regisss/math_qa huggingface dataset:
Problem: the value of ( 34.31 * 0.5 * 1.567 ) / ( 0.0673 * 23.25 * 7.57 ) is close to
Options: a ) 2 , b ) 1.15 , c ) 2.05 , d ) 2.27 , e ) 2.35
Rationale: "( 34.31 * 0.5 * 1.567 ) / ( 0.0673 * 23.25 * 7.57 ) = 26.882 / 11.845 = 2.27 answer : d"
Answer: d
Problem: the average age of 15 students of a class is 15 years . out of these , the average age of 5 students is 14 years and that of the other 9 students is 16 years . the age of the 15 th student is
Options: a ) 9 years , b ) 11 years , c ) 14 years , d ) 21 years , e ) 25 years
Rationale: "solution age of the 15 th student = [ 15 x 15 - ( 14 x 5 + 16 x 9 ) ] = ( 225 - 214 ) = 11 years . answer b"
Answer: b
Problem: the population of a town is 10000 . it increases annually at the rate of 20 % p . a . what will be its population after 2 years ?
Options: a ) 14300 , b ) 14400 , c ) 14500 , d ) 14600 , e ) 15400
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 10000 × 120 / 100 × 120 / 100 = 14400 b )"
Answer: b
Problem: what is the decimal equivalent of ( 1 / 4 ) ^ 3 ?
Options: a ) 0.0016 , b ) 0.0625 , c ) 0.16 , d ) 0.25 , e ) 0.0156
Rationale: ( 1 / 4 ) ^ 3 = 1 / 64 = 0.0156 answer : e
Answer: e
Problem: a student took 6 courses last year and received an average ( arithmetic mean ) grade of 100 points . the year before , the student took 5 courses and received an average grade of 40 points . to the nearest tenth of a point , what was the student ’ s average grade for the entire two - year period ?
Options: a ) 79 , b ) 89 , c ) 95 , d ) 72.72 , e ) 97.2
Rationale: "let the 6 courses that were taken last year be a 1 , a 2 , a 3 , a 4 , a 5 , a 6 a 1 + a 2 + a 3 + a 4 + a 5 + a 6 = 100 * 6 = 600 the year before , the 5 courses be b 1 , b 2 , b 3 , b 4 , b 5 b 1 + b 2 + b 3 + b 4 + b 5 = 40 * 5 = 200 student ' s average = ( 600 + 200 ) / 11 = 72.72 answer d"
Answer: d
Problem: at what price must an article costing rs . 66.5 be marked in order that after deducting 5 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 87.5 , b ) 89.5 , c ) 82.3 , d ) 82.1 , e ) 92.4
Rationale: "cp = 66.5 sp = 66.5 * ( 125 / 100 ) = 83.125 mp * ( 95 / 100 ) = 59.375 mp = 87.5 answer : a"
Answer: a
Problem: three 6 faced dice are thrown together . the probability that all the three show the same number on them is - .
Options: a ) 1 / 36 , b ) 1 / 216 , c ) 1 / 48 , d ) 1 / 55 , e ) 1 / 90
Rationale: "it all 3 numbers have to be same basically we want triplets . 111 , 222 , 333 , 444 , 555 and 666 . those are six in number . further the three dice can fall in 6 * 6 * 6 = 216 ways . hence the probability is 6 / 216 = 1 / 36 answer a"
Answer: a
Problem: the smallest number which when diminished by 7 , is divisible 12 , 16 , 18 , 21 and 28 is :
Options: a ) 1008 , b ) 1015 , c ) 1022 , d ) 1032 , e ) none of these
Rationale: "explanation required number = ( l . c . m . of 12,16 , 18 , 21 , 28 ) + 7 = 1008 + 7 = 1015 answer b"
Answer: b
Problem: the average of first 15 even numbers is ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 16 , e ) 14
Rationale: "sum of 15 even numbers = 15 * 16 = 240 average = 240 / 15 = 16 answer : d"
Answer: d
Problem: in 100 litres mixture milk and water are in the ratio 3 : 2 . after adding how many liters of water its ratio will become 3 : 4
Options: a ) 48 , b ) 50 , c ) 62 , d ) 78 , e ) 100
Rationale: milk quantity = 3 / 5 * 60 = 36 water quantity = 100 - 36 = 64 new ratio of m : w = 36 : 64 + x = 3 : 4 192 + 3 x = 144 x = 48 answer is a
Answer: a
Problem: a sum fetched a total simple interest of 4034.25 at the rate of 9 % . p . a . in 5 years . what is the sum ?
