Cheukting/mathqa huggingface dataset:
Question (general): in a village there are 150 men and 90 women in present time . if in next year population will be p = ( a ^ 2 + b ^ 2 ) ^ 1 / 2 , and in every year men are reduces 5 % . what is population of after 2 year .
Options: a ) 140 , b ) 141 , c ) 142 , d ) 143 , e ) 146
Rationale: "next year total population = [ 150 ^ 2 + 90 ^ 2 ] ^ . 5 = 174.92 = 175 man decreased by 5 % so total man = 150 * . 95 = 142.5 women will be = 175 - 142.5 = 32.5 so population after two years = [ 135 ^ 2 + 32.5 ^ 2 ] ^ . 5 = 146.15 = 146 so population after two year = 146 answer : e"
Answer: e
Question (physics): if an object travels 200 feet in 4 seconds , what is the object ' s approximate speed in miles per hour ? ( note : 1 mile = 5280 feet )
Options: a ) 36 , b ) 34 , c ) 356 , d ) 12 , e ) 45
Rationale: 1 mile = 5280 feet = > 1 feet = 1 / 5280 miles if the object travels 200 feet in 4 sec then it travels 200 / 4 * 60 * 60 feet in 1 hour ( 1 hr = 60 min * 60 sec ) = 3600 * 50 feet in 1 hour = 180000 feet in 1 hr = 180000 / 5280 miles in 1 hour = 18000 / 528 miles / hr ~ 34 miles / hr answer - b
Answer: b
Question (physics): a cube of side 3 meter length is cut into small cubes of side 15 cm each . how many such small cubes can be obtained ?
Options: a ) 8078 , b ) 1040 , c ) 1058 , d ) 1021 , e ) 8000
Rationale: "along one edge , the number of small cubes that can be cut = 300 / 15 = 20 along each edge 20 cubes can be cut . ( along length , breadth and height ) . total number of small cubes that can be cut = 20 * 20 * 20 = 8000 answer : e"
Answer: e
Question (geometry): a hall is 15 m long and 12 m broad . if the sum of the areas of the floor and the ceiling is equal to the sum of the areas of 4 walls , the volume of the hall is :
Options: a ) 3348 , b ) 3898 , c ) 1200 , d ) 2881 , e ) 7881
Rationale: answer : c ) 1200
Answer: c
Question (geometry): if the sides of a triangle are 30 cm , 28 cm and 12 cm , what is its area ?
Options: a ) 120 cm 2 , b ) 112 cm 2 , c ) 776 cm 2 , d ) 666 cm 2 , e ) 168 cm 2
Rationale: "the triangle with sides 30 cm , 28 cm and 12 cm is right angled , where the hypotenuse is 30 cm . area of the triangle = 1 / 2 * 28 * 12 = 168 cm 2 answer : e"
Answer: e
Question (general): the avg weight of a , b & c is 84 kg . if d joins the group , the avg weight of the group becomes 80 kg . if another man e who weights is 3 kg more than d replaces a , then the avgof b , c , d & e becomes 79 kg . what is the weight of a ?
Options: a ) 45 , b ) 65 , c ) 75 , d ) 89 , e ) 90
Rationale: "a + b + c = 3 * 84 = 252 a + b + c + d = 4 * 80 = 320 - - - - ( i ) so , d = 68 & e = 68 + 3 = 71 b + c + d + e = 79 * 4 = 316 - - - ( ii ) from eq . ( i ) & ( ii ) a - e = 320 – 316 = 4 a = e + 4 = 71 + 4 = 75 c"
Answer: c
Question (general): if the price of a certain computer increased 30 percent from d dollars to 377 dollars , then 2 d =
Options: a ) 540 , b ) 570 , c ) 619 , d ) 649 , e ) 580
Rationale: "before price increase price = d after 30 % price increase price = d + ( 30 / 100 ) * d = 1.3 d = 377 ( given ) i . e . d = 377 / 1.3 = $ 290 i . e . 2 d = 2 * 290 = 580 answer : option e"
Answer: e
Question (general): you have been given a physical balance and 7 weights of 52 , 50 , 48 , 44 , 45 , 46 , and 78 kgs . . keeping weights on one pan and object on the other , what is the maximum you can weigh less than 183 kgs . ?
