Question: a company wants to spend equal amounts of money for the purchase of two types of computer printers costing $ 400 and $ 350 per unit , respectively . what is the fewest number of computer printers that the company can purchase ?

<gadget id="calculator">lcm(400, 350)</gadget>
<output>2_800</output>

<gadget id="calculator">2_800 / 400</gadget>
<output>7</output>

<gadget id="calculator">2_800 / 350</gadget>
<output>8</output>

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

Choices:
A. 11
B. 13
C. 15
D. 17
E. 19

Explanation: "the smallest amount that the company can spend is the lcm of 400 and 350 , which is 2800 for each , which is total 5600 . the number of 1 st type of computers which costing $ 400 = 2800 / 400 = 7 . the number of 2 nd type of computers which costing $ 350 = 2800 / 350 = 8 . total = 7 + 8 = 15 answer is c ."


Question: a man can row upstream at 25 kmph and downstream at 55 kmph , and then find the speed of the man in still water ?

<gadget id="calculator">25 + 55</gadget>
<output>80</output>

<gadget id="calculator">80 / 2</gadget>
<output>40</output>
<result>40</result>

Choices:
A. 65
B. 40
C. 30
D. 78
E. 38

Explanation: "us = 25 ds = 55 m = ( 55 + 25 ) / 2 = 40 answer : b"


Question: what will be the cost of building a fence around a square plot with area equal to 289 sq ft , if the price per foot of building the fence is rs . 60 ?

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

<gadget id="calculator">4 * 17</gadget>
<output>68</output>

<gadget id="calculator">68 * 60</gadget>
<output>4_080</output>
<result>4_080</result>

Choices:
A. s . 3944
B. s . 3948
C. s . 4080
D. s . 3965
E. s . 3929

Explanation: "let the side of the square plot be a ft . a 2 = 289 = > a = 17 length of the fence = perimeter of the plot = 4 a = 68 ft . cost of building the fence = 68 * 60 = rs . 4080 . answer : c"


Question: an electrical appliances store sold this month 400 % more than the average of all the other months in the year . the sales total for this month was approximately what percent of total sales for this year ?

<gadget id="calculator">100 + 400</gadget>
<output>500</output>

<gadget id="calculator">100 * 12</gadget>
<output>1_200</output>

<gadget id="calculator">1_200 + 400</gadget>
<output>1_600</output>

<gadget id="calculator">500 / 1_600</gadget>
<output>5/16 = around 0.3125</output>

<gadget id="calculator">(5/16) * 100</gadget>
<output>125/4 = around 31.25</output>

<gadget id="calculator">(125/4) - 10</gadget>
<output>85/4 = around 21.25</output>
<result>85/4 = around 21.25</result>

Choices:
A. 14 %
B. 21 % .
C. 31 % .
D. 37 % .
E. 43 % .

subtract(multiply(divide(add(const_100, 400), add(multiply(const_100, const_12), 400)), const_100), const_10)

Explanation: the average sales for all the other months ( 11 months ) of the year is x . so , the total sales of those 11 months will be = 11 x now , this month ' s sales , which is 400 % more than the average of other months ' sales , is 5 x , ( x + 400 % of x ) . thus , this month ' s ' sales are ( 5 x / 16 x ) * 100 = 31.25 % of the total yearly sales . [ total sales = 11 x + 5 x = 16 x ] answer is b


Question: a bag contains 10 green and 8 white balls . if two balls are drawn simultaneously , the probability that both are of the same colour is

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

<gadget id="calculator">8 / 18</gadget>
<output>4/9 = around 0.444444</output>

<gadget id="calculator">8 - 1</gadget>
<output>7</output>

<gadget id="calculator">18 - 1</gadget>
<output>17</output>

<gadget id="calculator">7 / 17</gadget>
<output>7/17 = around 0.411765</output>

<gadget id="calculator">(4/9) * (7/17)</gadget>
<output>28/153 = around 0.183007</output>

<gadget id="calculator">10 / 18</gadget>
<output>5/9 = around 0.555556</output>

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

<gadget id="calculator">9 / 17</gadget>
<output>9/17 = around 0.529412</output>

<gadget id="calculator">(5/9) * (9/17)</gadget>
<output>5/17 = around 0.294118</output>

<gadget id="calculator">(28/153) + (5/17)</gadget>
<output>73/153 = around 0.477124</output>
<result>73/153 = around 0.477124</result>

Choices:
A. 8 / 15
B. 21 / 44
C. 3 / 5
D. 11 / 15
E. 7 / 15

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

Explanation: drawing two balls of same color from ten green balls can be done in 10 c ₂ ways . similarly from eight white balls two can be drawn in ⁸ c ₂ ways . p = 10 c ₂ / ¹ ⁵ c ₂ + ⁸ c ₂ / ¹ ⁵ c ₂ = 21 / 44 answer : b


Question: two bike riders ride in opposite directions around a circular track , starting at the same time from the same point . biker a rides at a speed of 16 kmph and biker b rides at a speed of 14 kmph . if the track has a diameter of 40 km , after how much time ( in hours ) will the two bikers meet ?

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

<gadget id="calculator">12 * 2</gadget>
<output>24</output>

<gadget id="calculator">24 - 2</gadget>
<output>22</output>

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

<gadget id="calculator">22 / 7</gadget>
<output>22/7 = around 3.142857</output>

<gadget id="calculator">16 + 14</gadget>
<output>30</output>

<gadget id="calculator">40 / 30</gadget>
<output>4/3 = around 1.333333</output>

<gadget id="calculator">(22/7) * (4/3)</gadget>
<output>88/21 = around 4.190476</output>
<result>88/21 = around 4.190476</result>

Choices:
A. 8.18 hrs .
B. 6.18 hrs .
C. 4.18 hrs .
D. 1.18 hrs .
E. 7.18 hrs .

multiply(divide(subtract(multiply(multiply(const_3, const_4), const_2), const_2), add(const_3, const_4)), divide(40, add(16, 14)))

Explanation: explanation : distance to be covered = = 40 km relative speed of bikers = 16 + 14 = 30 kmph . now , = = 4.18 hrs . answer : c


Question: a cistern 12 m long and 14 m wide contains water up to a depth of 1 m 25 cm . the total area of the wet surface is :

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

<gadget id="calculator">(1/4) + 1</gadget>
<output>5/4 = around 1.25</output>

<gadget id="calculator">(5/4) * 14</gadget>
<output>35/2 = around 17.5</output>

<gadget id="calculator">(5/4) * 12</gadget>
<output>15</output>

<gadget id="calculator">(35/2) + 15</gadget>
<output>65/2 = around 32.5</output>

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

<gadget id="calculator">14 * 12</gadget>
<output>168</output>

<gadget id="calculator">65 + 168</gadget>
<output>233</output>
<result>233</result>

Choices:
A. 224 m 2
B. 250 m 2
C. 220 m 2
D. 230 m 2
E. 233 m 2

add(multiply(const_2, add(multiply(add(divide(25, const_100), 1), 14), multiply(add(divide(25, const_100), 1), 12))), multiply(14, 12))

Explanation: "area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 14 x 1.25 + 12 x 1.25 ) + 12 x 14 ] m 2 = 233 m 2 . answer : e"


Question: if a / b = 1 / 3 , b / c = 2 , c / d = 1 / 2 , d / e = 3 and e / f = 1 / 10 , then what is the value of abc / def ?

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

<gadget id="calculator">3 * 10</gadget>
<output>30</output>

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

<gadget id="calculator">9 / 60</gadget>
<output>3/20 = around 0.15</output>
<result>3/20 = around 0.15</result>

Choices:
A. 27 / 4
B. 27 / 8
C. 3 / 4
D. 3 / 20
E. 1 / 4

divide(multiply(3, 3), multiply(2, multiply(3, 10)))

Explanation: say a = 2 . then : a / b = 1 / 3 - - > b = 6 ; b / c = 2 - - > c = 3 ; c / d = 1 / 2 - - > d = 6 ; d / e = 3 - - > e = 2 ; e / f = 1 / 10 - - > f = 20 . abc / def = ( 2 * 6 * 3 ) / ( 6 * 2 * 20 ) = 3 / 20 . answer : d .


Question: find the compound interest on $ 10000 in 2 years at 4 % per annum , the interest being compounded half - yearly ?

Choices:
A. $ 645.56
B. $ 824.32
C. $ 954.26
D. $ 745.69
E. $ 1020.45

subtract(multiply(power(add(divide(divide(4, const_100), 2), const_1), 4), 10000), 10000)

Explanation: "principle = $ 10000 rate = 2 % half yearly = 4 half years amount = 10000 * ( 1 + 2 / 100 ) ^ 4 = 10000 * 51 / 50 * 51 / 50 * 51 / 50 * 51 / 50 = $ 10824.32 c . i . = 10824.32 - 10000 = $ 824.32 answer is b"


Question: if a = 105 and a ^ 3 = 21 × 25 × 45 × z , what is the value of z ?

<gadget id="calculator">105 ** 3</gadget>
<output>1_157_625</output>

<gadget id="calculator">21 * 25</gadget>
<output>525</output>

<gadget id="calculator">525 * 45</gadget>
<output>23_625</output>

<gadget id="calculator">1_157_625 / 23_625</gadget>
<output>49</output>
<result>49</result>

Choices:
A. 35
B. 42
C. 45
D. 49
E. 54

divide(power(105, 3), multiply(multiply(21, 25), 45))

Explanation: "a = 105 = 3 * 5 * 7 a ^ 3 = 21 × 25 × 45 × z = > a ^ 3 = ( 7 * 3 ) x ( 5 * 5 ) x ( 3 ^ 2 * 5 ) x z = > a ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x z = > ( 3 * 5 * 7 ) ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x z z = 7 ^ 2 = 49 answer d"


Question: if the cost price of 50 articles is equal to the selling price of 45 articles , then the gain or loss percent is ?

<gadget id="calculator">100 * 45</gadget>
<output>4_500</output>

<gadget id="calculator">4_500 / 50</gadget>
<output>90</output>

<gadget id="calculator">100 - 90</gadget>
<output>10</output>

<gadget id="calculator">10 / 90</gadget>
<output>1/9 = around 0.111111</output>

<gadget id="calculator">100 * (1/9)</gadget>
<output>100/9 = around 11.111111</output>
<result>100/9 = around 11.111111</result>

Choices:
A. 11.11
B. 65
C. 78
D. 33
E. 25

multiply(const_100, divide(subtract(const_100, divide(multiply(const_100, 45), 50)), divide(multiply(const_100, 45), 50)))

Explanation: "given that , cost price of 50 article is equal to selling price of 45 articles . let cost price of one article = rs . 1 selling price of 45 articles = rs . 50 but cost price of 45 articles = rs . 45 therefore , the trader made profit . \ percentage of profit = 5 / 45 * 100 = 11.11 % answer : a"


Question: a train moves with a speed of 162 kmph . its speed in metres per second is

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

<gadget id="calculator">162 * (5/18)</gadget>
<output>45</output>
<result>45</result>

Choices:
A. 10.8
B. 18
C. 30
D. 38.8
E. 45

Explanation: "solution speed = 108 kmph = ( 162 x 5 / 18 ) m / sec = 45 m / sec . answer e"


Question: which number should replace both the asterisks in ( * / 20 ) x ( * / 80 ) = 1 ?

<gadget id="calculator">80 * 20</gadget>
<output>1_600</output>

<gadget id="calculator">1_600 ** (1/2)</gadget>
<output>40</output>
<result>40</result>

Choices:
A. 20
B. 40
C. 60
D. 80
E. 120

Explanation: "let ( y / 20 ) x ( y / 80 ) = 1 y ^ 2 = 20 x 80 = 20 x 20 x 4 y = ( 20 x 2 ) = 40 the answer is b ."


Question: a couple spent $ 211.20 in total while dining out and paid this amount using a credit card . the $ 211.20 figure included a 20 percent tip which was paid on top of the price which already included a sales tax of 10 percent on top of the price of the food . what was the actual price of the food before tax and tip ?

<gadget id="calculator">211.2 * 100</gadget>
<output>21_120</output>

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

<gadget id="calculator">21_120 / 120</gadget>
<output>176</output>

<gadget id="calculator">176 * 100</gadget>
<output>17_600</output>

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

<gadget id="calculator">17_600 / 110</gadget>
<output>160</output>
<result>160</result>

Choices:
A. $ 120
B. $ 140
C. $ 150
D. $ 160
E. $ 180

divide(multiply(divide(multiply(211.20, const_100), add(const_100, 20)), const_100), add(const_100, 10))

Explanation: "let the price of the meal be x . after a 10 % sales tax addition , the price is 1.1 * x after a 20 % tip on this amount , the total is 1.2 * 1.1 * x = 1.32 x 1.32 x = $ 211.20 x = $ 160 the correct answer is d ."