Options: a ) 5768 , b ) 8925 , c ) 8965 , d ) 6474 , e ) 8723
Rationale: "principal = ( 100 x 4034.25 ) / ( 9 x 5 ) = 403425 / 45 = 8965 . answer c"
Answer: c
Problem: 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 w .
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 % w = ( 97 / 556 ) * 100 = 17.4 % answer : b"
Answer: b
Problem: cereal a is 9 % sugar by weight , whereas healthier but less delicious cereal b is 2 % sugar by weight . to make a delicious and healthy mixture that is 4 % sugar , what should be the ratio of cereal a to cereal b , by weight ?
Options: a ) 2 : 9 , b ) 2 : 5 , c ) 1 : 6 , d ) 1 : 4 , e ) 1 : 3
Rationale: "( 9 / 100 ) a + ( 2 / 100 ) b = ( 4 / 100 ) ( a + b ) 5 a = 2 b = > a / b = 2 / 5 answer is b ."
Answer: b
Problem: how long does a train 180 meters long running at the rate of 54 kmph take to cross a bridge 660 meters in length ?
Options: a ) 33 , b ) 56 , c ) 55 , d ) 82 , e ) 62
Rationale: "explanation : t = ( 660 + 180 ) / 54 * 18 / 5 t = 56 answer : option b"
Answer: b
Problem: a profit of rs . 500 is divided between x and y in the ratio of 1 / 2 : 1 / 3 . what is the difference between their profit shares ?
Options: a ) rs . 200 , b ) rs . 100 , c ) rs . 300 , d ) rs . 50 , e ) rs . 90
Rationale: "a profit of rs . 500 is divided between x and y in the ratio of 1 / 2 : 1 / 3 or 3 : 2 . so profits are 300 and 200 . difference in profit share = 300 - 200 = 100 answer : b"
Answer: b
Problem: a man buys rs . 56 shares paying 9 % dividend . the man wants to have an interest of 12 % on his money . the market value of each share is :
Options: a ) s . 12 , b ) s . 15 , c ) s . 18 , d ) s . 21 , e ) s . 42
Rationale: "dividend on rs . 56 = rs . 9 / 100 x 56 = rs . 5.04 . rs . 12 is an income on rs . 100 . rs . 5.04 is an income on rs . 100 / 12 x 5.04 = rs . 42 . answer : option e"
Answer: e
Problem: of 440 surveyed students , 20 % of those who read book a also read book b and 25 % of those who read book b also read book a . if each student read at least one of the books , what is the difference between the number of students who read only book a and the number of students who read only book b ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 35 , e ) 55
Rationale: "say the number of students who read book a is a and the number of students who read book b is b . given that 20 % of those who read book a also read book b and 25 % of those who read book b also read book a , so the number of students who read both books is 0.2 a = 0.25 b - - > a = 1.25 b . since each student read at least one of the books then { total } = { a } + { b } - { both } - - > 440 = 1.25 b + b - 0.25 b - - > b = 220 , a = 1.25 b = 275 and { both } = 0.25 b = 55 . the number of students who read only book a is { a } - { both } = 125 - 25 = 100 ; the number of students who read only book b is { b } - { both } = 275 - 55 - 220 ; the difference is 220 - 55 = 165 . answer : e ."