Options: a ) 178 , b ) 180 , c ) 181 , d ) 182 , e ) 183
Rationale: "balance = 52 + 50 + 48 + 44 + 45 + 46 + 78 - 183 answer : e"
Answer: e
Question (gain): on a sum of money , the s . i . for 2 years is $ 600 , while the c . i . is $ 615 , the rate of interest being the same in both the cases . the rate of interest is ?
Options: a ) 4 % , b ) 5 % , c ) 6 % , d ) 7 % , e ) 8 %
Rationale: "difference in c . i . and s . i for 2 years = $ 615 - $ 600 = $ 15 s . i for one year = $ 300 s . i . on $ 300 for 1 year = $ 15 rate = ( 100 * 15 ) / ( 300 ) = 5 % the answer is b ."
Answer: b
Question (gain): a is a working partner and b is a sleeping partner in the business . a puts in rs . 2000 and b rs . 3000 , a receives 10 % of the profit for managing the business the rest being divided in proportion of their capitals . out of a total profit of rs . 9600 , money received by a is ?
Options: a ) 1978 , b ) 2707 , c ) 7728 , d ) 4416 , e ) 7291
Rationale: "2 : 3 = > 2 : 3 9600 * 10 / 100 = 960 9600 - 960 = 8640 8640 * 2 / 5 = 3456 + 960 = 4416 answer : d"
Answer: d
Question (physics): annie and sam set out together on bicycles traveling at 15 and 12 km per hour respectively . after 40 minutes , annie stops to fix a flat tire . if it takes annie 35 minutes to fix the flat tire and sam continues to ride during this time , how many minutes will it take annie to catch up with sam assuming that annie resumes riding at 15 km per hour ?
Options: a ) 20 , b ) 40 , c ) 60 , d ) 80 , e ) 100
Rationale: "annie gains 3 km per hour ( or 1 km every 20 minutes ) on sam . after 40 minutes annie is 2 km ahead . sam rides 1 km every 5 minutes . in the next 35 minutes , sam rides 7 km so sam will be 5 km ahead . it will take annie 100 minutes to catch sam . the answer is e ."
Answer: e
Question (general): find the unknown term 8 , 86 , x , - 4 , - 12
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 9
Rationale: 8 , 86 , x , - 4 , - 12 i guess each differ in d range of 2 8 - 8 = 0 8 - 6 = 2 6 - 2 = 4 2 - 6 = - 4 - 4 - 8 = - 12 answer : a
Answer: a
Question (physics): if a train , travelling at a speed of 360 kmph , crosses a pole in 5 sec , then the length of train is ?
Options: a ) 381 m , b ) 112 m , c ) 500 m , d ) 125 m , e ) 433 m
Rationale: "c c = 360 * 5 / 18 * 5 = 500 m"
Answer: c
Question (geometry): if y is the smallest positive integer such that 1260 multiplied by y is the square of an integer , then y must be
Options: a ) 25 , b ) 35 , c ) 60 , d ) 75 , e ) 140
Rationale: "1260 = 2 ^ 2 * 3 ^ 2 * 5 * 7 to be perfect square , we need to multiply by at least 5 * 7 = 35 . the answer is b ."
Answer: b
Question (general): a certain company retirement plan has arule of 70 provision that allows an employee to retire when the employee ' s age plus years of employment with the company total at least 70 . in what year could a female employee hired in 1988 on her 32 nd birthday first be eligible to retire under this provision ?
Options: a ) 2003 , b ) 2004 , c ) 2005 , d ) 2006 , e ) 2007
Rationale: "she must gain at least 70 points , now she has 32 and every year gives her two more points : one for age and one for additional year of employment , so 32 + 2 * ( # of years ) = 70 - - > ( # of years ) = 19 - - > 1988 + 19 = 2007 . answer : e ."
Answer: e
Question (probability): a coin is tossed 3 times . what is the probability of getting exactly 2 heads ?
