Question: the area of a square land is a square feet and the perimeter is p feet . if 5 a = 10 p + 45 , what is the perimeter of the land , in feet ?

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

<gadget id="calculator">40 / 5</gadget>
<output>8</output>

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

<gadget id="calculator">45 / 5</gadget>
<output>9</output>

<gadget id="calculator">9 * 4</gadget>
<output>36</output>

<gadget id="calculator">64 + 36</gadget>
<output>100</output>

<gadget id="calculator">100 ** (1/2)</gadget>
<output>10</output>

<gadget id="calculator">8 + 10</gadget>
<output>18</output>

<gadget id="calculator">18 / 2</gadget>
<output>9</output>
<result>36</result>

Choices:
A. 18
B. 56
C. 40
D. 36
E. 64

multiply(divide(add(divide(multiply(10, const_4), 5), sqrt(add(power(divide(multiply(10, const_4), 5), const_2), multiply(divide(45, 5), const_4)))), const_2), const_4)

Explanation: you can also solve this via using the given numbers in the answer choices ! of course you need to be aware of the basic properties as outlined by the other posts above ( a = x ^ 2 and p = 4 x ) starting with b you will notice that x = 14 is way too big for your area ( 14 ^ 2 ) and will not satisfy : 5 a = 10 p + 45 or a = 2 p + 9 - - > eliminate b and e now pick d ( its either too big , then its a , or too small then you know its c or it is b itsself ) and picking d indeed solves the problem ! ( 36 / 4 - - > 9 ; a = 9 ^ 2 = 81 and 81 = 2 x 36 + 9 )


Question: a cube of edge 16 cm is immersed completely in a rectangular vessel containing water . if the dimensions of the base of vessel are 20 cm * 15 cm , find the rise in water level ?

<gadget id="calculator">16 ** 3</gadget>
<output>4_096</output>

<gadget id="calculator">20 * 15</gadget>
<output>300</output>

<gadget id="calculator">4_096 / 300</gadget>
<output>1_024/75 = around 13.653333</output>
<result>1_024/75 = around 13.653333</result>

Choices:
A. 6 cm
B. 8.25 cm
C. 13.65 cm
D. 15.12 cm
E. 20.62 cm

Explanation: "increase in volume = volume of the cube = 16 * 16 * 16 cm ^ 3 rise in water level = volume / area = 16 * 16 * 16 / 20 * 15 = 13.65 cm answer is c"


Question: find the value of ( 45 + 23 / 89 ) × 89

<gadget id="calculator">23 / 89</gadget>
<output>23/89 = around 0.258427</output>

<gadget id="calculator">(23/89) + 45</gadget>
<output>4_028/89 = around 45.258427</output>

<gadget id="calculator">(4_028/89) * 89</gadget>
<output>4_028</output>
<result>4_028</result>

Choices:
A. 4028
B. 4026
C. 4248
D. 4538
E. 9028

Explanation: "= ( 45 + 23 / 89 ) × 89 = ( 4005 + 23 ) / 89 × 89 = 4028 / 89 × 89 = 4028 answer is a ."


Question: the average age of father and his two sons is 24 years . 5 years ago , the average age of the two sons was 15 years . if the difference between the ages of the two sons is 4 years , what is the present age of the father ?

<gadget id="calculator">24 * 3</gadget>
<output>72</output>

<gadget id="calculator">15 * 2</gadget>
<output>30</output>

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

<gadget id="calculator">30 + 10</gadget>
<output>40</output>

<gadget id="calculator">72 - 40</gadget>
<output>32</output>
<result>32</result>

Choices:
A. 45
B. 32
C. 47
D. 48
E. 49

subtract(multiply(24, const_3), add(multiply(15, const_2), multiply(5, const_2)))

Explanation: the total present age of father and two sons is 3 x 24 = 72 yrs the total present age of sons is ( 15 + 5 ) x 2 = 40 years so , present age of father is 72 â € “ 40 = 32 yrs answer b


Question: a caterer ordered 225 ice - cream bars and 125 sundaes . if the total price was $ 200.00 and the price of each ice - cream bar was $ 0.60 , what was the price of each sundae ?

<gadget id="calculator">225 * 0.6</gadget>
<output>135</output>

<gadget id="calculator">200 - 135</gadget>
<output>65</output>

<gadget id="calculator">65 / 125</gadget>
<output>13/25 = around 0.52</output>
<result>13/25 = around 0.52</result>

Choices:
A. $ 0.52
B. $ 0.80
C. $ 1.00
D. $ 1.20
E. $ 1.60

divide(subtract(200, multiply(225, 0.6)), 125)

Explanation: let price of a sundae = s price of ice cream bar = . 6 $ 225 * . 6 + 125 * s = 200 = > 125 * s = 65 = > s = 0.52 answer a


Question: a no . when divided by the sum of 555 and 445 gives 2 times their difference as quotient & 50 as remainder . find the no . is ?

<gadget id="calculator">555 + 445</gadget>
<output>1_000</output>

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

<gadget id="calculator">555 - 445</gadget>
<output>110</output>

<gadget id="calculator">2_000 * 110</gadget>
<output>220_000</output>

<gadget id="calculator">220_000 + 50</gadget>
<output>220_050</output>
<result>220_050</result>

Choices:
A. 145646
B. 236578
C. 645353
D. 456546
E. 220050

add(multiply(multiply(add(555, 445), 2), subtract(555, 445)), 50)

Explanation: "( 555 + 445 ) * 2 * 110 + 50 = 220000 + 50 = 220050 e"


Question: if p and q are prime numbers , how many divisors does the product p ^ 4 * q ^ 5 have ?

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

<gadget id="calculator">5 + 1</gadget>
<output>6</output>

<gadget id="calculator">5 * 6</gadget>
<output>30</output>
<result>30</result>

Choices:
A. 30
B. 40
C. 45
D. 50
E. 56

multiply(add(4, const_1), add(5, const_1))

Explanation: when a number n = a ^ x * b ^ y , where a and b are prime numbers , and x , y are positive integers , the number of divisors of n = ( x + 1 ) ( y + 1 ) therefore , the answer is a . 5 * 6 = 30


Question: if 20 % of a number = 300 , then 120 % of that number will be ?

<gadget id="calculator">120 * 300</gadget>
<output>36_000</output>

<gadget id="calculator">36_000 / 20</gadget>
<output>1_800</output>
<result>1_800</result>

Choices:
A. 20
B. 120
C. 360
D. 1800
E. 1820

Explanation: "let the number x . then , 20 % of x = 300 x = ( 300 * 100 ) / 20 = 1500 120 % of x = ( 120 / 100 * 1500 ) = 1800 . answer : d"


Question: a contractor undertook to do a certain piece of work in 6 days . he employed certain number of men , but 5 of them being absent from the very first day , the rest could finish the work in 10 days . the number of men originally employed were :

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

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

Choices:
A. 12
B. 10
C. 13
D. 11
E. none of these

Explanation: explanation : let there be x men at the beginning . less men , more days ( indirect proportion ) 12 : 6 : : x : ( x - 5 ) 12 ( x - 5 ) = 6 x < = > 6 x = 60 x = 10 answer : b


Question: one gear of pulley rotates at a speed of 3 rev / sec another gear roates at 5 rev / sec . if both start together after how many seconds will they be together again

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

Choices:
A. 3 sec
B. 5 sec
C. 15 sec
D. 20 sec
E. 25 sec

Explanation: 3 rotates 3 , 6,9 , 12,15 5 rotates 5 , 10,15 ans is 15 answer : c


Question: one type of liquid contains 10 % of water and the second type of liquid contains 15 % of water . a glass is filled with 5 parts of 1 st liquid and 2 parts of 2 nd liquid . the percentage of water in the new mixture in the glass is ?

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

<gadget id="calculator">100 / 7</gadget>
<output>100/7 = around 14.285714</output>

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

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

<gadget id="calculator">15 * 2</gadget>
<output>30</output>

<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>

<gadget id="calculator">(1/2) + (3/10)</gadget>
<output>4/5 = around 0.8</output>

<gadget id="calculator">(100/7) * (4/5)</gadget>
<output>80/7 = around 11.428571</output>
<result>80/7 = around 11.428571</result>

Choices:
A. 5.6 %
B. 11.4 %
C. 15.6 %
D. 21.3 %
E. 18.9 %

multiply(divide(const_100, add(5, 2)), add(divide(multiply(10, 5), const_100), divide(multiply(15, 2), const_100)))

Explanation: "required percentage = ( 10 % of 5 + 15 % of 2 ) / 5 + 2 * 100 = 0.8 / 7 * 100 = 11.4 % answer is b"


Question: mala and usha shared their water from a bottle . if mala and usha both drank for the same amount of time , but usha only drank 2 / 10 of the total bottle , what was the ratio of mala and usha speed ?

<gadget id="calculator">10 - 2</gadget>
<output>8</output>

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

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

Explanation: the answer is suppose to be c . 4 : 1 . it ' s from the gmatprep answer : option c


Question: the floor of a rectangular room is 18 m long and 12 m wide . the room is surrounded by a veranda of width 2 m on all its sides . the area of the veranda is :

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

<gadget id="calculator">4 + 18</gadget>
<output>22</output>

<gadget id="calculator">12 + 4</gadget>
<output>16</output>

<gadget id="calculator">22 * 16</gadget>
<output>352</output>

<gadget id="calculator">18 * 12</gadget>
<output>216</output>

<gadget id="calculator">352 - 216</gadget>
<output>136</output>
<result>136</result>

Choices:
A. 124 m 2
B. 126 m 2
C. 136 m 2
D. 158 m 2
E. none of these

subtract(rectangle_area(add(multiply(2, 2), 18), add(12, multiply(2, 2))), rectangle_area(18, 12))

Explanation: "area of the outer rectangle = 22 ã — 16 = 352 m 2 area of the inner rectangle = 18 ã — 12 = 216 m 2 required area = ( 352 â € “ 216 ) = 136 m 2 answer c"


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 84 , 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">84 * 8</gadget>
<output>672</output>

<gadget id="calculator">720 - 672</gadget>
<output>48</output>

<gadget id="calculator">92 - 90</gadget>
<output>2</output>

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

Choices:
A. 8
B. 9
C. 10
D. 21
E. 24

divide(subtract(multiply(90, 8), multiply(84, 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 = 84 thus m = 672 - - - - - - - - - 2 also , f / f = 92 thus f = 92 f - - - - - - - - - 3 put 2 and 3 in 1 : we get ( 672 + 92 f ) / ( 8 + f ) = 90 solving this we get f = 24 ans : e"


Question: a box contains 21 electric bulbs , out of which 4 are defective . two bulbs are chosen at random from this box . the probability that at least one of these is defective is

<gadget id="calculator">21 - 4</gadget>
<output>17</output>

<gadget id="calculator">binomial(17, 2)</gadget>
<output>136</output>

<gadget id="calculator">binomial(21, 2)</gadget>
<output>210</output>

<gadget id="calculator">136 / 210</gadget>
<output>68/105 = around 0.647619</output>

<gadget id="calculator">1 - (68/105)</gadget>
<output>37/105 = around 0.352381</output>
<result>37/105 = around 0.352381</result>

Choices:
A. 4 / 19
B. 7 / 19
C. 12 / 19
D. 21 / 95
E. 31 / 88

subtract(const_1, divide(choose(subtract(21, 4), const_2), choose(21, const_2)))

Explanation: "solution p ( none is defective ) = 17 c 2 / 21 c 2 = 57 / 88 . p ( at least one is defective ) = ( 1 - 57 / 88 ) = 31 / 88 . answer e"


Question: p , q and r together earn rs . 1710 in 9 days . p and r can earn rs . 600 in 5 days . q and r in 7 days can earn rs . 910 . how much amount does r can earn per day ?

<gadget id="calculator">600 / 5</gadget>
<output>120</output>

<gadget id="calculator">910 / 7</gadget>
<output>130</output>

<gadget id="calculator">120 + 130</gadget>
<output>250</output>

<gadget id="calculator">1_710 / 9</gadget>
<output>190</output>

<gadget id="calculator">250 - 190</gadget>
<output>60</output>
<result>60</result>

Choices:
A. s . 40
B. s . 60
C. s . 90
D. s . 100
E. s . 120

subtract(add(divide(600, 5), divide(910, 7)), divide(1710, 9))

Explanation: "explanation : amount earned by p , q and r in 1 day = 1710 / 9 = 190 - - - ( 1 ) amount earned by p and r in 1 day = 600 / 5 = 120 - - - ( 2 ) amount earned by q and r in 1 day = 910 / 7 = 130 - - - ( 3 ) ( 2 ) + ( 3 ) - ( 1 ) = > amount earned by p , q and 2 r in 1 day - amount earned by p , q and r in 1 day = 120 + 130 - 190 = 60 = > amount earned by r in 1 day = 60 answer : option b"


Question: a dealer purchases 15 articles for rs . 25 and sells 12 articles for rs . 32 . find the profit percentage ?