Answer: e
Problem: on a certain road , 10 % of the motorists exceed the posted speed limit and receive speeding tickets , but 30 % of the motorists who exceed the posted speed limit do not receive speeding tickets . what percent of the motorists on that road exceed the posted speed limit ?
Options: a ) 10.5 % , b ) 12.5 % , c ) 14.3 % , d ) 22 % , e ) 30 %
Rationale: "suppose there are x motorists . 10 % of them exceeded the speed limit and received the ticket , i . e . x / 10 . again , suppose total no . of motorists who exceeded the speed limit are y . 30 % of y exceeded the speed limit but did n ' t received the ticket , i . e . 3 y / 10 . it means 7 y / 10 received the ticket . hence , 7 y / 10 = x / 10 or y / x = 1 / 7 or y / x * 100 = 1 / 7 * 100 = 14.3 % c"
Answer: c
Problem: ajay can ride 50 km in 1 hour . in how many hours he can ride 750 km ?
Options: a ) 10 hrs , b ) 15 hrs , c ) 20 hrs , d ) 25 hrs , e ) 18 hrs
Rationale: "1 hour he ride 50 km he ride 750 km in = 750 / 50 * 1 = 15 hours answer is b"
Answer: b
Problem: a number of 47 marbles is to be divided and contain with boxes . if each box is to contain 3 , 4 , or 5 marbles , what is the largest possible number of boxes ?
Options: a ) 10 , b ) 12 , c ) 15 , d ) 16 , e ) 17
Rationale: "to maximize # of boxes we should minimize marbles per box : 14 * 3 + 1 * 5 = 47 - - > 14 + 1 = 15 . answer : c ."
Answer: c
Problem: 12 is subtracted from 95 % of a number , the result is 178 . find the number ?
Options: a ) 200 , b ) 240 , c ) 198 , d ) 190 , e ) 322
Rationale: "( 95 / 100 ) * x â € “ 12 = 178 9.5 x = 1900 x = 200 answer : a"
Answer: a
Problem: a man invests rs . 8000 at the rate of 5 % per annum . how much more should he invest at the rate of 8 % , so that he can earn a total of 6 % per annum ?
Options: a ) rs . 1200 , b ) rs . 1300 , c ) rs . 1500 , d ) rs . 4000 , e ) none of these
Rationale: explanation : interest on rs . 8000 at 5 % per annum = ( 8000 × 5 × 1 ) / 100 = rs . 400 let his additional investment at 8 % = x interest on rs . x at 8 % per annum = ( x × 8 × 1 ) / 100 = 2 x / 25 . to earn 6 % per annum for the total , interest = ( 8000 + x ) × 6 × 1 / 100 . = > 400 + 2 x / 25 = ( 8000 + x ) × 6 × 1 / 100 . = > 40000 + 8 x = ( 8000 + x ) × 6 . = > 40000 + 8 x = 48000 + 6 x . = > 2 x = 8000 . = > x = 4000 . answer : d
Answer: d
Problem: the cost per unit of electricity during a 4 year period is as follows : year 1 , $ 3 per unit ; year 2 , $ 4 per unit ; year 3 , $ 5 per unit ; year 4 , $ 6 per unit . if a factory spent equal dollars on electricity each year , what was the average cost of a unit of electricity during the 4 year period ?
Options: a ) $ 4.31 , b ) $ 4.51 , c ) $ 4.21 , d ) $ 5.21 , e ) $ 5.61
Rationale: let money spent each year = $ 60 units bought first year = 20 units bought second year = 15 units bought third year = 12 units bought fourth year = 10 total number of units = 57 total money spent = 60 * 4 = 240 average = 240 / 57 = 4.21 answer : c
Answer: c
Problem: in what time will a train 45 m long cross an electric pole , it its speed be 108 km / hr ?