Question: at a school , 3 - fifths of the male students and two - thirds of the female students speak a foreign language . if the number of males is equal to the number of females , what fraction of the students speak a foreign language ?

<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">100 / 2</gadget>
<output>50</output>

<gadget id="calculator">(3/5) * 50</gadget>
<output>30</output>

<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>

<gadget id="calculator">(2/3) * 50</gadget>
<output>100/3 = around 33.333333</output>

<gadget id="calculator">30 + (100/3)</gadget>
<output>190/3 = around 63.333333</output>

<gadget id="calculator">(190/3) / 100</gadget>
<output>19/30 = around 0.633333</output>
<result>19/30 = around 0.633333</result>

Choices:
A. 17 / 30
B. 19 / 30
C. 11 / 15
D. 7 / 15
E. 2 / 5

divide(add(multiply(divide(3, add(const_2, const_3)), divide(const_100, const_2)), multiply(divide(const_2, const_3), divide(const_100, const_2))), const_100)

Explanation: let x be the number of students in the school . the number of males who speak a foreign language is ( 3 / 5 ) ( 1 / 2 ) x = ( 3 / 10 ) x the number of females who speak a foreign language is ( 2 / 3 ) ( 1 / 2 ) x = ( 1 / 3 ) x the total number of students who speak a foreign language is ( 3 / 10 ) x + ( 1 / 3 ) x = ( 19 / 30 ) x the answer is b .


Question: the time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream . if the speed of the boat in still water is 60 kmph , find the speed of the stream ?

<gadget id="calculator">60 * 2</gadget>
<output>120</output>

<gadget id="calculator">120 / 3</gadget>
<output>40</output>

<gadget id="calculator">60 - 40</gadget>
<output>20</output>
<result>20</result>

Choices:
A. 18 kmph
B. 19 kmph
C. 21 kmph
D. 22 kmph
E. 20 kmph

subtract(60, divide(multiply(60, const_2), const_3))

Explanation: "the ratio of the times taken is 2 : 1 . the ratio of the speed of the boat in still water to the speed of the stream = ( 2 + 1 ) / ( 2 - 1 ) = 3 / 1 = 3 : 1 speed of the stream = 60 / 3 = 20 kmph . answer : e"


Question: the length of a rectangular plot is thrice its width . if the area of the rectangular plot is 432 sq meters , then what is the width ( in meters ) of the rectangular plot ?

<gadget id="calculator">432 / 3</gadget>
<output>144</output>

<gadget id="calculator">144 / 3</gadget>
<output>48</output>

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

Choices:
A. 10
B. 11
C. 12
D. 13
E. 14

divide(divide(divide(432, const_3), const_3), const_4)

Explanation: area = l * w = 3 w ^ 2 = 432 w ^ 2 = 144 w = 12 the answer is c .


Question: a certain car uses 12 gallons of gasoline in traveling 120 miles . in order for the car to travel the same distance using 10 gallons of gasoline , by how many miles per gallon must the car ’ s gas mileage be increased ?

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

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

<gadget id="calculator">12 - 10</gadget>
<output>2</output>
<result>2</result>

Choices:
A. 2
B. 4
C. 6
D. 8
E. 10

subtract(divide(120, 10), divide(120, 12))

Explanation: 120 / 10 = 12 . the difference is 12 - 10 = 2 . answer a


Question: the captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . find out the average age of the team .

<gadget id="calculator">26 + 3</gadget>
<output>29</output>

<gadget id="calculator">26 + 29</gadget>
<output>55</output>

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

<gadget id="calculator">55 - 9</gadget>
<output>46</output>

<gadget id="calculator">46 / 2</gadget>
<output>23</output>
<result>23</result>

Choices:
A. 20
B. 21
C. 22
D. 23
E. 25

divide(subtract(add(26, add(26, 3)), multiply(3, 3)), const_2)

Explanation: "number of members in the team = 11 let the average age of of the team = x = > ( sum of ages of all 11 members ) / 11 = x = > sum of the ages of all 11 members = 11 x age of the captain = 26 age of the wicket keeper = 26 + 3 = 29 sum of the ages of 9 members of the team excluding captain and wicket keeper = 11 x − 26 − 29 = 11 x − 55 average age of 9 members of the team excluding captain and wicket keeper = ( 11 x − 55 ) / 9 given that ( 11 x − 55 ) / 9 = ( x − 1 ) ⇒ 11 x − 55 = 9 ( x − 1 ) ⇒ 11 x − 55 = 9 x − 9 ⇒ 2 x = 46 ⇒ x = 46 / 2 = 23 years answer is d ."


Question: a box contains 7 pairs of shoes ( 14 shoes in total ) . if two shoes are selected at random , what it is the probability that they are matching shoes ?

<gadget id="calculator">14 - 1</gadget>
<output>13</output>

<gadget id="calculator">1 / 13</gadget>
<output>1/13 = around 0.076923</output>
<result>1/13 = around 0.076923</result>

Choices:
A. 1 / 190
B. 1 / 20
C. 1 / 19
D. 1 / 13
E. 1 / 9

Explanation: "the problem with your solution is that we do n ' t choose 1 shoe from 14 , but rather choose the needed one after we just took one and need the second to be the pair of it . so , the probability would simply be : 1 / 1 * 1 / 13 ( as after taking one at random there are 13 shoes left and only one is the pair of the first one ) = 1 / 13 answer : d ."


Question: when positive integer x is divided by positive integer y , the remainder is 3 . if x / y = 96.12 , what is the value of y ?

<gadget id="calculator">floor(96.12)</gadget>
<output>96</output>

<gadget id="calculator">96.12 - 96</gadget>
<output>0.12</output>

<gadget id="calculator">3 / 0.12</gadget>
<output>25</output>
<result>25</result>

Choices:
A. 96
B. 75
C. 48
D. 25
E. 12

Explanation: "when positive integer x is divided by positive integer y , the remainder is 3 - - > x = qy + 3 ; x / y = 96.12 - - > x = 96 y + 0.12 y ( so q above equals to 96 ) ; 0.12 y = 3 - - > y = 25 . answer : d ."


Question: if john makes a contribution to a charity fund at school , the average contribution size will increase by 50 % reaching $ 75 per person . if there were 1 other contributions made before john ' s , what is the size of his donation ?

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

<gadget id="calculator">2 * 75</gadget>
<output>150</output>

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

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

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

Choices:
A. $ 100
B. $ 150
C. $ 200
D. $ 250
E. $ 450

add(subtract(multiply(add(1, const_1), 75), multiply(add(1, const_1), 50)), 50)

Explanation: "cavg = average contribution before john cavg * 1.5 = 75 , therefore the average cont is $ 50 before john . if he needs to increase the average contribution by $ 25 , he must put in $ 25 for each of the 1 people . so $ 25 . but , he also has to put in the average for himself ( the twoth person ) , so add $ 75 . so $ 100 is your answer . answer a"


Question: 15 men can complete a work in 10 days while 20 boys can complete the same work in 15 days . how many days will 10 men and 10 boys together take to complete the same work

<gadget id="calculator">15 * 10</gadget>
<output>150</output>

<gadget id="calculator">150 / 10</gadget>
<output>15</output>

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

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

<gadget id="calculator">1 / 30</gadget>
<output>1/30 = around 0.033333</output>

<gadget id="calculator">(1/15) + (1/30)</gadget>
<output>1/10 = around 0.1</output>

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

Choices:
A. 9 days
B. 10 days
C. 11 days
D. 12 days
E. 13 days

inverse(add(divide(const_1, divide(multiply(15, 10), 10)), divide(const_1, multiply(15, const_2))))

Explanation: solution : work done by one man in one day = 1 / ( 15 * 10 ) work done by one boy in one day = 1 / ( 20 * 15 ) work done by 10 men and 10 boys in one day = 10 [ 1 / ( 15 * 10 ) + 1 / ( 20 * 15 ) ] days taken = 1 / work done by 10 men and 10 boys in one day answer b


Question: a rectangular tiled patio is composed of 96 square tiles . the rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles . after the change in layout , the patio will still have 96 tiles , and it will still be rectangular . how many rows are in the tile patio before the change in layout ?

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

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

<gadget id="calculator">96 * 2</gadget>
<output>192</output>

<gadget id="calculator">4 * 192</gadget>
<output>768</output>

<gadget id="calculator">16 + 768</gadget>
<output>784</output>

<gadget id="calculator">784 ** (1/2)</gadget>
<output>28</output>

<gadget id="calculator">(-4) + 28</gadget>
<output>24</output>

<gadget id="calculator">24 / 2</gadget>
<output>12</output>

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

Choices:
A. 5
B. 6
C. 8
D. 13
E. 28

divide(96, divide(add(negate(4), sqrt(add(power(4, 2), multiply(4, multiply(96, 2))))), 2))

Explanation: "suppose there are c columns and there are r rows original situation so , number of tiles = c * r = 96 also . reach column has r tiles and each row has c tiles new situation number of tiles in each column is r - 2 and number of tiles in each row is c + 4 so , number of rows = r - 2 and number of columns is c + 4 so , number of tiles = ( r - 2 ) * ( c + 4 ) = 96 comparing both of them we get c * r = ( r - 2 ) * ( c + 4 ) = > 4 r - 2 c = 8 c = 2 r - 4 putting it in c * r = 96 ( 2 r - 4 ) * r = 96 2 r ^ 2 - 4 r - 96 = 0 r can not be negative so r = 8 and c = 12 so , answer will be c"


Question: find the area of a parallelogram with base 12 cm and height 48 cm ?

<gadget id="calculator">12 * 48</gadget>
<output>576</output>
<result>576</result>

Choices:
A. 122 cm 2
B. 576 cm 2
C. 246 cm 2
D. 42 cm 2
E. 39 cm 2

Explanation: "area of a parallelogram = base * height = 12 * 48 = 576 cm 2 answer : b"


Question: of the diplomats attending a summit conference , 25 speak french , 32 do not speak russian , and 20 % of the diplomats speak neither french nor russian . if 10 % of the diplomats speak both languages , then how many diplomats attended the conference ?

<gadget id="calculator">32 - 25</gadget>
<output>7</output>

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

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

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

<gadget id="calculator">7 / (1/10)</gadget>
<output>70</output>
<result>70</result>

Choices:
A. 72
B. 70
C. 108
D. 120
E. 150

divide(subtract(32, 25), subtract(divide(20, const_100), divide(10, const_100)))

Explanation: "{ total } = { french } + { russian } - { both } + { neither } { total } = 25 + ( { total } - 32 ) - ( 0.1 * { total } ) + 0.2 * { total } solving gives { total } = 70 . answer : b ."


Question: a vendor buys 10 t - shirts at an average price of $ 14 per t - shirt . he then buys 15 more t - shirts at an average price of $ 11 per t - shirt . what is the average price q per t - shirt that the vendor paid for these purchases ?

<gadget id="calculator">10 + 14</gadget>
<output>24</output>

<gadget id="calculator">24 / 2</gadget>
<output>12</output>

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

<gadget id="calculator">(1/4) + (1/4)</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">12 + (1/2)</gadget>
<output>25/2 = around 12.5</output>
<result>25/2 = around 12.5</result>

Choices:
A. $ 12.20
B. $ 12.50
C. $ 12.55
D. $ 12.70
E. $ 13.00

add(divide(add(10, 14), const_2), add(const_0_25, const_0_25))

Explanation: "correct answer : a explanation : the relevant formula for this problem is average q = ( sum ) / ( number of terms ) . another way to look at the formula is sum = average x number of terms . for the first purchase , the vendor ' s sum ( total cost ) was $ 140 , since 14 x 10 = 140 . for the second purchase , the vendor ' s cost was $ 165 , since 11 x 15 = 165 . the grand sum is then $ 140 + $ 165 , which equals $ 305 . the total number of shirts purchased was 25 , so to get the average price per shirt , we divide 305 by 25 , which equals $ 12.20 . as a result , the correct answer is a . note : a relative understanding of weighted average offers a shortcut to this problem . because the true average of 11 and 14 is 12.5 , but the vendor sells more shirts at the lower price than at the higher price , the weighted average must be less than $ 12.50 ; only answer choice a is a possibility ."