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 3 / 8 , d ) 5 / 8 , e ) 3 / 16
Rationale: "the number of possible outcomes is 2 ^ 3 = 8 there are 3 ways to get exactly 2 heads . p ( exactly 2 heads ) = 3 / 8 the answer is c ."
Answer: c
Question (general): 3 , 4.5 , 6.75 , 10.13 , 15.18 , ( . . . )
Options: a ) 60 , b ) 60.75 , c ) 22.78 , d ) 32.52 , e ) 88
Rationale: "3 ( 3 ã — 3 ) ã · 2 = 4.5 ( 4.5 ã — 3 ) ã · 2 = 6.75 ( 6.75 ã — 3 ) ã · 2 = 10.13 ( 10.18 ã — 3 ) ã · 2 = 15.18 ( 15.18 ã — 3 ) ã · 2 = 60.75 answer is c"
Answer: c
Question (general): a certain protective additive increases from 45 days to 60 days the time between required maintenance checks on an industrial vehicle . by what percent is the time between maintenance checks increased by using the additive ?
Options: a ) 25 % , b ) 33 1 / 3 % , c ) 50 % , d ) 66 2 / 3 % , e ) 75 %
Rationale: "general formula for percent increase or decrease , ( percent change ) : percent = change / original ∗ 100 so , the time between maintenance checks increased by 60 − 45 / 45 ∗ 100 = 33 1 / 3 answer : b ."
Answer: b
Question (general): if x * y = xy + 2 ( x + y ) for all integers x and y , then 2 * ( – 3 ) =
Options: a ) – 16 , b ) – 11 , c ) – 8 , d ) 4 , e ) 16
Rationale: 2 * ( - 3 ) = 2 * ( - 3 ) + 2 ( 2 + ( - 3 ) ) = - 6 - 2 = - 8 option ( c )
Answer: c
Question (physics): a can run 4.5 km distance in 1 min 30 seconds , while b can run this distance in 3 min . by how much distance can a beat b ?
Options: a ) 2250 m , b ) 1000 m , c ) 1250 m , d ) 1800 m , e ) 2000 m
Rationale: a takes time 1.30 minutes = 90 sec b takes time 3 minutes = 180 sec diffrence = 180 - 90 = 90 sec now we are to find distance covered in 90 sec by b 180 sec = 4500 m 1 sec = 25 m 90 sec = 25 x 90 = 2250 m answer : a
Answer: a
Question (general): a , b and c rents a pasture for rs . 957 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should c pay ?
Options: a ) 270 , b ) 289 , c ) 297 , d ) 255 , e ) 552
Rationale: "12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 9 / 29 * 957 = 297 answer : c"
Answer: c
Question (general): a student got 74 % in math and 84 % in history . to get an overall average of 75 % , how much should the student get in the third subject ?
Options: a ) 61 % , b ) 63 % , c ) 65 % , d ) 67 % , e ) 69 %
Rationale: 74 + 84 + x = 3 * 75 x = 67 the answer is d .
Answer: d
Question (physics): the sector of a circle has radius of 7 cm and central angle 135 o . find its perimeter ?
Options: a ) 91.5 cm , b ) 92.2 cm , c ) 28.9 cm , d ) 30.5 cm , e ) 98.2 cm
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 135 / 360 * 2 * 22 / 7 * 7 ) + 2 ( 7 ) = 16.5 + 14 = 30.5 cm answer : d"
Answer: d
Question (geometry): the width of a rectangular hall is ½ of its length . if the area of the hall is 128 sq . m , what is the difference between its length and breadth ?