Options: a ) 0.5 , b ) 1.25 , c ) 1.5 , d ) 2.5 , e ) 3.5
Rationale: "speed = 108 * 5 / 18 = 30 m / sec time taken = 45 / 30 = 1.5 sec . answer : c"
Answer: c
Problem: in township k , 1 / 5 of the housing units are equiped with cable tv . if 1 / 10 of the housing units , including 1 / 4 of those that are equiped with cable tv , are equipped with videocassette recorders , what fraction of the housing units have neither cable tv nor videocassette recorders ?
Options: a ) 3 / 4 , b ) 11 / 15 , c ) 7 / 10 , d ) 1 / 6 , e ) 2 / 15
Rationale: 1 / 5 - - cable tv ( this includes some data from video cassette recorder ) 1 / 10 - - video cassette recorder including 1 / 4 ( equiped with cable tv ) i . e . 1 / 4 ( 1 / 5 ) = 1 / 20 therefore only video cassette recorder = 1 / 10 - 1 / 20 = 1 / 20 total = 1 / 5 + 1 / 20 + neither cable tv nor videocassette recorders 1 = 1 / 4 + neither cable tv nor videocassette recorders therefore neither cable tv nor videocassette recorders = 1 - 1 / 4 = 3 / 4 hence a .
Answer: a
Problem: two trains of equal are running on parallel lines in the same direction at 46 km / hr and 36 km / hr . the faster train passes the slower train in 45 sec . the length of each train is ?
Options: a ) 50 , b ) 26 , c ) 27 , d ) 62.5 , e ) 21
Rationale: "let the length of each train be x m . then , distance covered = 2 x m . relative speed = 46 - 36 = 10 km / hr . = 10 * 5 / 18 = 25 / 9 m / sec . 2 x / 45 = 25 / 9 = > x = 65.5 . answer : d"
Answer: d
Problem: a batsman makes a score of 87 runs in the 17 th inning and thus increases his averages by 3 . find his average after 17 th inning ?
Options: a ) 19 , b ) 29 , c ) 39 , d ) 49 , e ) 59
Rationale: "solution let the average after 17 th inning = x . then , average after 16 th inning = ( x - 3 ) average = 16 ( x - 3 ) + 87 = 17 x or x = ( 87 - 48 ) = 39 . answer c"
Answer: c
Problem: in what time will a train 100 meters long cross an electric pole , if its speed is 360 km / hr
Options: a ) 1 second , b ) 4.5 seconds , c ) 3 seconds , d ) 2.5 seconds , e ) none of these
Rationale: "explanation : first convert speed into m / sec speed = 360 * ( 5 / 18 ) = 100 m / sec time = distance / speed = 100 / 100 = 1 second answer : a"
Answer: a
Problem: a 340 - liter solution of kola is made from 64 % water , 9 % concentrated kola and the rest is made from sugar . if 3.2 liters of sugar , 8 liter of water and 6.8 liters of concentrated kola were added to the solution , what percent of the solution is made from sugar ?
Options: a ) 6 % . , b ) 7.5 % . , c ) 9.2 % . , d ) 10.5 % . , e ) 26.5 % .
Rationale: "denominator : 340 + 8 + 3.2 + 6.8 = 358 numerator : 340 ( 1 - . 64 - . 09 ) + 3.2 340 ( 0.27 ) + 3.2 91.8 + 3.2 95 ratio : 95 / 358 = 0.265 answer : e"
Answer: e
Problem: if ( 5 ^ 11 ) ( 9 ^ 6 ) = 3 ( 15 ^ x ) , what is the value of x ?