Question: excluding the stoppages , the speed of a bus is 48 km / hr and including the stoppages the speed of the bus is 12 km / hr . for how many minutes does the bus stop per hour ?

<gadget id="calculator">12 / 48</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">(1/4) * 60</gadget>
<output>15</output>

<gadget id="calculator">60 - 15</gadget>
<output>45</output>
<result>45</result>

Choices:
A. 45 min
B. 10 min
C. 12 min
D. 20 min
E. 18 min

subtract(const_60, multiply(divide(12, 48), const_60))

Explanation: "speed of the bus without stoppage = 48 km / hr speed of the bus with stoppage = 12 km / hr difference in speed = 36 km / hr so , the time taken in the stoppages = time taken to cover 36 km = ( 36 / 48 ) hr = 3 / 4 hr = 45 min answer : a"


Question: the area of the square formed on the diagonal of a rectangle as its side is 108 1 / 3 % more than the area of the rectangle . if the perimeter of the rectangle is 28 units , find the difference between the sides of the rectangle ?

<gadget id="calculator">108 / 3</gadget>
<output>36</output>

<gadget id="calculator">36 - 28</gadget>
<output>8</output>

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

Choices:
A. 5
B. 4
C. 7
D. 2
E. 1

divide(subtract(divide(108, 3), 28), const_4)

Explanation: let the sides of the rectangle be l and b respectively . from the given data , ( √ l 2 + b 2 ) = ( 1 + 108 1 / 3 % ) lb = > l 2 + b 2 = ( 1 + 325 / 3 * 1 / 100 ) lb = ( 1 + 13 / 12 ) lb = 25 / 12 lb = > ( l 2 + b 2 ) / lb = 25 / 12 12 ( l 2 + b 2 ) = 25 lb adding 24 lb on both sides 12 l 2 + 12 b 2 + 24 lb = 49 lb 12 ( l 2 + b 2 + 2 lb ) = 49 lb but 2 ( l + b ) = 28 = > l + b = 14 12 ( l + b ) 2 = 49 lb = > 12 ( 14 ) 2 = 49 lb = > lb = 48 since l + b = 14 , l = 8 and b = 6 l - b = 8 - 6 = 2 m . answer : d


Question: the owner of a furniture shop charges his customer 10 % more than the cost price . if a customer paid rs . 8800 for a computer table , then what was the cost price of the computer table ?

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

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

<gadget id="calculator">8_800 / (11/10)</gadget>
<output>8_000</output>
<result>8_000</result>

Choices:
A. rs . 6725
B. rs . 6727
C. rs . 8000
D. rs . 6725
E. rs . 6728

divide(8800, add(const_1, divide(10, const_100)))

Explanation: "cp = sp * ( 100 / ( 100 + profit % ) ) = 8800 ( 100 / 110 ) = rs . 8000 . answer : c"


Question: if sharon ' s weekly salary increased by 16 percent , she would earn $ 348 per week . if instead , her weekly salary were to increase by 15 percent , how much would she earn per week ?

<gadget id="calculator">16 / 100</gadget>
<output>4/25 = around 0.16</output>

<gadget id="calculator">1 + (4/25)</gadget>
<output>29/25 = around 1.16</output>

<gadget id="calculator">348 / (29/25)</gadget>
<output>300</output>

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

<gadget id="calculator">(3/20) * 300</gadget>
<output>45</output>

<gadget id="calculator">300 + 45</gadget>
<output>345</output>
<result>345</result>

Choices:
A. $ 374
B. $ 382
C. $ 345
D. $ 392
E. $ 399

add(divide(348, add(const_1, divide(16, const_100))), multiply(divide(15, const_100), divide(348, add(const_1, divide(16, const_100)))))

Explanation: "( 348 / 116 ) 115 = 345 in this case long division does not take much time . ( 348 / 116 ) = 3 3 * 115 = 345 ( 300 + 45 ) answer c"


Question: the average monthly salary of 8 workers and one supervisor in a factory was 430 . @ sswhen @ ssthe @ sssupervisor @ cc @ sswhose @ sssalary @ sswas @ ss 430 . @ sswhen @ ssthe @ sssupervisor @ cc @ sswhose @ sssalary @ sswas @ ss 430 . whenthesupervisor , whosesalarywas 430 . when the supervisor , whose salary was 870 per month , retired , a new person was appointed and then the average salary of 9 people was $ $ 440 per month . the salary of the new supervisor is :

<gadget id="calculator">440 * 9</gadget>
<output>3_960</output>

<gadget id="calculator">430 * 9</gadget>
<output>3_870</output>

<gadget id="calculator">3_870 - 870</gadget>
<output>3_000</output>

<gadget id="calculator">3_960 - 3_000</gadget>
<output>960</output>
<result>960</result>

Choices:
A. 233
B. 960
C. 287
D. 771
E. 191

subtract(multiply(440, 9), subtract(multiply(430, 9), 870))

Explanation: explanation : total salary of 8 workers and supervisor together = 9 ã — 430 = 3870 now total salary of 8 workers = 3870 â ˆ ’ 870 = 3000 total salary of 9 workers including the new supervisor = 9 ã — 440 = 3960 salary of the new supervisor = 3960 â ˆ ’ 3000 = 960 answer : b


Question: if ( m - 8 ) is a factor of m ^ 2 - hm - 24 , then h =

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

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

Choices:
A. 3
B. 5
C. 6
D. 11
E. 16

Explanation: ( m - 8 ) ( m - a ) = m ^ 2 - hm - 24 a = - 3 h = 8 + a = 5 = b


Question: the length of the bridge , which a train 500 metres long and travelling at 42 km / hr can cross in 60 seconds , is ?

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

<gadget id="calculator">42 * 1_000</gadget>
<output>42_000</output>

<gadget id="calculator">3_600 / 1</gadget>
<output>3_600</output>

<gadget id="calculator">42_000 / 3_600</gadget>
<output>35/3 = around 11.666667</output>

<gadget id="calculator">(35/3) * 60</gadget>
<output>700</output>

<gadget id="calculator">700 - 500</gadget>
<output>200</output>
<result>200</result>

Choices:
A. 100 m
B. 200 m
C. 300 m
D. 250 m
E. 350 m

subtract(multiply(divide(multiply(42, speed(const_1000, const_1)), speed(const_3600, const_1)), 60), 500)

Explanation: "speed = [ 42 x 5 / 18 ] m / sec = [ 35 / 3 ] m / sec time = 30 sec let the length of bridge be x metres . then , ( 130 + x ) / 60 35 / 3 = ( 130 + x ) / 60 500 + x = 700 = > x = 200 m answer : b"


Question: a bowl contains equal numbers of red , orange , green , blue , and yellow candies . kaz eats all of the green candies and half of the orange ones . next , he eats half of the remaining pieces of each color . finally , he eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 20 % of the original number . what percent of the red candies remain ?

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

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

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

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

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

<gadget id="calculator">20 - 15</gadget>
<output>5</output>

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

<gadget id="calculator">(5/2) / 20</gadget>
<output>1/8 = around 0.125</output>

<gadget id="calculator">(1/8) * 100</gadget>
<output>25/2 = around 12.5</output>
<result>25/2 = around 12.5</result>

Choices:
A. 5 %
B. 7.5 %
C. 10 %
D. 12.5 %
E. 15 %

multiply(divide(divide(subtract(20, add(divide(divide(const_100, add(const_2, const_3)), const_2), divide(divide(divide(const_100, add(const_2, const_3)), const_2), const_2))), const_2), divide(const_100, add(const_2, const_3))), const_100)

Explanation: "let x be the original number of each color . kaz eats all of the green candies and half of the orange ones . there are 0 green candies and 0.5 x orange candies remaining . he eats half of the remaining pieces of each color . there are 0.25 x orange candies , and 0.5 x each of red , yellow , and blue candies . he eats red and yellow candies in equal proportions . orange + blue + red + yellow = 0.75 x + red + yellow = x red + yellow = 0.25 x red = 0.125 x , since red = yellow . the answer is d ."


Question: the average of 2 , 76 and x is 5 . find the value of x ?

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

<gadget id="calculator">76 / 10</gadget>
<output>38/5 = around 7.6</output>

<gadget id="calculator">floor(38/5)</gadget>
<output>7</output>

<gadget id="calculator">76 % 10</gadget>
<output>6</output>

<gadget id="calculator">7 + 6</gadget>
<output>13</output>

<gadget id="calculator">13 + 2</gadget>
<output>15</output>

<gadget id="calculator">20 - 15</gadget>
<output>5</output>
<result>5</result>

Choices:
A. 10
B. 8
C. 12
D. 15
E. 5

subtract(multiply(5, const_4), add(add(floor(divide(76, const_10)), reminder(76, const_10)), 2))

Explanation: average = ( 2 + 7 + 6 + x ) / 4 = 5 x = 5 answer is e


Question: if y > 0 , ( 6 y ) / 20 + ( 3 y ) / 10 is what percent of y ?

<gadget id="calculator">6 / 20</gadget>
<output>3/10 = around 0.3</output>

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

<gadget id="calculator">(3/10) + (3/10)</gadget>
<output>3/5 = around 0.6</output>

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

Choices:
A. 40 %
B. 50 %
C. 60 %
D. 70 %
E. 80 %

multiply(const_100, add(divide(6, 20), divide(3, 10)))

Explanation: "can be reduced to 3 y / 10 + 3 y / 10 = 3 y / 5 = 60 % c"


Question: if the number is divided by 3 , it reduced by 36 . the number is

<gadget id="calculator">36 * 3</gadget>
<output>108</output>

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

<gadget id="calculator">108 / 2</gadget>
<output>54</output>
<result>54</result>

Choices:
A. 51
B. 50
C. 45
D. 54
E. 36

divide(multiply(36, 3), subtract(3, const_1))

Explanation: "explanation : let the number be x . then , x - ( x / 3 ) = 36 = > 2 x / 3 = 36 = > x = 54 answer : option d"


Question: in a group of 150 readers who read science fiction or literacy works or both , 120 read science fiction and 90 read literacy works . how many read both science fiction and literacy works ?

<gadget id="calculator">120 + 90</gadget>
<output>210</output>

<gadget id="calculator">210 - 150</gadget>
<output>60</output>
<result>60</result>

Choices:
A. 70
B. 60
C. 90
D. 100
E. 110

Explanation: consider total number of reader n ( s u l ) = 150 people who read science fiction n ( s ) = 120 people who read literacy works n ( l ) = 90 both science fiction and literacy n ( s â ˆ © l ) = ? n ( s u l ) = n ( s ) + n ( l ) - n ( s â ˆ © l ) 150 = 120 + 90 - n ( s â ˆ © l ) n ( s â ˆ © l ) = 210 - 150 n ( s â ˆ © l ) = 60 so people read both science fiction and literacy works are 160 answer : b


Question: the speed of a boat in still water in 30 km / hr and the rate of current is 7 km / hr . the distance travelled downstream in 36 minutes is :

<gadget id="calculator">30 + 7</gadget>
<output>37</output>

<gadget id="calculator">36 / 60</gadget>
<output>3/5 = around 0.6</output>

<gadget id="calculator">37 * (3/5)</gadget>
<output>111/5 = around 22.2</output>
<result>111/5 = around 22.2</result>

Choices:
A. 18.4 km
B. 20.6 km
C. 21.4 km
D. 1111 km
E. 22.2 km

multiply(add(30, 7), divide(36, const_60))

Explanation: "explanation : speed downstream = ( 30 + 7 ) = 37 kmph time = 36 minutes = 36 / 60 hour = 3 / 5 hour distance travelled = time × speed = ( 3 / 5 ) × 37 = 22.2 km answer : option e"


Question: 39 persons can repair a road in 12 days , working 5 hours a day . in how many days will 30 persons , working 3 hours a day , complete the work ?

<gadget id="calculator">39 * 12</gadget>
<output>468</output>

<gadget id="calculator">468 * 5</gadget>
<output>2_340</output>

<gadget id="calculator">30 * 3</gadget>
<output>90</output>

<gadget id="calculator">2_340 / 90</gadget>
<output>26</output>
<result>26</result>

Choices:
A. 10
B. 26
C. 14
D. 15
E. 16

divide(multiply(multiply(39, 12), 5), multiply(30, 3))

Explanation: "let the required number of days be x . less persons , more days ( indirect proportion ) more working hours per day , less days ( indirect proportion ) persons 30 : 39 : : 12 : x working hours / day 3 : 5 30 x 3 x x = 39 x 5 x 12 x = ( 39 x 5 x 12 ) / ( 30 x 3 ) x = 26 . answer : b"


Question: cole drove from home to work at an average speed of 80 kmh . he then returned home at an average speed of 120 kmh . if the round trip took a total of 2 hours , how many minutes did it take cole to drive to work ?

