Question: two dogsled teams raced across a 300 mile course in wyoming . team a finished the course in 3 fewer hours than team q . if team a ' s average speed was 5 mph greater than team q ' s , what was team q ' s average mph ?

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

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

Choices:
A. 12
B. 15
C. 18
D. 20
E. 25

Explanation: "this is a very specific format that has appeared in a handful of real gmat questions , and you may wish to learn to recognize it : here we have a * fixed * distance , and we are given the difference between the times and speeds of two things that have traveled that distance . this is one of the very small number of question formats where backsolving is typically easier than solving directly , since the direct approach normally produces a quadratic equation . say team q ' s speed was s . then team q ' s time is 300 / s . team a ' s speed was then s + 5 , and team a ' s time was then 300 / ( s + 5 ) . we need to find an answer choice for s so that the time of team a is 3 less than the time of team q . that is , we need an answer choice so that 300 / ( s + 5 ) = ( 300 / s ) - 3 . you can now immediately use number properties to zero in on promising answer choices : the times in these questions will always work out to be integers , and we need to divide 300 by s , and by s + 5 . so we want an answer choice s which is a factor of 300 , and for which s + 5 is also a factor of 300 . so you can rule out answers a and c immediately , since s + 5 wo n ' t be a divisor of 300 in those cases ( sometimes using number properties you get to the correct answer without doing any other work , but unfortunately that ' s not the case here ) . testing the other answer choices , if you try answer d , you find the time for team q is 15 hours , and for team a is 12 hours , and since these differ by 3 , as desired , d is correct ."


Question: the average salary of the employees in a office is rs . 120 / month . the avg salary of officers is rs . 460 and of non officers is rs 110 . if the no . of officers is 15 , then find the no of nonofficers in the office .

<gadget id="calculator">15 * 460</gadget>
<output>6_900</output>

<gadget id="calculator">15 * 120</gadget>
<output>1_800</output>

<gadget id="calculator">6_900 - 1_800</gadget>
<output>5_100</output>

<gadget id="calculator">120 - 110</gadget>
<output>10</output>

<gadget id="calculator">5_100 / 10</gadget>
<output>510</output>
<result>510</result>

Choices:
A. 400
B. 420
C. 430
D. 450
E. 510

divide(subtract(multiply(15, 460), multiply(15, 120)), subtract(120, 110))

Explanation: "let no . of non - officers be x 15 * 460 + x * 110 = ( x + 15 ) 120 x = 510 e"


Question: the h . c . f . of two numbers is 10 and the other two factors of their l . c . m . are 13 and 14 . the larger of the two numbers is :

<gadget id="calculator">10 * 14</gadget>
<output>140</output>
<result>140</result>

Choices:
A. 100
B. 120
C. 180
D. 140
E. 60

Explanation: "clearly , the numbers are ( 10 x 13 ) and ( 10 x 14 ) . larger number = ( 10 x 14 ) = 140 . answer : option d"


Question: a and b began business with rs . 3000 and rs . 4000 after 8 months , a withdraws rs . 1000 and b advances rs . 1000 more . at the end of the year , their profits amounted to rs . 672 find the share of a .

<gadget id="calculator">3_000 * 8</gadget>
<output>24_000</output>

<gadget id="calculator">3_000 - 1_000</gadget>
<output>2_000</output>

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

<gadget id="calculator">2_000 * 4</gadget>
<output>8_000</output>

<gadget id="calculator">24_000 + 8_000</gadget>
<output>32_000</output>

<gadget id="calculator">4_000 * 8</gadget>
<output>32_000</output>

<gadget id="calculator">4_000 + 1_000</gadget>
<output>5_000</output>

<gadget id="calculator">5_000 * 4</gadget>
<output>20_000</output>

<gadget id="calculator">32_000 + 20_000</gadget>
<output>52_000</output>

<gadget id="calculator">32_000 + 52_000</gadget>
<output>84_000</output>

<gadget id="calculator">672 / 84_000</gadget>
<output>1/125 = around 0.008</output>

<gadget id="calculator">(1/125) * 32_000</gadget>
<output>256</output>
<result>256</result>

Choices:
A. 256
B. 388
C. 379
D. 277
E. 122

multiply(divide(672, add(add(multiply(3000, 8), multiply(subtract(3000, 1000), subtract(const_12, 8))), add(multiply(4000, 8), multiply(add(4000, 1000), subtract(const_12, 8))))), add(multiply(3000, 8), multiply(subtract(3000, 1000), subtract(const_12, 8))))

Explanation: "explanation : ( 3 * 8 + 2 * 4 ) : ( 4 * 8 + 5 * 4 ) 8 : 13 8 / 21 * 672 = 256 answer : a"


Question: a cricketer whose bowling average is 12.4 runs per wicket takes 5 wickets for 26 runs and there by decreases his average by 0.4 . the number age of the family now is ?

<gadget id="calculator">12.4 - 0.4</gadget>
<output>12</output>

<gadget id="calculator">5 * 12</gadget>
<output>60</output>

<gadget id="calculator">60 - 26</gadget>
<output>34</output>

<gadget id="calculator">34 / 0.4</gadget>
<output>85</output>
<result>85</result>

Choices:
A. 17
B. 98
C. 88
D. 85
E. 83

divide(subtract(multiply(5, subtract(12.4, 0.4)), 26), 0.4)

Explanation: let the number of wickets taken till the last match be x . then , ( 12.4 x + 26 ) / ( x + 5 ) = 12 = 12.4 x + 26 = 12 x + 60 = 0.4 x = 34 = x = 340 / 4 = 85 . answer : d


Question: a began business with rs . 27000 and was joined afterwards by b with rs . 54000 . when did b join if the profits at the end of the year were divided in the ratio of 2 : 1 ?

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

<gadget id="calculator">27_000 * 12</gadget>
<output>324_000</output>

<gadget id="calculator">324_000 / 54_000</gadget>
<output>6</output>

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

<gadget id="calculator">12 - 3</gadget>
<output>9</output>
<result>9</result>

Choices:
A. 9
B. 6
C. 7
D. 8
E. 2

subtract(multiply(const_4, const_3), divide(divide(multiply(27000, multiply(const_4, const_3)), 54000), 2))

Explanation: 27 * 12 : 54 * x = 2 : 1 x = 3 12 - 3 = 9 answer : a


Question: a , band c can do a piece of work in 11 days , 20 days and 20 days respectively , working alone . how soon can the work be done if a is assisted by band c on alternate days ?

<gadget id="calculator">20 / 11</gadget>
<output>20/11 = around 1.818182</output>

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

<gadget id="calculator">(20/11) + 1</gadget>
<output>31/11 = around 2.818182</output>

<gadget id="calculator">(31/11) + (31/11)</gadget>
<output>62/11 = around 5.636364</output>

<gadget id="calculator">(62/11) / 2</gadget>
<output>31/11 = around 2.818182</output>

<gadget id="calculator">20 / (31/11)</gadget>
<output>220/31 = around 7.096774</output>
<result>220/31 = around 7.096774</result>

Choices:
A. 7 days
B. 8 days
C. 9 days
D. 10 days
E. 11 days

divide(20, divide(add(add(divide(20, 11), divide(20, 20)), add(divide(20, 11), divide(20, 20))), const_2))

Explanation: "( a + b ) ' s 1 day ' s work = 1 / 11 + 1 / 20 = 31 / 220 ( a + c ) ' s 1 day ' s work = 1 / 11 + 1 / 20 = 31 / 220 work done in 2 day ' s = 31 / 220 + 31 / 220 = 31 / 110 31 / 110 th work done in 2 days work done = 110 / 31 * 2 = 7 days ( approx ) answer : a"


Question: out of 40 applicants to a law school , 15 majored in political science , 20 had a grade point average higher than 3.0 , and 10 did not major in political science and had a gpa equal to or lower than 3.0 . how many t applicants majored in political science and had a gpa higher than 3.0 ?

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

<gadget id="calculator">40 - 25</gadget>
<output>15</output>

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

Choices:
A. 5
B. 10
C. 15
D. 25
E. 35

Explanation: "total applicants = 40 political science = 15 and non political science = 40 - 15 = 25 gpa > 3.0 = 20 and gpa < = 3.0 = 20 10 non political science students had gpa < = 3.0 - - > 15 non political science students had gpa > 3.0 gpa > 3.0 in political science = total - ( gpa > 3.0 in non political science ) t = 20 - 15 = 5 answer : a"


Question: two numbers a and b are such that the sum of 5 % of a and 2 % of b is two - third of the sum of 6 % of a and 8 % of b . find the ratio of a : b .

<gadget id="calculator">8 / 100</gadget>
<output>2/25 = around 0.08</output>

<gadget id="calculator">(2/25) * 2</gadget>
<output>4/25 = around 0.16</output>

<gadget id="calculator">(4/25) / 3</gadget>
<output>4/75 = around 0.053333</output>

<gadget id="calculator">2 / 100</gadget>
<output>1/50 = around 0.02</output>

<gadget id="calculator">(4/75) - (1/50)</gadget>
<output>1/30 = around 0.033333</output>

<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>

<gadget id="calculator">6 / 100</gadget>
<output>3/50 = around 0.06</output>

<gadget id="calculator">(3/50) * 2</gadget>
<output>3/25 = around 0.12</output>

<gadget id="calculator">(3/25) / 3</gadget>
<output>1/25 = around 0.04</output>

<gadget id="calculator">(1/20) - (1/25)</gadget>
<output>1/100 = around 0.01</output>

<gadget id="calculator">(1/30) / (1/100)</gadget>
<output>10/3 = around 3.333333</output>
<result>10/3 = around 3.333333</result>

Choices:
A. 2 : 1
B. 1 : 2
C. 4 : 3
D. 10 : 3
E. 3 : 2

divide(subtract(divide(multiply(divide(8, const_100), const_2), const_3), divide(2, const_100)), subtract(divide(5, const_100), divide(multiply(divide(6, const_100), const_2), const_3)))

Explanation: explanation : 5 % of a + 2 % of b = 2 / 3 ( 6 % of a + 8 % of b ) 5 a / 100 + 2 b / 100 = 2 / 3 ( 6 a / 100 + 8 b / 100 ) ⇒ 5 a + 2 b = 2 / 3 ( 6 a + 8 b ) ⇒ 15 a + 6 b = 12 a + 16 b ⇒ 3 a = 10 b ⇒ ab = 10 / 3 ⇒ a : b = 10 : 3 answer : option d


Question: 20 men do a work in 20 days . how many men are needed to finish the work in 10 days ?

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

<gadget id="calculator">400 / 10</gadget>
<output>40</output>
<result>40</result>

Choices:
A. 50
B. 20
C. 30
D. 10
E. 40

Explanation: "men required to finish the work in 10 days = 20 * 20 / 10 = 40 answer is e"


Question: if 5 a = 6 b and ab ≠ 0 , what is the ratio of a / 6 to b / 5 ?

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

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

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

Choices:
A. 36 / 25
B. 10 / 12
C. 1
D. 1 / 5
E. 25 / 36

Explanation: "a nice fast approach is the first find a pair of numbers that satisfy the given equation : 5 a = 6 b here ' s one pair : a = 6 and b = 5 what is the ratio of a / 6 to b / 5 ? in other words , what is the value of ( a / 6 ) / ( b / 5 ) ? plug in values to get : ( a / 6 ) / ( b / 5 ) = ( 6 / 6 ) / ( 5 / 5 ) = 1 / 1 = 1 c"


Question: x does a work in 20 days . y does the same work in 30 days . in how many days they together will do the same work ?