Options: a ) 7 , b ) 9 , c ) 11 , d ) 13 , e ) 15
Rationale: "( 5 ^ 11 ) ( 9 ^ 6 ) = 3 ( 15 ^ x ) = > 5 ^ 11 * 3 ^ 12 = 3 * 3 ^ x * 5 ^ x = > 5 ^ 11 * 3 ^ 12 = 3 ^ ( x + 1 ) * 5 ^ x value of x = 11 answer c"
Answer: c
Problem: find the total number of prime factors in the expression ( 4 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 5
Options: a ) 26 , b ) 32 , c ) 25 , d ) 27 , e ) 29
Rationale: "( 4 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 5 = ( 2 x 2 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 5 = 2 ^ 11 x 2 ^ 11 x 7 ^ 5 x 11 ^ 5 = 2 ^ 22 x 7 ^ 5 x 11 ^ 5 total number of prime factors = ( 22 + 5 + 5 ) = 32 . answer is b ."
Answer: b
Problem: a rectangular photograph is surrounded by a border that is 1 inch wide on each side . the total area of the photograph and the border is m square inches . if the border had been 5 inches wide on each side , the total area would have been ( m + 180 ) square inches . what is the perimeter of the photograph , in inches ?
Options: a ) 21 , b ) 36 , c ) 38 , d ) 40 , e ) 42
Rationale: "let length and breadth of photograph be l and b respectively . perimeter is given by 2 * ( l + b ) - - - - - ( 1 ) according to the question : ( l + 2 ) ( b + 2 ) = m - - - - ( 2 ) and ( l + 10 ) ( b + 10 ) = m + 180 - - - - - - - - - > ( l + 10 ) ( b + 10 ) - 180 = m - - - - - - ( 3 ) equating ( 2 ) and ( 3 ) ( l + 2 ) ( b + 2 ) = ( l + 10 ) ( b + 10 ) - 180 lb + 2 l + 2 b + 4 = lb + 10 l + 10 b + 100 - 180 simplify 8 l + 8 b = 84 - - - - - - > 2 ( l + b ) = 21 ( check eq ( 1 ) ) answer is a"
Answer: a
Problem: a student took 6 courses last year and received an average ( arithmetic mean ) grade of 100 points . the year before , the student took 5 courses and received an average grade of 50 points . to the nearest tenth of a point , what was the student ’ s average grade for the entire two - year period ?
Options: a ) 79 , b ) 89 , c ) 95 , d ) 77.27 , e ) 97.2
Rationale: "let the 6 courses that were taken last year be a 1 , a 2 , a 3 , a 4 , a 5 , a 6 a 1 + a 2 + a 3 + a 4 + a 5 + a 6 = 100 * 6 = 600 the year before , the 5 courses be b 1 , b 2 , b 3 , b 4 , b 5 b 1 + b 2 + b 3 + b 4 + b 5 = 50 * 5 = 250 student ' s average = ( 600 + 250 ) / 11 = 77.27 answer d"
Answer: d
Problem: jim ’ s taxi service charges an initial fee of $ 2.35 at the beginning of a trip and an additional charge of $ 0.35 for each 2 / 5 of a mile traveled . what is the total charge for a trip of 3.6 miles ?
Options: a ) $ 3.15 , b ) $ 4.45 , c ) $ 4.80 , d ) $ 5.5 , e ) $ 5.40
Rationale: "let the fixed charge of jim ’ s taxi service = 2.35 $ and charge per 2 / 5 mile ( . 4 mile ) = . 35 $ total charge for a trip of 3.6 miles = 2.35 + ( 3.6 / . 4 ) * . 35 = 2.35 + 9 * . 35 = 5.5 $ answer d"
Answer: d
Problem: a miniature roulette wheel is divided into 9 equal sectors , each bearing a distinct integer from 1 to 9 , inclusive . each time the wheel is spun , a ball randomly determines the winning sector by settling in that sector . if the wheel is spun three times , approximately what is the probability that the product of the three winning sectors ’ integers will be even ?
Options: a ) 50 % , b ) 67 % , c ) 83 % , d ) 90 % , e ) 96 %
Rationale: "the only way to have an odd product is if all 3 integers are odd . p ( odd product ) = 5 / 9 * 5 / 9 * 5 / 9 = 125 / 729 p ( even product ) = 1 - 125 / 729 = 604 / 729 which is about 83 % the answer is c ."