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

<gadget id="calculator">80 + 120</gadget>
<output>200</output>

<gadget id="calculator">240 / 200</gadget>
<output>6/5 = around 1.2</output>

<gadget id="calculator">(6/5) * 60</gadget>
<output>72</output>
<result>72</result>

Choices:
A. 66
B. 70
C. 72
D. 75
E. 78

multiply(divide(multiply(120, 2), add(80, 120)), const_60)

Explanation: "first round distance travelled ( say ) = d speed = 80 k / h time taken , t 2 = d / 80 hr second round distance traveled = d ( same distance ) speed = 120 k / h time taken , t 2 = d / 120 hr total time taken = 2 hrs therefore , 2 = d / 80 + d / 120 lcm of 80 and 120 = 240 2 = d / 80 + d / 120 = > 2 = 3 d / 240 + 2 d / 240 = > d = 240 * 2 / 5 km therefore , t 1 = d / 80 = > t 1 = ( 240 * 2 ) / ( 5 x 80 ) = > t 1 = ( 6 x 60 ) / 5 - - in minutes = > t 1 = 72 minutes . c"


Question: a trader mixes 80 kg of tea at 15 per kg with 20 kg of tea at cost price of 20 per kg . in order to earn a profit of 25 % , what should be the sale price of the mixed tea ?

<gadget id="calculator">80 * 15</gadget>
<output>1_200</output>

<gadget id="calculator">20 * 20</gadget>
<output>400</output>

<gadget id="calculator">1_200 + 400</gadget>
<output>1_600</output>

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

<gadget id="calculator">1_600 / 100</gadget>
<output>16</output>

<gadget id="calculator">16 * 25</gadget>
<output>400</output>

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

<gadget id="calculator">4 + 16</gadget>
<output>20</output>
<result>20</result>

Choices:
A. 23.75
B. 22
C. 20
D. 19.20
E. none of these

add(divide(multiply(divide(add(multiply(80, 15), multiply(20, 20)), add(80, 20)), 25), const_100), divide(add(multiply(80, 15), multiply(20, 20)), add(80, 20)))

Explanation: "c . p . of mixture = 80 × 15 + 20 × 20 / 80 + 20 = 16 ∴ s . p . = ( 100 + 25 ) / 100 × 16 = 20 answer c"


Question: pipe a fills a tank of capacity 800 liters at the rate of 40 liters a minute . another pipe b fills the same tank at the rate of 30 liters a minute . a pipe at the bottom of the tank drains the tank at the rate of 20 liters a minute . if pipe a is kept open for a minute and then closed and pipe b is open for a minute and then closed and then pipe c is open for a minute and then closed and the cycle is repeated , when will the tank be full ?

<gadget id="calculator">40 + 30</gadget>
<output>70</output>

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

<gadget id="calculator">800 / 50</gadget>
<output>16</output>

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

Choices:
A. 48 minutes
B. 14 minutes
C. 39 minutes
D. 40 minutes 20 seconds
E. none of these

multiply(divide(800, subtract(add(40, 30), 20)), const_3)

Explanation: "in one cycle they fill 40 + 30 - 20 = 50 liters 800 = 50 * n = > n = 16 here n = number of cycles . total time = 16 * 3 = 48 as in one cycle there are 3 minutes . thus 48 minutes answer : a"


Question: if w / x = 1 / 3 and w / y = 3 / 4 , then ( x + y ) / y =

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

<gadget id="calculator">4 / 3</gadget>
<output>4/3 = around 1.333333</output>

<gadget id="calculator">3 / (4/3)</gadget>
<output>9/4 = around 2.25</output>

<gadget id="calculator">(9/4) + 1</gadget>
<output>13/4 = around 3.25</output>
<result>13/4 = around 3.25</result>

Choices:
A. 13 / 4
B. 6 / 5
C. 7 / 5
D. 8 / 5
E. 9 / 5

add(divide(divide(3, 1), divide(4, 3)), const_1)

Explanation: "w / x = 1 / 3 = > x = 3 w and w / y = 3 / 4 = > y = ( 4 / 3 ) w ( x + y ) / y = ( 3 w + 4 / 3 w ) / ( 4 / 3 w ) = ( 13 / 3 w ) / ( 4 / 3 w ) = 13 / 4 correct option : a"


Question: the speed of a boat in still water is 15 km / hr and the rate of current is 3 km / hr . the distance travelled downstream in 24 minutes is

<gadget id="calculator">24 / 60</gadget>
<output>2/5 = around 0.4</output>

<gadget id="calculator">15 + 3</gadget>
<output>18</output>

<gadget id="calculator">(2/5) * 18</gadget>
<output>36/5 = around 7.2</output>
<result>36/5 = around 7.2</result>

Choices:
A. 17.2 km
B. 7.2 km
C. 7.6 km
D. 17.6 km
E. 27.2 km

multiply(divide(24, const_60), add(15, 3))

Explanation: "speed of a boat in still water = 15 km / hr speed of the current = 3 km / hr speed downstream = ( 15 + 3 ) = 18 km / hr distance travelled downstream in 24 minutes = ( 24 / 60 ) × 18 = ( 2 × 18 ) / 5 = 7.2 km answer is b"


Question: a man is 20 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is ?

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

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

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

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

<gadget id="calculator">18 / 1</gadget>
<output>18</output>
<result>18</result>

Choices:
A. 11
B. 25
C. 27
D. 18
E. 91

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

Explanation: "let the son ' s present age be x years . then , man ' s present age = ( x + 20 ) years . ( x + 20 ) + 2 = 2 ( x + 2 ) x + 22 = 2 x + 4 = > x = 18 . answer : d"


Question: a gardener grows cabbages in her garden that is in the shape of a square . each cabbage takes 1 square feet of area in her garden . this year , she has increased her output by 193 cabbages as compared to last year . the shape of the area used for growing the cabbages has remained a square in both these years . how many cabbages did she produce this year ?

<gadget id="calculator">193 / 2</gadget>
<output>193/2 = around 96.5</output>

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

<gadget id="calculator">(1/4) + (1/4)</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">(193/2) + (1/2)</gadget>
<output>97</output>

<gadget id="calculator">97 ** 2</gadget>
<output>9_409</output>
<result>9_409</result>

Choices:
A. 8,208
B. 9,409
C. 11,424
D. 12,586
E. can not be determined

power(add(divide(193, const_2), add(const_0_25, const_0_25)), const_2)

Explanation: "let the side for growing cabbages this year be x ft . thus the area is x ^ 2 . let the side for growing cabbages last year be y ft . thus , the area was y ^ 2 . the area would have increased by 193 sq ft as each cabbage takes 1 sq ft space . x ^ 2 - y ^ 2 = 193 ( x + y ) ( x - y ) = 193 193 is a prime number and thus it will be ( 97 + 96 ) * ( 97 - 96 ) . thus x = 97 and y = 96 x ^ 2 = 97 ^ 2 = 9409 the answer is b ."


Question: if d is the smallest positive integer such that 3150 multiplied by d is the square of an integer , then d must be

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

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

<gadget id="calculator">5 ** 2</gadget>
<output>25</output>

<gadget id="calculator">9 * 25</gadget>
<output>225</output>

<gadget id="calculator">3_150 / 225</gadget>
<output>14</output>
<result>14</result>

Choices:
A. 2
B. 5
C. 6
D. 7
E. 14

divide(3150, multiply(power(const_3, const_2), power(add(const_4, const_1), const_2)))

Explanation: solution : this problem is testing us on the rule that when we express a perfect square by its unique prime factors , every prime factor ' s exponent is an even number . let ’ s start by prime factorizing 3150 . 3150 = 315 x 10 = 5 x 63 x 10 = 5 x 7 x 3 x 3 x 5 x 2 3150 = 2 ^ 1 x 3 ^ 2 x 5 ^ 2 x 7 ^ 1 ( notice that the exponents of both 2 and 7 are not even numbers . this tells us that 3150 itself is not a perfect square . ) we also are given that 3150 multiplied by d is the square of an integer . we can write this as : 2 ^ 1 x 3 ^ 2 x 5 ^ 2 x 7 ^ 1 x d = square of an integer according to our rule , we need all unique prime factors ' exponents to be even numbers . thus , we need one more 2 and one more 7 . therefore , d = 7 x 2 = 14 answer is e .


Question: at garage sale , all of the prices of the items sold were different . if the price of a radio sold at the garage sale was both the 9 th highest price and the 35 th lowest price among the prices of the items sold , how many items were sold at the garage sale ?

<gadget id="calculator">9 + 35</gadget>
<output>44</output>

<gadget id="calculator">44 - 1</gadget>
<output>43</output>
<result>43</result>

Choices:
A. 43
B. 28
C. 44
D. 49
E. 46

Explanation: 8 + 34 + 1 = 43 answer : a


Question: excluding the stoppages , the speed of a bus is 12 km / hr and including the stoppages the speed of the bus is 6 km / hr . for how many minutes does the bus stop per hour ?

<gadget id="calculator">6 / 12</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">(1/2) * 60</gadget>
<output>30</output>

<gadget id="calculator">60 - 30</gadget>
<output>30</output>
<result>30</result>

Choices:
A. 15 min
B. 30 min
C. 12 min
D. 20 min
E. 18 min

subtract(const_60, multiply(divide(6, 12), const_60))

Explanation: "speed of the bus without stoppage = 12 km / hr speed of the bus with stoppage = 6 km / hr difference in speed = 6 km / hr so , the time taken in the stoppages = time taken to cover 6 km = ( 6 / 12 ) hr = 1 / 2 hr = 30 min answer : b"


Question: in a park there are two ponds with both brown ducks and green ducks . in the smaller pond there are 45 ducks and in the larger pond there are 55 ducks . if 20 % of the ducks in the smaller pond are green and 40 % of the ducks in the larger pond are green , then what percentage of ducks are green ?

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

<gadget id="calculator">45 * (1/5)</gadget>
<output>9</output>

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

<gadget id="calculator">55 * (2/5)</gadget>
<output>22</output>

<gadget id="calculator">9 + 22</gadget>
<output>31</output>

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

<gadget id="calculator">31 / 100</gadget>
<output>31/100 = around 0.31</output>

<gadget id="calculator">(31/100) * 100</gadget>
<output>31</output>
<result>31</result>

Choices:
A. 25 %
B. 27 %
C. 29 %
D. 31 %
E. 33 %

multiply(divide(add(multiply(45, divide(20, const_100)), multiply(55, divide(40, const_100))), add(45, 55)), const_100)

Explanation: "number of ducks in small pond = 45 green ducks in small pond = 20 % of 45 = 9 ducks number of ducks in large pond = 55 green ducks in large pond = 40 % of 55 = 22 ducks total number of ducks = 45 + 55 = 100 total number of green ducks = 9 + 22 = 31 ducks percentage of green ducks = 31 / 100 * 100 = 31 % answer : d"


Question: rice weighing 35 / 2 pounds was divided equally and placed in 4 containers . how many ounces of rice were in each container ? ( note that 1 pound = 16 ounces )

<gadget id="calculator">35 / 2</gadget>
<output>35/2 = around 17.5</output>

<gadget id="calculator">(35/2) * 16</gadget>
<output>280</output>

<gadget id="calculator">280 / 4</gadget>
<output>70</output>
<result>70</result>

Choices:
A. 40
B. 50
C. 60
D. 70
E. 80

Explanation: 35 / 2 ÷ 4 = 35 / 8 pounds in each container 35 / 8 pounds * 16 ounces / pound = 70 ounces in each container the answer is d .


Question: ashok secured average of 74 marks in 6 subjects . if the average of marks in 5 subjects is 74 , how many marks did he secure in the 6 th subject ?