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

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

<gadget id="calculator">(1/20) + (1/30)</gadget>
<output>1/12 = around 0.083333</output>

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

Choices:
A. 10
B. 12
C. 20
D. 30
E. 15

inverse(add(divide(const_1, 20), divide(const_1, 30)))

Explanation: "x ' s 1 day ' s work = 1 / 20 y ' s 1 day ' s work = 1 / 30 ( x + y ) ' s 1 day ' s work = ( 1 / 20 + 1 / 30 ) = 1 / 12 both together will finish the work in 12 days . correct option is b"


Question: jack and jill are marathon runners . jack can finish a marathon ( 42 km ) in 3.5 hours and jill can run a marathon in 4.2 hours . what is the ratio of their average running speed ? ( jack : jill )

<gadget id="calculator">42 / 3.5</gadget>
<output>12</output>

<gadget id="calculator">42 / 4.2</gadget>
<output>10</output>

<gadget id="calculator">12 / 10</gadget>
<output>6/5 = around 1.2</output>
<result>6/5 = around 1.2</result>

Choices:
A. 14 / 15
B. 15 / 14
C. 4 / 5
D. 6 / 5
E. can not be determined

Explanation: average speed of jack = distance / time = 42 / ( 7 / 2 ) = 84 / 7 average speed of jill = 42 / ( 4.2 ) = 10 ratio of average speed of jack to jill = ( 84 / 7 ) / 10 = 84 / 70 = 6 / 5 answer d


Question: a container contains 1000 liters of milk , from this container 10 liters of milk was taken out and replaced by water . this process was repeated further 2 times . how much milk is now contained by the container ?

<gadget id="calculator">1_000 - 10</gadget>
<output>990</output>

<gadget id="calculator">990 - 10</gadget>
<output>980</output>

<gadget id="calculator">980 - 10</gadget>
<output>970</output>
<result>970</result>

Choices:
A. 970.3 liters
B. 1000.45 liters
C. 879.65 liters
D. 1020.56 liters
E. 910.95 liters

subtract(subtract(subtract(1000, 10), 10), 10)

Explanation: amount of milk left after 3 operations = 1000 ( 1 - 10 / 1000 ) ^ 3 = 1000 * 99 / 100 * 99 / 100 * 99 / 100 = 970.3 liters answer is a


Question: a squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 3 feet . how many feet does the squirrel travels if the post is 18 feet tall and 3 feet in circumference ?

<gadget id="calculator">18 / 3</gadget>
<output>6</output>

<gadget id="calculator">6 * 3</gadget>
<output>18</output>
<result>18</result>

Choices:
A. 10 feet
B. 12 feet
C. 13 feet
D. 15 feet
E. 18 feet

Explanation: "total circuit = 18 / 3 = 6 total feet squirrel travels = 6 * 3 = 18 feet answer : e"


Question: in an electric circuit , two resistors with resistances 3 ohm and 5 ohm are connected in parallel . in this case , if r is the combined resistance of these two resistors , then the reciprocal of r is equal to the sum of the reciprocals of two resistors . what is the value ?

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

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

<gadget id="calculator">15 / 8</gadget>
<output>15/8 = around 1.875</output>
<result>15/8 = around 1.875</result>

Choices:
A. 15 ohms
B. 15 / 8 ohms
C. 1 / 8 ohms
D. 8 / 15 ohms
E. 8 ohms

Explanation: the wording is a bit confusing , though basically we are told that 1 / r = 1 / 3 + 1 / 5 , from which it follows that r = 15 / 8 ohms . answer : b .


Question: a and b enterd into a partnership investing rs . 16000 and rs . 12000 respectively . after 3 months , a withdrew rs . 5000 while b invested rs . 5000 more . after 3 more months . c joins the business with a capital of rs . 21000 . the share of b exceeds that of c , out of a total profit of rs . 26400 after one year by

<gadget id="calculator">12_000 * 3</gadget>
<output>36_000</output>

<gadget id="calculator">12_000 + 5_000</gadget>
<output>17_000</output>

<gadget id="calculator">12 - 3</gadget>
<output>9</output>

<gadget id="calculator">17_000 * 9</gadget>
<output>153_000</output>

<gadget id="calculator">36_000 + 153_000</gadget>
<output>189_000</output>

<gadget id="calculator">16_000 * 3</gadget>
<output>48_000</output>

<gadget id="calculator">16_000 - 5_000</gadget>
<output>11_000</output>

<gadget id="calculator">11_000 * 9</gadget>
<output>99_000</output>

<gadget id="calculator">48_000 + 99_000</gadget>
<output>147_000</output>

<gadget id="calculator">147_000 + 189_000</gadget>
<output>336_000</output>

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

<gadget id="calculator">21_000 * 6</gadget>
<output>126_000</output>

<gadget id="calculator">336_000 + 126_000</gadget>
<output>462_000</output>

<gadget id="calculator">189_000 / 462_000</gadget>
<output>9/22 = around 0.409091</output>

<gadget id="calculator">26_400 * (9/22)</gadget>
<output>10_800</output>

<gadget id="calculator">126_000 / 462_000</gadget>
<output>3/11 = around 0.272727</output>

<gadget id="calculator">26_400 * (3/11)</gadget>
<output>7_200</output>

<gadget id="calculator">10_800 - 7_200</gadget>
<output>3_600</output>
<result>3_600</result>

Choices:
A. rs . 2400
B. rs . 3000
C. rs . 3600
D. rs . 4800
E. none of these

subtract(multiply(26400, divide(add(multiply(12000, 3), multiply(add(12000, 5000), subtract(const_12, 3))), add(add(add(multiply(16000, 3), multiply(subtract(16000, 5000), subtract(const_12, 3))), add(multiply(12000, 3), multiply(add(12000, 5000), subtract(const_12, 3)))), multiply(21000, subtract(subtract(const_12, 3), 3))))), multiply(26400, divide(multiply(21000, subtract(subtract(const_12, 3), 3)), add(add(add(multiply(16000, 3), multiply(subtract(16000, 5000), subtract(const_12, 3))), add(multiply(12000, 3), multiply(add(12000, 5000), subtract(const_12, 3)))), multiply(21000, subtract(subtract(const_12, 3), 3))))))

Explanation: solution a : b : c = ( 16000 x 3 + 11000 x 9 ) : ( 12000 x 3 + 17000 x 9 ) : ( 21000 x 6 ) = 147 : 180 : 126 = 7 : 9 : 6 . ∴ difference of b and c ’ s shares = rs . ( 26400 x 9 / 22 - 26400 x 6 / 22 ) = rs . 3600 . answer c


Question: in a 500 m race , the ratio of the speeds of two contestants a and b is 3 : 4 . a has a start of 155 m . then , a wins by :

<gadget id="calculator">500 - 155</gadget>
<output>345</output>

<gadget id="calculator">345 * 4</gadget>
<output>1_380</output>

<gadget id="calculator">1_380 / 3</gadget>
<output>460</output>

<gadget id="calculator">500 - 460</gadget>
<output>40</output>
<result>40</result>

Choices:
A. 60 m
B. 20 m
C. 40 m
D. 20 m
E. 23 m

subtract(500, divide(multiply(subtract(500, 155), 4), 3))

Explanation: "to reach the winning post a will have to cover a distance of ( 500 - 155 ) m , i . e . , 345 m . while a covers 3 m , b covers 4 m . while a covers 345 m , b covers 4 x 345 / 3 m = 460 m . thus , when a reaches the winning post , b covers 460 m and therefore remains 40 m behind . a wins by 40 m . answer : c"


Question: dan ' s age after 16 years will be 6 times his age 4 years ago . what is the present age of dan ?

<gadget id="calculator">4 * 6</gadget>
<output>24</output>

<gadget id="calculator">16 + 24</gadget>
<output>40</output>

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

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

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

divide(add(16, multiply(4, 6)), subtract(6, const_1))

Explanation: "let dan ' s present age be x . x + 16 = 6 ( x - 4 ) 5 x = 40 x = 8 the answer is a ."


Question: by selling 20 pencils for a rupee a man loses 60 % . how many for a rupee should he sell in order to gain 60 % ?

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

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

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

<gadget id="calculator">160 * (1/40)</gadget>
<output>4</output>

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

<gadget id="calculator">(1/4) * 20</gadget>
<output>5</output>
<result>5</result>

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

multiply(divide(const_1, multiply(add(const_100, 60), divide(const_1, subtract(const_100, 60)))), 20)

Explanation: "40 % - - - 20 160 % - - - ? 40 / 160 * 20 = 5 answer : e"


Question: after decreasing 24 % in the price of an article costs rs . 1216 . find the actual cost of an article ?

<gadget id="calculator">24 / 100</gadget>
<output>6/25 = around 0.24</output>

<gadget id="calculator">1 - (6/25)</gadget>
<output>19/25 = around 0.76</output>

<gadget id="calculator">1_216 / (19/25)</gadget>
<output>1_600</output>
<result>1_600</result>

Choices:
A. 1667
B. 6789
C. 1200
D. 1600
E. 1421

divide(1216, subtract(const_1, divide(24, const_100)))

Explanation: "cp * ( 76 / 100 ) = 1216 cp = 16 * 100 = > cp = 1600 answer : d"


Question: if ( 18 ^ a ) * 9 ^ ( 3 a – 1 ) = ( 2 ^ 3 ) ( 3 ^ b ) and a and b are positive integers , what is the value of a ?

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

Choices:
A. 22
B. 11
C. 9
D. 6
E. 3

Explanation: 18 ^ a ) * 9 ^ ( 3 a – 1 ) = ( 2 ^ 3 ) ( 3 ^ b ) = 2 ^ a . 9 ^ a . 9 ^ ( 3 a – 1 ) = ( 2 ^ 3 ) ( 3 ^ b ) just compare powers of 2 from both sides ( no need to calculate powers of 3 , 9 as value of b is not asked ) answer = 3 answer : e


Question: a student traveled 10 percent of the distance of the trip alone , continued another 30 miles with a friend , and then finished the last half of the trip alone . how many miles long was the trip ?

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

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

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

<gadget id="calculator">(9/10) - (1/2)</gadget>
<output>2/5 = around 0.4</output>

<gadget id="calculator">30 / (2/5)</gadget>
<output>75</output>
<result>75</result>

Choices:
A. 75
B. 100
C. 125
D. 150
E. 175

divide(30, subtract(subtract(const_1, inverse(10)), divide(const_1, const_2)))

Explanation: let x be the total length of the trip . 0.1 x + 30 miles + 0.5 x = x 30 miles = 0.4 x x = 75 miles the answer is a .


Question: a bag marked at $ 250 is sold for $ 120 . the rate of discount is ?

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

<gadget id="calculator">130 / 250</gadget>
<output>13/25 = around 0.52</output>

<gadget id="calculator">(13/25) * 100</gadget>
<output>52</output>
<result>52</result>

Choices:
A. 10 %
B. 25 %
C. 20 %
D. 52 %
E. 45 %

multiply(divide(subtract(250, 120), 250), const_100)

Explanation: "rate of discount = 130 / 250 * 100 = 52 % answer is d"


Question: a can do a piece of work 30 days . b can do work in 45 days . in how many days they will complete the work together ?

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

<gadget id="calculator">1 / 45</gadget>
<output>1/45 = around 0.022222</output>

<gadget id="calculator">(1/30) + (1/45)</gadget>
<output>1/18 = around 0.055556</output>

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

Choices:
A. 15 days
B. 16 days
C. 19 days
D. 17 days
E. 18 days

divide(const_1, add(divide(const_1, 30), divide(const_1, 45)))

Explanation: "lcm = 90 , ratio = 30 : 45 = 2 : 3 no of days = 90 / ( 2 + 3 ) = 90 / 5 = 18 days answer : e"


Question: average between two sets of numbers is closer to the set with morenumbers ?

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

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

Choices:
A. 70
B. 80
C. 85
D. 90
E. 95

Explanation: "if on a test three people answered 90 % of the questions correctly and two people answered 80 % correctly , then the average for the group is not 85 % but rather 3 × 90 + 2 × 805 = 4305 = 86.3 × 90 + 2 × 805 = 4305 = 86 . here , 90 has a weight of 3 = > it occurs 3 times . whereas 80 has a weight of 2 = > it occurs 2 times . so the average is closer to 90 than to 80 as we have just calculated . b"


Question: what is the probability that the sum of two dice will yield a 6 , and then when both are thrown again , their sum will again yield a 6 ? assume that each die has 5 sides with faces numbered 1 to 5 .

