</gadget>
<output>10/299 = around 0.033445</output>

<gadget id="calculator">(1/23) + (10/299)</gadget>
<output>1/13 = around 0.076923</output>

<gadget id="calculator">1 / (1/13)</gadget>
<output>13</output>
<result>13</result>

Choices:
A. 25 days
B. 13 days
C. 14 days
D. 20 days
E. 15 days

inverse(add(divide(const_1, 23), divide(const_1, multiply(add(divide(30, const_100), const_1), 23))))

Explanation: "the ratio of times taken by a and b = 100 : 130 = 10 : 13 suppose b can do work in x days then 10 : 13 : : 23 : x x = ( 23 * 13 ) / 10 x = 299 / 10 a ' s 1 day ' s work = 1 / 23 b ' s 1 day ' s work = 10 / 299 ( a + b ) ' s 1 day ' s work = 1 / 23 + 10 / 299 = 23 / 299 = 1 / 13 a and b together can do work in 13 days answer ( b )"


Question: this year , mbb consulting fired 6 % of its employees and left remaining employee salaries unchanged . sally , a first - year post - mba consultant , noticed that that the average ( arithmetic mean ) of employee salaries at mbb was 10 % more after the employee headcount reduction than before . the total salary pool allocated to employees after headcount reduction is what percent of that before the headcount reduction ?

<gadget id="calculator">100 * 10</gadget>
<output>1_000</output>

<gadget id="calculator">100 + 1_000</gadget>
<output>1_100</output>

<gadget id="calculator">100 - 6</gadget>
<output>94</output>

<gadget id="calculator">94 + 4</gadget>
<output>98</output>

<gadget id="calculator">1_100 * 98</gadget>
<output>107_800</output>

<gadget id="calculator">107_800 / 1_000</gadget>
<output>539/5 = around 107.8</output>
<result>539/5 = around 107.8</result>

Choices:
A. 98.5 %
B. 100.0 %
C. 102.8 %
D. 103.4 %
E. 105.0 %

divide(multiply(add(const_100, multiply(const_100, 10)), add(subtract(const_100, 6), const_4)), multiply(const_100, 10))

Explanation: "100 employees getting 1000 $ avg , so total salary for 100 ppl = 100000 6 % reduction in employees lead to 94 employees and a salary increase of 10 % of previous avg salary thus the new avg salary is = 10 % ( 1000 ) + 1000 = 1100 so total salary of 94 employees is 94 * 1100 = 103400 now the new salary is more than previous salary by x % . x = ( 103400 / 100000 ) * 100 = 103.4 % so the answer is d"


Question: find the cost of fencing around a circular field of diameter 12 m at the rate of rs . 3.50 a meter ?

<gadget id="calculator">12 / 2</gadget>
<output>6</output>

<gadget id="calculator">2 * pi * 6</gadget>
<output>12*pi = around 37.699112</output>

<gadget id="calculator">(12*pi) * 3.5</gadget>
<output>42.0*pi = around 131.946891</output>
<result>42.0*pi = around 131.946891</result>

Choices:
A. 131.95
B. 132.9
C. 140.33
D. 123.4
E. 190.4

Explanation: "2 * 22 / 7 * 6 = 37.7 37.7 * 3 1 / 2 = rs . 131.95 answer : a"


Question: a group of 55 adults and 70 children go for trekking . if there is meal for either 70 adults or 90 children and if 28 adults have their meal , find the total number of children that can be catered with the remaining food .

<gadget id="calculator">70 - 28</gadget>
<output>42</output>

<gadget id="calculator">90 / 70</gadget>
<output>9/7 = around 1.285714</output>

<gadget id="calculator">42 * (9/7)</gadget>
<output>54</output>
<result>54</result>

Choices:
A. 33
B. 54
C. 18
D. 17
E. 01

multiply(subtract(70, 28), divide(90, 70))

Explanation: "explanation : as there is meal for 70 adults and 28 have their meal , the meal left can be catered to 42 adults . now , 70 adults = 90 children 7 adults = 9 children therefore , 42 adults = 54 children hence , the meal can be catered to 54 children . answer : b"


Question: a side of beef lost 25 percent of its weight in processing . if the side of beef weighed 540 pounds after processing , how many pounds did it weigh before processing ?

<gadget id="calculator">540 * 100</gadget>
<output>54_000</output>

<gadget id="calculator">100 - 25</gadget>
<output>75</output>

<gadget id="calculator">54_000 / 75</gadget>
<output>720</output>
<result>720</result>

Choices:
A. 191
B. 355
C. 720
D. 840
E. 1,560

divide(multiply(540, const_100), subtract(const_100, 25))

Explanation: "let weight of side of beef before processing = x ( 75 / 100 ) * x = 540 = > x = ( 540 * 100 ) / 75 = 720 answer c"


Question: when a random experiment is conducted , the probability that event a occurs is 1 / 3 . if the random experiment is conducted 5 independent times , what is the probability that event a occurs exactly twice ?

<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>

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

Choices:
A. 5 / 243
B. 25 / 243
C. 64 / 243
D. 80 / 243
E. 16 / 17

Explanation: one case is : 1 / 3 * 1 / 3 * 2 / 3 * 2 / 3 * 2 / 3 = 2 ^ 3 / 3 ^ 5 we have 5 ! / 2 ! * 3 ! = 10 such cases so , 2 ^ 3 * 10 / 3 ^ 5 = 80 / 243 answer : d .