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

<gadget id="calculator">32 * 5</gadget>
<output>160</output>

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

<gadget id="calculator">160 - 100</gadget>
<output>60</output>
<result>60</result>

Choices:
A. 80 %
B. 50 %
C. 59 %
D. 40 %
E. 60 %

subtract(multiply(32, 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 . 160 ( 32 * 5 ) profit percentage = ( 160 - 100 ) / 100 * 100 = 60 % answer : e"


Question: a fraudulent dairy guy declares to market his dairy at price range but he combined it with water and therefore benefits 25 % . the percentage of water in the combination is :

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

<gadget id="calculator">100 / 125</gadget>
<output>4/5 = around 0.8</output>

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

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

Choices:
A. 20 %
B. 30 %
C. 50 %
D. 35 %
E. 60 %

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

Explanation: explanation : - > if capability price of 1 l of milk = rs . 1 and s . price of 1 l of combination = rs . 1 benefits = 20 % capability price of 1 l of combination = [ ( 100 / 100 + 25 ) * 1 ] = rs . 100 / 125 = rs . 4 / 5 - > from the rule of allegation i . capability price of 1 l of water = 0 ii . capability price of 1 l of milk = 1 iii . ( p ) = 4 / 5 iv . d – m = 1 – 4 / 5 = 1 / 5 v . m – c = 4 / 5 – 0 = 4 / 5 ratio of milk to water = 4 / 5 : 1 / 5 = 4 : 1 % of water in the combination = ( 1 / 5 x 100 ) % = 20 % answer : a


Question: 49 ã — 49 = 7 ^ ?

<gadget id="calculator">log(49)</gadget>
<output>log(49) = around 3.89182</output>

<gadget id="calculator">log(49) + log(49)</gadget>
<output>2*log(49) = around 7.783641</output>

<gadget id="calculator">log(7)</gadget>
<output>log(7) = around 1.94591</output>

<gadget id="calculator">(2*log(49)) / log(7)</gadget>
<output>2*log(49)/log(7) = around 4</output>
<result>2*log(49)/log(7) = around 4</result>

Choices:
A. 4
B. 7
C. 8
D. 16
E. none of these

Explanation: 49 ã — 49 = 7 ? or , 7 ( 2 ) ã — 7 ( 2 ) = 7 ? or 7 ( 4 ) = 7 ? or , ? = 4 answer a


Question: a batsman in his 12 th inning makes a score of 60 and their by increasing his average by 4 . what is his average after the 12 th inning ?

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

<gadget id="calculator">60 - 48</gadget>
<output>12</output>

<gadget id="calculator">12 + 4</gadget>
<output>16</output>
<result>16</result>

Choices:
A. 12
B. 16
C. 20
D. 24
E. 28

Explanation: "11 x + 60 = 12 ( x + 4 ) x = 12 + 4 = 16 answer : b"


Question: find the ones digit of 73 ^ 351

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

<gadget id="calculator">7 * 10</gadget>
<output>70</output>

<gadget id="calculator">73 - 70</gadget>
<output>3</output>

<gadget id="calculator">351 / 4</gadget>
<output>351/4 = around 87.75</output>

<gadget id="calculator">floor(351/4)</gadget>
<output>87</output>

<gadget id="calculator">87 * 4</gadget>
<output>348</output>

<gadget id="calculator">351 - 348</gadget>
<output>3</output>

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

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

<gadget id="calculator">27 - 20</gadget>
<output>7</output>
<result>7</result>

Choices:
A. 3
B. 5
C. 6
D. 7
E. 9

subtract(power(subtract(73, multiply(add(const_3, const_4), const_10)), subtract(351, multiply(floor(divide(351, const_4)), const_4))), multiply(const_2, const_10))

Explanation: "the units digit of 73 ^ 351 will be the same as the units digit of 3 ^ 351 3 ^ 1 = 3 - - > the units digit is 3 ; 3 ^ 2 = 9 - - > the units digit is 9 ; 3 ^ 3 = 27 - - > the units digit is 7 ; 3 ^ 4 = 81 - - > the units digit is 1 ; 3 ^ 5 = 243 - - > the units digit is 3 again ; . . . so , as you can see the units digit repeats in blocks of 4 : { 3 , 9 , 7 , 1 } , { 3 , 9 , 7 , 1 } , . . . now , since 351 = 348 + 3 = ( multiple of 4 ) + 3 , then the units digit of 3 ^ 351 will be the third number in the pattern thus 7 . answer : d ."


Question: 5 is added to a certain number , the sum is multiplied by 7 , the product is divided by 5 and 5 is subtracted from the quotient . the remainder left is half of 66 . what is the number ?

<gadget id="calculator">66 / 2</gadget>
<output>33</output>

<gadget id="calculator">33 + 5</gadget>
<output>38</output>

<gadget id="calculator">38 * 5</gadget>
<output>190</output>

<gadget id="calculator">190 / 7</gadget>
<output>190/7 = around 27.142857</output>

<gadget id="calculator">(190/7) - 5</gadget>
<output>155/7 = around 22.142857</output>
<result>155/7 = around 22.142857</result>

Choices:
A. 21
B. 20
C. 22
D. 30
E. 45

subtract(divide(multiply(add(divide(66, const_2), 5), 5), 7), 5)

Explanation: let number is x . when 5 added to it , = ( x + 5 ) 7 multiplied to sum , = 7 * ( x + 5 ) now , = [ { 7 * ( x + 5 ) } / 5 ] and , = [ { 7 * ( x + 5 ) } / 5 ] - 5 according to question , [ { 7 * ( x + 10 ) } / 5 ] - 5 = half of 66 [ ( 7 x + 35 ) / 5 ) = 33 + 5 7 x + 35 = 38 * 5 x = 155 / 7 x = 22.14 = 22 so , required number is : 22 . answer : c


Question: john bought a shirt on sale for 25 % off the original price and another 25 % off the discounted price . if the final price was $ 17 , what was the price before the first discount ?

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

<gadget id="calculator">10_000 * 17</gadget>
<output>170_000</output>

<gadget id="calculator">100 - 25</gadget>
<output>75</output>

<gadget id="calculator">75 * 100</gadget>
<output>7_500</output>

<gadget id="calculator">75 * 25</gadget>
<output>1_875</output>

<gadget id="calculator">7_500 - 1_875</gadget>
<output>5_625</output>

<gadget id="calculator">170_000 / 5_625</gadget>
<output>272/9 = around 30.222222</output>
<result>272/9 = around 30.222222</result>

Choices:
A. $ 45.10
B. $ 30.22
C. $ 28.44
D. $ 67.54
E. $ 65.23

divide(multiply(multiply(const_100, const_100), 17), subtract(multiply(subtract(const_100, 25), const_100), multiply(subtract(const_100, 25), 25)))

Explanation: "let x be the price before the first discount . the price after the first discount is x - 25 % x ( price after first discount ) a second discount of 25 % of the discounted price after which the final price is 17 ( x - 25 % x ) - 25 % ( x - 25 % x ) = 17 solve for x x = $ 30.22 correct answer b"


Question: if a trader sold two cars each at rs . 325475 and gains 15 % on the first and loses 15 % on the second , then his profit or loss percent on the whole is ?

<gadget id="calculator">15 * 15</gadget>
<output>225</output>

<gadget id="calculator">225 / 100</gadget>
<output>9/4 = around 2.25</output>
<result>9/4 = around 2.25</result>

Choices:
A. 1.44 %
B. 1.74 %
C. 1.84 %
D. 1.97 %
E. 2.25 %

Explanation: "sp of each car is rs . 325475 , he gains 15 % on first car and losses 15 % on second car . in this case , there will be loss and percentage of loss is given by = [ ( profit % ) ( loss % ) ] / 100 = ( 15 ) ( 15 ) / 100 % = 1.44 % answer : e"


Question: in township k , 1 / 5 of the housing units are equipped with cable television . if 1 / 10 of the housing units , including 1 / 3 of those that are equipped with cable television , are equipped with videocassette recorders , what fraction of the housing units have neither cable television nor videocassette recorders ?

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

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

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

<gadget id="calculator">(4/5) - (1/10)</gadget>
<output>7/10 = around 0.7</output>

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

<gadget id="calculator">(1/5) * (1/3)</gadget>
<output>1/15 = around 0.066667</output>

<gadget id="calculator">(7/10) + (1/15)</gadget>
<output>23/30 = around 0.766667</output>
<result>23/30 = around 0.766667</result>

Choices:
A. 23 / 30
B. 11 / 15
C. 7 / 10
D. 1 / 6
E. 2 / 15

add(subtract(subtract(const_1, divide(1, 5)), divide(1, 10)), multiply(divide(1, 5), divide(1, 3)))

Explanation: let total housing units = 5 x . as per question , equipped with cable tv = x equipped with vcr = x / 2 , which includes x / 3 ctv . so , only vcr = x / 2 - x / 3 = x / 6 . so , cable tv + vcr = x + x / 6 = 7 x / 6 no cable tv and vcr = 5 x - 7 x / 6 = 23 x / 6 . fraction = 23 x / ( 6 * 5 x ) = 23 / 30 . hence , a


Question: it is the new year and mandy has made a resolution to lose weight this year . she plans to exercise and do yoga . for exercise she plans to workout at the gym and ride her bicycle in the ratio of 2 : 3 everyday . she will also do yoga in the ratio , yoga : exercise = 2 : 3 . if she rides her bike for 16 minutes , how much time will she spend doing yoga ? ( rounded to minutes )

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

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

<gadget id="calculator">16 * (3/5)</gadget>
<output>48/5 = around 9.6</output>

<gadget id="calculator">(3/5) * (3/5)</gadget>
<output>9/25 = around 0.36</output>

<gadget id="calculator">(48/5) / (9/25)</gadget>
<output>80/3 = around 26.666667</output>
<result>80/3 = around 26.666667</result>

Choices:
A. 10 min .
B. 41 min .
C. 27 min .
D. 23 min .
E. 25 min .

divide(multiply(16, divide(3, add(2, 3))), multiply(divide(3, add(2, 3)), divide(3, add(2, 3))))

Explanation: "the ratio is 2 : 3 = gym : ride , so ( 16 ) ( 3 / 2 ) = 24 minutes at the gym , and 24 + 16 = 40 minutes exercise , so ( 2 / 3 ) ( 40 ) = 27 minutes yoga . answer : c"


Question: a cistern which could be filled in 8 hours takes one hour more to be filled owing to a leak in its bottom . if the cistern is full in what time will the leak empty it ?

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

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

<gadget id="calculator">(1/8) - (1/10)</gadget>
<output>1/40 = around 0.025</output>

<gadget id="calculator">1 / (1/40)</gadget>
<output>40</output>
<result>40</result>

Choices:
A. 76 hrs
B. 99 hrs
C. 55 hrs
D. 90 hrs
E. 40 hrs

inverse(subtract(divide(const_1, 8), divide(const_1, const_10)))

Explanation: "1 / 8 - 1 / x = 1 / 10 = > 40 hrs answer : e"


Question: a sum fetched a total simple interest of rs . 4016.25 at the rate of 1 % p . a . in 9 years . what is the sum ?

<gadget id="calculator">4_016.25 * 100</gadget>
<output>401_625</output>

<gadget id="calculator">401_625 / 1</gadget>
<output>401_625</output>

<gadget id="calculator">401_625 / 9</gadget>
<output>44_625</output>
<result>44_625</result>

Choices:
A. 42315
B. 42877
C. 44625
D. 38925
E. 22887

divide(divide(multiply(4016.25, const_100), 1), 9)

Explanation: "principal = ( 100 * 4016.25 ) / ( 1 * 9 ) = rs . 44625 . answer : c"


Question: average expenditure of a person for the first 3 days of a week is rs . 320 and for the next 4 days is rs . 420 . average expenditure of the man for the whole week is :

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

<gadget id="calculator">4 * 100</gadget>
<output>400</output>

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

<gadget id="calculator">400 / 7</gadget>
<output>400/7 = around 57.142857</output>

<gadget id="calculator">320 + (400/7)</gadget>
<output>2_640/7 = around 377.142857</output>
<result>2_640/7 = around 377.142857</result>

Choices:
A. 350
B. 370
C. 390
D. 360
E. none

add(320, divide(multiply(4, subtract(420, 320)), add(3, 4)))

Explanation: explanation : assumed mean = rs . 320 total excess than assumed mean = 4 × ( rs . 420 - rs . 350 ) = rs . 280 therefore , increase in average expenditure = rs . 280 / 7 = rs . 40 therefore , average expenditure for 7 days = rs . 320 + rs . 40 = rs . 360 correct option : d


Question: in a certain school , the ratio of boys to girls is 5 to 13 . if there are 64 more girls than boys , how many boys are there ?