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

<gadget id="calculator">5 / 25</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">(1/5) * (1/5)</gadget>
<output>1/25 = around 0.04</output>
<result>1/25 = around 0.04</result>

Choices:
A. 1 / 144
B. 1 / 25
C. 1 / 12
D. 1 / 6
E. 1 / 3

multiply(divide(5, power(5, const_2)), divide(5, power(5, const_2)))

Explanation: solution - rolling dices is an independent event . the combinations to get 6 are ( 1,5 ) , ( 5,1 ) , ( 2,4 ) , ( 4,2 ) , ( 3,3 ) and total combinations of both dices is 25 . the probability of getting 6 in first attempt is 5 / 25 = 1 / 5 . probability of getting 6 again in second attempt = ( 1 / 5 ) * ( 1 / 5 ) = 1 / 25 . ans b


Question: the average of runs of a cricket player of 10 innings was 34 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?

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

<gadget id="calculator">4 + 34</gadget>
<output>38</output>

<gadget id="calculator">11 * 38</gadget>
<output>418</output>

<gadget id="calculator">10 * 34</gadget>
<output>340</output>

<gadget id="calculator">418 - 340</gadget>
<output>78</output>
<result>78</result>

Choices:
A. 78
B. 79
C. 85
D. 87
E. 89

subtract(multiply(add(10, const_1), add(4, 34)), multiply(10, 34))

Explanation: "explanation : average = total runs / no . of innings = 34 so , total = average x no . of innings = 34 x 10 = 340 . now increase in avg = 4 runs . so , new avg = 34 + 4 = 38 runs total runs = new avg x new no . of innings = 38 x 11 = 418 runs made in the 11 th inning = 418 - 340 = 78 answer : a"


Question: a truck covers a distance of 288 km at a certain speed in 8 hours . how much time would a car take at an average speed which is 18 kmph more than that of the speed of the truck to cover a distance which is 90 km more than that travelled by the truck ?

<gadget id="calculator">288 + 90</gadget>
<output>378</output>

<gadget id="calculator">288 / 8</gadget>
<output>36</output>

<gadget id="calculator">36 + 18</gadget>
<output>54</output>

<gadget id="calculator">378 / 54</gadget>
<output>7</output>
<result>7</result>

Choices:
A. 6 hours
B. 5 hours
C. 7 hours
D. 8 hours
E. none

Explanation: "explanation : speed of the truck = distance / time = 288 / 8 = 36 kmph now , speed of car = ( speed of truck + 18 ) kmph = ( 36 + 18 ) = 54 kmph distance travelled by car = 288 + 90 = 378 km time taken by car = distance / speed = 378 / 54 = 7 hours . answer – c"


Question: a , b and c play a cricket match . the ratio of the runs scored by them in the match is a : b = 2 : 3 and b : c = 2 : 5 . if the total runs scored by all of them are 75 , the runs scored by b are ? a . 15 b . 18

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

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

<gadget id="calculator">(2/3) * (2/5)</gadget>
<output>4/15 = around 0.266667</output>

<gadget id="calculator">(4/15) + (2/5)</gadget>
<output>2/3 = around 0.666667</output>

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

<gadget id="calculator">75 / (5/3)</gadget>
<output>45</output>

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

Choices:
A. 22
B. 18
C. 99
D. 77
E. 24

multiply(divide(75, add(add(multiply(divide(2, 3), divide(2, 5)), divide(2, 5)), const_1)), divide(2, 5))

Explanation: a : b = 2 : 3 b : c = 2 : 5 a : b : c = 4 : 6 : 15 6 / 25 * 75 = 18 answer : b


Question: if 65 percent of a class answered the first question on a certain test correctly , 50 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ?

<gadget id="calculator">65 + 50</gadget>
<output>115</output>

<gadget id="calculator">115 + 20</gadget>
<output>135</output>

<gadget id="calculator">135 - 100</gadget>
<output>35</output>
<result>35</result>

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

subtract(add(add(65, 50), 20), const_100)

Explanation: "65 % answered the first question correctly and 20 % answered neither correctly . then 15 % missed the first question but answered the second question correctly . then the percent who answered both correctly is 50 % - 15 % = 35 % . the answer is c ."


Question: john and ingrid pay 30 % and 40 % tax annually , respectively . if john makes $ 56000 and ingrid makes $ 73000 , what is their combined tax rate ?

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

<gadget id="calculator">(3/10) * 56_000</gadget>
<output>16_800</output>

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

<gadget id="calculator">(2/5) * 73_000</gadget>
<output>29_200</output>

<gadget id="calculator">16_800 + 29_200</gadget>
<output>46_000</output>

<gadget id="calculator">73_000 + 56_000</gadget>
<output>129_000</output>

<gadget id="calculator">46_000 / 129_000</gadget>
<output>46/129 = around 0.356589</output>

<gadget id="calculator">(46/129) * 100</gadget>
<output>4_600/129 = around 35.658915</output>
<result>4_600/129 = around 35.658915</result>

Choices:
A. 32 %
B. 34.4 %
C. 35 %
D. 35.6 %
E. 36.4 %

multiply(divide(add(multiply(divide(30, const_100), 56000), multiply(divide(40, const_100), 73000)), add(73000, 56000)), const_100)

Explanation: "( 1 ) when 30 and 40 has equal weight or weight = 1 / 2 , the answer would be 35 . ( 2 ) when 40 has larger weight than 30 , the answer would be in between 35 and 40 . unfortunately , we have 2 answer choices d and e that fit that condition so we need to narrow down our range . ( 3 ) get 73000 / 129000 = 73 / 129 is a little above 1 / 2 . thus , our answer is just a little above 35 . answer : d"


Question: the average ( arithmetic mean ) of 20 , 40 , and 60 is 6 more than the average of 10 , 70 , and what number ?

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

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

<gadget id="calculator">6 * 3</gadget>
<output>18</output>

<gadget id="calculator">18 + 10</gadget>
<output>28</output>

<gadget id="calculator">28 + 70</gadget>
<output>98</output>

<gadget id="calculator">120 - 98</gadget>
<output>22</output>
<result>22</result>

Choices:
A. 15
B. 25
C. 35
D. 22
E. 55

subtract(add(add(20, 40), 60), add(add(multiply(6, const_3), 10), 70))

Explanation: "a 1 = 120 / 3 = 40 a 2 = a 1 - 6 = 34 sum of second list = 34 * 3 = 102 therefore the number = 102 - 80 = 22 answer : d"


Question: if 150 ! / 10 ^ n is an integer , what is the largest possible value of n ?

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

<gadget id="calculator">150 / 5</gadget>
<output>30</output>

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

<gadget id="calculator">6 + 30</gadget>
<output>36</output>
<result>36</result>

Choices:
A. 38
B. 47
C. 32
D. 36
E. 37

add(divide(divide(150, add(const_4, const_1)), add(const_4, const_1)), divide(150, add(const_4, const_1)))

Explanation: the question actually asks the highest power of 10 which divides 150 ! ( for a number to be an integer - without any remainder all the trailing zeroe ' s must be divided by the denominator ) 10 = 2 x 5 150 factorial will have 37 as - 150 / 5 = 30 30 / 5 = 6 6 / 5 = 1 so answer will be ( e ) 37


Question: the average height of 20 students in a class was calculated as 175 cm . it has later found that the height of one of the students in the class was incorrectly written as 151 cm whereas the actual height was 131 cm . what was the actual average height of the students in the class ?

<gadget id="calculator">20 * 175</gadget>
<output>3_500</output>

<gadget id="calculator">151 - 131</gadget>
<output>20</output>

<gadget id="calculator">3_500 - 20</gadget>
<output>3_480</output>

<gadget id="calculator">3_480 / 20</gadget>
<output>174</output>
<result>174</result>

Choices:
A. 174 cm
B. 173 cm
C. 172 cm
D. 171 cm
E. 170 cm

divide(subtract(multiply(20, 175), subtract(151, 131)), 20)

Explanation: "the total height was 20 cm too much . the average height should be reduced by 20 cm / 20 = 1 cm the answer is a ."


Question: a certain number of workers can do a work in 85 days . if there were 10 workers more it could be finished in 10 days less . how many workers are there ?

<gadget id="calculator">85 - 10</gadget>
<output>75</output>

<gadget id="calculator">75 * 10</gadget>
<output>750</output>

<gadget id="calculator">85 - 75</gadget>
<output>10</output>

<gadget id="calculator">750 / 10</gadget>
<output>75</output>
<result>75</result>

Choices:
A. 75
B. 30
C. 28
D. 24
E. 32

divide(multiply(subtract(85, 10), 10), subtract(85, subtract(85, 10)))

Explanation: "number of workers = 10 * ( 85 - 10 ) / 10 = 75 answer is a"


Question: car z travels 48 miles per gallon of gasoline when driven at a constant rate of 45 miles per hour , but travels 20 percent fewer miles per gallon of gasoline when driven at a constant rate of 60 miles per hour . how many miles does car z travel on 10 gallons of gasoline when driven at a constant rate of 60 miles per hour ?

<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">(4/5) * 48</gadget>
<output>192/5 = around 38.4</output>

<gadget id="calculator">(192/5) * 10</gadget>
<output>384</output>
<result>384</result>

Choices:
A. 320
B. 384
C. 400
D. 408.3
E. 440

multiply(multiply(subtract(const_1, divide(20, const_100)), 48), 10)

Explanation: "the question stem asks us for the distance possible with 10 gallons of fuel at a constant speed of 60 miles per hour . we therefore first calculate the fuel efficiency at that speed . the stem tells us that at 45 miles / hour , the car will run 48 miles / gallon and at 60 miles / hour , that distance decreases by 20 % . we can therefore conclude that the car will travel 38.4 miles / gallon at a constant speed of 60 miles / gallon . with 10 gallons of fuel , the car can therefore travel 38.4 miles / gallon * 10 gallons = 384 miles . answer b ."


Question: mr yadav spends 60 % of his monthly salary on consumable items and 50 % of the remaining on clothes and transport . he saves the remaining amount . if his savings at the end of the year were 24000 , how much amount per month would he have spent on clothes and transport ?

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

<gadget id="calculator">40 * 50</gadget>
<output>2_000</output>

<gadget id="calculator">2_000 / 100</gadget>
<output>20</output>

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

<gadget id="calculator">24_000 / (1/5)</gadget>
<output>120_000</output>

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

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

<gadget id="calculator">10_000 * (1/5)</gadget>
<output>2_000</output>
<result>2_000</result>

Choices:
A. 2000
B. 8076
C. 9691.2
D. 4845.6
E. none of these

multiply(divide(divide(24000, divide(divide(multiply(subtract(const_100, 60), 50), const_100), const_100)), multiply(const_3, const_4)), divide(divide(multiply(subtract(const_100, 60), 50), const_100), const_100))

Explanation: "∵ amount , he have spent in 1 month on clothes transport = amount spent on saving per month ∵ amount , spent on clothes and transport = 24000 ⁄ 12 = 2000 answer a"


Question: in the class of 50 students , 30 speak tamil and 40 speak telugu . what is the lowest possible number of students who speak both the languages ?

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

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

Choices:
A. 8
B. 10
C. 20
D. 30
E. 32

Explanation: let the student who speaks tamil - x let the student who speaks telugu - y as ( xuy ) - ( xny ) = total 30 + 40 - ( xny ) = 50 = 20 c )


Question: two trains start simultaneously from opposite ends of a 175 - km route and travel toward each other on parallel tracks . train x , traveling at a constant rate , completes the 175 - km trip in 4 hours . train y , travelling at a constant rate , completes the 175 - km trip in 3 hours . how many kilometers had train x traveled when it met train y ?

<gadget id="calculator">175 / 4</gadget>
<output>175/4 = around 43.75</output>

<gadget id="calculator">175 / 3</gadget>
<output>175/3 = around 58.333333</output>

<gadget id="calculator">(175/4) + (175/3)</gadget>
<output>1_225/12 = around 102.083333</output>

<gadget id="calculator">175 / (1_225/12)</gadget>
<output>12/7 = around 1.714286</output>

<gadget id="calculator">(175/4) * (12/7)</gadget>
<output>75</output>
<result>75</result>

Choices:
A. 66
B. 69
C. 72
D. 75
E. 78

multiply(divide(175, 4), divide(175, add(divide(175, 4), divide(175, 3))))

Explanation: if the two trains cover a total distance d , then train x travels ( 3 / 7 ) * d while train y travels ( 4 / 7 ) * d . if the trains travel 175 km to the meeting point , then train x travels ( 3 / 7 ) * 175 = 75 km . the answer is d .