Answer: c
Problem: local kennel has cats and dogs in the ratio of 2 : 3 . if there are 6 fewer cats than dogs , how many dogs are in the kennel ?
Options: a ) 24 , b ) 18 , c ) 30 , d ) 15 , e ) 12
Rationale: lets work with the data given to us . we know that there ratio of cats to dogs is 2 : 3 or cats 2 dogs 3 we can write number of cats as 2 x and number of dogs as 3 x and we know that 3 x - 2 x = 6 ( therefore x = 6 ) then # of dogs = 3 x 6 = 18 answer is b
Answer: b
Problem: in the coordinate plane a slope of the line k is 3 / 2 times the y - intercept of the line k . what is the x - intercept of the line k ?
Options: a ) - 2 , b ) 2 / 3 , c ) - 2 / 3 , d ) 1 / 4 , e ) 3 / 2
Rationale: as y = 3 / 2 mx + m , from 0 = 3 / 2 mx + m we get x = 2 / 3 . hence , the correct answer choice is b .
Answer: b
Problem: 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 . 140000 , find the cost of a camel ?
Options: a ) s . 9800 , b ) s . 3800 , c ) s . 9800 , d ) s . 6800 , e ) s . 5600
Rationale: cost of the camel = p 10 camels = 24 horses 16 horses = 4 oxen 6 oxen = 4 elephants 10 elephants = rs . 140000 p = rs . [ ( 24 * 4 * 4 * 140000 ) / ( 10 * 16 * 6 * 10 ) ] p = rs . ( 53760000 / 9600 ) = > p = rs . 5600 answer : e
Answer: e
Problem: a watch was sold at a loss of 10 % . if it was sold for rs . 140 more , there would have been a gain of 5 % . what is the cost price ?
Options: a ) s . 933.33 , b ) s . 1009 , c ) s . 1007 , d ) s . 1006 , e ) s . 1002
Rationale: "explanation : 90 % 105 % - - - - - - - - 15 % - - - - 140 100 % - - - - ? = > rs . 933.33 answer : a"
Answer: a
Problem: how many positive integers less than 15 can be expressed as the sum of a positive multiple of 2 and a positive multiple of 3 ?
Options: a ) 14 , b ) 13 , c ) 12 , d ) 8 , e ) 10
Rationale: the number = 2 a + 3 b < 20 when a = 1 , b = 1 , 2 , 3 , 4 , 5 - > 2 a = 2 ; 3 b = 3 , 6 , 9 - > the number = 5 , 8 , 11 - - > 3 numbers when a = 2 , b = 1 , 2,3 - > . . . . - - > 3 numbers when a = 3 , b = 1,2 , 3,4 - - > . . . . - - > 2 numbers total number is already 8 . look at the answer there is no number greater than 8 - - > we dont need to try any more answer must be d
Answer: d
Problem: the sum of all consecutive odd integers from − 31 to 41 , inclusive , is
Options: a ) 110 , b ) 135 , c ) 150 , d ) 165 , e ) 185
Rationale: "the sum of the odd numbers from - 31 to + 31 is 0 . let ' s add the remaining numbers . 33 + 35 + 37 + 39 + 41 = 5 ( 37 ) = 185 the answer is e ."
Answer: e
Problem: find the compound ratio of ( 2 : 5 ) , ( 6 : 11 ) and ( 11 : 2 ) is
Options: a ) 3 : 2 , b ) 2 : 1 , c ) 1 : 2 , d ) 6 : 5 , e ) 2 : 3
Rationale: "required ratio = 2 / 5 * 6 / 11 * 11 / 2 = 2 / 1 = 6 : 5 answer is d"
Answer: d
Problem: if a man lost 4 % by selling oranges at the rate of 24 a rupee at how many a rupee must he sell them to gain 44 % ?