<gadget id="calculator">5 / 13</gadget>
<output>5/13 = around 0.384615</output>

<gadget id="calculator">1 - (5/13)</gadget>
<output>8/13 = around 0.615385</output>

<gadget id="calculator">64 / (8/13)</gadget>
<output>104</output>

<gadget id="calculator">104 - 64</gadget>
<output>40</output>
<result>40</result>

Choices:
A. 27
B. 40
C. 45
D. 72
E. 117

subtract(divide(64, subtract(const_1, divide(5, 13))), 64)

Explanation: the ratio of b to g is 5 : 13 and the other data point is g are more than boys by 64 . . . looking at the ratio we can say that the 8 ( 13 - 5 ) extra parts caused this diff of 64 . so 1 part corresponds to 64 / 8 = 8 and so 5 parts correspond to 5 * 8 = 40 . b


Question: a computer manufacturer produces a certain electronic component at a cost of $ 80 per component . shipping costs for delivering the components are $ 3 per unit . further , the manufacturer has costs of $ 16,500 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 150 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ?

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

<gadget id="calculator">16 * 1_000</gadget>
<output>16_000</output>

<gadget id="calculator">3 * 100</gadget>
<output>300</output>

<gadget id="calculator">16_000 + 300</gadget>
<output>16_300</output>

<gadget id="calculator">80 + 3</gadget>
<output>83</output>

<gadget id="calculator">83 * 150</gadget>
<output>12_450</output>

<gadget id="calculator">16_300 + 12_450</gadget>
<output>28_750</output>

<gadget id="calculator">28_750 / 150</gadget>
<output>575/3 = around 191.666667</output>
<result>575/3 = around 191.666667</result>

Choices:
A. $ 28
B. $ 82
C. $ 110
D. $ 138
E. $ 193

divide(add(add(multiply(multiply(const_4, const_4), const_1000), multiply(3, const_100)), multiply(add(80, 3), 150)), 150)

Explanation: "by the question , the equation would be 150 p - 83 * 150 - 16500 = 0 p being the price we want to find and equation resulting zero means revenue and costs are equal so we can get the minimum price of the component . solving the equation , we get p = $ 193 . answer e for me ."


Question: two cyclist start on a circular track from a given point but in opposite direction with speeds of 7 m / s and 8 m / s . if the circumference of the circle is 630 meters , after what time will they meet at the starting point ?

<gadget id="calculator">8 + 7</gadget>
<output>15</output>

<gadget id="calculator">630 / 15</gadget>
<output>42</output>
<result>42</result>

Choices:
A. 20 sec
B. 15 sec
C. 42 sec
D. 50 sec
E. 1 min

Explanation: "they meet every 630 / 7 + 8 = 42 sec answer is c"


Question: calculate the sum of first 60 natural numbers .

<gadget id="calculator">60 + 1</gadget>
<output>61</output>

<gadget id="calculator">60 / 2</gadget>
<output>30</output>

<gadget id="calculator">61 * 30</gadget>
<output>1_830</output>
<result>1_830</result>

Choices:
A. 1839
B. 2830
C. 1830
D. 1831
E. 1835

multiply(add(60, const_1), divide(60, const_2))

Explanation: "solution we know that ( 1 + 2 + 3 + . . . . . + 60 ) = n ( n + 1 ) / 2 therefore ( 1 + 2 + 3 + . . . . + 60 ) = ( 60 × 61 / 2 ) = 1830 . answer c"


Question: buffalo gives 4 liter milk , cow gives ( 1 / 2 ) liter milk and goat gives 1 / 4 liter milk . you have to get 20 liter milk by 20 animals . what is the number of goats ?

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

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

Explanation: assume number of respective animals are x , y , z . x + y + z = 20 - - - ( 1 ) as the total number of animal has to be 20 amt of milk will be 4 x + ( 1 / 2 ) y + ( 1 / 4 ) z = 20 - - - ( 2 ) solving equation 1 and 2 we get 15 x + y = 60 - - - - ( 3 ) since buffalo gives 4 litre and total milk is 20 , x < 5 but from eq 3 , x can not be more than 4 ; further if x = 1 or 2 ; y > 20 . . . not possible , since total animal is 20 thus , x = 3 , y = 15 , z = 2 2 goats answer : b


Question: a batsman makes a score of 85 runs in the 11 th inning and thus increases his average by 5 . find his average after 11 th inning .

<gadget id="calculator">11 * 5</gadget>
<output>55</output>

<gadget id="calculator">85 - 55</gadget>
<output>30</output>

<gadget id="calculator">30 + 5</gadget>
<output>35</output>
<result>35</result>

Choices:
A. 40
B. 50
C. 62
D. 45
E. 35

Explanation: "let the average after 11 th inning = x then , average after 10 th inning = x - 5 10 ( x - 5 ) + 85 = 11 x x = 85 - 50 = 35 answer is e"


Question: each of the three people individually can complete a certain job in 3 , 4 , and 6 hours , respectively . what is the lowest fraction of the job that can be done in 1 hour by 2 of the people working together at their respective rates ?

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

<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>

<gadget id="calculator">(1/4) + (1/6)</gadget>
<output>5/12 = around 0.416667</output>
<result>5/12 = around 0.416667</result>

Choices:
A. 1 / 3
B. 9 / 20
C. 8 / 15
D. 5 / 12
E. 2 / 3

add(divide(const_1, 4), divide(const_1, 6))

Explanation: the two slowest people work at rates of 1 / 4 and 1 / 6 of the job per hour . the sum of these rates is 1 / 4 + 1 / 6 = 5 / 12 of the job per hour . the answer is d .


Question: in what ratio mental a at rs . 68 per kg be mixed with another metal at rs . 96 per kg so that cost of alloy ( mixture ) is rs . 80 per kg ?

<gadget id="calculator">96 - 80</gadget>
<output>16</output>

<gadget id="calculator">96 - 68</gadget>
<output>28</output>

<gadget id="calculator">16 / 28</gadget>
<output>4/7 = around 0.571429</output>

<gadget id="calculator">1 - (4/7)</gadget>
<output>3/7 = around 0.428571</output>

<gadget id="calculator">(4/7) / (3/7)</gadget>
<output>4/3 = around 1.333333</output>
<result>4/3 = around 1.333333</result>

Choices:
A. 5 : 8
B. 4 : 7
C. 4 : 3
D. 9 : 5
E. 9 : 8

divide(divide(subtract(96, 80), subtract(96, 68)), subtract(const_1, divide(subtract(96, 80), subtract(96, 68))))

Explanation: ( 96 - 80 ) / ( 80 - 68 ) = 16 / 12 = 4 / 3 answer : c


Question: if a man lost 4 % by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44 % ?

<gadget id="calculator">100 - 4</gadget>
<output>96</output>

<gadget id="calculator">96 * 12</gadget>
<output>1_152</output>

<gadget id="calculator">100 + 44</gadget>
<output>144</output>

<gadget id="calculator">1_152 / 144</gadget>
<output>8</output>
<result>8</result>

Choices:
A. 8
B. 7
C. 5
D. 2
E. 1

divide(multiply(subtract(const_100, 4), 12), add(const_100, 44))

Explanation: "96 % - - - - 12 144 % - - - - ? 96 / 144 * 12 = 8 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 6 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 - 6</gadget>
<output>6</output>
<result>6</result>

Choices:
A. 2
B. 4
C. 12
D. 6
E. 160

Explanation: "actual miles / gallon is = 480 / 40 = 12 miles / gallon . current engine miles / gallon is 6 miles / gallon . additional 6 miles / gallon is required to match the actual mileage . imo option d ."


Question: every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 70400 ?

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

<gadget id="calculator">(1/8) * 70_400</gadget>
<output>8_800</output>

<gadget id="calculator">70_400 + 8_800</gadget>
<output>79_200</output>

<gadget id="calculator">(1/8) * 79_200</gadget>
<output>9_900</output>

<gadget id="calculator">79_200 + 9_900</gadget>
<output>89_100</output>
<result>89_100</result>

Choices:
A. 89100
B. 81028
C. 27772
D. 29889
E. 22312

Explanation: 70400 * 9 / 8 * 9 / 8 = 89100 . answer : a


Question: an empty fuel tank is filled with brand z gasoline . when the tank is 1 / 4 empty , it is filled with brand y gasoline . when the tank is half empty again , it is filled with brand z gasoline . when the tank is half empty again , it is filled with brand y gasoline . at this time , what percent of the gasoline in the tank is brand z ?

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

<gadget id="calculator">(1/4) * 100</gadget>
<output>25</output>

<gadget id="calculator">100 - 25</gadget>
<output>75</output>

<gadget id="calculator">75 / 2</gadget>
<output>75/2 = around 37.5</output>

<gadget id="calculator">100 - (75/2)</gadget>
<output>125/2 = around 62.5</output>

<gadget id="calculator">(125/2) / 2</gadget>
<output>125/4 = around 31.25</output>
<result>125/4 = around 31.25</result>

Choices:
A. 31.25 %
B. 30 %
C. 40 %
D. 50 %
E. 45 %

divide(subtract(const_100, divide(subtract(const_100, multiply(divide(1, 4), const_100)), const_2)), const_2)

Explanation: work with fraction of brand z in the tank . 1 st step : brand z is 1 2 nd step : brand z is 1 / 4 3 rd step : brand z is ( 1 / 2 ) * ( 1 / 4 ) + 1 / 2 = 5 / 8 4 th step : brand z is ( 1 / 2 ) * ( 5 / 8 ) = 5 / 16 answer ( a )


Question: if a - b = 3 and a ( power 2 ) + b ( power 2 ) = 29 , find the value of ab .

<gadget id="calculator">3 ** 2</gadget>
<output>9</output>

<gadget id="calculator">29 - 9</gadget>
<output>20</output>

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

Choices:
A. 5
B. 8
C. 4
D. 10
E. 3

Explanation: "2 ab = ( a ( power 2 ) + b ( power 2 ) - ( a - b ) ( power 2 ) = 29 - 9 = 20 ab = 10 . answer is d ."


Question: in an election , candidate a got 55 % of the total valid votes . if 15 % of the total votes were declared invalid and the total numbers of votes is 560000 , find the number of valid vote polled in favor of candidate ?

<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>

<gadget id="calculator">1 - (3/20)</gadget>
<output>17/20 = around 0.85</output>

<gadget id="calculator">560_000 * (17/20)</gadget>
<output>476_000</output>

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

<gadget id="calculator">476_000 * (11/20)</gadget>
<output>261_800</output>
<result>261_800</result>

Choices:
A. 261800
B. 355800
C. 356500
D. 356800
E. 357000

multiply(multiply(560000, subtract(const_1, divide(15, const_100))), divide(55, const_100))

Explanation: "total number of invalid votes = 15 % of 560000 = 15 / 100 × 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 – 84000 = 476000 percentage of votes polled in favour of candidate a = 55 % therefore , the number of valid votes polled in favour of candidate a = 55 % of 476000 = 55 / 100 × 476000 = 26180000 / 100 = 261800 a )"


Question: a certain number when divided by 39 leaves a remainder 20 , what is the remainder when the same number is divided by 13 ?

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

Choices:
A. 7
B. 8
C. 9
D. 0
E. 1

Explanation: "39 + 20 = 59 / 13 = 7 ( remainder ) answer : a"


Question: a sum fetched a total simple interest of $ 4196.25 at the rate of 9 p . c . p . a . in 5 years . what is the sum ?

<gadget id="calculator">4_196.25 * 100</gadget>
<output>419_625</output>

<gadget id="calculator">419_625 / 9</gadget>
<output>46_625</output>

<gadget id="calculator">46_625 / 5</gadget>
<output>9_325</output>
<result>9_325</result>

Choices:
A. $ 8829
B. $ 2840
C. $ 6578
D. $ 7782
E. $ 8929

divide(divide(multiply(4196.25, const_100), 9), 5)

Explanation: "e 8929 principal = $ 100 x 4196.25 / 9 x 5 = $ 419625 / 45 = $ 8929 ."


Question: if the sum of 5 consecutive even positive integers is a , then the sum of the next 5 even consecutive integers in terms of a is :

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

Choices:
A. a + 5
B. a + 10
C. a + 25
D. a + 50
E. 2 a + 5

Explanation: in case of consecutive integers or integers in arithmetic progression mean = median i . e . median = a / 5 = mean = third integer first integer = a / 5 - 4 second integer = a / 5 - 2 third integer = a / 5 fourth integer = a / 5 + 2 fifth integer = a / 5 + 4 i . e . sixth integer = a / 5 + 6 seventh integer = a / 5 + 8 eighth integer = a / 5 + 10 ninth integer = a / 5 + 12 tenth integer = a / 5 + 14 now mean of next 5 integers = median = a / 5 + 5 i . e . sum of next 5 integers = ( a / 5 + 10 ) * 5 = a + 50 answer : option d


Question: an escalator moves towards the top level at the rate of 12 ft . sec and its length is 196 feet . if a person walks on the moving escalator at the rate of 2 feet per second towards the top level , how much time does he take to cover the entire length .