Options: a ) 8 m , b ) 10 m , c ) 12 m , d ) 15 m , e ) 17 m
Rationale: "let the length of the hall be x m breadth of the hall = 1 x / 2 m area of the hall = length * breadth 128 = x * 1 x / 2 x ² = 256 x = 16 difference between the length and breadth of the hall = x - 1 x / 2 = x / 2 = 16 / 2 = 8 m answer : a"
Answer: a
Question (physics): two trains running in opposite directions cross a man standing on the platform in 47 seconds and 38 seconds respectively and they cross each other in 40 seconds . the ratio of their speeds is :
Options: a ) 3 : 1 , b ) 3 : 2 , c ) 2 : 7 , d ) 3 : 25 , e ) 3 : 4
Rationale: "let the speeds of the two trains be x m / sec and y m / sec respectively . then , length of the first train = 47 x meters , and length of the second train = 38 y meters . ( 47 x + 37 y ) / ( x + y ) = 40 = = > 47 x + 38 y = 40 x + 40 y = = > 7 x = 2 y = = > x / y = 2 / 7 answer : option c"
Answer: c
Question (physics): the ratio between the length and the breadth of a rectangular park is 3 : 2 . if a man cycling along the boundary of the park at the speed of 13 km / hr completes one round in 8 minutes , then the area of the park ( in sq . m ) is
Options: a ) 345600 , b ) 153400 , c ) 153600 , d ) 154000 , e ) 154200
Rationale: "perimeter = distance covered in 8 min . = 18000 x 8 m = 2400 m . 60 let length = 3 x metres and breadth = 2 x metres . then , 2 ( 3 x + 2 x ) = 2400 or x = 240 . length = 720 m and breadth = 480 m . area = ( 720 x 480 ) m 2 = 345600 m 2 . a"
Answer: a
Question (physics): a train 200 m long running at 80 kmph crosses a platform in 22 sec . what is the length of the platform ?
Options: a ) 338 , b ) 277 , c ) 350 , d ) 288 , e ) 271
Rationale: "d = 80 * 5 / 18 = 22 = 488 – 200 = 288 answer : d"
Answer: d
Question (gain): a fruit seller sells mangoes at the rate of rs . 9 per kg and thereby loses 20 % . at what price per kg , he should have sold them to make a profit of 5 % ?
Options: a ) rs . 11.81 , b ) rs . 12 , c ) rs . 12.25 , d ) rs . 12.31 , e ) none
Rationale: "solution 85 : 9 = 105 : x x = ( 9 × 105 / 80 ) = rs . 11.81 hence , s . p per kg = rs . 11.81 answer a"
Answer: a
Question (gain): if the simple interest on a certain sum of money for 8 years is one – fifth of the sum , then the rate of interest per annum is
Options: a ) 4.1 % , b ) 7 % , c ) 2.5 % , d ) 2.8 % , e ) 3 %
Rationale: explanation : let the principal ( p ) be x then , simple interest ( si ) = x / 5 time ( t ) = 8 years rate of interest per annum ( r ) = ( 100 × si ) / pt = ( 100 × ( x / 5 ) / ( x × 8 ) = 20 / 8 = 2.5 % answer : option c
Answer: c
Question (physics): two pipes a and b can fill a tank in 20 and 30 minutes respectively . if both the pipes are used together , then how long will it take to fill the tank ?
Options: a ) 12 min , b ) 15 min , c ) 25 min , d ) 50 min , e ) 55 min
Rationale: "part filled by a in 1 min = 1 / 20 part filled by b in 1 min = 1 / 30 part filled by ( a + b ) in 1 min = ( 1 / 20 + 1 / 30 ) = 1 / 12 so both pipes can fill the tank in 12 minutes . answer : a"
Answer: a
Question (general): the captain of a cricket team of 11 members is 24 years old and the wicket keeper is 3 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average age of the team ?
Options: a ) 20 years , b ) 21 years , c ) 22 years , d ) 23 years , e ) 24 years
Rationale: "explanation : let the average age of the whole team by x years . 11 x â € “ ( 24 + 27 ) = 9 ( x - 1 ) 11 x â € “ 9 x = 42 2 x = 42 x = 21 . so , average age of the team is 21 years . answer b"
Answer: b
Question (physics): the sum of 111 consecutive integers is 11211 . what is the greatest integer in the set ?
Options: a ) 148 , b ) 150 , c ) 152 , d ) 154 , e ) 156
Rationale: "let x be the first integer in the set , then x + 110 is the largest integer . the sum is : x + ( x + 1 ) + ( x + 2 ) + . . . + ( x + 110 ) = 111 x + 110 * 111 / 2 = 111 ( x + 55 ) then x + 55 = 101 x = 46 the largest integer in the set is 46 + 110 = 156 the answer is e ."