<gadget id="calculator">74 * 6</gadget>
<output>444</output>

<gadget id="calculator">74 * 5</gadget>
<output>370</output>

<gadget id="calculator">444 - 370</gadget>
<output>74</output>
<result>74</result>

Choices:
A. 66
B. 74
C. 78
D. 80
E. none of these

subtract(multiply(74, 6), multiply(74, 5))

Explanation: "explanation : number of subjects = 6 average of marks in 6 subjects = 74 therefore total marks in 6 subjects = 74 * 6 = 444 now , no . of subjects = 5 total marks in 5 subjects = 74 * 5 = 370 therefore marks in 6 th subject = 444 – 370 = 74 answer b"


Question: susan made a block with small cubes of 5 cubic cm volume to make a block 7 small cubes long , 7 small cubes wide and 6 small cubes deep . she realise that she has used more small cubes than she really needed . she realised that she could have glued a fewer number of cubes together ot look like a block with same dimensions , if it were made

<gadget id="calculator">7 * 7</gadget>
<output>49</output>

<gadget id="calculator">49 * 6</gadget>
<output>294</output>

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

<gadget id="calculator">5 * 5</gadget>
<output>25</output>

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

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

<gadget id="calculator">294 - 100</gadget>
<output>194</output>
<result>194</result>

Choices:
A. 194
B. 195
C. 196
D. 197
E. 198

subtract(multiply(multiply(7, 7), 6), multiply(multiply(subtract(7, const_2), subtract(7, const_2)), subtract(6, const_2)))

Explanation: volume of cube of dimensions 7 7 6 is 7 * 7 * 6 = 294 if it were to look hollow the imaginary inside cube volume is to be deducted which is ( 7 - 2 ) * ( 7 - 2 ) * ( 6 - 2 ) = 100 ( here 2 is deducted because the inside cube which has to be hollow is 2 cubes more on every dimension ) so minimum number of cubes required to make hollow cube is 294 - 100 = 194 cubes answer : a


Question: in a dairy farm , 55 cows eat 55 bags of husk in 55 days . in how many days one cow will eat one bag of husk ?

<gadget id="calculator">55 / 55</gadget>
<output>1</output>

<gadget id="calculator">1 * 55</gadget>
<output>55</output>
<result>55</result>

Choices:
A. 34 days
B. 40 days
C. 46 days
D. 50 days
E. 55 days

Explanation: "explanation : less cows , more days ( indirect proportion ) less bags , less days ( direct proportion ) [ cows 1 55 bags 55 1 ] : : 55 : x = > x ∗ 55 ∗ 1 = 55 ∗ 1 ∗ 55 = > x = 55 option e"


Question: a tank is filled in 10 hours by 3 pipes a , b and c . the pipe c is twice as fast as b and b is twice as fast as a . how much time will pipe a alone take to fill the tank ?

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

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

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

Choices:
A. 70 hours
B. 30 hours
C. 35 hours
D. 50 hours
E. 60 hours

multiply(add(const_4, add(const_1, const_2)), 10)

Explanation: 1 / a + 1 / b + 1 / c = 1 / 10 ( a , b and c 1 hour work ) given . . 1 / b = 2 / a and 1 / c = 2 / b = 4 / a hence 1 / a + 2 / a + 4 / a = 1 / 10 on solving . . . . we get 1 / a = 1 / 70 ( work done by a in 1 hour ) therefore time taken by a is 70 hours to finish the whole work answer : a


Question: in a certain production lot , 40 percent of the toys are red and the remaining toys are green . half of toys are small and half are large . if 10 percent of the toys are red and small , and 40 toys are green and large . how many of the toys are red and large ?

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

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

<gadget id="calculator">(2/5) - (1/10)</gadget>
<output>3/10 = around 0.3</output>

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

<gadget id="calculator">(2/5) + (1/2)</gadget>
<output>9/10 = around 0.9</output>

<gadget id="calculator">(9/10) - (1/10)</gadget>
<output>4/5 = around 0.8</output>

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

<gadget id="calculator">40 / (1/5)</gadget>
<output>200</output>

<gadget id="calculator">(3/10) * 200</gadget>
<output>60</output>
<result>60</result>

Choices:
A. 40
B. 60
C. 70
D. 80
E. 90

multiply(subtract(divide(40, const_100), divide(10, const_100)), divide(40, subtract(const_1, subtract(add(divide(40, const_100), divide(const_1, const_2)), divide(10, const_100)))))

Explanation: 40 % toys are red . 50 % toys are small - 50 % are large red and small - 10 % red and large must be 30 % ( since there are total 40 % red toys ) but 50 % toys are large . if 30 % are red and large , the rest 20 % large toys must be green . so large and green toys are 20 % . these 20 % large and green toys are actually 40 so total number of toys must be 200 . since red and large toys are 30 % , they must be 60 . answer : b


Question: if 4 ( p ' s capital ) = 6 ( q ' s capital ) = 10 ( r ' s capital ) , then out of the total profit of rs 4030 , r will receive

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

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

<gadget id="calculator">15 + 10</gadget>
<output>25</output>

<gadget id="calculator">25 + 6</gadget>
<output>31</output>

<gadget id="calculator">6 / 31</gadget>
<output>6/31 = around 0.193548</output>

<gadget id="calculator">4_030 * (6/31)</gadget>
<output>780</output>
<result>780</result>

Choices:
A. 600
B. 780
C. 800
D. 900
E. none of these

multiply(4030, divide(6, add(add(add(10, add(4, const_1)), 10), 6)))

Explanation: "explanation : let p ' s capital = p , q ' s capital = q and r ' s capital = r then 4 p = 6 q = 10 r = > 2 p = 3 q = 5 r = > q = 2 p / 3 r = 2 p / 5 p : q : r = p : 2 p / 3 : 2 p / 5 = 15 : 10 : 6 r ' s share = 4030 * ( 6 / 31 ) = 130 * 6 = 780 . answer : option b"


Question: mark and ann together were allocated n boxes of cookies to sell for a club project . mark sold 11 boxes less than n and ann sold 2 boxes less than n . if mark and ann have each sold at least one box of cookies , but together they have sold less than n boxes , what is the value of n ?

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

Choices:
A. 10
B. 11
C. 12
D. 13
E. 14

Explanation: if n = 12 mark sold 1 box and ann sold 10 boxes total 11 < 12 answer : c


Question: in a forest 10 rabbits were caught , tagged with electronic markers , then released . a month later , 10 rabbits were captured in the same forest . of these 10 rabbits , it was found that 2 had been tagged with the electronic markers . if the percentage of tagged rabbits in the second sample approximates the percentage of tagged rabbits in the forest , and if no rabbits had either left or entered the forest over the preceding month , what is the approximate number of rabbits in the forest ?

<gadget id="calculator">10 + 10</gadget>
<output>20</output>

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

<gadget id="calculator">2 / 10</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">(1/5) * 100</gadget>
<output>20</output>

<gadget id="calculator">30 + 20</gadget>
<output>50</output>
<result>50</result>

Choices:
A. 150
B. 70
C. 50
D. 1500
E. 500

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

Explanation: given that 10 rabbits were caught and tagged in the first sample , and 10 were caught in the second sample of which 2 had tags , then 2 / 10 approximates the fraction of the population of tagged rabbits in the forest . proportion : a / x = c / d a = rabbits tagged first sample c / d = the fraction of the population of tagged rabbits in the forest x = the population of rabbits in the forest proportion : 10 / x = 1 / 5 x = ( 1 ) ( 10 ) ( 5 ) = 50 . there are approximately 50 rabbits in the forest . answer is c


Question: train a leaves the station traveling at 30 miles per hour . two hours later train в leaves the same station traveling in the same direction at 45 miles per hour . how many miles from the station was train a overtaken by train b ?

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

<gadget id="calculator">45 - 30</gadget>
<output>15</output>

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

<gadget id="calculator">4 * 45</gadget>
<output>180</output>
<result>180</result>

Choices:
A. 100
B. 120
C. 140
D. 160
E. 180

multiply(divide(multiply(30, const_2), subtract(45, 30)), 45)

Explanation: "after two hours , train a is ahead by 60 miles . train b can catch up at a rate of 15 miles per hour . the time to catch up is 60 / 15 = 4 hours . in 4 hours , train a travels another 30 * 4 = 120 miles for a total of 180 miles . the answer is e ."


Question: micheal and adam can do together a piece of work in 20 days . after they have worked together for 15 days micheal stops and adam completes the remaining work in 10 days . in how many days micheal complete the work separately .

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

<gadget id="calculator">(1/20) * 15</gadget>
<output>3/4 = around 0.75</output>

<gadget id="calculator">1 - (3/4)</gadget>
<output>1/4 = around 0.25</output>

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

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

<gadget id="calculator">1 / 40</gadget>
<output>1/40 = around 0.025</output>

<gadget id="calculator">(1/20) - (1/40)</gadget>
<output>1/40 = around 0.025</output>

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

Choices:
A. 40 days
B. 100 days
C. 120 days
D. 110 days
E. 90 days

inverse(subtract(inverse(20), inverse(multiply(inverse(subtract(const_1, multiply(inverse(20), 15))), 10))))

Explanation: "rate of both = 1 / 20 together they do = 1 / 20 * 15 = 3 / 4 left work = 1 - 3 / 4 = 1 / 4 adam completes 1 / 4 work in 10 day so he took 10 * 4 = 40 days to complete the left work alone . thus the rate of adam is 40 / 1 rate of micheal = 1 / 20 - 1 / 40 = 1 / 40 thus micheal takes 40 days to complete the whole work . ans . a ."


Question: pipe a can fill a tank in 6 hours . due to a leak at the bottom , it takes 10 hours for the pipe a to fill the tank . in what time can the leak alone empty the full tank ?

<gadget id="calculator">10 * 6</gadget>
<output>60</output>

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

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

Choices:
A. 13
B. 17
C. 15
D. 19
E. 12

divide(multiply(10, 6), subtract(10, 6))

Explanation: "let the leak can empty the full tank in x hours 1 / 6 - 1 / x = 1 / 10 = > 1 / x = 1 / 6 - 1 / 10 = ( 5 - 3 ) / 30 = 2 / 30 = 1 / 15 = > x = 15 . answer : c"


Question: how many terminating zeroes w does 200 ! have ?

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

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

<gadget id="calculator">5 * 5</gadget>
<output>25</output>

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

<gadget id="calculator">40 + 8</gadget>
<output>48</output>
<result>48</result>

Choices:
A. 40
B. 48
C. 49
D. 55
E. 64

add(divide(200, add(const_4, const_1)), divide(200, multiply(add(const_4, const_1), add(const_4, const_1))))

Explanation: you have 40 multiples of 5 , 8 of 25 and 1 of 125 . this will give 49 zeros . c


Question: two trains 500 m and 750 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?

<gadget id="calculator">500 + 750</gadget>
<output>1_250</output>

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

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

<gadget id="calculator">100 * (5/18)</gadget>
<output>250/9 = around 27.777778</output>

<gadget id="calculator">1_250 / (250/9)</gadget>
<output>45</output>
<result>45</result>

Choices:
A. 10.6
B. 45
C. 10.4
D. 10.8
E. 10.1

Explanation: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 500 + 750 = 1250 m . required time = 1250 * 9 / 250 = 45 sec . answer : b"


Question: a train 110 m long is running with a speed of 36 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?

<gadget id="calculator">36 + 6</gadget>
<output>42</output>

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

<gadget id="calculator">42 * (5/18)</gadget>
<output>35/3 = around 11.666667</output>

<gadget id="calculator">110 / (35/3)</gadget>
<output>66/7 = around 9.428571</output>
<result>66/7 = around 9.428571</result>

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

divide(110, multiply(add(36, 6), const_0_2778))

Explanation: "speed of train relative to man = 36 + 6 = 42 km / hr . = 42 * 5 / 18 = 35 / 3 m / sec . time taken to pass the men = 110 * 3 / 35 = 9 sec . answer : d"


Question: tough and tricky questions : remainders . 1 ^ 1 + 2 ^ 2 + 3 ^ 3 + . . . + 7 ^ 7 is divided by 7 . what is the remainder ?