Question: what is the rate percent when the simple interest on rs . 2000 amount to rs . 320 in 4 years ?

<gadget id="calculator">100 * 320</gadget>
<output>32_000</output>

<gadget id="calculator">2_000 * 4</gadget>
<output>8_000</output>

<gadget id="calculator">32_000 / 8_000</gadget>
<output>4</output>
<result>4</result>

Choices:
A. 4.5 %
B. 4.25 %
C. 4 %
D. 4.3 %
E. 4.1 %

divide(multiply(const_100, 320), multiply(2000, 4))

Explanation: "interest for 1 year = 320 / 4 = 80 interest on rs 2000 p / a = 80 interest rate = 80 / 2000 * 100 = 4 % answer : c"


Question: a ratio between two numbers is 4 : 5 and their l . c . m . is 200 . the first number is

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

<gadget id="calculator">200 / 20</gadget>
<output>10</output>

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

Choices:
A. 60
B. 40
C. 20
D. 15
E. none

multiply(divide(200, multiply(4, 5)), 4)

Explanation: "sol . let the required numbers be 4 x and 5 x . then , their l . c . m . is 20 x . ∴ 20 x = 200 ⇔ x = 10 . hence , the first number is 40 . answer b"


Question: 10 camels cost as much as 24 horses , 16 horses cost as much as 4 oxen and 6 oxen as much as 4 elephants . if the cost of 10 elephants is rs . 170000 , find the cost of a camel ?

<gadget id="calculator">24 * 4</gadget>
<output>96</output>

<gadget id="calculator">96 * 4</gadget>
<output>384</output>

<gadget id="calculator">384 * 170_000</gadget>
<output>65_280_000</output>

<gadget id="calculator">10 * 16</gadget>
<output>160</output>

<gadget id="calculator">160 * 6</gadget>
<output>960</output>

<gadget id="calculator">960 * 10</gadget>
<output>9_600</output>

<gadget id="calculator">65_280_000 / 9_600</gadget>
<output>6_800</output>
<result>6_800</result>

Choices:
A. rs . 9800
B. rs . 3800
C. rs . 9800
D. rs . 6800
E. rs . 6880

divide(multiply(multiply(multiply(24, 4), 4), 170000), multiply(multiply(multiply(10, 16), 6), 10))

Explanation: "cost of the camel = p 10 camels = 24 horses 16 horses = 4 oxen 6 oxen = 4 elephants 10 elephants = rs . 170000 p = rs . [ ( 24 * 4 * 4 * 170000 ) / ( 10 * 16 * 6 * 10 ) ] p = rs . ( 65280000 / 9600 ) = > p = rs . 6800 answer : d"


Question: when the positive integer k is divided by the positive integer n , the remainder is 11 . if k / n = 81.1 , what is the value of n ?

<gadget id="calculator">81.1 * 10</gadget>
<output>811</output>

<gadget id="calculator">811 - 2</gadget>
<output>809</output>

<gadget id="calculator">809 / 10</gadget>
<output>809/10 = around 80.9</output>

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

<gadget id="calculator">11 / (1/5)</gadget>
<output>55</output>

<gadget id="calculator">(809/10) * 55</gadget>
<output>8_899/2 = around 4_449.5</output>

<gadget id="calculator">(8_899/2) + 11</gadget>
<output>8_921/2 = around 4_460.5</output>

<gadget id="calculator">(8_921/2) / 55</gadget>
<output>811/10 = around 81.1</output>
<result>811/10 = around 81.1</result>

Choices:
A. 9
B. 20
C. 55
D. 70
E. 81

divide(add(multiply(divide(subtract(multiply(81.1, const_10), const_2), const_10), divide(11, divide(const_2, const_10))), 11), divide(11, divide(const_2, const_10)))

Explanation: "here ' s an approach that ' s based on number properties and a bit ofbrute forcemath : we ' re told that k and n are both integers . since k / n = 81.2 , we can say that k = 81.2 ( n ) n has tomultiply outthe . 2 so that k becomes an integer . with the answers that we have to work with , n has to be a multiple of 5 . eliminate a and e . with the remaining answers , we can test the answers and find the one that fits the rest of the info ( k / n = 81.2 and k / n has a remainder of 11 ) answer b : if n = 20 , then k = 1624 ; 1624 / 20 has a remainder of 4 not a match answer c : if n = 55 , then k = 4466 ; 4466 / 55 has a remainder of 11 match . final answer : e"


Question: if a person walks at 10 km / hr instead of 8 km / hr , he would have walked 14 km more . the actual distance traveled by him is ?

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

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

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

Choices:
A. 50
B. 40
C. 56
D. 16
E. 20

multiply(8, divide(14, subtract(10, 8)))

Explanation: "let the actual distance traveled be x km . then , x / 8 = ( x + 14 ) / 10 2 x - 112 = > x = 56 km . answer : c"


Question: if twice of a number divided by 3 d gives 20 as the remainder , and 5 times of the same number gives 32 as the remainder . what will be the value of d ?

<gadget id="calculator">32 / 5</gadget>
<output>32/5 = around 6.4</output>

<gadget id="calculator">(32/5) * 2</gadget>
<output>64/5 = around 12.8</output>

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

<gadget id="calculator">(64/5) - (1/4)</gadget>
<output>251/20 = around 12.55</output>
<result>251/20 = around 12.55</result>

Choices:
A. 11
B. 12
C. 15
D. 14
E. 18

subtract(multiply(divide(32, 5), const_2), divide(const_1, const_4))

Explanation: remainder in second case is , 32 . so , 3 d > = 33 . so , minimum value of d should 11 . if number = 28 . double of number = 56 and take d = 12 so 56 / 36 remainder = 20 . now 5 times of number = 140 . so 140 / 36 remainder = 32 . that is , 3 d = 36 satisfy the conditions . so d = 12 . answer : b


Question: 3 people candidates contested an election and they received 1136 , 7636 and 11628 votes respectively . what is the percentage of the total votes did the winning candidate get ?

<gadget id="calculator">1_136 + 7_636</gadget>
<output>8_772</output>

<gadget id="calculator">8_772 + 11_628</gadget>
<output>20_400</output>

<gadget id="calculator">11_628 / 20_400</gadget>
<output>57/100 = around 0.57</output>

<gadget id="calculator">(57/100) * 100</gadget>
<output>57</output>
<result>57</result>

Choices:
A. 40 %
B. 45 %
C. 57 %
D. 58 %
E. 60 %

Explanation: tot no of votes = ( 1136 + 7636 + 11628 ) = 20400 req = > ( 11628 / 20400 * 100 ) = > 57 % answer c


Question: a spirit and water solution is sold in a market . the cost per liter of the solution is directly proportional to the part ( fraction ) of spirit ( by volume ) the solution has . a solution of 1 liter of spirit and 1 liter of water costs 40 cents . how many cents does a solution of 1 liter of spirit and 2 liters of water cost ?

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

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

<gadget id="calculator">40 * (1/3)</gadget>
<output>40/3 = around 13.333333</output>

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

Choices:
A. 40
B. 33
C. 50
D. 51
E. 52

multiply(multiply(40, divide(1, add(1, 2))), add(1, 2))

Explanation: "yes , ensure that you understand the relation thoroughly ! cost per liter = k * fraction of spirit 40 cents is the cost of 2 liters of solution ( 1 part water , 1 part spirit ) . so cost per liter is 20 cents . fraction of spirit is 1 / 2 . 20 = k * ( 1 / 2 ) k = 40 cost per liter = 40 * ( 1 / 3 ) ( 1 part spirit , 2 parts water ) cost for 3 liters = 40 * ( 1 / 3 ) * 3 = 40 cents a . 40 cents"


Question: if 12 men or 20 women can do a piece of work in 54 days , then in how many days can 9 men and 12 women together do the work ?

<gadget id="calculator">12 * 54</gadget>
<output>648</output>

<gadget id="calculator">9 / 648</gadget>
<output>1/72 = around 0.013889</output>

<gadget id="calculator">20 * 54</gadget>
<output>1_080</output>

<gadget id="calculator">12 / 1_080</gadget>
<output>1/90 = around 0.011111</output>

<gadget id="calculator">(1/72) + (1/90)</gadget>
<output>1/40 = around 0.025</output>

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

Choices:
A. 10 days
B. 30 days
C. 20 days
D. 80 days
E. 40 days

inverse(add(divide(9, multiply(12, 54)), divide(12, multiply(20, 54))))

Explanation: "e 40 days given that 12 m = 20 w = > 3 m = 5 w 9 men + 12 women = 15 women + 12 women = 27 women 20 women can do the work in 54 days . so , 27 women can do it in ( 20 * 54 ) / 27 = 40 days ."


Question: gold is 19 times as heavy as water and copper is 9 times as heavy as water . in what ratio should these be mixed to get an alloy 13 times as heavy as water ?

<gadget id="calculator">13 - 9</gadget>
<output>4</output>

<gadget id="calculator">19 - 13</gadget>
<output>6</output>

<gadget id="calculator">4 / 6</gadget>
<output>2/3 = around 0.666667</output>
<result>2/3 = around 0.666667</result>

Choices:
A. 1 : 2
B. 2 : 3
C. 4 : 1
D. 5 : 2
E. 6 : 5

divide(subtract(13, 9), subtract(19, 13))

Explanation: "g = 19 w c = 9 w let 1 gm of gold mixed with x gm of copper to get 1 + x gm of the alloy 1 gm gold + x gm copper = x + 1 gm of alloy 19 w + 9 wx = x + 1 * 13 w 19 + 9 x = 13 ( x + 1 ) x = 3 / 2 ratio of gold with copper = 1 : 3 / 2 = 2 : 3 answer is b"


Question: a and b started a business jointly a ' s investment was thrice the investment of b and the period of his investment was two times the period of investment of b . if b received rs . 4000 as profit , then their total profit is

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

<gadget id="calculator">6 + 1</gadget>
<output>7</output>

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

Choices:
A. 23477
B. 28000
C. 28877
D. 1987
E. 1771

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

Explanation: "explanation : suppose b invested rs . x for y months . then , a invested rs . 3 x for 2 y months . so , a : b = ( 3 x * 2 y ) : ( x * y ) = 6 xy : xy = 6 : 1 . b ' s profit : total profit = 1 : 7 . let the total profit be rs . x then , 1 / 7 = 4000 / x or x = 28000 . answer : b ) 28000"


Question: excluding stoppages , the average speed of a bus is 100 km / hr and including stoppages , the average speed of the bus is 40 km / hr . for how many minutes does the bus stop per hour ?

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

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

<gadget id="calculator">(2/5) * 60</gadget>
<output>24</output>

<gadget id="calculator">60 - 24</gadget>
<output>36</output>
<result>36</result>

Choices:
A. 15 min
B. 18 min
C. 16 min
D. 20 min
E. 36 min

subtract(multiply(const_1, const_60), multiply(divide(40, 100), const_60))

Explanation: in 1 hr , the bus covers 100 km without stoppages and 40 km with stoppages . stoppage time = time take to travel ( 100 - 40 ) km i . e 60 km at 100 km / hr . stoppage time = 60 / 100 hrs = 36 min answer : e


Question: tom traveled the entire 60 miles trip . if he did the first 15 miles of at a constant rate 24 miles per hour and the remaining trip of at a constant rate 45 miles per hour , what is the his average speed , in miles per hour ?

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

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

<gadget id="calculator">15 / 24</gadget>
<output>5/8 = around 0.625</output>

<gadget id="calculator">1 + (5/8)</gadget>
<output>13/8 = around 1.625</output>

<gadget id="calculator">60 / (13/8)</gadget>
<output>480/13 = around 36.923077</output>
<result>480/13 = around 36.923077</result>

Choices:
A. 35.62 mph
B. 25.45 mph
C. 34.52 mph
D. 36.92 mph
E. 36.29 mph

divide(60, add(divide(45, subtract(60, 15)), divide(15, 24)))

Explanation: avg speed = total distance / total time = ( d 1 + d 2 ) / ( t 1 + t 2 ) = ( 15 + 45 ) / ( ( 15 / 24 ) + ( 45 / 45 ) ) = 60 * 2 / 3 = 36.92 mph d


Question: if w is the set of all the integers between 49 and 114 , inclusive , that are either multiples of 3 or multiples of 2 or multiples of both , then w contains how many numbers ?