Answer: e
Question (general): according to the formula f = 9 / 5 ( c ) + 32 , if the temperature in degrees farenheit ( f ) increases by 28 , by how much does the temperature in degrees celsius ( c ) increase ?
Options: a ) 9 , b ) 15.55 , c ) 47 , d ) 48 3 / 5 , e ) 59
Rationale: you can plug in values . c = 5 / 9 * ( f - 32 ) f = 32 - - > c = 0 ; f = 32 + 28 = 60 - - > c = 5 / 9 * 28 = 15.55 . increase = 15.55 degrees . answer : b .
Answer: b
Question (general): how many positive integers less than 24 are prime numbers , odd multiples of 5 , or the sum of a positive multiple of 2 and a positive multiple of 4 ?
Options: a ) 19 , b ) 25 , c ) 24 , d ) 22 , e ) 20
Rationale: "9 prime numbers less than 28 : { 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 } 2 odd multiples of 5 : { 5 , 15 } 9 numbers which are the sum of a positive multiple of 2 and a positive multiple of 4 : { 6 , 8 , 10 , 12 , 14 , 16 , 18 , 20 , 22 } notice , that 5 is in two sets , thus total # of integers satisfying the given conditions is 9 + 2 + 9 - 1 = 19 . answer : a ."
Answer: a
Question (physics): without stoppages , a train travels certain distance with an average speed of 250 km / h , and with stoppages , it covers the same distance with an average speed of 125 km / h . how many minutes per hour the train stops ?
Options: a ) 25 , b ) 30 , c ) 35 , d ) 40 , e ) 45
Rationale: "due to stoppages , it covers 125 km less . time taken to cover 125 km = 125 â  „ 250 h = 1 â  „ 2 h = 1 â  „ 2 ã — 60 min = 30 min answer b"
Answer: b
Question (general): cara took out a charge account at the general store and agreed to pay 5 % simple annual interest . if she charges $ 54 on her account in january , how much will she owe a year later , assuming she does not make any additional charges or payments ?
Options: a ) $ 55.70 , b ) $ 56.20 , c ) $ 56.70 , d ) $ 57.20 , e ) $ 57.70
Rationale: 1.05 * $ 54 = $ 56.70 the answer is c .
Answer: c
Question (other): a can contains a mixture of liquids a and b is the ratio 7 : 5 . when 9 litres of mixture are drawn off and the can is filled with b , the ratio of a and b becomes 7 : 9 . how many liter t of liquid a was contained by the can initially ?
Options: a ) 10 , b ) 20 , c ) 21 , d ) 25 , e ) 27
Rationale: "as a : b : : 7 : 5 - - - > only option c is a multiple of 7 and hence it is a good place to start . also a : b : : 7 : 5 means that , a = ( 712 ) * total and b = ( 5 / 12 ) * total if a = 21 , b = 15 - - - > remove 9 litres - - - > you remove ( 7 / 12 ) * 9 of a - - - > a remaining = 21 - ( 7 / 12 ) * 9 = 63 / 4 similarly , for b , you remove ( 5 / 12 ) * 9 - - - > b remaining = 15 - ( 5 / 12 ) * 9 = 45 / 4 and then add 9 more litres of b - - - > 9 + 45 / 4 = 81 / 4 thus a / b ( final ratio ) = ( 45 / 4 ) / ( 81 / 4 ) = 7 : 9 , the same as the final ratio mentioned in the question . hence c is the correct answer . a / b = 7 / 9 = ( 7 x - ( 7 / 12 ) * 9 ) / ( 5 x - ( 5 / 12 ) * 9 + 9 ) , where 7 x and 5 x are initial quantities of a and b respectively . thus , 7 / 9 = ( 7 x - ( 7 / 12 ) * 9 ) / ( 5 x - ( 5 / 12 ) * 9 + 9 ) - - - > giving you x = 3 . thus a ( original ) t = 7 * 3 = 21 . c"
Answer: c
Question (geometry): the length of a rectangle is double its width . if the length is diminished by 5 cm and the width is increased by 5 cm then its area is increased by 75 cm square . what is the length of the rectangle ?