<gadget id="calculator">12 + 2</gadget>
<output>14</output>

<gadget id="calculator">196 / 14</gadget>
<output>14</output>
<result>14</result>

Choices:
A. 14 sec
B. 10 sec
C. 12 sec
D. 8 sec
E. 9 sec

Explanation: "time taken to cover the entire length = tot . dist / resultant speed = 196 / ( 12 + 2 ) = 14 sec answer : a"


Question: pipe a fills a tank in 12 minutes . pipe b can fill the same tank 3 times as fast as pipe a . if both the pipes are kept open when the tank is empty , how many minutes will it take to fill the tank ?

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

<gadget id="calculator">3 / 12</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">(1/12) + (1/4)</gadget>
<output>1/3 = around 0.333333</output>

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

Choices:
A. 4 mins
B. 6 mins
C. 5 mins
D. 3 mins
E. 7 mins

inverse(add(divide(const_1, 12), divide(3, 12)))

Explanation: "a ' s rate is 1 / 12 and b ' s rate is 1 / 4 . the combined rate is 1 / 12 + 1 / 4 = 1 / 3 the pipes will fill the tank in 3 minutes . the answer is d ."


Question: a sum of rs . 2730 is lent into two parts so that the interest on the first part for 8 years at 3 % per annum may be equal to the interest on the second part for 3 years at 5 % per annum . find the second sum ?

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

<gadget id="calculator">15 * 2_730</gadget>
<output>40_950</output>

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

<gadget id="calculator">15 + 24</gadget>
<output>39</output>

<gadget id="calculator">40_950 / 39</gadget>
<output>1_050</output>

<gadget id="calculator">2_730 - 1_050</gadget>
<output>1_680</output>
<result>1_680</result>

Choices:
A. 1629
B. 1680
C. 1677
D. 1698
E. 1679

subtract(2730, divide(multiply(multiply(3, 5), 2730), add(multiply(3, 5), multiply(8, 3))))

Explanation: ( x * 8 * 3 ) / 100 = ( ( 2730 - x ) * 3 * 5 ) / 100 24 x / 100 = 40950 / 100 - 15 x / 100 39 x = 40950 = > x = 1050 second sum = 2730 â € “ 1050 = 1680 answer : b


Question: the speed at which a man can row a boat in still water is 22 kmph . if he rows downstream , where the speed of current is 3 kmph , what time will he take to cover 80 metres ?

<gadget id="calculator">22 + 3</gadget>
<output>25</output>

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

<gadget id="calculator">25 * (5/18)</gadget>
<output>125/18 = around 6.944444</output>

<gadget id="calculator">80 / (125/18)</gadget>
<output>288/25 = around 11.52</output>
<result>288/25 = around 11.52</result>

Choices:
A. 12.59
B. 11.53
C. 15.69
D. 14.56
E. 18.98

divide(80, multiply(add(22, 3), const_0_2778))

Explanation: speed of the boat downstream = 22 + 3 = 25 kmph = 25 * 5 / 18 = 6.94 m / s hence time taken to cover 80 m = 80 / 6.94 = 11.53 seconds . answer : b


Question: on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.70 per glass on the first day , what was the price per glass on the second day ?

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

<gadget id="calculator">2 * 0.7</gadget>
<output>1.4</output>

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

<gadget id="calculator">1.4 / 3</gadget>
<output>0.466667</output>
<result>0.466667</result>

Choices:
A. $ 0.15
B. $ 0.20
C. $ 0.30
D. $ 0.40
E. $ 0.46

divide(multiply(add(const_1, const_1), 0.70), add(const_1, const_2))

Explanation: "on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.7 = 3 * x - - > x = $ 0.46 . answer : e ."


Question: if one - third of one - fourth of a number is 18 , then 3 - tenth of that number is : a . 35

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

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

<gadget id="calculator">12 * 18</gadget>
<output>216</output>

<gadget id="calculator">(3/10) * 216</gadget>
<output>324/5 = around 64.8</output>
<result>324/5 = around 64.8</result>

Choices:
A. 23
B. 87
C. 26
D. 64.8
E. 01

multiply(divide(const_3, const_10), multiply(multiply(3, const_4), 18))

Explanation: explanation : the number is 1 / 3 of 1 / 4 is = 15 then 1 / 3 ã — 1 / 4 = 18 number is 216 then 216 ã — 3 / 10 = 64.8 answer : d


Question: during a certain season , a team won 75 percent of its first 100 games and 50 percent of its remaining games . if the team won 70 percent of its games for the entire season , what was the total number of games that the team played ?

<gadget id="calculator">75 - 70</gadget>
<output>5</output>

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

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

<gadget id="calculator">(7/10) - (1/2)</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">5 / (1/5)</gadget>
<output>25</output>

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

Choices:
A. 180
B. 170
C. 156
D. 150
E. 125

add(100, divide(subtract(75, 70), subtract(divide(70, const_100), divide(50, const_100))))

Explanation: we are first given that a team won 75 percent of its first 100 games . this means the team won 0.75 x 100 = 75 games out of its first 100 games . we are next given that the team won 50 percent of its remaining games . if we use variable t to represent the total number of games in the season , then we can say t – 100 equals the number of remaining games in the season . thus we can say : 0.5 ( t – 100 ) = number of wins for remaining games 0.5 t – 50 = number of wins for remaining games lastly , we are given that team won 70 percent of all games played in the season . that is , they won 0.7 t games in the entire season . with this we can set up the equation : number of first 100 games won + number of games won for remaining games = total number of games won in the entire season 75 + 0.5 t – 50 = 0.7 t 25 = 0.2 t 250 = 2 t 125 = t answer is e .


Question: if a number n is chosen at random from the set of two - digit integers whose digits are both prime numbers , what is the probability e that n is divisible by 3 ?

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

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

<gadget id="calculator">5 / 16</gadget>
<output>5/16 = around 0.3125</output>
<result>5/16 = around 0.3125</result>

Choices:
A. 1 / 3
B. ¼
C. 9 / 25
D. 5 / 16
E. 0

divide(add(3, const_2), multiply(const_4, const_4))

Explanation: "prime digits are : 2 , 3 , 5 , 7 total number of 2 digit # s with both digits prime are : 4 * 4 = 16 out of these numbers divisible by 3 = 33 , 27 , 57 , 72 and 75 . i had to find the numbers manually using the 4 numbers above . = > prob = 5 / 16 . ans d . took me 3 : 20 mins ."


Question: p , q and r together earn rs . 1890 in 9 days . p and r can earn rs . 600 in 5 days . q and r in 7 days can earn rs . 910 . how much amount does r can earn per day ?

<gadget id="calculator">600 / 5</gadget>
<output>120</output>

<gadget id="calculator">910 / 7</gadget>
<output>130</output>

<gadget id="calculator">120 + 130</gadget>
<output>250</output>

<gadget id="calculator">1_890 / 9</gadget>
<output>210</output>

<gadget id="calculator">250 - 210</gadget>
<output>40</output>
<result>40</result>

Choices:
A. s . 40
B. s . 70
C. s . 90
D. s . 100
E. s . 120

subtract(add(divide(600, 5), divide(910, 7)), divide(1890, 9))

Explanation: "explanation : amount earned by p , q and r in 1 day = 1890 / 9 = 210 - - - ( 1 ) amount earned by p and r in 1 day = 600 / 5 = 120 - - - ( 2 ) amount earned by q and r in 1 day = 910 / 7 = 130 - - - ( 3 ) ( 2 ) + ( 3 ) - ( 1 ) = > amount earned by p , q and 2 r in 1 day - amount earned by p , q and r in 1 day = 120 + 130 - 210 = 40 = > amount earned by r in 1 day = 40 answer : option a"


Question: the greatest number that divides 690 and 875 leaving remainders 10 and 25 respectively is :

<gadget id="calculator">875 - 25</gadget>
<output>850</output>

<gadget id="calculator">gcd(690, 875)</gadget>
<output>5</output>

<gadget id="calculator">850 / 5</gadget>
<output>170</output>
<result>170</result>

Choices:
A. 170
B. 130
C. 150
D. 120
E. 180

Explanation: "explanation : 690 - 10 = 680 , 875 – 25 = 850 highest number that can divide 680 and 850 exactly is hcm of the numbers . hcf of 680 and 850 = 170 answer : a"


Question: a group of students was interviewed for that if it was asked whether or not they speak french and / or english . among those who speak french , 25 speak english well , while 65 of them do not speak english . if 55 % of students do not speak french , how many students were surveyed ?

<gadget id="calculator">25 + 65</gadget>
<output>90</output>

<gadget id="calculator">100 - 55</gadget>
<output>45</output>

<gadget id="calculator">45 / 100</gadget>
<output>9/20 = around 0.45</output>

<gadget id="calculator">90 / (9/20)</gadget>
<output>200</output>
<result>200</result>

Choices:
A. 190
B. 175
C. 225
D. 200
E. 250

divide(add(25, 65), divide(subtract(const_100, 55), const_100))

Explanation: number of students who speak french are 65 + 25 = 90 of total students , the percentage of students who do not speak french was 55 % - - > percentage of who do is 45 % 90 - - - - - - - 45 % x - - - - - - - 100 % x = 90 * 100 / 45 = 200 = number of all students answer is d


Question: a salesman sold twice as much pears in the afternoon than in the morning . if he sold $ 510 kilograms of pears that day , how many kilograms did he sell in the afternoon ?

<gadget id="calculator">510 / 3</gadget>
<output>170</output>

<gadget id="calculator">170 * 2</gadget>
<output>340</output>
<result>340</result>

Choices:
A. 120
B. 180
C. 340
D. 280
E. 320

Explanation: "3 x = 510 x = 170 therefore , the salesman sold 170 kg in the morning and 2 ⋅ 170 = 340 kg in the afternoon . so answer is c ."


Question: find the sum of all 3 digit natural numbers , which are divisible by 8 .

<gadget id="calculator">100 + 4</gadget>
<output>104</output>

<gadget id="calculator">100 * 10</gadget>
<output>1_000</output>

<gadget id="calculator">1_000 - 8</gadget>
<output>992</output>

<gadget id="calculator">104 + 992</gadget>
<output>1_096</output>

<gadget id="calculator">992 - 104</gadget>
<output>888</output>

<gadget id="calculator">888 / 8</gadget>
<output>111</output>

<gadget id="calculator">111 + 1</gadget>
<output>112</output>

<gadget id="calculator">112 / 2</gadget>
<output>56</output>

<gadget id="calculator">1_096 * 56</gadget>
<output>61_376</output>
<result>61_376</result>

Choices:
A. 61376
B. 54411
C. 612314
D. 64170
E. 64171

multiply(add(add(const_100, const_4), subtract(multiply(const_100, const_10), 8)), divide(add(divide(subtract(subtract(multiply(const_100, const_10), 8), add(const_100, const_4)), 8), const_1), const_2))

Explanation: the three digit natural numbers divisible by 8 are 104 , 112 , 120 , … . 992 . let sndenote their sum . that is , sn = 104 112 120 128 , 992 g + + + + + . now , the sequence 104 , 112 , 120 , g , 992 forms an a . p . a = 104 , d = 8 , l = 992 n = l - a / d n = 112 s 112 = n / 2 ( a + l ) = 61376 option a


Question: each of the products produced yesterday was checked by worker x or worker y . 0.5 % of the products checked by worker x are defective and 0.8 % of the products checked by worker y are defective . if the total defective rate of all the products checked by worker x and worker y is 0.65 % , what fraction of the products was checked by worker y ?

<gadget id="calculator">0.65 - 0.5</gadget>
<output>0.15</output>

<gadget id="calculator">0.8 - 0.5</gadget>
<output>0.3</output>

<gadget id="calculator">0.15 / 0.3</gadget>
<output>0.5</output>
<result>0.5</result>

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

divide(subtract(0.65, 0.5), subtract(0.8, 0.5))

Explanation: "x : 0.5 % is 0.15 % - points from 0.65 % . y : 0.8 % is 0.15 % - points from 0.65 % . therefore the ratio of products checked by y : x is 1 : 1 . thus , worker y checked 1 / 2 of the products . the answer is b ."


Question: the radius of the two circular fields is in the ratio 4 : 10 the area of the second field is what percent greater than the area of the first ?