<gadget id="calculator">114 - 49</gadget>
<output>65</output>

<gadget id="calculator">65 / 3</gadget>
<output>65/3 = around 21.666667</output>

<gadget id="calculator">floor(65/3)</gadget>
<output>21</output>

<gadget id="calculator">65 / 2</gadget>
<output>65/2 = around 32.5</output>

<gadget id="calculator">21 + (65/2)</gadget>
<output>107/2 = around 53.5</output>

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

<gadget id="calculator">65 / 6</gadget>
<output>65/6 = around 10.833333</output>

<gadget id="calculator">floor(65/6)</gadget>
<output>10</output>

<gadget id="calculator">(107/2) - 10</gadget>
<output>87/2 = around 43.5</output>
<result>87/2 = around 43.5</result>

Choices:
A. 34
B. 44
C. 45
D. 55
E. 72

subtract(add(floor(divide(subtract(114, 49), 3)), divide(subtract(114, 49), 2)), floor(divide(subtract(114, 49), multiply(2, 3))))

Explanation: "official solution : number of multiples of 3 step 1 . subtract the extreme multiples of 3 within the range ( the greatest is 114 , the smallest is 51 ) : 114 - 51 = 63 step 2 . divide by 3 : 63 / 3 = 21 step 3 . add 1 : 21 + 1 = 22 . so there are 22 multiples of 3 within the range : examples are 51 , 54 , 57 , 60 , etc . number of multiples of 2 step 1 . subtract the extreme multiples of 2 within the range ( the greatest is 114 , the smallest is 50 ) : 114 - 50 = 64 step 2 . divide by 2 : 64 / 2 = 32 step 3 . add 1 : 32 + 1 = 33 . so there are 33 multiples of 2 within the range : examples are 50 , 52 , 54 , 56 , 58 , 60 etc . add the 22 multiples of 3 and the 33 multiples of 2 : 22 + 33 = 55 . however , by adding the multiples of 2 and the multiples of 3 , we are effectively counting several numbers twice : for example , 54 and 60 are parts of both the lists above . so we ca n ' t just take 22 + 33 = 55 . find the number of multiples of 6 ( which are the double counted , as 6 is divisible by both 2 and 3 ) , and subtract it from 55 : step 1 . subtract the extreme multiples of 6 within the range ( the greatest is 72 , the smallest is 54 ) : 114 - 54 = 60 step 2 . divide by 6 : 60 / 6 = 10 step 3 . add 1 : 10 + 1 = 11 . so there are 11 multiples of 6 within the range : we counted 11 numbers twice . subtract the 11 multiples of 6 from the sum of the multiples of 2 and 3 : = 22 + 33 - 11 = 55 - 11 = 44 therefore , the final number of multiples of 2 , 3 or 6 is 44 . hence , this is the correct answer . ( b )"


Question: a shopkeeper sold 8 articles at the cost price of 10 articles . then find the profit % or lost %

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

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

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

Choices:
A. 10 %
B. 25 %
C. 20 %
D. 30 %
E. 50 %

multiply(divide(subtract(10, 8), 8), const_100)

Explanation: "here 8 articles selling price = 10 articles cost price so the difference = 10 - 8 = 2 % of profit = 2 * 100 / 8 = 25 % correct option is b"


Question: the general hospital is comprised of , 3 / 5 pediatricians , 1 / 4 surgeons , and the rest are gp doctors . if 1 / 4 of the surgeons are heart surgeons , and the hospital doubles the number of gp doctors , what proportion of the hospital are now heart surgeons ?

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

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

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

<gadget id="calculator">20 + 4</gadget>
<output>24</output>

<gadget id="calculator">1 / 24</gadget>
<output>1/24 = around 0.041667</output>
<result>1/24 = around 0.041667</result>

Choices:
A. 2 / 5
B. 1 / 4
C. 1 / 2
D. 1 / 24
E. 1 / 25

divide(subtract(3, add(1, 1)), add(multiply(4, 5), 4))

Explanation: ped = 3 / 5 = 12 / 20 sur = 1 / 4 = 4 / 20 gp = 1 - ( 12 / 20 + 4 / 20 ) = 1 - 16 / 20 = 4 / 20 hsur = ( 1 / 4 ) ( 4 / 20 ) = 1 / 20 if gp doubled = > ( 2 ) ( 4 ) = 8 ; then , total = 12 + 4 + 8 = 24 , and 1 is hsur = > proportion = 1 / 24 . answer : d


Question: 45 pupil , out of them 12 in debate only and 22 in singing only . then how many in both ?

<gadget id="calculator">12 + 22</gadget>
<output>34</output>

<gadget id="calculator">45 - 34</gadget>
<output>11</output>
<result>11</result>

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

Explanation: the intersection for two = 45 - 12 - 22 = 11 play both games . answer : c


Question: of the 75 cars on a car lot , 45 have air - conditioning , 35 have power steering , and 12 have both air - conditioning and power steering . how many of the cars on the lot have neither air - conditioning nor power steering ?

<gadget id="calculator">45 + 35</gadget>
<output>80</output>

<gadget id="calculator">80 - 12</gadget>
<output>68</output>

<gadget id="calculator">75 - 68</gadget>
<output>7</output>
<result>7</result>

Choices:
A. 7
B. 8
C. 10
D. 15
E. 18

Explanation: "total - neither = all air conditioning + all power steering - both or 75 - neither = 45 + 35 - 12 = 68 . = > neither = 7 , hence a . answer : a"


Question: a corporation 5 times its annual bonus to 10 of its employees . what percent of the employees ’ new bonus is the increase ?

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

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

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

Choices:
A. 12 %
B. 18 %
C. 80 %
D. 20 %
E. 15 %

multiply(divide(subtract(5, const_1), 5), const_100)

Explanation: let the annual bonus be x . a corporation triples its annual bonus . so new bonus = 5 x . increase = 5 x - x = 4 x the increase is what percent of the employees ’ new bonus = ( 4 x / 5 x ) * 100 = 80 % hence c .


Question: the sum of ages of 5 children born at the intervals of 3 years each is 50 years . what is the age of the youngest child ?

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

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

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

Choices:
A. 4 years
B. 8 years
C. 10 years
D. none of these
E. can not be determined

Explanation: "explanation let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 50 5 x = 20 x = 4 . age of the youngest child = x = 4 years . answer a"


Question: yearly subscription to professional magazines cost a company $ 940.00 . to make a 25 % cut in the magazine budget , how much less must be spent ?

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

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

<gadget id="calculator">(3/4) * 940</gadget>
<output>705</output>
<result>705</result>

Choices:
A. 705
B. 655
C. 656
D. 657
E. 658

multiply(divide(subtract(const_100, 25), const_100), 940)

Explanation: total cost 940 940 * 25 / 100 = 235 so the cut in amount is 235 the less amount to be spend is 940 - 235 = 705 answer : a


Question: the mean of 50 observations was 40 . it was found later that an observation 48 was wrongly taken as 23 . the corrected new mean is

<gadget id="calculator">40 * 50</gadget>
<output>2_000</output>

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

<gadget id="calculator">48 - 23</gadget>
<output>25</output>

<gadget id="calculator">2_000 + 25</gadget>
<output>2_025</output>

<gadget id="calculator">2_025 / 50</gadget>
<output>81/2 = around 40.5</output>
<result>81/2 = around 40.5</result>

Choices:
A. 40.46
B. 36.1
C. 36.5
D. 39.1
E. none

divide(add(multiply(40, 50), subtract(subtract(50, const_2), 23)), 50)

Explanation: "sol . therefore correct sum = ( 40 × 50 + 48 – 23 ) = 2023 . therefore correct mean = 2023 / 50 = 40.46 . answer a"


Question: a certain tests consists 8 sections with 25 questions , numbered from 1 to 25 , in each section . if a student answered all of the even - numbered questions correctly and 3 / 4 of the odd - numbered questions correctly , what was the total number of questions he answered correctly ? a . 150 b . 172 c . 174 d . 175 e . 176

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

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

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

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

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

Choices:
A. 174
B. 150
C. 180
D. 175
E. 190

add(divide(multiply(8, 25), const_2), multiply(divide(multiply(8, 25), const_2), divide(3, 4)))

Explanation: each set has 12 even and 13 odd numbered questions leading to total 96 even and 104 odd questions . 96 + 3 / 4 â ˆ — 104 = 96 + 78 = 17496 + 3 / 4 â ˆ — 104 = 96 + 78 = 174 answer : a


Question: a train running at the speed of 60 km / hr crosses a pole in 30 seconds . what is the length of the train ?

<gadget id="calculator">60 * 1_000</gadget>
<output>60_000</output>

<gadget id="calculator">60_000 / 3_600</gadget>
<output>50/3 = around 16.666667</output>

<gadget id="calculator">(50/3) * 30</gadget>
<output>500</output>
<result>500</result>

Choices:
A. 500 m
B. 620 m
C. 872 m
D. 150 m
E. 765 m

multiply(divide(multiply(60, const_1000), const_3600), 30)

Explanation: "speed = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec length of the train = ( speed x time ) = ( 50 / 3 * 30 ) m = 500 m . answer : a"


Question: when greenville state university decided to move its fine arts collection to a new library , it had to package the collection in 20 - inch by 20 - inch by 15 - inch boxes . if the university pays $ 0.60 for every box , and if the university needs 3.06 million cubic inches to package the collection , what is the minimum amount the university must spend on boxes ?

<gadget id="calculator">1_000 * 1_000</gadget>
<output>1_000_000</output>

<gadget id="calculator">3.06 * 1_000_000</gadget>
<output>3_060_000</output>

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

<gadget id="calculator">400 * 15</gadget>
<output>6_000</output>

<gadget id="calculator">3_060_000 / 6_000</gadget>
<output>510</output>

<gadget id="calculator">510 * 0.6</gadget>
<output>306</output>
<result>306</result>

Choices:
A. $ 306
B. $ 275
C. $ 510
D. $ 1,250
E. $ 2,550

multiply(divide(multiply(3.06, multiply(const_1000, const_1000)), multiply(multiply(20, 20), 15)), 0.60)

Explanation: "total no . of boxes = 3060000 / ( 20 × 20 × 15 ) = 510 total cost = 510 × $ 0.6 = $ 306 answer a"


Question: the sum of ages of 5 children born at the intervals of 3 years each is 80 years . what is the age of the youngest child ?

<gadget id="calculator">80 / 5</gadget>
<output>16</output>

<gadget id="calculator">16 - 3</gadget>
<output>13</output>

<gadget id="calculator">13 - 3</gadget>
<output>10</output>
<result>10</result>

Choices:
A. 3 years
B. 4 years
C. 6 years
D. 7 years
E. 10 years

Explanation: "let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 80 5 x = 50 x = 10 . age of the youngest child = x = 10 years . e )"


Question: 2 is what percent of 40 ?