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

<gadget id="calculator">5 + 7</gadget>
<output>12</output>

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

<gadget id="calculator">12 + 6</gadget>
<output>18</output>

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

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

<gadget id="calculator">23 + 6</gadget>
<output>29</output>

<gadget id="calculator">29 + 3</gadget>
<output>32</output>

<gadget id="calculator">32 / 7</gadget>
<output>32/7 = around 4.571429</output>

<gadget id="calculator">floor(32/7)</gadget>
<output>4</output>

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

<gadget id="calculator">32 - 28</gadget>
<output>4</output>
<result>4</result>

Choices:
A. 0
B. 1
C. 2
D. 3
E. 4

subtract(add(add(add(add(add(add(1, const_4), 7), add(const_4, const_2)), add(const_4, const_1)), add(const_4, const_2)), const_3), multiply(7, floor(divide(add(add(add(add(add(add(1, const_4), 7), add(const_4, const_2)), add(const_4, const_1)), add(const_4, const_2)), const_3), 7))))

Explanation: a number is divisible by 5 , if its last digit is divisible by 5 let ' s look into the sum of last digits of each term of the given expression 1 ^ 1 = 1 2 ^ 2 = 4 3 ^ 3 = 7 4 ^ 4 = 6 5 ^ 5 = 5 6 ^ 6 = 6 7 ^ 7 = 3 adding all these numbers we get 32 which gives a remainder of 4 when divided by 7 . so answer must be 4 . bunuel , can you please confirm the answer of this question . yes , the oa is c . clicked the wrong button when posting . edited . thank you . e


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

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

<gadget id="calculator">125 / 100</gadget>
<output>5/4 = around 1.25</output>

<gadget id="calculator">225 / (5/4)</gadget>
<output>180</output>

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

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

<gadget id="calculator">180 / (3/2)</gadget>
<output>120</output>
<result>120</result>

Choices:
A. 237
B. 126
C. 971
D. 611
E. 120

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

Explanation: "explanation : let cp be 100 a sells at 50 % profit so sp = 150 b sells at 25 % profit = 150 x ( 1 + 25 / 100 ) = 187.50 cp - - - sp 100 - - - 187.50 x - - - 225 cp = 225 x 100 / 187.50 = 120 answer : e"


Question: average marks of a , b , c is 48 . when d joins average becomes 47 . e has 3 more marks than d . average marks of b , c , d , e is 48 . what is the marks of a ?

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

<gadget id="calculator">48 * 4</gadget>
<output>192</output>

<gadget id="calculator">47 * 4</gadget>
<output>188</output>

<gadget id="calculator">188 - 144</gadget>
<output>44</output>

<gadget id="calculator">44 + 3</gadget>
<output>47</output>

<gadget id="calculator">47 + 44</gadget>
<output>91</output>

<gadget id="calculator">192 - 91</gadget>
<output>101</output>

<gadget id="calculator">144 - 101</gadget>
<output>43</output>
<result>43</result>

Choices:
A. 43
B. 44
C. 45
D. 46
E. 47

subtract(multiply(const_3, 48), subtract(multiply(48, const_4), add(add(subtract(multiply(47, const_4), multiply(const_3, 48)), 3), subtract(multiply(47, const_4), multiply(const_3, 48)))))

Explanation: a + b + c = 144 a + b + c + d = 188 d = 44 e = 47 b + c + d + e = 192 b + c = 101 a = 43 answer : a


Question: 3 candidates in an election and received 3136 , 7636 and 11628 votes respectively . what % of the total votes did the winning candidate got in that election ?

Choices:
A. 45 %
B. 49 %
C. 52 %
D. 59 %
E. 61 %

Explanation: "total number of votes polled = ( 3136 + 7636 + 11628 ) = 22400 so , required percentage = 11628 / 22400 * 100 = 52 % c"


Question: two pipes p and q can fill a cistern in 12 and 15 minutes respectively . both are opened together , but at the end of 2 minutes the first is turned off . how many more minutes will it take for the cistern to fill after the first pipe is turned off ?

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

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

<gadget id="calculator">(1/12) + (1/15)</gadget>
<output>3/20 = around 0.15</output>

<gadget id="calculator">(3/20) * 2</gadget>
<output>3/10 = around 0.3</output>

<gadget id="calculator">1 - (3/10)</gadget>
<output>7/10 = around 0.7</output>

<gadget id="calculator">(7/10) * 15</gadget>
<output>21/2 = around 10.5</output>
<result>21/2 = around 10.5</result>

Choices:
A. 8.5
B. 9.5
C. 10.5
D. 11.5
E. 12.5

multiply(subtract(const_1, multiply(add(divide(const_1, 12), divide(const_1, 15)), 2)), 15)

Explanation: "let x be the total time it takes for the cistern to fill . 2 / 12 + x / 15 = 1 x / 15 = 5 / 6 x = 12.5 after the first pipe is turned off , it takes 10.5 more minutes to fill the cistern . the answer is c ."


Question: a company conducted a survey about its two brands , a and b . x percent of respondents liked product a , ( x – 20 ) percent liked product b , 23 percent liked both products , and 23 percent liked neither product . what is the minimum number g of people surveyed by the company ?

<gadget id="calculator">100 - 23</gadget>
<output>77</output>

<gadget id="calculator">77 + 23</gadget>
<output>100</output>

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

<gadget id="calculator">120 / 2</gadget>
<output>60</output>

<gadget id="calculator">60 - 20</gadget>
<output>40</output>

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

Choices:
A. 46
B. g = 80
C. g = 90
D. g = 100
E. 200

add(subtract(divide(add(add(subtract(const_100, 23), 23), 20), const_2), 20), divide(add(add(subtract(const_100, 23), 23), 20), const_2))

Explanation: "100 = x + x - 20 + 23 - 23 x = 60 , so , product a = 60 % , product b = 40 % , both = 23 % , neither = 23 % 23 % of the total no . of people should be an integer . so , a , bc are out . 60 % of d and 40 % of d are both integers . so , d satisfies all conditions . so , answer is d ."


Question: a train traveling at 72 kmph crosses a platform in 33 seconds and a man standing on the platform in 18 seconds . what is the length of the platform in meters ?

<gadget id="calculator">72 * 1_000</gadget>
<output>72_000</output>

<gadget id="calculator">72_000 / 3_600</gadget>
<output>20</output>

<gadget id="calculator">20 * 33</gadget>
<output>660</output>

<gadget id="calculator">20 * 18</gadget>
<output>360</output>

<gadget id="calculator">660 - 360</gadget>
<output>300</output>
<result>300</result>

Choices:
A. 240 meters
B. 360 meters
C. 420 meters
D. 300 meters
E. can not be determined

subtract(multiply(divide(multiply(72, const_1000), const_3600), 33), multiply(divide(multiply(72, const_1000), const_3600), 18))

Explanation: "speed of train = 72 * ( 5 / 18 ) = 20 m / s lets consider the man as a stationery point on the platform . crossing the point gives us the length of the train . lt = 20 * 18 = 360 m . crossing the platform gives us the length of trainlength of platform . l ( t + p ) = 20 * 33 = 660 m . so , length of platform = 660 - 360 = 300 m imo , answer d"


Question: the weights of one liter vegetable ghee packet of two brands ‘ a ’ and ‘ b ’ are 800 gm and 850 gm respectively . if they are mixed in the ratio of 3 : 2 by volumes to form a mixture of 3 liters , what is the weight ( in kg ) of the mixture ?

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

<gadget id="calculator">2 * 850</gadget>
<output>1_700</output>

<gadget id="calculator">2_400 + 1_700</gadget>
<output>4_100</output>

<gadget id="calculator">3 * 4_100</gadget>
<output>12_300</output>

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

<gadget id="calculator">12_300 / 5</gadget>
<output>2_460</output>

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

Choices:
A. 3.84
B. 1.75
C. 3.52
D. 2.46
E. none of these

divide(divide(multiply(3, add(multiply(3, 800), multiply(2, 850))), add(3, 2)), const_1000)

Explanation: "here ' s how i did it . my notes from reading the problem were : 1 l a = 800 gm 1 l b = 850 gm we are mixing five parts ( 3 parts a plus 2 parts b , 5 parts total ) to get 3 l , so 5 x = 3 - - - > x = 3 / 5 . each part is 3 / 5 of a liter . so if we have 3 parts a , we have 800 * 3 * ( 3 / 5 ) = 1440 if we have 2 parts b , we have 850 * 2 * ( 3 / 5 ) = 1020 1440 + 1020 = 2460 solving for units gives us 2.46 so the answer is d"


Question: $ 9,000 is deposited in a savings account that pays 14 % annual interest compounded semiannually . to the nearest dollar , how much is in the account at the end of the year ?

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

Choices:
A. $ 11304.12
B. $ 12304.54
C. $ 11604.14
D. $ 10304.10
E. $ 9304.41

Explanation: this is the case of semi - annual compoundingso , multiply time period by 2 and divide rate by 2 so , new time = 2 periods and new rate = 14 / 2 = 7 % now , ca = 9000 ( 1 + 7 / 100 ) ^ 2 = $ 10304.10 hence answer is d


Question: a certain bacteria colony doubles in size every day for 25 days , at which point it reaches the limit of its habitat and can no longer grow . if two bacteria colonies start growing simultaneously , how many days will it take them to reach the habitat ’ s limit ?

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

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

Choices:
A. 6.33
B. 7.5
C. 10
D. 15
E. 24

Explanation: "if there is one bacteria colony , then it will reach the limit of its habitat in 25 days . if there are two bacteria colonies , then in order to reach the limit of habitat they would need to double one time less than in case with one colony . thus colonies need to double 24 times . answer : e . similar questions to practice : hope it helps ."


Question: if daily wages of a man is 4 times to that of a woman , how many men should work for 25 days to earn rs . 14400 ? given that wages for 40 women for 30 days are rs . 21600 .

<gadget id="calculator">40 * 30</gadget>
<output>1_200</output>

<gadget id="calculator">21_600 / 1_200</gadget>
<output>18</output>

<gadget id="calculator">18 * 4</gadget>
<output>72</output>

<gadget id="calculator">72 * 25</gadget>
<output>1_800</output>

<gadget id="calculator">14_400 / 1_800</gadget>
<output>8</output>
<result>8</result>

Choices:
A. 12
B. 4
C. 6
D. 8
E. 20

divide(14400, multiply(multiply(divide(21600, multiply(40, 30)), 4), 25))

Explanation: explanation : wages of 1 woman for 1 day = 21600 / 40 ã — 30 wages of 1 man for 1 day = 21600 ã — 4 / 40 ã — 30 wages of 1 man for 25 days = 21600 ã — 4 ã — 25 / 40 ã — 30 number of men = 14400 / ( 21600 ã — 4 ã — 25 / 40 ã — 30 ) = 144 / ( 216 ã — 100 / 40 ã — 30 ) = 8 answer : option d


Question: jerry went to a shop and bought things worth rs . 20 , out of which 30 % went on sales tax on taxable purchases . if the tax rate was 6 % , then what was the cost of the tax free items ?

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

<gadget id="calculator">100 / 6</gadget>
<output>50/3 = around 16.666667</output>

<gadget id="calculator">(3/10) * (50/3)</gadget>
<output>5</output>

<gadget id="calculator">5 + (3/10)</gadget>
<output>53/10 = around 5.3</output>

<gadget id="calculator">20 - (53/10)</gadget>
<output>147/10 = around 14.7</output>
<result>147/10 = around 14.7</result>

Choices:
A. 14
B. 14.7
C. 21.3
D. 21.5
E. 21.7

subtract(20, add(multiply(divide(30, const_100), divide(const_100, 6)), divide(30, const_100)))

Explanation: total cost of the items he purchased = rs . 20 given that out of this rs . 20 , 30 % is given as tax = > total tax incurred = 30 % = rs . 30 / 100 let the cost of the tax free items = x given that tax rate = 6 % ∴ ( 20 − 30 / 100 − x ) 6 / 100 = 30 / 100 ⇒ 6 ( 20 − 0.3 − x ) = 30 ⇒ ( 20 − 0.3 − x ) = 5 ⇒ x = 20 − 0.3 − 5 = 14.7 b )


Question: a random 10 - letter code is to be formed using the letters a , b , c , d , e , f , g , h , i and i ( only the “ i ” will be used twice ) . what is the probability that a code that has the two i ’ s adjacent to one another will be formed ?