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

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

<gadget id="calculator">100 - 16</gadget>
<output>84</output>
<result>84</result>

Choices:
A. 72 %
B. 96 %
C. 94 %
D. 84 %
E. 82 %

subtract(power(10, const_2), power(4, const_2))

Explanation: r = 4 ï € r 2 = 16 r = 10 ï € r 2 = 100 100 ï € â € “ 84 ï € 100 - - - - ? = > 84 % . answer : d


Question: a river 2 m deep and 45 m wide is flowing at the rate of 5 kmph the amount of water that runs into the sea per minute is ?

<gadget id="calculator">2 * 45</gadget>
<output>90</output>

<gadget id="calculator">5 * 1_000</gadget>
<output>5_000</output>

<gadget id="calculator">90 * 5_000</gadget>
<output>450_000</output>

<gadget id="calculator">1 * 60</gadget>
<output>60</output>

<gadget id="calculator">450_000 / 60</gadget>
<output>7_500</output>
<result>7_500</result>

Choices:
A. 4500 m 3
B. 4580 m 3
C. 7500 m 3
D. 4900 m 3
E. 4700 m 3

divide(multiply(multiply(2, 45), multiply(5, const_1000)), multiply(const_1, const_60))

Explanation: "explanation : ( 5000 * 2 * 45 ) / 60 = 7500 m 3 answer : option c"


Question: if the range q of the 6 numbers 4 , 314 , 710 and x is 12 , what is the difference between the greatest possible value of x and least possible value of x ?

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

<gadget id="calculator">12 + 2</gadget>
<output>14</output>

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

<gadget id="calculator">21 + 7</gadget>
<output>28</output>

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

<gadget id="calculator">28 + 10</gadget>
<output>38</output>

<gadget id="calculator">38 + 12</gadget>
<output>50</output>

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

<gadget id="calculator">50 - 11</gadget>
<output>39</output>

<gadget id="calculator">39 / 3</gadget>
<output>13</output>
<result>13</result>

Choices:
A. 0
B. 2
C. 12
D. 13
E. 15

divide(subtract(add(add(add(add(add(4, const_3), add(const_12, const_2)), add(const_4, const_3)), add(4, 6)), 12), add(const_10, const_1)), const_3)

Explanation: the range q of a set is the difference between the largest and smallest elements of a set . without x , the difference between the largest and smallest elements of a set is 14 - 3 = 11 < 12 , which means that in order 12 to be the range of the set x must be either the smallest element so that 14 - x = 12 - - - > x = 2 or x must the largest element so that x - 3 = 12 - - > x = 15 . the the difference between the greatest possible value of x and least possible value of x is 15 - 2 = 13 . answer : d .


Question: if 80 percent of a class answered the first question on a certain test correctly , 55 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ?

<gadget id="calculator">80 + 55</gadget>
<output>135</output>

<gadget id="calculator">135 + 20</gadget>
<output>155</output>

<gadget id="calculator">155 - 100</gadget>
<output>55</output>
<result>55</result>

Choices:
A. 10 %
B. ( 8 ) 20 %
C. 30 %
D. 50 %
E. 55 %

subtract(add(add(80, 55), 20), const_100)

Explanation: "i did n ' t understand how to connect 20 percent with the whole equation . why 20 is out of the percentile diagram ( circles ) but inside of 100 ? 20 % appeared in the exam ; however did not answer question aquestion b correctly so they are out of the two circles , however as they have appeared in the exam , they have to be taken into consideration for calculation purpose i am doing it this way : suppose the total class size is 100 , then 20 percent of the class answered incorrectly and rest 80 percent answered correctly in question 1 or 2 or both . now , 100 - [ ( 80 - x ) + x + ( 55 - x ) ] = 20 . . . . . . . . . . values are in percent x = 20 - 100 + 135 x = 55 ans : e"


Question: a train 300 m long can cross an electric pole in 20 sec and then find the speed of the train ?

<gadget id="calculator">300 / 1_000</gadget>
<output>3/10 = around 0.3</output>

<gadget id="calculator">20 / 3_600</gadget>
<output>1/180 = around 0.005556</output>

<gadget id="calculator">(3/10) / (1/180)</gadget>
<output>54</output>
<result>54</result>

Choices:
A. 72
B. 67
C. 54
D. 26
E. 27

divide(divide(300, const_1000), divide(20, const_3600))

Explanation: "length = speed * time speed = l / t s = 300 / 20 s = 15 m / sec speed = 15 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 54 kmph answer : c"


Question: a train is 385 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">385 + 140</gadget>
<output>525</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">525 / (25/2)</gadget>
<output>42</output>
<result>42</result>

Choices:
A. 42 seconds
B. 30 seconds
C. 40 seconds
D. 50 seconds
E. none of these

divide(add(385, 140), divide(multiply(45, const_1000), const_3600))

Explanation: "explanation : speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 385 + 140 = 525 meter time = distance / speed = 525 ∗ 2 / 25 = 42 seconds option a"


Question: the distance between two cities a and b is 330 km . a train starts from a at 8 a . m . and travel towards b at 60 km / hr . another train starts from b at 9 a . m and travels towards a at 75 km / hr . at what time do they meet ?

<gadget id="calculator">330 + 75</gadget>
<output>405</output>

<gadget id="calculator">60 + 75</gadget>
<output>135</output>

<gadget id="calculator">405 / 135</gadget>
<output>3</output>

<gadget id="calculator">3 + 8</gadget>
<output>11</output>
<result>11</result>

Choices:
A. 10 a . m
B. 10.30 a . m
C. 11 a . m
D. 11.30 a . m
E. none of these

Explanation: explanation : suppose they meet x hrs after 8 a . m then , [ distance moved by first in x hrs ] + [ distance moved by second in ( x - 1 ) hrs ] = 330 . therefore , 60 x + 75 ( x - 1 ) = 330 . = > x = 3 . so , they meet at ( 8 + 3 ) i . e , 11 a . m . answer : c


Question: there are 10 stations between hyderabad and bangalore . how many second class tickets have to be printed , so that a passenger can travel from any station to any other station ?

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

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

<gadget id="calculator">11 * 12</gadget>
<output>132</output>
<result>132</result>

Choices:
A. 156
B. 167
C. 132
D. 352
E. 380

multiply(add(10, const_1), add(add(10, const_1), const_1))

Explanation: "the total number of stations = 12 from 12 stations we have to choose any two stations and the direction of travel ( i . e . , hyderabad to bangalore is different from bangalore to hyderabad ) in 12 p ₂ ways . ² ⁰ p ₂ = 12 * 11 = 132 . answer : c"


Question: total dinning bill of 9 people was $ 139.00 and 10 % tip divided the bill evenly ? what is the bill amount each person shared .

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

<gadget id="calculator">(1/10) + 1</gadget>
<output>11/10 = around 1.1</output>

<gadget id="calculator">139 * (11/10)</gadget>
<output>1_529/10 = around 152.9</output>

<gadget id="calculator">(1_529/10) / 9</gadget>
<output>1_529/90 = around 16.988889</output>
<result>1_529/90 = around 16.988889</result>

Choices:
A. 21.84
B. 12.84
C. 16.98
D. 24.84
E. 15.84

divide(multiply(139.00, add(divide(const_1, 10), const_1)), 9)

Explanation: "dinner bill of 9 person = 139 + 10 % tip so , 10 % of 139 = ( 139 * 10 ) / 100 = 13.9 so , the actual total amount = 139 + 13.9 = $ 152.9 so per head bill = 152.9 / 9 = $ 16.98 answer : c"


Question: find the length of the longest pole that can be placed in a room 12 m long 8 m broad and 9 m high .

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

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

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

<gadget id="calculator">144 + 64</gadget>
<output>208</output>

<gadget id="calculator">81 + 208</gadget>
<output>289</output>

<gadget id="calculator">289 ** (1/2)</gadget>
<output>17</output>
<result>17</result>

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

sqrt(add(power(9, const_2), add(power(12, const_2), power(8, const_2))))

Explanation: "length of longest pole = length of the diagonal of the room = sqrt ( 12 ^ 2 + 8 ^ 2 + 9 ^ 2 = sqrt ( 289 ) = 17 m . answer is e ."


Question: if 9 ^ y = 3 ^ 14 , what is y ?

<gadget id="calculator">14 / 2</gadget>
<output>7</output>
<result>7</result>

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

Explanation: "9 ^ y = 3 ^ 2 y = 3 ^ 14 2 y = 14 y = 7 the answer is e ."


Question: how many zeroes are there at the end of the number n , if n = 90 ! + 180 ! ?

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

<gadget id="calculator">90 / 5</gadget>
<output>18</output>

<gadget id="calculator">18 + 2</gadget>
<output>20</output>
<result>20</result>

Choices:
A. 15
B. 18
C. 21
D. 24
E. 27

add(divide(90, add(const_4, const_1)), const_2)

Explanation: "the number of zeroes at the end of 90 ! will be less than the number of zeroes at the end of 180 ! hence it is sufficient to calculate the number of zeroes at the end of 90 ! the number of zeroes = [ 90 / 5 ] + [ 90 / 25 ] + [ 90 / 125 ] = 18 + 3 + 0 = 21 the answer is c ."


Question: ms . harris invested in fund x and fund b . the total amount she invested , in both funds combined , was $ 100000 . in one year , fund x paid 23 % and fund b paid 17 % . the interest earned in fund b was exactly $ 200 greater than the interest earned in fund x . how much did ms . morris invest in fund x ?

<gadget id="calculator">23 * 100_000</gadget>
<output>2_300_000</output>

<gadget id="calculator">2_300_000 + 200</gadget>
<output>2_300_200</output>

<gadget id="calculator">23 + 17</gadget>
<output>40</output>

<gadget id="calculator">2_300_200 / 40</gadget>
<output>57_505</output>

<gadget id="calculator">100_000 - 57_505</gadget>
<output>42_495</output>
<result>42_495</result>

Choices:
A. $ 32000
B. $ 36000
C. $ 40000
D. $ 42000
E. $ 45,000

Explanation: 0.17 b - 0.23 x = 200 | * 100 17 b - 23 x = 20,000 x + b = 100,000 b = 100,000 - x 17 ( 100,000 - x ) - 23 x = 20,000 1 , 700,000 - 17 x - 23 x = 20,000 1 , 680,000 = 40 x divide by 40 first two digits : 42 . . . so answer is d .


Question: if the price of a certain computer increased 30 percent from b dollars to 351 dollars , then 2 b =

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

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

<gadget id="calculator">351 / (13/10)</gadget>
<output>270</output>

<gadget id="calculator">270 * 2</gadget>
<output>540</output>
<result>540</result>

Choices:
A. 540
B. 570
C. 619
D. 649
E. 700

multiply(divide(351, divide(add(const_100, 30), const_100)), 2)

Explanation: "before price increase price = b after 30 % price increase price = b + ( 30 / 100 ) * b = 1.3 b = 351 ( given ) i . e . b = 351 / 1.3 = $ 270 i . e . 2 b = 2 * 270 = 540 answer : option a"


Question: vishal invested 10 % more than trishul . trishul invested 10 % less than raghu . if the total sum of their investments is rs . 5780 , how much amount did raghu invest ?

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

<gadget id="calculator">1 - (1/10)</gadget>
<output>9/10 = around 0.9</output>

<gadget id="calculator">1 + (1/10)</gadget>
<output>11/10 = around 1.1</output>

<gadget id="calculator">(9/10) * (11/10)</gadget>
<output>99/100 = around 0.99</output>

<gadget id="calculator">(99/100) + (9/10)</gadget>
<output>189/100 = around 1.89</output>

<gadget id="calculator">(189/100) + 1</gadget>
<output>289/100 = around 2.89</output>

<gadget id="calculator">5_780 / (289/100)</gadget>
<output>2_000</output>
<result>2_000</result>

Choices:
A. 1287
B. 2887
C. 2000
D. 1129
E. 1192

divide(5780, add(add(multiply(subtract(const_1, divide(10, const_100)), add(const_1, divide(10, const_100))), subtract(const_1, divide(10, const_100))), const_1))

Explanation: "let money invested by raghu = rs . x money invested by trishul = 9 / 10 x = 0.9 x money invested by vishal = 9 / 10 x * 110 / 100 = 0.99 x also , x + 0.9 x + 0.99 x = 5780 = x = 5780 / 2.89 = 2000 therefore , amount invested by raghu is rs . 2000 . answer : c"


Question: how many seconds will a train 100 meters long take to cross a bridge 170 meters long if the speed of the train is 36 kmph ?

<gadget id="calculator">170 + 100</gadget>
<output>270</output>

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

<gadget id="calculator">36 * (5/18)</gadget>
<output>10</output>

<gadget id="calculator">270 / 10</gadget>
<output>27</output>
<result>27</result>

Choices:
A. 54 sec
B. 65 sec
C. 25 sec
D. 45 sec
E. 27 sec

Explanation: "d = 100 + 170 = 270 s = 36 * 5 / 18 = 10 mps t = 270 / 10 = 27 sec answer : e"


Question: in a bus left side are 15 seats available , 3 few seats in right side because in rear exit door . each seat hold 3 people . in addition , there is a seat back can sit 12 people all together . how many people can sit in a bus ?