Options: a ) 20
b ) 30
c ) 40
d ) 56
e ) 65
Rationale: sol . according to question ( l - 5 ) ( b + 5 ) - lb = 75 and l = 2 b so , b = 20 , l = 40 ans . ( c )
Answer: c
Question (physics): a and b go around a circular track of length 1500 m on a cycle at speeds of 36 kmph and 54 kmph . after how much time will they meet for the first time at the starting point ?
Options: a ) 120 sec , b ) 165 sec , c ) 300 sec , d ) 167 sec , e ) 168 sec
Rationale: "time taken to meet for the first time at the starting point = lcm { length of the track / speed of a , length of the track / speed of b } = lcm { 1500 / ( 36 * 5 / 18 ) , 1500 / ( 54 * 5 / 18 ) } = lcm ( 150 , 100 ) = 300 sec . answer : c"
Answer: c
Question (physics): a train 300 m long takes 9 sec to cross a man walking at 3 kmph in a direction opposite to that of the train . find the speed of the train ?
Options: a ) 100 kmph , b ) 90 kmph , c ) 120 kmph , d ) 117 kmph , e ) 125 kmph
Rationale: "let the speed of the train be x kmph speed of the train relative to man = x + 3 = ( x + 3 ) * 5 / 18 m / sec 300 / [ ( x + 3 ) * 5 / 18 ] = 9 9 ( x + 3 ) = 1080 x = 117 kmph answer is d"
Answer: d
Question (geometry): the perimeters of 2 squares are 40 cm and 32 cm . find the perimeter of a third square whose area is equal to the difference of the areas of the two squares ?
Options: a ) 20 cm , b ) 24 cm , c ) 32 cm , d ) 28 cm , e ) 30 cm
Rationale: "side of the 1 st square = 40 / 4 = 10 cm side of the 2 nd square = 32 / 4 = 8 cm area of the 3 rd square = 10 ^ 2 - 8 ^ 2 = 36 cm ^ 2 side of the 3 rd square = 6 cm required perimeter = 6 * 4 = 24 cm answer is b"
Answer: b
Question (physics): if there are 210 workers in a factory , and on a certain day , 198 were present . calculate the percentage that showed up for work ? ( round to the nearest tenth ) .
Options: a ) 94.3 % , b ) 95.3 % , c ) 93.3 % , d ) 92.3 % , e ) 91.3 %
Rationale: 198 / 210 * 100 = 94.28 94.3 % correct answer a
Answer: a
Question (physics): a car gets 40 kilometers per gallon of gasoline . how many gallons of gasoline would the car need to travel 210 kilometers ?
Options: a ) 8.25 gallons , b ) 7.5 gallons , c ) 6.55 gallons , d ) 5.25 gallons , e ) 4.5 gallons
Rationale: "each 40 kilometers , 1 gallon is needed . we need to know how many 40 kilometers are there in 210 kilometers ? 210 / 40 = 5.25 * 1 gallon = 5.25 gallons correct answer d"
Answer: d
Question (other): on a certain farm the ratio of horses to cows is 4 : 1 . if the farm were to sell 15 horses and buy 15 cows , the ratio of horses to cows would then be 7 : 3 . after the transaction , how many more horses than cows would the farm own ?
Options: a ) 20 , b ) 40 , c ) 50 , d ) 60 , e ) 80
Rationale: "originally , there were 4 k horses and k cows . 3 ( 4 k - 15 ) = 7 ( k + 15 ) 12 k - 7 k = 105 + 45 5 k = 150 k = 30 the difference between horses and cows is ( 4 k - 15 ) - ( k + 15 ) = 3 k - 30 = 60 the answer is d ."
Answer: d
Question (physics): two pipes p and q can fill a cistern in 11 and 15 minutes respectively . both are opened together , but at the end of 3 minutes the first is turned off . how much longer will the cistern take to fill ?
Options: a ) 1 / 8 , b ) 1 / 4 , c ) 2 / 4 , d ) 10 / 11 , e ) 1 / 4
Rationale: "3 / 11 + x / 15 = 1 x = 10 10 / 11 answer : d"
Answer: d
Question (gain): rani bought more apples than oranges . she sells apples at ₹ 23 apiece and makes 15 % profit . she sells oranges at ₹ 10 apiece and makes 25 % profit . if she gets ₹ 653 after selling all the apples and oranges , find her profit percentage q .