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

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

<gadget id="calculator">factorial(8)</gadget>
<output>40_320</output>

<gadget id="calculator">9 * 40_320</gadget>
<output>362_880</output>

<gadget id="calculator">factorial(10)</gadget>
<output>3_628_800</output>

<gadget id="calculator">3_628_800 / 40_320</gadget>
<output>90</output>

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

<gadget id="calculator">45 * 40_320</gadget>
<output>1_814_400</output>

<gadget id="calculator">362_880 / 1_814_400</gadget>
<output>1/5 = around 0.2</output>
<result>1/5 = around 0.2</result>

Choices:
A. 1 / 10
B. 1 / 8
C. 1 / 5
D. 1 / 4
E. 1 / 2

divide(multiply(subtract(10, const_1), factorial(subtract(10, const_2))), multiply(divide(divide(factorial(10), factorial(subtract(10, const_2))), const_2), factorial(subtract(10, const_2))))

Explanation: total number of combinations possible = 10 ! / 2 ! 10 ! / 2 ! total favorable combinations = 9 ! 9 ! - we have considered the two is as one element . since we have two is , they can interchange their positions , without affecting the code . probability = 9 ! / ( 10 ! / 2 ! ) = 9 ! ∗ 2 ! / 10 ! = 1 / 59 ! / ( 10 ! / 2 ! ) = 9 ! ∗ 2 ! / 10 ! = 1 / 5 ans : c


Question: at the end of the day , february 14 th , a florist had 90 roses left in his shop , all of which were red , white or pink in color and either long or short - stemmed . a third of the roses were short - stemmed , 15 of which were white and 10 of which were pink . the percentage of pink roses that were short - stemmed equaled the percentage of red roses that were short - stemmed . if none of the long - stemmed roses were white , what percentage of the long - stemmed roses were red ?

<gadget id="calculator">90 / 3</gadget>
<output>30</output>

<gadget id="calculator">90 - 30</gadget>
<output>60</output>

<gadget id="calculator">30 - 15</gadget>
<output>15</output>

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

<gadget id="calculator">60 * 5</gadget>
<output>300</output>

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

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

<gadget id="calculator">20 / 60</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">(1/3) * 100</gadget>
<output>100/3 = around 33.333333</output>
<result>100/3 = around 33.333333</result>

Choices:
A. 20 %
B. 75 %
C. 50 %
D. 33.3 %
E. 80 %

multiply(divide(divide(multiply(subtract(90, divide(90, const_3)), subtract(subtract(divide(90, const_3), 15), 10)), add(10, subtract(subtract(divide(90, const_3), 15), 10))), subtract(90, divide(90, const_3))), const_100)

Explanation: r + w + p = 90 s + l = 90 1 / 3 * 90 = 30 short - stemmed white = 15 short - stemmed pink = 10 = > short - stemmed red = 5 10 / p = 5 / r = > r = p / 2 , p = 2 r so total long stemmed = 60 and long stemmed red + long stemmed pink = 60 so long stemmed red / long stemmed = ? total white = 15 ( as no long stemmed white ) = > r + 2 r + 15 = 90 = > 3 r = 75 and r = 25 long stemmed r = 25 - 5 = 20 so long stemmed red / r = 20 / 60 = 33.3 % answer - d


Question: the average salary / head of allthe workers in a workshop is rs . 1200 , if the average salary / head of 10 technician is rs . 1400 and the average salary / head of the rest is rs . 900 , the total no . of workers in the work - shop is ?

<gadget id="calculator">10 * 1_400</gadget>
<output>14_000</output>

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

<gadget id="calculator">14_000 - 9_000</gadget>
<output>5_000</output>

<gadget id="calculator">1_200 - 900</gadget>
<output>300</output>

<gadget id="calculator">5_000 / 300</gadget>
<output>50/3 = around 16.666667</output>
<result>50/3 = around 16.666667</result>

Choices:
A. 18
B. 17
C. 15
D. 19
E. 21

divide(subtract(multiply(10, 1400), multiply(10, 900)), subtract(1200, 900))

Explanation: let the total number of workers be y . so sum of salary for all workers = sum of salary of 10 technician + sum of salary for other y - 10 workers . 10 x 1400 + 900 ( y - 10 ) = 1200 y ⇒ 14000 + 900 y - 9000 = 1200 y ⇒ 300 y = 5000 ∴ y = 17 so total number of workers = 17 b


Question: two cubes have their volumes are in the ratio 1 : 27 . find the ratio of their surface area ?

<gadget id="calculator">1 / 27</gadget>
<output>1/27 = around 0.037037</output>

<gadget id="calculator">(1/27) * 3</gadget>
<output>1/9 = around 0.111111</output>
<result>1/9 = around 0.111111</result>

Choices:
A. 1 : 2
B. 2 : 3
C. 1 : 9
D. 2 : 7
E. 3 : 11

Explanation: let their edges be a and b then , a ^ 3 / b ^ 3 = 1 / 27 ( a / b ) ^ 3 = ( 1 / 3 ) ^ 3 a / b = 1 / 3 ratio of their surface areas = 6 a ^ 2 / 6 b ^ 2 = ( a / b ) ^ 2 = 1 / 9 = 1 : 9 answer is c


Question: if the integer n has exactly 4 positive divisors , including 1 and n , how many positive divisors does n ^ 3 have ?

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

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

Choices:
A. 16
B. 11
C. 10
D. 20
E. 9

Explanation: take the example of 6 . . . it has 4 positive divisors ( 1,2 , 3,4 ) now , take the example of 216 . . . it has 16 divisors . . so a is the ans


Question: a father and his son are waiting at a bus stop in the evening . there is a lamp post behind them . the lamp post , the father and his son stand on the same straight line . the father observes that the shadows of his head and his son ’ s head are incident at the same point on the ground . if the heights of the lamp post , the father and his son are 6 metres , 1.8 metres and 0.9 metres respectively , and the father is standing 2.1 metres away from the post , then how far ( in metres ) is the son standing from his father ?

<gadget id="calculator">0.9 * 2.1</gadget>
<output>1.89</output>

<gadget id="calculator">6 - 1.8</gadget>
<output>4.2</output>

<gadget id="calculator">1.89 / 4.2</gadget>
<output>0.45</output>
<result>0.45</result>

Choices:
A. 0.9
B. 0.75
C. 0.6
D. 0.45
E. none of these

divide(multiply(0.9, 2.1), subtract(6, 1.8))

Explanation: explanation : l is the lamp post position , f is father and s is son ’ s position . x is the point where the shadow falls . ld = 0.9 = son ’ s height , lb = 1.8 = father ’ s height . so ab = 6 – 1.8 = 4.2 also bc = lf = 2.1 we observe that ∆ abc ~ ∆ ade ( two triangles are similar ) . hence , the corresponding sides are proportional . so , ab / ad = dc / de . 4.2 / 5.1 = 2.1 / de . de = 5.1 * 2.1 / 4.2 = 5.1 / 2 = 2.55 . ls = de = 2.55 fs = ls – lf = 2.55 – 2.1 = 0.45 . answer : d


Question: a rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn , one parallel to the length and the other parallel to the breadth . what is the cost of traveling the two roads at rs . 5 per sq m ?

<gadget id="calculator">80 + 60</gadget>
<output>140</output>

<gadget id="calculator">140 - 10</gadget>
<output>130</output>

<gadget id="calculator">130 * 10</gadget>
<output>1_300</output>

<gadget id="calculator">1_300 * 5</gadget>
<output>6_500</output>
<result>6_500</result>

Choices:
A. 6500
B. 2779
C. 2779
D. 3900
E. 2781

multiply(multiply(subtract(add(80, 60), 10), 10), 5)

Explanation: "area = ( l + b â € “ d ) d ( 80 + 60 â € “ 10 ) 10 = > 1300 m 2 1300 * 5 = rs . 6500 answer : a"


Question: at their respective rates , pump a , b , and c can fulfill an empty tank , or pump - out the full tank in 2 , 3 , and 6 hours . if a and b are used to pump - out water from the half - full tank , while c is used to fill water into the tank , in how many hours , the tank will be empty ?

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

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

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

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

<gadget id="calculator">6 / 4</gadget>
<output>3/2 = around 1.5</output>

<gadget id="calculator">(3/2) / 2</gadget>
<output>3/4 = around 0.75</output>
<result>3/4 = around 0.75</result>

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

divide(divide(6, subtract(add(divide(6, 2), divide(6, 3)), const_1)), const_2)

Explanation: rate of a = 1 / 2 tank / hour ; rate of b = 1 / 3 tank / hour ; rate of c = 1 / 6 tank / hour . combined rate when a and b are used to pump - out water , while c is used to fill water into the tank is 1 / 2 + 1 / 3 - 1 / 6 = 2 / 3 tank hour . so , to empty the full tank 3 / 2 hours ( reciprocal of rate ) are needed . to empty the half - full tank half of that time would be needed : 1 / 2 * 3 / 2 = 3 / 4 hours . answer : c .


Question: a boat can travel with a speed of 22 km / hr in still water . if the speed of the stream is 5 km / hr , find the time taken by the boat to go 108 km downstream

<gadget id="calculator">22 + 5</gadget>
<output>27</output>

<gadget id="calculator">108 / 27</gadget>
<output>4</output>
<result>4</result>

Choices:
A. 5 hours
B. 4 hours
C. 3 hours
D. 2 hours
E. none of these

Explanation: "explanation : speed of the boat in still water = 22 km / hr speed of the stream = 5 km / hr speed downstream = ( 22 + 5 ) = 27 km / hr distance travelled downstream = 108 km time taken = distance / speed = 108 / 27 = 4 hours . answer : option b"


Question: company c sells a line of 25 products with an average retail price of $ 1,200 . if none of these products sells for less than $ 400 , and exactly 10 of the products sell for less than $ 1,000 , what is the greatest possible selling price of the most expensive product ?

<gadget id="calculator">12 * 100</gadget>
<output>1_200</output>

<gadget id="calculator">1_200 * 25</gadget>
<output>30_000</output>

<gadget id="calculator">400 * 10</gadget>
<output>4_000</output>

<gadget id="calculator">25 - 10</gadget>
<output>15</output>

<gadget id="calculator">15 - 1</gadget>
<output>14</output>

<gadget id="calculator">14 * 1_000</gadget>
<output>14_000</output>

<gadget id="calculator">4_000 + 14_000</gadget>
<output>18_000</output>

<gadget id="calculator">30_000 - 18_000</gadget>
<output>12_000</output>
<result>12_000</result>

Choices:
A. 12000
B. 13000
C. 14000
D. 15000
E. 16000

subtract(multiply(multiply(const_12, const_100), 25), add(multiply(400, 10), multiply(subtract(subtract(25, 10), const_1), 1,000)))

Explanation: "the average price of 25 products is $ 1,200 means that the total price of 25 products is 25 * 1,200 = $ 30,000 . next , since exactly 10 of the products sell for less than $ 1,000 , then let ' s make these 10 items to be at $ 400 each ( min possible ) . now , the remaining 14 items can not be priced less than $ 1,000 , thus the minimum possible price of each of these 14 items is $ 1,000 . thus the minimum possible value of 24 products is 10 * 400 + 14 * 1,000 = $ 18,000 . therefore , the greatest possible selling price of the most expensive product is $ 30,000 - $ 18,000 = $ 12,000 . answer : a ."


Question: a man purchased earphone on friday . but he forgot how much it cost . the data he have are mean expenditure of all 7 days is 500 . expenditure on mon , tue , wed , thurs , sat , sun are 450600 , 400500 , 550300 . on friday he purchased 3 things one earphone , one pen and one notebook . pen cost 30 and notebook cost 50 . then what is cost of earphone ?

<gadget id="calculator">7 * 500</gadget>
<output>3_500</output>

<gadget id="calculator">500 - 50</gadget>
<output>450</output>

<gadget id="calculator">500 + 100</gadget>
<output>600</output>

<gadget id="calculator">450 + 600</gadget>
<output>1_050</output>

<gadget id="calculator">500 - 100</gadget>
<output>400</output>

<gadget id="calculator">1_050 + 400</gadget>
<output>1_450</output>

<gadget id="calculator">1_450 + 500</gadget>
<output>1_950</output>

<gadget id="calculator">500 + 50</gadget>
<output>550</output>

<gadget id="calculator">1_950 + 550</gadget>
<output>2_500</output>

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

<gadget id="calculator">2_500 + 300</gadget>
<output>2_800</output>

<gadget id="calculator">3_500 - 2_800</gadget>
<output>700</output>

<gadget id="calculator">700 - 30</gadget>
<output>670</output>

<gadget id="calculator">670 - 50</gadget>
<output>620</output>
<result>620</result>

Choices:
A. 620
B. 530
C. 450
D. 470
E. 500

subtract(subtract(subtract(multiply(7, 500), add(add(add(add(add(subtract(500, 50), add(500, const_100)), subtract(500, const_100)), 500), add(500, 50)), subtract(subtract(500, const_100), const_100))), 30), 50)

Explanation: solution let expenditure on friday be x ( 450 + 600 + 400 + 500 + x + 550 + 300 ) / 7 = 500 2800 + x = 3500 x = 700 pen + notebook + earphone = 700 earphone = 700 - 80 = 620 answer a


Question: how many prime numbers are between 51 / 13 and 89 / 9 ?