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

<gadget id="calculator">15 + 12</gadget>
<output>27</output>

<gadget id="calculator">27 * 3</gadget>
<output>81</output>

<gadget id="calculator">81 + 12</gadget>
<output>93</output>
<result>93</result>

Choices:
A. 52
B. 49
C. 95
D. 88
E. 93

add(multiply(add(15, subtract(15, 3)), 3), 12)

Explanation: "right side = 15 seat left side = 15 - 3 ( 3 few seat in right side ) = 12 seat total = 15 + 12 = 27 people can seat in 27 seat = 27 * 3 = 81 people can seat in last seat = 12 total people can seat = 81 + 12 = 93 answer : e"


Question: some persons can do a piece of work in 16 days . two times the number of these people will do half of that work in ?

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

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

<gadget id="calculator">8 * (1/2)</gadget>
<output>4</output>
<result>4</result>

Choices:
A. 3
B. 4
C. 5
D. 6
E. 8

multiply(multiply(16, divide(const_1, const_2)), divide(const_1, const_2))

Explanation: "16 / ( 2 * 2 ) = 4 days answer : b"


Question: if an average hard drive had a capacity of 0.4 tb in 2000 , and average hard drive capacities double every 5 years , what will be the average hard drive capacity in 2050 ?

<gadget id="calculator">0.4 * 2</gadget>
<output>0.8</output>

<gadget id="calculator">0.8 * 2</gadget>
<output>1.6</output>

<gadget id="calculator">1.6 * 2</gadget>
<output>3.2</output>

<gadget id="calculator">3.2 * 2</gadget>
<output>6.4</output>

<gadget id="calculator">6.4 * 2</gadget>
<output>12.8</output>

<gadget id="calculator">12.8 * 2</gadget>
<output>25.6</output>

<gadget id="calculator">25.6 * 2</gadget>
<output>51.2</output>

<gadget id="calculator">51.2 * 2</gadget>
<output>102.4</output>

<gadget id="calculator">102.4 * 2</gadget>
<output>204.8</output>

<gadget id="calculator">204.8 * 2</gadget>
<output>409.6</output>

<gadget id="calculator">409.6 + 0.4</gadget>
<output>410</output>

<gadget id="calculator">410 * 10</gadget>
<output>4_100</output>
<result>4_100</result>

Choices:
A. 256
B. 512
C. 4096
D. 1024
E. 1536

multiply(add(multiply(multiply(multiply(multiply(multiply(multiply(multiply(multiply(multiply(multiply(0.4, const_2), const_2), const_2), const_2), const_2), const_2), const_2), const_2), const_2), const_2), 0.4), const_10)

Explanation: "0.4 * 2 ^ 10 = 0.4 * 1024 = 409.6 the answer is c ."


Question: find the remainder when 6 ^ 50 is divided by 215

Choices:
A. 34
B. 35
C. 36
D. 37
E. 38

Explanation: "( 6 ^ 3 ) ^ 16 * 6 ^ 2 / 215 ( 215 + 1 ) ^ 16 * 6 ^ 2 / 215 1 ^ 16 * 6 ^ 2 / 215 = 36 answer : c"


Question: a train 140 m long is running at 60 kmph . in how much time wiu it pass a platform 260 m long ?

<gadget id="calculator">140 + 260</gadget>
<output>400</output>

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

<gadget id="calculator">60 * (5/18)</gadget>
<output>50/3 = around 16.666667</output>

<gadget id="calculator">400 / (50/3)</gadget>
<output>24</output>
<result>24</result>

Choices:
A. 21 sec
B. 22 sec
C. 23 sec
D. 24 sec
E. 26 sec

Explanation: "s = d / t d = 140 + 260 = 400 m s = 60 * 5 / 18 m / sec = 50 / 3 m / sec t = 400 / ( 50 / 3 ) = 1200 / 50 = 24 sec answer : d"


Question: the total marks obtained by a student in mathematics and physics is 50 and his score in chemistry is 20 marks more than that in physics . find the average marks scored in mathamatics and chemistry together .

<gadget id="calculator">50 + 20</gadget>
<output>70</output>

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

Choices:
A. 15
B. 25
C. 35
D. 45
E. 55

Explanation: "let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 50 and c - p = 20 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 50 + 20 ) / 2 = 35 . answer : c"


Question: a rectangular grassy plot 110 m . by 65 m has a gravel path 2.5 m wide all round it on the inside . find the cost of gravelling the path at 70 paise per sq . metre

<gadget id="calculator">110 * 65</gadget>
<output>7_150</output>

<gadget id="calculator">2.5 * 2</gadget>
<output>5</output>

<gadget id="calculator">110 - 5</gadget>
<output>105</output>

<gadget id="calculator">65 - 5</gadget>
<output>60</output>

<gadget id="calculator">105 * 60</gadget>
<output>6_300</output>

<gadget id="calculator">7_150 - 6_300</gadget>
<output>850</output>

<gadget id="calculator">850 * 70</gadget>
<output>59_500</output>

<gadget id="calculator">59_500 / 100</gadget>
<output>595</output>
<result>595</result>

Choices:
A. s 595
B. s 780
C. s 880
D. s 480
E. s 980

divide(multiply(subtract(multiply(110, 65), multiply(subtract(110, multiply(2.5, const_2)), subtract(65, multiply(2.5, const_2)))), 70), const_100)

Explanation: "area of the plot = 110 m * 65 m = 7150 sq . m area of plot excluding gravel = 105 m * 60 m = 6300 sq . m area of gravel = 7150 sq . m - 6300 sq . m = 850 sq . m cost of building it = 850 sq . m * 70 = 59500 p in rs = 59500 / 100 = rs 595 answer : a"


Question: rahul played weel in this season . his current batting averagge is 46 . if he score 78 runs in today match . his batting average will become 54 . how many matches had he played in this season .

<gadget id="calculator">78 - 54</gadget>
<output>24</output>

<gadget id="calculator">54 - 46</gadget>
<output>8</output>

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

Choices:
A. 8
B. 10
C. 3
D. 6
E. 5

divide(subtract(78, 54), subtract(54, 46))

Explanation: "46 x + 78 = 54 ( x + 1 ) = > 8 x = 24 = > x = 3 answer : c"


Question: find the simple interest on rs . 69,000 at 16 2 / 3 % per year for 9 months .

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

<gadget id="calculator">6 * 100</gadget>
<output>600</output>

<gadget id="calculator">600 * 100</gadget>
<output>60_000</output>

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

<gadget id="calculator">9 * 100</gadget>
<output>900</output>

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

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

<gadget id="calculator">900 * 10</gadget>
<output>9_000</output>

<gadget id="calculator">60_000 + 9_000</gadget>
<output>69_000</output>

<gadget id="calculator">16 * 3</gadget>
<output>48</output>

<gadget id="calculator">48 + 2</gadget>
<output>50</output>

<gadget id="calculator">50 / 3</gadget>
<output>50/3 = around 16.666667</output>

<gadget id="calculator">69_000 * (50/3)</gadget>
<output>1_150_000</output>

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

<gadget id="calculator">9 / 12</gadget>
<output>3/4 = around 0.75</output>

<gadget id="calculator">1_150_000 * (3/4)</gadget>
<output>862_500</output>

<gadget id="calculator">1 / 100</gadget>
<output>1/100 = around 0.01</output>

<gadget id="calculator">862_500 * (1/100)</gadget>
<output>8_625</output>
<result>8_625</result>

Choices:
A. 7500
B. 6500
C. 8625
D. 9500
E. none of them

multiply(multiply(multiply(add(multiply(multiply(multiply(const_2, const_3), const_100), const_100), multiply(multiply(multiply(const_3, const_3), const_100), multiply(add(const_3, const_2), const_2))), divide(add(multiply(16, 3), 2), 3)), divide(multiply(const_3, const_3), multiply(2, multiply(const_2, const_3)))), divide(const_1, const_100))

Explanation: p = rs . 69000 , r = 50 / 3 % p . a and t = 9 / 12 years = 3 / 4 years . simple interest = ( p * r * t ) / 100 = rs . ( 69,000 * ( 50 / 3 ) * ( 3 / 4 ) * ( 1 / 100 ) ) = rs . 8625 answer is c .


Question: malar and roja combined will complete a task in 35 days , but malar alone can complete same work in 60 days . calculate in how many days roja can complete this work ?

<gadget id="calculator">35 * 60</gadget>
<output>2_100</output>

<gadget id="calculator">60 - 35</gadget>
<output>25</output>

<gadget id="calculator">2_100 / 25</gadget>
<output>84</output>
<result>84</result>

Choices:
A. 85 days
B. 45 days
C. 90 days
D. 84 days
E. 95 days

divide(multiply(35, 60), subtract(60, 35))

Explanation: malar - 35 days = > 1 / 35 roja - 60 days = > 1 / 60 malar one day work = 1 / 35 - 1 / 60 = 1 / 84 = = > 84 days answer d


Question: the measure of the side of a square is quadrupled . if x represents the perimeter of the original square , what is the value of the new perimeter ?

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

Choices:
A. 3 x
B. 4 x
C. 9 x
D. 12 x
E. 27 x

Explanation: original perimeter = x hence original side = x / 4 new side = 4 x / 4 new perimeter = 4 * 4 x / 4 = 4 x correct option : b


Question: tough and tricky questions : word problems . micheal , saren and donald decided to club together to buy a present . each of them gave equal amount of money . luckily saren negotiated a 20 % discount for the present so that each of them paid 4 dollars less . how much did they pay for a present ?

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

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

<gadget id="calculator">12 / (1/5)</gadget>
<output>60</output>

<gadget id="calculator">60 - 12</gadget>
<output>48</output>
<result>48</result>

Choices:
A. 20
B. 36
C. 48
D. 60
E. 72

subtract(divide(multiply(4, const_3), divide(20, const_100)), multiply(4, const_3))

Explanation: answer c . we know that saren negotiated a discount of 20 % , so each of them paid $ 4 less . since there are three people , the 20 % of the original price amounts to $ 12 . 5 times 12 $ is 60 $ , so the original price , before saren negotiated the discount , had been $ 60 . they paid $ 12 less than the base price , so they spent $ 48 .


Question: a club wants to mix 25 pounds of candy worth $ 8.00 per pound with candy worth $ 5.00 per pound to reduce the cost of the mixture to $ 6.00 per pound . how many pounds of the $ 5.00 per pound candy should be used ?

<gadget id="calculator">25 * 8</gadget>
<output>200</output>

<gadget id="calculator">6 * 25</gadget>
<output>150</output>

<gadget id="calculator">200 - 150</gadget>
<output>50</output>
<result>50</result>

Choices:
A. 30
B. 40
C. 50
D. 60
E. 70

subtract(multiply(25, 8.00), multiply(6.00, 25))

Explanation: "let number of pounds of 5 $ candy to be used be w 6 = ( 25 * 8 + 5 * w ) / ( 25 + w ) = > 150 + 6 w = 200 + 5 w = > w = 50 answer c"


Question: pradeep has to obtain 20 % of the total marks to pass . he got 390 marks and failed by 25 marks . the maximum marks are

<gadget id="calculator">390 + 25</gadget>
<output>415</output>

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

<gadget id="calculator">415 / (1/5)</gadget>
<output>2_075</output>
<result>2_075</result>

Choices:
A. 300
B. 2075
C. 800
D. 1000
E. 3900

divide(add(390, 25), divide(20, const_100))

Explanation: "explanation : let their maximum marks be x . then , 20 % of x = 390 + 25 = > 20 / 100 x = 415 x = ( 41500 / 20 ) x = 2075 . answer : b"


Question: a grocer has a sale of rs . 5420 , rs . 5660 , rs . 6200 , rs . 6350 and rs . 6500 for 5 consecutive months . find the sale he should have in the sixth month , so that he gets an average sale of rs . 6500 ?

<gadget id="calculator">5 + 1</gadget>
<output>6</output>

<gadget id="calculator">6 * 6_500</gadget>
<output>39_000</output>

<gadget id="calculator">5_420 + 5_660</gadget>
<output>11_080</output>

<gadget id="calculator">11_080 + 6_200</gadget>
<output>17_280</output>

<gadget id="calculator">17_280 + 6_350</gadget>
<output>23_630</output>

<gadget id="calculator">23_630 + 6_500</gadget>
<output>30_130</output>

<gadget id="calculator">39_000 - 30_130</gadget>
<output>8_870</output>
<result>8_870</result>

Choices:
A. rs . 5870
B. rs . 5991
C. rs . 8870
D. rs . 6850
E. none of these

Explanation: "explanation : total sale for 5 months = rs . ( 5420 + 5660 + 6200 + 6350 + 6500 ) = rs . 30,130 therefore , required sale = rs . [ ( 6500 * 6 ) – 30,130 ] = rs . ( 39000 – 30,130 ) = rs . 8870 answer c"


Question: if 30 men take 15 days to to complete a job , in how many days can 25 men finish that work ?