Options: a ) 16.8 % , b ) 17.4 % , c ) 17.9 % , d ) 18.5 % , e ) 19.1 %
Rationale: given : selling price of an apple = 23 - - > cost price = 23 / 1.15 = 20 selling price of an orange = 10 - - > cost price = 10 / 1.25 = 8 a > o 23 * ( a ) + 10 * ( o ) = 653 653 - 23 * ( a ) has to be divisible by 10 - - > units digit has to be 0 values of a can be 1 , 11 , 21 , 31 , . . . . - - > 1 can not be the value between 11 and 21 , if a = 11 , o = 30 - - > not possible if a = 21 , o = 17 - - > possible cost price = 20 * 21 + 8 * 17 = 420 + 136 = 556 profit = 653 - 556 = 97 profit % q = ( 97 / 556 ) * 100 = 17.4 % answer : b
Answer: b
Question (general): at a summer camp with 1,800 participants , 1 / 2 of the campers are aged 8 to 12 . next year , the number of campers aged 8 to 12 will increase by 1 / 3 . after this change , what percentage of the total 1,800 campers will the 8 - to 12 - year - olds represent ?
Options: a ) 68 % , b ) 66 % , c ) 66 2 / 3 % , d ) 60 % , e ) 70 %
Rationale: total - 1,800 participants campers are aged 8 to 12 = ( 1 / 2 ) * 1800 = 900 next year , campers are aged 8 to 12 = ( 4 / 3 ) * 900 = 1200 percentage = ( 1200 / 1800 ) * 100 = 66 2 / 3 % answer : option c
Answer: c
Question (general): village p ’ s population is 800 greater than village q ' s population . if village q ’ s population were reduced by 500 people , then village p ’ s population would be 3 times as large as village q ' s population . what is village q ' s current population ?
Options: a ) 1100 , b ) 1150 , c ) 1200 , d ) 1250 , e ) 1300
Rationale: "p = q + 800 . p = 3 ( q - 500 ) . 3 ( q - 500 ) = q + 800 . 2 q = 2300 . q = 1150 . the answer is b ."
Answer: b
Question (gain): the sale price of a trolley bag including the sale tax is rs . 420 . the rate of sale tax is 12 % . if the shopkeeper has made a profit of 25 % , the cost price of the trolley bag is :
Options: a ) rs 625 , b ) rs 300 , c ) rs 350 , d ) rs 375 , e ) none of these
Rationale: explanation : 112 % of s . p . = 420 s . p . = rs . ( 420 x 100 / 112 ) = rs . 375 . c . p . = rs ( 100 / 125 x 375 ) = rs 300 answer : b
Answer: b
Question (physics): how many bricks each measuring 20 cm x 13.25 cm x 8 cm , will be needed to build a wall 7 m x 8 m x 15.5 m
Options: a ) 5600 , b ) 4600 , c ) 4094 , d ) 7200 , e ) none of these
Rationale: "explanation : no . of bricks = volume of the wall / volume of 1 brick = ( 700 x 800 x 15.5 ) / ( 20 x 13.25 x 8 ) = 4094 answer : c"
Answer: c
Question (general): one - tenth of the students at a nursery school are 4 years old or older . if 20 students have not yet reached their third birthday , and a total of 50 students are not between 3 years old and 4 years old , how many children are in the nursery school ?
Options: a ) 150 , b ) 300 , c ) 450 , d ) 490 , e ) 620
Rationale: x / 10 students are > 4 yrs 20 students are < 3 yrs x / 10 + 20 = 50 x / 10 = 30 x = 300 answer : b
Answer: b
Question (general): if p / q = 3 / 4 then 3 p + 4 q = ?
Options: a ) 25 / 4 , b ) 25 / 2 , c ) 20 / 4 , d ) 35 / 4 , e ) 25 / 3
Rationale: 3 p + 4 q = ? divided by q , 3 ( p / q ) + 4 = x 3 * ( 3 / 4 ) + 4 = 25 / 4 answer : a
Answer: a