<gadget id="calculator">floor(2)</gadget>
<output>2</output>
<result>2</result>

Choices:
A. 0
B. 1
C. 2
D. 3
E. 4

Explanation: "51 / 13 = 4 - 89 / 9 = 10 - prime numbers between 4 and 10 are 5 and 7 - sign signifies that the number is marginally less . answer c"


Question: a soccer team played 130 games and won 60 percent of them . how many games did it win ?

<gadget id="calculator">60 * 130</gadget>
<output>7_800</output>

<gadget id="calculator">7_800 / 100</gadget>
<output>78</output>
<result>78</result>

Choices:
A. 84
B. 94
C. 100
D. 125
E. 78

Explanation: "60 % of 130 = x 0.60 * 130 = x 78 = x answer : e"


Question: what least no . must be subtracted from 5026 so that remaining no . is divisible by 5 ?

<gadget id="calculator">5_026 / 5</gadget>
<output>5_026/5 = around 1_005.2</output>

<gadget id="calculator">floor(5_026/5)</gadget>
<output>1_005</output>

<gadget id="calculator">1_005 * 5</gadget>
<output>5_025</output>

<gadget id="calculator">5_026 - 5_025</gadget>
<output>1</output>
<result>1</result>

Choices:
A. 3
B. 4
C. 5
D. 6
E. 1

subtract(5026, multiply(floor(divide(5026, 5)), 5))

Explanation: explanation : on dividing 5026 by 5 we get the remainder 1 , so 1 should be subtracted option e


Question: a gambler has won 40 % of his 40 poker games for the week so far . if , all of a sudden , his luck changes and he begins winning 70 % of the time , how many more games must he play to end up winning 60 % of all his games for the week ?

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

<gadget id="calculator">40 * (3/5)</gadget>
<output>24</output>

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

<gadget id="calculator">40 * (2/5)</gadget>
<output>16</output>

<gadget id="calculator">24 - 16</gadget>
<output>8</output>

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

<gadget id="calculator">(7/10) - (3/5)</gadget>
<output>1/10 = around 0.1</output>

<gadget id="calculator">8 / (1/10)</gadget>
<output>80</output>
<result>80</result>

Choices:
A. 50
B. 60
C. 70
D. 80
E. 90

divide(subtract(multiply(40, divide(60, const_100)), multiply(40, divide(40, const_100))), subtract(divide(70, const_100), divide(60, const_100)))

Explanation: "let x be the number of additional games the gambler needs to play . 0.4 ( 40 ) + 0.7 x = 0.6 ( x + 40 ) 0.1 x = 8 x = 80 the answer is d ."


Question: when 2 / 9 of the votes on a certain resolution have been counted , 3 / 4 of those counted are in favor of the resolution . what fraction x of the remaining votes must be against the resolution so that the total count will result in a vote of 2 to 1 against the resolution ?

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

<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>

<gadget id="calculator">2 / 9</gadget>
<output>2/9 = around 0.222222</output>

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

<gadget id="calculator">(2/9) * (3/4)</gadget>
<output>1/6 = around 0.166667</output>

<gadget id="calculator">(2/9) - (1/6)</gadget>
<output>1/18 = around 0.055556</output>

<gadget id="calculator">(2/3) - (1/18)</gadget>
<output>11/18 = around 0.611111</output>

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

<gadget id="calculator">7 / 9</gadget>
<output>7/9 = around 0.777778</output>

<gadget id="calculator">(11/18) / (7/9)</gadget>
<output>11/14 = around 0.785714</output>
<result>11/14 = around 0.785714</result>

Choices:
A. 11 / 14
B. 13 / 18
C. 4 / 7
D. 3 / 7
E. 3 / 14

divide(subtract(divide(2, add(1, 2)), subtract(divide(2, 9), multiply(divide(2, 9), divide(3, 4)))), divide(subtract(9, 2), 9))

Explanation: "if we use variable for total votes there will be too many fractions to manipulate with , so pick some smart # : let set total # of votes is 18 . 2 / 9 of the votes on a certain resolution have been counted - - > 4 counted and 18 - 4 = 14 votes left to be counted ; 3 / 4 of those counted are in favor of the resolution - - > 3 in favor and 1 against ; ratio of those who voted against to those who voted for to be 2 to 1 there should be total of 18 * 2 / 3 = 12 people who voted against , so in the remaining 14 votes there should be 12 - 1 = 11 people who voted against . thus x = 11 / 14 of the remaining votes must be against . answer : a ."


Question: the speed of the boat in still water in 12 kmph . it can travel downstream through 54 kms in 3 hrs . in what time would it cover the same distance upstream ?

<gadget id="calculator">54 / 3</gadget>
<output>18</output>

<gadget id="calculator">18 - 12</gadget>
<output>6</output>

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

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

Choices:
A. 8 hours
B. 6 hours
C. 4 hours
D. 5 hours
E. 9 hours

divide(54, subtract(12, subtract(divide(54, 3), 12)))

Explanation: "still water = 12 km / hr downstream = 54 / 3 = 18 km / hr upstream = > > still water = ( u + v / 2 ) = > > 12 = u + 18 / 2 = 6 km / hr so time taken in upstream = 545 / 6 = 9 hrs answer : e"


Question: if shares of two persons in profits are rs . 400 and rs . 600 then ratio of their capitals is

<gadget id="calculator">400 / 600</gadget>
<output>2/3 = around 0.666667</output>
<result>2/3 = around 0.666667</result>

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

Explanation: "profit = time * capital so 400 : 600 = 2 : 3 answer : b"


Question: f ( x ) is a function such that f ( 2 x + 1 ) = 2 f ( x ) + 1 for all real numbers x and f ( 0 ) = 2 . find the value of f ( 3 ) .

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

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

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

Choices:
A. 10
B. 11
C. 12
D. 13
E. 14

subtract(multiply(multiply(2, 3), 2), 1)

Explanation: f ( 2 x + 1 ) = 2 f ( x ) + 1 : given f ( 3 ) = 2 f ( 1 ) + 1 : x = 1 in a f ( 1 ) = 2 f ( 0 ) + 1 : x = 0 in a f ( 3 ) = 11 : substitute correct answer b


Question: a sum of money deposited at c . i . amounts to rs . 2420 in 2 years and to rs . 2662 in 3 years . find the rate percent ?

<gadget id="calculator">2_662 - 2_420</gadget>
<output>242</output>

<gadget id="calculator">242 / 2_420</gadget>
<output>1/10 = around 0.1</output>

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

Choices:
A. 23 %
B. 10 %
C. 32 %
D. 98 %
E. 31 %

multiply(divide(subtract(2662, 2420), 2420), const_100)

Explanation: "2420 - - - 242 100 - - - ? = > 10 % answer : b"


Question: a car started running at a speed of 36 km / hr and the speed of the car was increased by 2 km / hr at the end of every hour . find the total distance covered by the car in the first 10 hours of the journey .

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

<gadget id="calculator">36 + 20</gadget>
<output>56</output>

<gadget id="calculator">56 + 36</gadget>
<output>92</output>

<gadget id="calculator">92 / 2</gadget>
<output>46</output>
<result>46</result>

Choices:
A. 45 km
B. 76 km
C. 25 km
D. 15 km
E. 30 km

divide(add(add(36, multiply(2, 10)), 36), 2)

Explanation: "a 45 km the total distance covered by the car in the first 10 hours = 36 + 38 + 40 + 42 + 44 + 46 + 48 + 50 + 52 + 54 = sum of 10 terms in ap whose first term is 36 and last term is 54 = 10 / 2 [ 36 + 54 ] = 450 km ."


Question: the profits of qrs company rose 30 % from march to april , then dropped 20 % from april to may , then rose 50 % from may to june . what was the percent increase for the whole quarter , from march to june ?

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

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

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

<gadget id="calculator">1 + (3/10)</gadget>
<output>13/10 = around 1.3</output>

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

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

<gadget id="calculator">(13/10) * (4/5)</gadget>
<output>26/25 = around 1.04</output>

<gadget id="calculator">(3/2) * (26/25)</gadget>
<output>39/25 = around 1.56</output>

<gadget id="calculator">(39/25) - 1</gadget>
<output>14/25 = around 0.56</output>

<gadget id="calculator">100 * (14/25)</gadget>
<output>56</output>
<result>56</result>

Choices:
A. 15 %
B. 32 %
C. 56 %
D. 62 %
E. 80 %

multiply(const_100, subtract(multiply(add(const_1, divide(50, const_100)), multiply(add(const_1, divide(30, const_100)), subtract(const_1, divide(20, const_100)))), const_1))

Explanation: "assume 100 in march , then 130 in april as 30 % increase , then 104 in may as 20 % decrease from april , and then 156 in june which is 150 % of 104 . so overall increase is from 100 to 156 is 56 % answer c"


Question: a pupil ' s marks were wrongly entered as 83 instead of 63 . due to that the average marks for the class got increased by half . the number of pupils in the class is :

<gadget id="calculator">83 - 63</gadget>
<output>20</output>

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

Choices:
A. 45
B. 40
C. 39
D. 37
E. 38

Explanation: "explanation : let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 . x / 2 = ( 83 - 63 ) = > x / 2 = 20 = > x = 40 . answer : b"


Question: if 40 % of ( x - y ) = 30 % of ( x + y ) then what percent of x is y ?

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

<gadget id="calculator">40 + 30</gadget>
<output>70</output>

<gadget id="calculator">10 / 70</gadget>
<output>1/7 = around 0.142857</output>

<gadget id="calculator">(1/7) * 100</gadget>
<output>100/7 = around 14.285714</output>
<result>100/7 = around 14.285714</result>

Choices:
A. 2.5 %
B. 10 %
C. 5 %
D. 14 %
E. 25 %

multiply(divide(subtract(40, 30), add(40, 30)), const_100)

Explanation: 40 % of ( x - y ) = 30 % of ( x + y ) ( 40 / 100 ) ( x - y ) = ( 30 / 100 ) ( x + y ) 4 ( x - y ) = 3 ( x + y ) x = 7 y x = 7 y therefore required percentage = ( ( y / x ) x 100 ) % = ( ( y / 7 y ) x 100 ) = 14 % answer is d .


Question: there are 20 players on a rugby team . if the average weight of the players is 180 pounds , what will be the new average height if a 210 pound player will join the team ?

<gadget id="calculator">20 * 180</gadget>
<output>3_600</output>

<gadget id="calculator">3_600 + 210</gadget>
<output>3_810</output>

<gadget id="calculator">20 + 1</gadget>
<output>21</output>

<gadget id="calculator">3_810 / 21</gadget>
<output>1_270/7 = around 181.428571</output>
<result>1_270/7 = around 181.428571</result>

Choices:
A. 185
B. 183.22
C. 184.96
D. 181.43
E. 182.78

divide(add(multiply(20, 180), 210), add(20, const_1))

Explanation: ( sum of the 20 weights ) / 20 = 180 sum of the 20 weights = 3600 new sum = 3600 + 210 = 3810 new average = 3810 / 21 = 181.43 ans : d


Question: if in a 20 over cricket match , there were no wide balls , no wides , no extras and no overthrows . what is the maximum number of runs that a batsman can score in an ideal case scenario ?

<gadget id="calculator">20 * 10</gadget>
<output>200</output>

<gadget id="calculator">200 + 20</gadget>
<output>220</output>

<gadget id="calculator">220 + 1</gadget>
<output>221</output>

<gadget id="calculator">3 * 221</gadget>
<output>663</output>
<result>663</result>

Choices:
A. 663
B. 720
C. 625
D. 640
E. none

multiply(const_3, add(add(multiply(20, const_10), 20), const_1))

Explanation: solution : 663 explanation : for an ideal case , the batsman will hit a six on each ball . but if he hits six on the last ball of the over , the strike will change in the next over . thus , the best he can do in the last ball is run 3 runs so that he retains the strike even in the next over . thus the total runs that he can score in each over : 6 * 5 + 3 = 33 but this will have to go like it only till the 19 th over . in the last over , he can hit a six in the last ball as well as that will be the last ball of the match . thus runs for the last over will be 6 * 6 = 36 . hence the maximum runs = 33 * 19 + 36 = 663 answer a