<gadget id="calculator">30 * 15</gadget>
<output>450</output>

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

Choices:
A. 18
B. 17
C. 16
D. 15
E. 14

Explanation: ans . 18 days


Question: if 7 a = 8 b and ab ≠ 0 , what is the ratio of a / 8 to b / 7 ?

<gadget id="calculator">7 * 8</gadget>
<output>56</output>

<gadget id="calculator">8 * 7</gadget>
<output>56</output>

<gadget id="calculator">56 / 56</gadget>
<output>1</output>
<result>1</result>

Choices:
A. 16 / 14
B. 8 / 7
C. 1
D. 7 / 8
E. 64 / 49

Explanation: "a nice fast approach is the first find a pair of numbers that satisfy the given equation : 7 a = 8 b here ' s one pair : a = 8 and b = 7 what is the ratio of a / 8 to b / 7 ? in other words , what is the value of ( a / 8 ) / ( b / 7 ) ? plug in values to get : ( a / 8 ) / ( b / 7 ) = ( 8 / 8 ) / ( 7 / 7 ) = 1 / 1 = 1 c"


Question: an empty fuel tank is filled with brand z gasoline . when the tank is 3 / 4 empty , it is filled with brand y gasoline . when the tank is half empty again , it is filled with brand z gasoline . when the tank is half empty again , it is filled with brand y gasoline . at this time , what percent of the gasoline in the tank is brand z ?

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

<gadget id="calculator">(3/4) * 100</gadget>
<output>75</output>

<gadget id="calculator">100 - 75</gadget>
<output>25</output>

<gadget id="calculator">25 / 2</gadget>
<output>25/2 = around 12.5</output>

<gadget id="calculator">100 - (25/2)</gadget>
<output>175/2 = around 87.5</output>

<gadget id="calculator">(175/2) / 2</gadget>
<output>175/4 = around 43.75</output>
<result>175/4 = around 43.75</result>

Choices:
A. 40 %
B. 41 %
C. 43.75 %
D. 42 %
E. 44 %

divide(subtract(const_100, divide(subtract(const_100, multiply(divide(3, 4), const_100)), const_2)), const_2)

Explanation: "work with fraction of brand z in the tank . 1 st step : brand z is 1 2 nd step : brand z is 1 / 2 3 rd step : brand z is ( 3 / 4 ) * ( 1 / 2 ) + 1 / 2 = 7 / 8 4 th step : brand z is ( 1 / 2 ) * ( 7 / 8 ) = 7 / 16 = 43.75 % answer ( c )"


Question: 3 candidates contested in an election and received 4136 , 7636 , 11628 votes respectively . what is the percentage of the total votes did the winning candidate get ?

<gadget id="calculator">4_136 + 7_636</gadget>
<output>11_772</output>

<gadget id="calculator">11_772 + 11_628</gadget>
<output>23_400</output>

<gadget id="calculator">11_628 / 23_400</gadget>
<output>323/650 = around 0.496923</output>

<gadget id="calculator">(323/650) * 100</gadget>
<output>646/13 = around 49.692308</output>
<result>646/13 = around 49.692308</result>

Choices:
A. 45 %
B. 49 %
C. 50 %
D. 51 %
E. 62 %

Explanation: total number of votes polled = 4136 + 7636 + 11628 = 23400 required percentage = 11628 * 100 / 23400 = 50 % answer is c


Question: in a hostel , the number of students decreased by 12 % and the price of food increased by 20 % over the previous year . if each student consumes the same amount of food then by how much should the consumption of food be cut short by every student , so that the total cost of the food remains the same as that of the previous year ?

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

<gadget id="calculator">100 - 12</gadget>
<output>88</output>

<gadget id="calculator">100 + 20</gadget>
<output>120</output>

<gadget id="calculator">88 * 120</gadget>
<output>10_560</output>

<gadget id="calculator">10_000 / 10_560</gadget>
<output>125/132 = around 0.94697</output>

<gadget id="calculator">1 - (125/132)</gadget>
<output>7/132 = around 0.05303</output>

<gadget id="calculator">(7/132) * 100</gadget>
<output>175/33 = around 5.30303</output>
<result>175/33 = around 5.30303</result>

Choices:
A. 19 %
B. 15 %
C. 25 %
D. 40 %
E. 5.3 %

multiply(subtract(const_1, divide(multiply(const_100, const_100), multiply(subtract(const_100, 12), add(const_100, 20)))), const_100)

Explanation: "cost of food ( c ) = food consumed per student ( f ) * number of students ( n ) * price of food ( p ) originally , c = fnp when number of students decrease by 12 % , and the price of food increases by 20 % , c = f ( new ) * ( 0.88 n ) * ( 1.2 p ) = > f ( new ) = f / ( 0.88 * 1.2 ) = > f ( new ) = 0.9469 f therefore the new cost of food must be 94.69 % of the old cost , or the cost of food must decrease by 5.3 % ( option e )"


Question: the sum of number of boys and girls in a school is 1150 . if the number of boys is x , then the number of girls becomes x % of the total number of students . the number of boys is ?

<gadget id="calculator">1_150 / 100</gadget>
<output>23/2 = around 11.5</output>

<gadget id="calculator">(23/2) + 1</gadget>
<output>25/2 = around 12.5</output>

<gadget id="calculator">1_150 / (25/2)</gadget>
<output>92</output>
<result>92</result>

Choices:
A. 50
B. 40
C. 60
D. 92
E. 70

divide(1150, add(divide(1150, const_100), const_1))

Explanation: "we have x + x % of 1150 = 1150 x + x / 100 * 1150 = 1150 25 / 2 * x = 1150 x = 1150 * 2 / 25 = 92 answer is d"


Question: p can do a work in the same time in which q and r together can do it . if p and q work together , the work can be completed in 10 days . r alone needs 35 days to complete the same work . then q alone can do it in

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

<gadget id="calculator">1 / 35</gadget>
<output>1/35 = around 0.028571</output>

<gadget id="calculator">(1/10) + (1/35)</gadget>
<output>9/70 = around 0.128571</output>

<gadget id="calculator">(9/70) / 2</gadget>
<output>9/140 = around 0.064286</output>

<gadget id="calculator">(9/140) - (1/35)</gadget>
<output>1/28 = around 0.035714</output>

<gadget id="calculator">1 / (1/28)</gadget>
<output>28</output>
<result>28</result>

Choices:
A. 20
B. 22
C. 25
D. 28
E. 30

divide(const_1, subtract(divide(add(divide(const_1, 10), divide(const_1, 35)), const_2), divide(const_1, 35)))

Explanation: "work done by p and q in 1 day = 1 / 10 work done by r in 1 day = 1 / 35 work done by p , q and r in 1 day = 1 / 10 + 1 / 35 = 9 / 70 but work done by p in 1 day = work done by q and r in 1 day . hence the above equation can be written as work done by p in 1 day ã — 2 = 9 / 70 = > work done by p in 1 day = 9 / 140 = > work done by q and r in 1 day = 9 / 140 hence work done by q in 1 day = 9 / 140 â € “ 1 / 35 = 1 / 28 so q alone can do the work in 28 days answer is d ."


Question: kim has 3 pairs of shoes ; each pair is a different color . if kim randomly selects 2 shoes without replacement from the 6 shoes , what is the probability that she will select 2 shoes of the same color ?

<gadget id="calculator">binomial(6, 2)</gadget>
<output>15</output>

<gadget id="calculator">3 / 15</gadget>
<output>1/5 = around 0.2</output>
<result>1/5 = around 0.2</result>

Choices:
A. 2 / 5
B. 1 / 5
C. 1 / 9
D. 1 / 10
E. 1 / 25

Explanation: "total pairs = 6 c 2 = 15 ; same color pairs = 3 c 1 * 1 c 1 = 3 ; prob = 1 / 5 ans b"


Question: simplify : 3005 - 3000 + 10

<gadget id="calculator">3_000 / 10</gadget>
<output>300</output>

<gadget id="calculator">3_005 - 300</gadget>
<output>2_705</output>
<result>2_705</result>

Choices:
A. 2505
B. 2509
C. 2705
D. 2508
E. none of them

Explanation: 3005 - 3000 + 10 = 3005 - ( 3000 / 10 ) = 3005 - 300 = 2705 . answer is c


Question: a sports retailer ordered white and yellow tennis balls in equal number but the dispatch clerk of the tennis ball company erred and dispatched 50 extra yellow balls and making ratio of white balls to yellow balls 8 / 15 . how many tennis balls did the retailer order originally .

<gadget id="calculator">8 * 50</gadget>
<output>400</output>

<gadget id="calculator">15 - 8</gadget>
<output>7</output>

<gadget id="calculator">400 / 7</gadget>
<output>400/7 = around 57.142857</output>

<gadget id="calculator">(400/7) * 2</gadget>
<output>800/7 = around 114.285714</output>
<result>800/7 = around 114.285714</result>

Choices:
A. 110
B. 114.28
C. 140
D. 160
E. 214

multiply(divide(multiply(8, 50), subtract(15, 8)), const_2)

Explanation: white : yellow = x : ( x + 50 ) = 8 : 15 - - > 15 x = 8 x + 400 - - > x = 57.14 . the total # of balls originally x + x = 57.14 + 57.14 = 114.28 . answer : b .


Question: how many numbers are divisible by both 2 and 3 up to 300 ?

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

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

Choices:
A. 50
B. 100
C. 150
D. 200
E. 250

Explanation: divide 300 by 6 , as the numbers which are divisible by both 2 and 3 are also divisible by 6 . the quotient obtained after dividing 300 by 6 is 50 , hence answer is 50 . option a


Question: the result when a number subtracted from 150 is the same as the number added to 68 . what is the number ?

<gadget id="calculator">150 - 68</gadget>
<output>82</output>

<gadget id="calculator">82 / 2</gadget>
<output>41</output>

<gadget id="calculator">41 + 68</gadget>
<output>109</output>
<result>109</result>

Choices:
A. 110
B. 100
C. 109
D. 218
E. 210

add(divide(subtract(150, 68), const_2), 68)

Explanation: answer let the number be x . then , x - 68 = 150 - x â ‡ ’ 2 x = 150 + 68 = 218 â ‡ ’ 2 x = 218 â ˆ ´ x = 109 correct option : c


Question: how many numbers up to 300 and 700 are divisible by 2 , 3 and 7 both together ?

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

<gadget id="calculator">lcm(2, 3)</gadget>
<output>6</output>

<gadget id="calculator">lcm(6, 7)</gadget>
<output>42</output>

<gadget id="calculator">400 / 42</gadget>
<output>200/21 = around 9.52381</output>

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

<gadget id="calculator">2 + 20</gadget>
<output>22</output>

<gadget id="calculator">22 / 42</gadget>
<output>11/21 = around 0.52381</output>

<gadget id="calculator">(200/21) - (11/21)</gadget>
<output>9</output>
<result>9</result>

Choices:
A. 9
B. 10
C. 11
D. 12
E. 13

subtract(divide(subtract(700, 300), lcm(lcm(2, 3), 7)), divide(add(2, multiply(const_2, const_10)), lcm(lcm(2, 3), 7)))

Explanation: ( 700 – 300 ) / 42 = 9 22 / 42 = > 9 numbers answer : a


Question: total 90 cows 30 cow gives each 2 liter milk 30 cow gives each 3 / 4 liter milk 30 cow gives each 1 / 4 liter milk this is split into 3 son per each 30 cows & 30 liter milk how ?

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

<gadget id="calculator">(3/4) * 30</gadget>
<output>45/2 = around 22.5</output>

<gadget id="calculator">(3/4) + (45/2)</gadget>
<output>93/4 = around 23.25</output>

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

<gadget id="calculator">(1/4) * 30</gadget>
<output>15/2 = around 7.5</output>

<gadget id="calculator">(93/4) + (15/2)</gadget>
<output>123/4 = around 30.75</output>
<result>123/4 = around 30.75</result>

Choices:
A. 10
B. 12
C. 15
D. 16
E. 30

add(add(divide(3, 4), multiply(divide(3, 4), 30)), multiply(const_0_25, 30))

Explanation: "30 cow 2 liter each = 60 liter 30 cow 3 / 4 liter each = 3 / 4 = 0.75 * 30 = 22.5 30 cow 1 / 4 liter each = 1 / 4 = 0.25 * 30 = 7.5 add 60 + 22.5 + 7.5 = 90 milk split into 3 son each 30 liter then 90 / 3 = 30 answer : e"


Question: the ratio between the length and the breadth of a rectangular park is 1 : 3 . if a man cycling along the boundary of the park at the speed of 12 km / hr completes one round in 8 min , then the area of the park ( in sq . m ) is ?