<gadget id="calculator">2 / 40</gadget>
<output>1/20 = around 0.05</output>

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

Choices:
A. 0.2 %
B. 2 %
C. 5 %
D. 20 %
E. 500 %

Explanation: "2 = x * 40 / 100 x = 5 % ans ; c"


Question: tea worth rs . 126 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . if the mixture is worth rs . 153 per kg , the price of the third variety per kg

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

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

<gadget id="calculator">153 * 4</gadget>
<output>612</output>

<gadget id="calculator">126 + 126</gadget>
<output>252</output>

<gadget id="calculator">612 - 252</gadget>
<output>360</output>

<gadget id="calculator">360 / 2</gadget>
<output>180</output>
<result>180</result>

Choices:
A. 175.59
B. 175.5
C. 175.57
D. 175.52
E. 175.11

divide(subtract(multiply(153, add(add(1, 1), 2)), add(126, 126)), 2)

Explanation: "explanation : since first second varieties are mixed in equal proportions , so their average price = rs . ( 126 + 135 / 2 ) = rs . 130.50 so , the mixture is formed by mixing two varieties , one at rs . 130.50 per kg and the other at say , rs . x per kg in the ratio 2 : 2 , i . e . , 1 : 1 . we have to find x . cost of 1 kg tea of 1 st kind cost of 1 kg tea of 2 nd kind x - 153 / 22.50 = 1 = > x - 153 = 22.50 = > x = 175.50 . hence , price of the third variety = rs . 175.50 per kg . answer : c ) rs . 175.50"


Question: in an examination , a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer . if he attempts all 80 questions and secures 120 marks , the number of questions he attempts correctly , is :

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

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

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

Choices:
A. 35
B. 46
C. 42
D. 30
E. 40

Explanation: "let the number of correct answers be x . number of incorrect answers = ( 80 â € “ x ) . 4 x â € “ 1 ( 80 â € “ x ) = 120 or 5 x = 200 or x = 40 . answer : e"


Question: a no . when divided by the sum of 555 and 445 gives 2 times their difference as quotient & 10 as remainder . find the no . is ?

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

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

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

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

<gadget id="calculator">220_000 + 10</gadget>
<output>220_010</output>
<result>220_010</result>

Choices:
A. 220010
B. 145778
C. 220110
D. 235467
E. 220001

add(multiply(multiply(add(555, 445), 2), subtract(555, 445)), 10)

Explanation: "( 555 + 445 ) * 2 * 110 + 10 = 220000 + 10 = 220010 a"


Question: in a sports club with 55 members , 23 play badminton and 29 play tennis and 7 do not play either . how many members play both badminton and tennis ?

<gadget id="calculator">23 + 29</gadget>
<output>52</output>

<gadget id="calculator">52 + 7</gadget>
<output>59</output>

<gadget id="calculator">59 - 55</gadget>
<output>4</output>
<result>4</result>

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

Explanation: "23 + 29 = 52 but where as total number is 55 - 7 = 48 therefore answer is 52 - 48 = 4 hence answer is c"


Question: a garrison of 500 men has provisions for 20 days . at the end of 14 days , a reinforcement arrives , and it is now found that the provisions will last only for 3 days more . what is the reinforcement ?

<gadget id="calculator">500 * 20</gadget>
<output>10_000</output>

<gadget id="calculator">500 * 14</gadget>
<output>7_000</output>

<gadget id="calculator">10_000 - 7_000</gadget>
<output>3_000</output>

<gadget id="calculator">3_000 / 3</gadget>
<output>1_000</output>

<gadget id="calculator">1_000 - 500</gadget>
<output>500</output>
<result>500</result>

Choices:
A. 500
B. 1000
C. 1500
D. 3000
E. 2000

subtract(divide(subtract(multiply(500, 20), multiply(500, 14)), 3), 500)

Explanation: "500 - - - - 20 500 - - - - 6 x - - - - - 3 x * 3 = 500 * 6 x = 1000 500 - - - - - - - 500 answer : a"


Question: how long does a train 165 meters long running at the rate of 54 kmph take to cross a bridge 660 meters in length ?

<gadget id="calculator">165 + 660</gadget>
<output>825</output>

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

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

<gadget id="calculator">825 / 15</gadget>
<output>55</output>
<result>55</result>

Choices:
A. 55 sec
B. 40 sec
C. 45 sec
D. 30 sec
E. 35 sec

Explanation: "t = ( 660 + 165 ) / 54 * 18 / 5 t = 55 answer a"


Question: in covering a distance of 54 km , abhay takes 2 hours more than sameer . if abhay doubles his speed , then he would take 1 hour less than sameer . abhay ' s speed is :

<gadget id="calculator">54 / 2</gadget>
<output>27</output>

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

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

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

Choices:
A. 5 kmph
B. 6 kmph
C. 6.25 kmph
D. 7.5 kmph
E. 9 kmph

divide(subtract(54, divide(54, 2)), add(1, 2))

Explanation: "let abhay ' s speed be x km / hr . then , 54 / x - 54 / 2 x = 3 6 x = 54 x = 9 km / hr . answer : option e"


Question: john has $ 1600 at the beginning of his trip , after spending money , he still has exactly $ 600 less than he spent on the trip . how much money does john still have ?

<gadget id="calculator">1_600 - 600</gadget>
<output>1_000</output>

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

Choices:
A. $ 200
B. $ 400
C. $ 600
D. $ 800
E. $ 500

Explanation: suppose total money spent = x not spend ( money he still has ) = x - 600 x + x - 600 = 1600 x = 1100 money not spend = 1100 - 600 = 500 answer : e


Question: students at a school were on average 180 cm tall . the average female height was 170 cm , and the average male height was 181 cms . what was the ratio of men to women ?

<gadget id="calculator">180 - 170</gadget>
<output>10</output>

<gadget id="calculator">181 - 180</gadget>
<output>1</output>

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

Choices:
A. 5 : 2
B. 5 : 1
C. 4 : 3
D. 4 : 1
E. 10 : 1

divide(subtract(180, 170), subtract(181, 180))

Explanation: we ' re given a few facts to work with : 1 ) the average height of the females is 170 cm 2 ) the average height of the males is 181 cm 3 ) the average of the group is 180 cm we ' re asked for the ratio of men to women . w = number of women m = number of men ( 170 w + 181 m ) / ( w + m ) = 180 170 w + 181 m = 180 w + 180 m 1 m = 10 w m / w = 10 / 1 the ratio of men to women is 10 to 1 . e


Question: if the length of the longest chord of a certain circle is 18 , what is the radius of that certain circle ?

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

Choices:
A. 2.5
B. 9
C. 10
D. 15
E. 20

Explanation: "longest chord of a circle is the diameter of the circle diameter = 2 * radius if diameter of the circle is given as 18 = 2 * 9 so radius of the circle = 9 correct answer - b"


Question: a cistern 10 meters long and 4 meters wide contains water up to a depth of 1 meter 25 cm . what is the total area of the wet surface ?

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

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

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

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

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

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

<gadget id="calculator">10 * (5/4)</gadget>
<output>25/2 = around 12.5</output>

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

<gadget id="calculator">50 + 25</gadget>
<output>75</output>
<result>75</result>

Choices:
A. 45
B. 55
C. 65
D. 75
E. 85

add(add(multiply(10, 4), multiply(const_2, multiply(4, add(1, divide(25, const_100))))), multiply(const_2, multiply(10, add(1, divide(25, const_100)))))

Explanation: area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 4 x 1.25 + 10 x 1.25 ) + 10 x 4 ] = 75 the answer is d .


Question: if 50 % of ( x - y ) = 30 % of ( x + y ) then what percent of x is y ?

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

<gadget id="calculator">50 + 30</gadget>
<output>80</output>

<gadget id="calculator">20 / 80</gadget>
<output>1/4 = around 0.25</output>

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

Choices:
A. 2.5 %
B. 10 %
C. 5 %
D. 15 %
E. 25 %

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

Explanation: "50 % of ( x - y ) = 30 % of ( x + y ) ( 50 / 100 ) ( x - y ) = ( 30 / 100 ) ( x + y ) 5 ( x - y ) = 3 ( x + y ) 2 x = 8 y x = 4 y therefore required percentage = ( ( y / x ) x 100 ) % = ( ( y / 4 y ) x 100 ) = 25 % answer is e ."


Question: how many seconds does sandy take to cover a distance of 600 meters , if sandy runs at a speed of 18 km / hr ?

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

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

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

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

Explanation: 18 km / hr = 18000 m / 3600 s = 5 m / s time = 600 / 5 = 120 seconds the answer is b .


Question: calculate how many days it will take for 10 boys to paint a 80 m long wall if 6 boys can paint a 70 m long wall in 8 days ,

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

<gadget id="calculator">48 * 80</gadget>
<output>3_840</output>

<gadget id="calculator">70 * 10</gadget>
<output>700</output>

<gadget id="calculator">3_840 / 700</gadget>
<output>192/35 = around 5.485714</output>
<result>192/35 = around 5.485714</result>

Choices:
A. 9.48 days
B. 3.48 days
C. 7.48 days
D. 5.48 days
E. 6.48 days

divide(multiply(multiply(6, 8), 80), multiply(70, 10))

Explanation: "the length of wall painted by one boy in one day = 70 / 6 * 1 / 8 = 1.46 m no . of days required to paint 50 m cloth by 8 boys = 80 / 10 * 1 / 1.46 = 5.48 days . d"


Question: a no . when divided by the sum of 555 and 445 gives 2 times their difference as quotient & 60 as remainder . find the no . is ?

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

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

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

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

<gadget id="calculator">220_000 + 60</gadget>
<output>220_060</output>
<result>220_060</result>

Choices:
A. 145646
B. 236578
C. 645353
D. 456546
E. 220060

add(multiply(multiply(add(555, 445), 2), subtract(555, 445)), 60)

Explanation: "( 555 + 445 ) * 2 * 110 + 60 = 220000 + 60 = 220060 e"


Question: a monkey start climbing up a tree 18 ft tall . each hour it hops 3 ft and slips back 2 ft . how much time would it take the monkey to reach the top .

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

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

<gadget id="calculator">18 - 2</gadget>
<output>16</output>
<result>16</result>

Choices:
A. 15 hrs
B. 18 hrs
C. 19 hrs
D. 17 hrs
E. 16 hrs

Explanation: "if monkey hops 3 ft and slips back 2 ft in a hour , it means the monkey hops ( 3 ft - 2 ft ) = 1 ft / hr . similarly in 15 hrs it wil be 15 ft . bt since the height of the tree is 18 ft , so if the monkey hops up the tree in the next hr i . e 16 th hr then it reaches at the top of the tree . hence it takes 16 hrs for monkey to reach at the top answer : e"


Question: jane and ashley take 8 days and 40 days respectively to complete a project when they work on it alone . they thought if they worked on the project together , they would take fewer days to complete it . during the period that they were working together , jane took an eight day leave from work . this led to jane ' s working for four extra days on her own to complete the project . how long did it take to finish the project ?

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

<gadget id="calculator">4 * (1/8)</gadget>
<output>1/2 = around 0.5</output>

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

<gadget id="calculator">4 + 4</gadget>
<output>8</output>

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

<gadget id="calculator">8 * (1/40)</gadget>
<output>1/5 = around 0.2</output>

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

<gadget id="calculator">(1/8) + (1/40)</gadget>
<output>3/20 = around 0.15</output>

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

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

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

Choices:
A. 14 days
B. 15 days
C. 16 days
D. 18 days
E. 20 days

add(add(divide(subtract(subtract(const_1, multiply(const_4, divide(const_1, 8))), multiply(add(const_4, const_4), divide(const_1, 40))), add(divide(const_1, 8), divide(const_1, 40))), add(const_4, const_4)), const_4)

Explanation: "let us assume that the work is laying 40 bricks . jane = 5 bricks per day ashley = 1 brick per day together = 6 bricks per day let ' s say first 8 days ashley works alone , no of bricks = 8 last 4 days jane works alone , no . of bricks = 20 remaining bricks = 40 - 28 = 12 so together , they would take 12 / 6 = 2 total no . of days = 8 + 4 + 2 = 14 answer is a"


Question: if an integer n is to be selected at random from 1 to 100 , inclusive , what is probability n ( n + 1 ) will be divisible by 32 ?

<gadget id="calculator">2 / 32</gadget>
<output>1/16 = around 0.0625</output>
<result>1/16 = around 0.0625</result>

Choices:
A. 2 / 7
B. 3 / 7
C. 1 / 16
D. 1 / 14
E. 1 / 12

Explanation: "because n ( n + 1 ) is always an even product of even * odd or odd * even factors , there is a probability of 1 that that it will be divisible by 2 , and , thus , a probability of 1 / 2 that it will be divisible by 4 and , thus , a probability of 1 / 4 that it will be divisible by 8 and , thus , a probability of 1 / 8 that it will be divisible by 16 and , thus , a probability of 1 / 16 that it will be divisible by 32 1 * 1 / 16 = 1 / 16 answer : c"


Question: today jim is twice as old as fred , and sam is 4 years younger than fred . 4 years ago jim was 8 times as old as sam . how old is jim now ?

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

<gadget id="calculator">64 - 4</gadget>
<output>60</output>

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

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

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

Choices:
A. 8
B. 12
C. 16
D. 20
E. 24

multiply(divide(subtract(multiply(8, 8), 4), subtract(8, const_2)), const_2)

Explanation: we ' re asked how old jim is now . we ' re given three facts to work with : 1 ) today , jim is twice as old as fred 2 ) today , sam is 4 years younger than fred 3 ) four years ago , jim was 8 times as old as sam . let ' s test answer d : 20 if . . . . jim is currently 20 years old . . . . fred is 10 years old sam is 6 years old 4 years ago , jim was 16 and sam was 2 , so jim was 8 times sam ' s age . this is an exact match for what we were told , so this must be the answer . d


Question: a bullet train 150 m long is running with a speed of 30 kmph . in what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the bullet train is going ?

<gadget id="calculator">30 + 6</gadget>
<output>36</output>

<gadget id="calculator">36 * 1_000</gadget>
<output>36_000</output>

<gadget id="calculator">36_000 / 3_600</gadget>
<output>10</output>

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

Choices:
A. 23 sec
B. 15 sec
C. 12 sec
D. 11 sec
E. 15 sec

divide(150, divide(multiply(add(30, 6), const_1000), const_3600))

Explanation: e 15 sec speed of the bullet train relative to man = ( 30 + 6 ) kmph = 36 * 5 / 18 m / sec = 30 / 3 m / sec . time taken by the bullet train to cross the man = time taken by it to cover 150 m at ( 30 / 3 ) m / sec = ( 150 * 3 / 30 ) sec = 15 sec


Question: the sum of all the integers k such that – 21 < k < 24 is

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

<gadget id="calculator">(-21) + 1</gadget>
<output>-20</output>

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

<gadget id="calculator">(-20) + (-19)</gadget>
<output>-39</output>
<result>-39</result>

Choices:
A. 0
B. - 2
C. - 25
D. - 39
E. - 51

add(add(negate(21), const_1), add(add(negate(21), const_1), const_1))

Explanation: "- 20 - - - - - - - - - - - - - - - - - - 0 - - - - - - - - - - - - - - - - - 23 values upto + 23 cancels outwe are left with only - 20 - 19 sum of which is - 39 . hence option d . d"


Question: a dealer purchases 15 articles for rs . 25 and sells 12 articles for rs . 30 . find the profit percentage ?

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

<gadget id="calculator">30 * 5</gadget>
<output>150</output>

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

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

Choices:
A. 25 %
B. 50 %
C. 20 %
D. 5 %
E. none of these

subtract(multiply(30, add(const_4, const_1)), multiply(25, const_4))

Explanation: "l . c . m of 15 and 12 = 60 cp of 60 articles = rs . 100 ( 25 * 4 ) sp of 60 articles = rs . 150 ( 30 * 5 ) profit percentage = ( 150 - 100 ) / 100 * 100 = 50 % answer : b"


Question: a worker ' s daily wage is increased by 50 % and the new wage is $ 30 per day . what was the worker ' s daily wage before the increase ?

<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 / (3/2)</gadget>
<output>20</output>
<result>20</result>

Choices:
A. $ 15
B. $ 18
C. $ 20
D. $ 22
E. $ 25

divide(30, add(const_1, divide(50, const_100)))

Explanation: let x be the daily wage before the increase . 1.5 x = $ 30 x = $ 20 the answer is c .


Question: if the weight of 12 meters long rod is 13.4 kg . what is the weight of 6 meters long rod ?

<gadget id="calculator">6 * 13.4</gadget>
<output>80.4</output>

<gadget id="calculator">80.4 / 12</gadget>
<output>6.7</output>
<result>6.7</result>

Choices:
A. 6.7 kg .
B. 10.8 kg .
C. 12.4 kg .
D. 18.0 kg
E. none

Explanation: "answer ∵ weight of 12 m long rod = 13.4 kg ∴ weight of 1 m long rod = 13.4 / 12 kg ∴ weight of 6 m long rod = 13.4 x 6 / 12 = 6.7 kg option : a"


Question: a store sells 2 kinds of jelly beans mixes ( a and b ) both made up of red and yellow beans . if b contains 20 % more red beans than a but 10 % fewer yellow beans . and jar a contains twice as many red beans as yellow by what percent is the number of beans in jar b larger than the number in jar a

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

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

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

<gadget id="calculator">210 / 100</gadget>
<output>21/10 = around 2.1</output>

<gadget id="calculator">(21/10) - 2</gadget>
<output>1/10 = around 0.1</output>

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

Choices:
A. 5
B. 6
C. 8
D. 9
E. 10

multiply(subtract(divide(add(add(const_100, 20), subtract(const_100, 10)), const_100), const_2), const_100)

Explanation: a has 10 yellows 20 reds total = 30 so b has 1.2 x 20 = 24 reds 0.9 x 10 = 9 yellows total = 33 difference = 3 / 30 = 10 % answer : e


Question: find the greatest common factor ( gfc ) of 24 , 40 and 60 .

<gadget id="calculator">gcd(24, 40)</gadget>
<output>8</output>

<gadget id="calculator">gcd(8, 60)</gadget>
<output>4</output>
<result>4</result>

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

Explanation: we first write the prime factorization of each given number 24 = 2 × 2 × 2 × 3 = 23 * cubic * × 3 40 = 2 × 2 × 2 × 5 = 23 * cubic * × 5 60 = 2 × 2 × 3 × 5 = 22 * square * × 3 × 5 gfc = 22 * square * = 4 corect answer is d ) 4


Question: when 242 is divided by a certain divisor the remainder obtained is 12 . when 698 is divided by the same divisor the remainder obtained is 16 . however , when the sum of the two numbers 242 and 698 is divided by the divisor , the remainder obtained is 10 . what is the value of the divisor ?

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

<gadget id="calculator">28 - 10</gadget>
<output>18</output>
<result>18</result>

Choices:
A. 11
B. 18
C. 13
D. 23
E. none of these

Explanation: "let that divisor be x since remainder is 12 or 16 it means divisor is greater than 16 . now 242 - 12 = 230 = kx ( k is an integer and 234 is divisble by x ) similarly 698 - 16 = 682 = lx ( l is an integer and 689 is divisible by x ) adding both 698 and 242 = ( 230 + 682 ) + 12 + 16 = x ( k + l ) + 28 when we divide this number by x then remainder will be equal to remainder of ( 28 divided by x ) = 10 hence x = 28 - 10 = 18 hence b"


Question: the cost price of an article is 64 % of the marked price . calculate the gain percent after allowing a discount of 20 % ?

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

<gadget id="calculator">80 / 64</gadget>
<output>5/4 = around 1.25</output>

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

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

Choices:
A. 37.5 %
B. 48 %
C. 50.5 %
D. 52 %
E. 25 %

multiply(subtract(divide(subtract(const_100, 20), 64), const_1), const_100)

Explanation: "explanation : let marked price = rs . 100 . then , c . p . = rs . 64 , s . p . = rs . 80 gain % = 16 / 64 * 100 = 25 % . answer : option e"


Question: by selling 22 pens for a rupee a woman loses 10 % . how many for a rupee should he sell in order to gain 50 % ?

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

<gadget id="calculator">100 / 90</gadget>
<output>10/9 = around 1.111111</output>

<gadget id="calculator">(10/9) / 22</gadget>
<output>5/99 = around 0.050505</output>

<gadget id="calculator">(5/99) * 50</gadget>
<output>250/99 = around 2.525253</output>

<gadget id="calculator">(250/99) / 100</gadget>
<output>5/198 = around 0.025253</output>

<gadget id="calculator">(5/99) + (5/198)</gadget>
<output>5/66 = around 0.075758</output>

<gadget id="calculator">1 / (5/66)</gadget>
<output>66/5 = around 13.2</output>
<result>66/5 = around 13.2</result>

Choices:
A. 12
B. 14
C. 45
D. 13
E. 65

inverse(add(divide(divide(const_100, subtract(const_100, 10)), 22), divide(multiply(divide(divide(const_100, subtract(const_100, 10)), 22), 50), const_100)))

Explanation: "d 90 % - - - 22 150 % - - - ? 90 / 150 * 22 = 13"


Question: a and b start a business jointly . a invests rs 16000 for 8 month and b remains in the business for 4 months . out of total profit , b claims 2 / 7 of the profit . how much money was contributed by b ?

<gadget id="calculator">16_000 * 8</gadget>
<output>128_000</output>

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

<gadget id="calculator">128_000 * 2</gadget>
<output>256_000</output>

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

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

<gadget id="calculator">256_000 / 20</gadget>
<output>12_800</output>
<result>12_800</result>

Choices:
A. 12800
B. 13000
C. 11500
D. 12500
E. 12000

divide(multiply(multiply(16000, 8), divide(8, 4)), multiply(4, add(4, const_1)))

Explanation: b claims 2 / 7 of the profit a claims remaining 5 / 7 of the profit = > a : b = 5 / 7 : 2 / 7 = 5 : 2 let the money contributed by b = b then a : b = 16000 × 8 : b × 4 therefore , 16000 × 8 : b × 4 = 5 : 2 16000 × 8 × 2 = b × 4 × 5 16000 × 2 × 2 = b × 5 3200 × 2 × 2 = b b = 12800 answer is a .


Question: john and steve are speed walkers in a race . john is 10 meters behind steve when he begins his final push . john blazes to the finish at a pace of 4.2 m / s , while steve maintains a blistering 3.7 m / s speed . if john finishes the race 2 meters ahead of steve , how long was john ’ s final push ?

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

<gadget id="calculator">3.7 * 12</gadget>
<output>44.4</output>

<gadget id="calculator">4.2 - 3.7</gadget>
<output>0.5</output>

<gadget id="calculator">44.4 / 0.5</gadget>
<output>88.8</output>

<gadget id="calculator">88.8 + 12</gadget>
<output>100.8</output>

<gadget id="calculator">100.8 / 4.2</gadget>
<output>24</output>
<result>24</result>

Choices:
A. 13 seconds
B. 17 seconds
C. 24 seconds
D. 34 seconds
E. 51 seconds

Explanation: "let t be the time that john spent for his final push . thus , per the question , 4.2 t = 3.7 t + 10 + 2 - - - > 0.5 t = 12 - - - > t = 24 seconds . c is the correct answer ."


Question: in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the ` ` sport ' ' formulation , the ratio of flavoring to corn syrup is three times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of the ` ` sport ' ' formulation contains 3 ounces of corn syrup , how many ounces of water does it contain ?

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

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

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

Choices:
A. 45
B. 50
C. 55
D. 60
E. 63

multiply(multiply(30, const_2), divide(3, const_4))

Explanation: f : c : w 1 : 12 : 30 sport version : f : c 3 : 12 f : w 1 : 60 or 3 : 180 so c : f : w = 12 : 3 : 180 c / w = 12 / 180 = 3 ounces / x ounces x = 3 * 180 / 12 = 45 ounces of water answer : a


Question: two employees x and y are paid a total of rs . 440 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?

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

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

<gadget id="calculator">440 * 10</gadget>
<output>4_400</output>

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

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

<gadget id="calculator">4_400 / 22</gadget>
<output>200</output>
<result>200</result>

Choices:
A. s . 150
B. s . 200
C. s . 250
D. s . 350
E. s . 400

divide(multiply(440, multiply(add(const_1, const_4), const_2)), multiply(add(multiply(add(const_1, const_4), const_2), const_1), const_2))

Explanation: "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 440 but x = 120 % of y = 120 y / 100 = 12 y / 10 â ˆ ´ 12 y / 10 + y = 440 â ‡ ’ y [ 12 / 10 + 1 ] = 440 â ‡ ’ 22 y / 10 = 440 â ‡ ’ 22 y = 4400 â ‡ ’ y = 4400 / 22 = 400 / 2 = rs . 200 b )"


Question: how many gallons of milk that is 10 percent butter - fat must be added to 8 gallons of milk that is 25 percent butterfat to obtain milk that is 20 percent butterfat ?