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

<gadget id="calculator">10 * 6</gadget>
<output>60</output>

<gadget id="calculator">12 / 60</gadget>
<output>1/5 = around 0.2</output>

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

<gadget id="calculator">(8/5) * 1_000</gadget>
<output>1_600</output>

<gadget id="calculator">1 + 3</gadget>
<output>4</output>

<gadget id="calculator">1_600 / 4</gadget>
<output>400</output>

<gadget id="calculator">400 / 2</gadget>
<output>200</output>

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

<gadget id="calculator">200 * 600</gadget>
<output>120_000</output>
<result>120_000</result>

Choices:
A. 124545 m
B. 134561 m
C. 156787 m
D. 15450 m
E. 120000 m

rectangle_area(divide(divide(multiply(multiply(divide(12, multiply(const_10, multiply(const_3, const_2))), 8), const_1000), add(1, 3)), const_2), multiply(divide(divide(multiply(multiply(divide(12, multiply(const_10, multiply(const_3, const_2))), 8), const_1000), add(1, 3)), const_2), 3))

Explanation: "perimeter = distance covered in 8 min . = 12000 x 8 m = 1600 m . 60 let length = 1 x metres and breadth = 3 x metres . then , 2 ( 1 x + 3 x ) = 1600 or x = 200 . length = 200 m and breadth = 600 m . area = ( 600 x 200 ) m 2 = 120000 m e"


Question: the ratio of two quantities is incorrect when written as 10 to 14 . how should this ratio be written ?

<gadget id="calculator">10 / 14</gadget>
<output>5/7 = around 0.714286</output>
<result>5/7 = around 0.714286</result>

Choices:
A. 5 : 14
B. 10 : 7
C. 20 : 24
D. 5 : 7
E. it can not be determined from the information given

Explanation: a ratio should be reduced to the lowest common denominator . 10 : 14 means 10 x : 14 x which can be written as 5 ( 2 ) : 7 ( 2 ) . . . answer : d


Question: cereal a is 11 % sugar by weight , whereas healthier but less delicious cereal b is 2 % sugar by weight . to make a delicious and healthy mixture that is 5 % sugar , what should be the ratio of cereal a to cereal b , by weight ?

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

<gadget id="calculator">11 - 5</gadget>
<output>6</output>

<gadget id="calculator">3 / 6</gadget>
<output>1/2 = around 0.5</output>
<result>1/2 = around 0.5</result>

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

Explanation: "2 % is 3 % - points below 5 % and 11 % is 6 % - points above 5 % . the ratio of a : b should be 3 : 6 = 1 : 2 . the answer is a ."


Question: in a family 16 people eat only vegetarian , 9 people eat only non veg . , 12 people eat both veg and non veg . . how many people eat veg in the family ?

<gadget id="calculator">16 + 12</gadget>
<output>28</output>
<result>28</result>

Choices:
A. 28
B. 26
C. 22
D. 31
E. 21

Explanation: total people eat veg = only veg + both veg and non veg total = 16 + 12 = 28 answer = a


Question: if the price of sugar rises from rs . 10 per kg to rs . 11 per kg , a person , to have no increase in the expenditure on sugar , will have to reduce his consumption of sugar by

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

<gadget id="calculator">10 / 11</gadget>
<output>10/11 = around 0.909091</output>

<gadget id="calculator">1 - (10/11)</gadget>
<output>1/11 = around 0.090909</output>

<gadget id="calculator">(1/11) * 100</gadget>
<output>100/11 = around 9.090909</output>
<result>100/11 = around 9.090909</result>

Choices:
A. 9 %
B. 20 %
C. 25 %
D. 30 %
E. none

multiply(subtract(const_1, divide(multiply(const_1, 10), 11)), const_100)

Explanation: "sol . let the original consumption = 100 kg and new consumption = x kg . so , 100 x 10 = x × 11 = x = 91 kg . ∴ reduction in consumption = 9 % . answer a"


Question: the sum of the even numbers between 1 and n is 85 * 86 , where n is an odd number , then n = ?

<gadget id="calculator">85 * 2</gadget>
<output>170</output>

<gadget id="calculator">170 + 1</gadget>
<output>171</output>
<result>171</result>

Choices:
A. 163
B. 171
C. 179
D. 185
E. 191

Explanation: "let n - 1 = 2 a . 2 + 4 + . . . + 2 a = 2 * ( 1 + 2 + . . . + a ) = 2 * ( a ) ( a + 1 ) / 2 = ( a ) ( a + 1 ) = 85 * 86 then a = 85 and n = 171 . the answer is b ."


Question: total dinning bill of 6 people was $ 139.00 and 10 % tip divided the bill evenly ? what is the bill amount each person shared .

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

<gadget id="calculator">(1/10) + 1</gadget>
<output>11/10 = around 1.1</output>

<gadget id="calculator">139 * (11/10)</gadget>
<output>1_529/10 = around 152.9</output>

<gadget id="calculator">(1_529/10) / 6</gadget>
<output>1_529/60 = around 25.483333</output>
<result>1_529/60 = around 25.483333</result>

Choices:
A. 21.84
B. 22.84
C. 23.84
D. 24.84
E. 25.48

divide(multiply(139, add(divide(const_1, 10), const_1)), 6)

Explanation: dinner bill of 6 person = 139 + 10 % tip so , 10 % of 139 = ( 139 * 10 ) / 100 = 13.9 so , the actual total amount = 139 + 13.9 = $ 152.9 so per head bill = 152.9 / 6 = $ 25.48 answer : e


Question: in a t . v . factory , an average of 63 tvs are produced per day for the fist 25 days of the months . a few workers fellill for the next 5 daysreducing the daily avg for the month to 58 sets / day . the average production per day for day last 5 days is ?

<gadget id="calculator">25 + 5</gadget>
<output>30</output>

<gadget id="calculator">30 * 58</gadget>
<output>1_740</output>

<gadget id="calculator">25 * 63</gadget>
<output>1_575</output>

<gadget id="calculator">1_740 - 1_575</gadget>
<output>165</output>

<gadget id="calculator">165 / 5</gadget>
<output>33</output>
<result>33</result>

Choices:
A. 35
B. 33
C. 48
D. 50
E. 52

divide(subtract(multiply(add(25, 5), 58), multiply(25, 63)), 5)

Explanation: production during these 5 days = total production in a month - production in first 25 days . = 30 x 58 - 25 x 63 = 165 â ˆ ´ average for last 5 days = 165 / 5 = 33 b


Question: a part - time employee ’ s hourly wage was increased by 25 % . she decided to decrease the number of hours worked per week so that her total income did not change . by approximately what percent should the number of hours worked be decreased ?

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

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

<gadget id="calculator">125 / 100</gadget>
<output>5/4 = around 1.25</output>

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

<gadget id="calculator">(1/5) * 100</gadget>
<output>20</output>
<result>20</result>

Choices:
A. 9 %
B. 15 %
C. 20 %
D. 50 %
E. 100 %

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

Explanation: "let ' s plug in somenicenumbers and see what ' s needed . let ' s say the employee used to make $ 1 / hour and worked 100 hours / week so , the total weekly income was $ 100 / week after the 25 % wage increase , the employee makes $ 1.25 / hour we want the employee ' s income to remain at $ 100 / week . so , we want ( $ 1.25 / hour ) ( new # of hours ) = $ 100 divide both sides by 1.25 to get : new # of hours = 100 / 1.25 ≈ 80 hours so , the number of hours decreases from 100 hours to ( approximately ) 80 hours . this represents a 20 % decrease ( approximately ) . answer : c"


Question: a is twice as good a workman as b and they took 10 days together to do the work b alone can do it in .

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

<gadget id="calculator">10 * 3</gadget>
<output>30</output>

<gadget id="calculator">30 / 2</gadget>
<output>15</output>

<gadget id="calculator">15 * 2</gadget>
<output>30</output>
<result>30</result>

Choices:
A. 25 days
B. 88 days
C. 30 days
D. 11 days
E. 13 days

multiply(divide(multiply(10, add(const_2, const_1)), const_2), const_2)

Explanation: wc = 2 : 1 2 x + x = 1 / 10 x = 1 / 30 = > 30 days answer : c


Question: which number can we add to 425897 to get a number exactly divisible by 456 ?

<gadget id="calculator">425_897 % 456</gadget>
<output>449</output>

<gadget id="calculator">456 - 449</gadget>
<output>7</output>
<result>7</result>

Choices:
A. 3
B. 5
C. 7
D. 9
E. 11

Explanation: "425897 / 456 = 933 with a remainder of 449 . we need to add 456 - 449 = 7 the answer is c ."


Question: the speed at which a man can row a boat in still water is 9 kmph . if he rows downstream , where the speed of current is 3 kmph , what time will he take to cover 60 metres ?

<gadget id="calculator">9 + 3</gadget>
<output>12</output>

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

<gadget id="calculator">12 * (5/18)</gadget>
<output>10/3 = around 3.333333</output>

<gadget id="calculator">60 / (10/3)</gadget>
<output>18</output>
<result>18</result>

Choices:
A. 16 seconds
B. 34 seconds
C. 14 seconds
D. 18 seconds
E. 15 seconds

divide(60, multiply(add(9, 3), const_0_2778))

Explanation: "speed of the boat downstream = 9 + 3 = 12 kmph = 12 * 5 / 18 = 10 / 3 m / s hence time taken to cover 60 m = 60 * 3 / 10 = 18 seconds . answer : d"


Question: the roof of an apartment building is rectangular and its length is 3 times longer than its width . if the area of the roof is 588 feet squared , what is the difference between the length and the width of the roof ?

<gadget id="calculator">588 / 3</gadget>
<output>196</output>

<gadget id="calculator">196 ** (1/2)</gadget>
<output>14</output>

<gadget id="calculator">14 * 3</gadget>
<output>42</output>

<gadget id="calculator">42 - 14</gadget>
<output>28</output>
<result>28</result>

Choices:
A. 28 .
B. 40 .
C. 42 .
D. 44 .
E. 46 .

subtract(multiply(sqrt(divide(588, 3)), 3), sqrt(divide(588, 3)))

Explanation: "answer is a : 28 let w be the width , so length is 3 w . therefore : w * 3 w = 588 , solving for , w = 14 , so 3 w - w = 2 w = 2 * 14 = 28"


Question: how many numbers from 15 to 65 are exactly divisible by 5 ?

<gadget id="calculator">65 / 5</gadget>
<output>13</output>

<gadget id="calculator">floor(13)</gadget>
<output>13</output>

<gadget id="calculator">13 * 5</gadget>
<output>65</output>

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

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

<gadget id="calculator">3 + 1</gadget>
<output>4</output>

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

<gadget id="calculator">65 - 20</gadget>
<output>45</output>

<gadget id="calculator">45 / 5</gadget>
<output>9</output>

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

Choices:
A. 5
B. 7
C. 9
D. 10
E. 12

add(divide(subtract(multiply(floor(divide(65, 5)), 5), multiply(add(floor(divide(15, 5)), const_1), 5)), 5), const_1)

Explanation: "option ' d ' 15 / 5 = 3 and 65 / 5 = 13 = = > 13 - 3 = 10 numbers"


Question: two cards are drawn together from a pack of 52 cards the probability that one is the spade and one is a heart is ?

<gadget id="calculator">52 / 4</gadget>
<output>13</output>

<gadget id="calculator">13 * 13</gadget>
<output>169</output>

<gadget id="calculator">52 * 52</gadget>
<output>2_704</output>

<gadget id="calculator">169 / 2_704</gadget>
<output>1/16 = around 0.0625</output>

<gadget id="calculator">(1/16) * 2</gadget>
<output>1/8 = around 0.125</output>
<result>1/8 = around 0.125</result>

Choices:
A. 85 / 852
B. 45 / 69
C. 18 / 456
D. 13 / 102
E. 23 / 125

multiply(divide(multiply(divide(52, const_4), divide(52, const_4)), multiply(52, 52)), const_2)

Explanation: "let s be the sample space then n ( s ) = 52 c 2 = ( 52 * 51 ) / ( 2 * 1 ) = 1326 let e be the event of getting 1 spade kings and 1 heart let n ( e ) = number of ways of chossing 1 spade out of 13 and 1 heart out of 13 = ( 13 c 1 * 13 c 1 ) = 13 * 13 = 169 p ( e ) = n ( e ) / n ( s ) = 169 / 1326 = 13 / 102 answer ( d )"