<gadget id="calculator">25 - 20</gadget>
<output>5</output>

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

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

Choices:
A. 4
B. 12
C. 14
D. 16
E. 28

divide(multiply(subtract(25, 20), 8), 10)

Explanation: "equate the fat : 0.1 x + 0.25 * 8 = 0.2 ( x + 8 ) - - > x = 4 . answer : a ."


Question: a envelop weight 8.5 gm , if 820 of these envelop are sent with an advertisement mail . how much wieght ?

<gadget id="calculator">8.5 * 820</gadget>
<output>6_970</output>

<gadget id="calculator">6_970 / 1_000</gadget>
<output>697/100 = around 6.97</output>
<result>697/100 = around 6.97</result>

Choices:
A. 6.6 kg
B. 6.8 kg
C. 6.7 kg
D. 6.97 kg
E. 7.8 kg

Explanation: "820 * 8.5 6970.0 gm 6.97 kg answer : d"


Question: the area of a rectangular field is equal to 500 square meters . its perimeter is equal to 90 meters . find the width of this rectangle .

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

<gadget id="calculator">45 * 45</gadget>
<output>2_025</output>

<gadget id="calculator">4 * 500</gadget>
<output>2_000</output>

<gadget id="calculator">2_025 - 2_000</gadget>
<output>25</output>

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

<gadget id="calculator">45 - 5</gadget>
<output>40</output>

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

Choices:
A. 5
B. 10
C. 15
D. 20
E. 25

divide(subtract(divide(90, const_2), sqrt(subtract(multiply(divide(90, const_2), divide(90, const_2)), multiply(const_4, 500)))), const_2)

Explanation: "l * w = 500 : area , l is the length and w is the width . 2 l + 2 w = 90 : perimeter l = 45 - w : solve for l ( 45 - w ) * w = 500 : substitute in the area equation w = 20 and l = 25 correct answer d"


Question: the angle between the minute hand and the hour hand of a clock when the time is 11.30 , is

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

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

<gadget id="calculator">12 / 11</gadget>
<output>12/11 = around 1.090909</output>

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

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

<gadget id="calculator">(12/11) * 55</gadget>
<output>60</output>

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

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

<gadget id="calculator">30 * 11</gadget>
<output>330</output>

<gadget id="calculator">330 / 2</gadget>
<output>165</output>
<result>165</result>

Choices:
A. 35 °
B. 65 °
C. 45 °
D. 165 °
E. 95 °

divide(multiply(subtract(multiply(divide(multiply(const_3, const_4), subtract(multiply(const_3, const_4), const_1)), multiply(add(const_4, const_1), subtract(multiply(const_3, const_4), const_1))), divide(const_60, const_2)), subtract(multiply(const_3, const_4), const_1)), const_2)

Explanation: angle between hands of a clock when the minute hand is behind the hour hand , the angle between the two hands at m minutes past h ' o clock = 30 ( h − m / 5 ) + m / 2 degree when the minute hand is ahead of the hour hand , the angle between the two hands at m minutes past h ' o clock = 30 ( m / 5 − h ) − m / 2 degree here h = 11 , m = 30 and minute hand is behind the hour hand . hence the angle = 30 ( h − m / 5 ) + m / 2 = 30 ( 11 − 30 / 5 ) + 30 / 2 = 30 ( 11 − 6 ) + 15 = 30 × 5 + 15 = 165 ° answer is d .


Question: there are 16 bees in the hive , then 6 more fly . how many bees are there in all ?

<gadget id="calculator">16 + 6</gadget>
<output>22</output>
<result>22</result>

Choices:
A. 7
B. 33
C. 22
D. 17
E. 25

Explanation: 16 + 6 = 22 . answer is c .


Question: a train moves with a speed of 108 kmph . its speed in metres per second is :

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

<gadget id="calculator">108 * (5/18)</gadget>
<output>30</output>
<result>30</result>

Choices:
A. 10.8
B. 18
C. 30
D. 38.8
E. none of these

Explanation: "explanation : 108 kmph = ( 108 x 5 / 18 ) m / sec = 30 m / s . answer : c"


Question: 20 is subtracted from 60 % of a number , the result is 88 . find the number ?

<gadget id="calculator">20 + 88</gadget>
<output>108</output>

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

<gadget id="calculator">108 / (3/5)</gadget>
<output>180</output>
<result>180</result>

Choices:
A. 120
B. 300
C. 180
D. 170
E. 148

divide(add(20, 88), divide(60, const_100))

Explanation: "( 60 / 100 ) * x â € “ 20 = 88 6 x = 1080 x = 180 answer : c"


Question: by how much is 50 % of 250 greater than 25 % of 400 .

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

<gadget id="calculator">250 * (1/2)</gadget>
<output>125</output>

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

<gadget id="calculator">(1/4) * 400</gadget>
<output>100</output>

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

Choices:
A. 25
B. 26
C. 29
D. 39
E. 26

subtract(multiply(250, divide(50, const_100)), multiply(divide(25, const_100), 400))

Explanation: "( 50 / 100 ) * 250 â € “ ( 25 / 100 ) * 400 125 - 100 = 25 answer : b"


Question: find the ratio in which rice at rs . 7.20 a kg be mixed with rice at rs . 5.70 a kg to produce a mixture worth rs . 6.30 a kg ?

<gadget id="calculator">6.3 - 5.7</gadget>
<output>0.6</output>

<gadget id="calculator">7.2 - 6.3</gadget>
<output>0.9</output>

<gadget id="calculator">0.6 / 0.9</gadget>
<output>0.666667</output>
<result>0.666667</result>

Choices:
A. 1 : 3
B. 2 : 3
C. 3 : 4
D. 4 : 5
E. none of these

divide(subtract(6.3, 5.7), subtract(7.2, 6.3))

Explanation: solution required ratio = 60 : 90 = 2 : 3 answer b


Question: a solution contains 8 parts of water for every 7 parts of lemonade syrup . how many parts of the solution should be removed and replaced with water so that the solution will now contain 35 % lemonade syrup ?

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

<gadget id="calculator">7 / 15</gadget>
<output>7/15 = around 0.466667</output>

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

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

<gadget id="calculator">(7/15) - (2/5)</gadget>
<output>1/15 = around 0.066667</output>

<gadget id="calculator">(1/15) / (7/15)</gadget>
<output>1/7 = around 0.142857</output>

<gadget id="calculator">(1/7) * 15</gadget>
<output>15/7 = around 2.142857</output>
<result>15/7 = around 2.142857</result>

Choices:
A. 1.5
B. 1.75
C. 2.14
D. 2.34
E. 2.64

multiply(divide(subtract(divide(7, add(8, 7)), divide(const_2, add(const_2, const_3))), divide(7, add(8, 7))), add(8, 7))

Explanation: "let the total solution is 150 l with 80 l water 70 l syrup . to make 35 % syrup solution , the result solution must have 97.5 l syrup and 52.5 l syrup . therefore we are taking 17.5 l of syrup from initial solution and replacing with water . using urinary method : 70 l syrup in 150 l solution 17.5 l syrup in 37.5 l solution we started by multiplying 10 now to get to the result we need to divide by 17.5 = > amount of solution to be replaced with water ( 37.5 / 17.5 ) = 2.14 . correct option : c"


Question: running at the same constant rate , 100 identical machines can produce a total of 500 coffee bar per minute . at this rate , how many bottles could 20 such machines produce in 2 minutes ?

<gadget id="calculator">500 / 100</gadget>
<output>5</output>

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

<gadget id="calculator">10 * 20</gadget>
<output>200</output>
<result>200</result>

Choices:
A. 110
B. 220
C. 330
D. 200
E. 789

multiply(multiply(divide(500, 100), 2), 20)

Explanation: let ' s take the approach that uses the answer choices to eliminate wasted time . 500 / 100 = 5 coffee bar per minute per machine . 20 machines = 100 per minute . 2 minutes worth = 200 coffe bar . looking at the answers it is clear . . . we can only choose ( d ) the correct answer is d .


Question: find the constant k so that : - x 2 - ( k + 8 ) x - 8 = - ( x - 2 ) ( x - 4 )

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

<gadget id="calculator">8 + 6</gadget>
<output>14</output>
<result>14</result>

Choices:
A. 11
B. 12
C. 14
D. 19
E. 15

Explanation: "- x 2 - ( k + 8 ) x - 8 = - ( x - 2 ) ( x - 4 ) : given - x 2 - ( k + 8 ) x - 8 = - x 2 + 6 x - 8 - ( k + 8 ) = 6 : two polynomials are equal if their corresponding coefficients are equal . k = - 14 : solve the above for k correct answer c"


Question: a , b and c invested rs . 6000 , rs . 4000 and rs . 10000 respectively , in a partnership business . find the share of a in profit of rs . 11000 after a year ?

<gadget id="calculator">6_000 + 4_000</gadget>
<output>10_000</output>

<gadget id="calculator">10_000 + 10_000</gadget>
<output>20_000</output>

<gadget id="calculator">6_000 / 20_000</gadget>
<output>3/10 = around 0.3</output>

<gadget id="calculator">(3/10) * 11_000</gadget>
<output>3_300</output>
<result>3_300</result>

Choices:
A. 3300
B. 1100
C. 2667
D. 600
E. 4000

Explanation: "explanation : 6000 : 4000 : 10000 3 : 2 : 5 3 / 10 * 11000 = 3300 answer : a"


Question: a group of people participate in some curriculum , 30 of them practice yoga , 20 study cooking , 15 study weaving , 5 of them study cooking only , 8 of them study both the cooking and yoga , 5 of them participate all curriculums . how many people study both cooking and weaving ?

<gadget id="calculator">20 - 8</gadget>
<output>12</output>

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

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

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

subtract(subtract(subtract(20, 8), 5), 5)

Explanation: "both cooking and weaving = 20 - ( 5 + 8 + 5 ) = 2 so , the correct answer is b ."


Question: at what rate percent on simple interest will rs . 750 amount to rs . 825 in 5 years ?

<gadget id="calculator">825 - 750</gadget>
<output>75</output>

<gadget id="calculator">75 / 750</gadget>
<output>1/10 = around 0.1</output>

<gadget id="calculator">(1/10) / 5</gadget>
<output>1/50 = around 0.02</output>

<gadget id="calculator">(1/50) * 100</gadget>
<output>2</output>
<result>2</result>

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

multiply(divide(divide(subtract(825, 750), 750), 5), const_100)

Explanation: "75 = ( 750 * 5 * r ) / 100 r = 2 % . answer : a"


Question: two ants , arthur and amy , have discovered a picnic and are bringing crumbs back to the anthill . amy makes twice as many trips and carries one and a half times as many crumbs per trip as arthur . if arthur carries a total of b crumbs to the anthill , how many crumbs will amy bring to the anthill , in terms of b ?

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

Choices:
A. b / 2
B. b
C. 3 b / 2
D. 2 b
E. 3 b

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

Explanation: lets do it by picking up numbers . let arthur carry 2 crumbs per trip , this means amy carries 3 crumbs per trip . also let arthur make 2 trips and so amy makes 4 trips . thus total crumbs carried by arthur ( b ) = 2 x 2 = 4 , total crumbs carried by amy = 3 x 4 = 12 . 12 is 3 times 4 , so e


Question: a certain number of badges were distributed among a class of students . the student who got 1 / 6 th of the total number of badges actually got 5 times the average number of badges the others got ! how many students were there in the class ?

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

<gadget id="calculator">30 - 5</gadget>
<output>25</output>

<gadget id="calculator">25 + 1</gadget>
<output>26</output>
<result>26</result>

Choices:
A. 30
B. 26
C. 11
D. 31
E. 32

Explanation: detailed solution let the total students be ( n + 1 ) let total badges be x let the average of ‘ n ’ students be y the student who got 1 / 6 th of x = 5 y or y = x / 30 therefore ‘ n ’ students got 1 / 30 th of total share each or n * x / 30 + 1 * x / 6 = x nx + 5 x = 30 x n + 5 = 30 or n = 25 total = n + 1 = 26 correct answer : b