Options: a ) 16 , b ) 8 , c ) 9 , d ) 4 , e ) 3
Rationale: "96 % - - - - 24 144 % - - - - ? 96 / 144 * 24 = 16 answer : a"
Answer: a
Problem: the ratio of the number of females to males at a party was 1 : 2 but when 6 females and 6 males left , the ratio became 1 : 3 . how many people were at the party originally ?
Options: a ) 24 , b ) 28 , c ) 32 , d ) 36 , e ) 40
Rationale: "the total number of people are x females + 2 x males . 3 * ( x - 6 ) = 2 x - 6 x = 12 there were 3 x = 36 people at the party originally . the answer is d ."
Answer: d
Problem: one robot builds a robot in 1 hour , another one builds a robot in 2 hours . the 2 robots work together and when a new robot is complete , it joins the others , working at a constant rate of one robot in 2 hours . how much time will it take until there are 6 robots altogether , if the robots build only one robot at a time ?
Options: a ) 70 min , b ) 94 min , c ) 109 min , d ) 114 min , e ) 120 min
Rationale: "first the 2 robots work at the rate of 1 + 1 / 2 = 3 / 2 so they complete one robot in 2 / 3 rd of an hour = 40 minutes - ( 1 ) now the 3 robots work together at the rate of 1 + 1 / 2 + 1 / 2 = 4 / 2 = 2 / 1 so they complete one robot in 1 / 2 an hour , i . e 30 minutes - ( 2 ) now the 4 robots work together at the rate of 1 + 1 / 2 + 1 / 2 + 1 / 2 = 5 / 2 so they complete one robot in 2 / 5 th of an hour , i . e . 24 minutes - ( 3 ) now the 4 robots work together at the rate of 1 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 = 3 so they complete one robot in 1 / 3 th of an hour , i . e . 20 minutes - ( 4 ) and now we have 5 robots so total = ( 1 ) + ( 2 ) + ( 3 ) + ( 4 ) = 114 minutes answer - d"
Answer: d
Problem: john had a stock of 1200 books in his bookshop . he sold 75 on monday , 50 on tuesday , 64 on wednesday , 78 on thursday and 135 on friday . what percentage of the books were not sold ?
Options: a ) 50.4 % , b ) 23.8 % , c ) 66.5 % , d ) 34.9 % , e ) 43.5 %
Rationale: let n be the total number of books sold . hence n = 75 + 50 + 64 + 78 + 135 = 402 let m be the books not sold m = 1200 - n = 1200 - 402 = 798 percentage books not sold / total number of books = 798 / 1200 = 0.665 = 66.5 % correct answer c
Answer: c
Problem: if @ is a binary operation defined as the difference between an integer n and the product of n and 5 , then what is the largest positive integer n such that the outcome of the binary operation of n is less than 16 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "@ ( n ) = 5 n - n we need to find the largest positive integer such that 5 n - n < 16 . then 4 n < 16 and n < 4 . the largest possible integer is n = 3 . the answer is c ."
Answer: c
Problem: find the average of all numbers between 2 and 63 which are divisible by 5
Options: a ) 15 , b ) 20 , c ) 25 , d ) 32.5 , e ) 35
Rationale: "explanation : average = ( 5 + 10 + 15 + 20 + 25 + 30 + 35 + 40 + 45 + 50 + 55 + 60 ) / 12 = 390 / 12 = 32.5 answer : option d"
Answer: d
Problem: a mixture contains alcohol and water in the ratio 4 : 3 . if 7 litres of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture
Options: a ) 15 litres , b ) 14 litres , c ) 30 litres , d ) 22 litres , e ) 8 litres
Rationale: "let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 4 x / ( 3 x + 7 ) = 4 / 5 20 x = 4 ( 3 x + 7 ) 8 x = 28 x = 3.5 quantity of alcohol = ( 4 x 3.5 ) litres = 14 litres . answer is b ."
Answer: b
Problem: a sum fetched total simple interest of 4016.25 at the rate of 12 p . c . p . a . in 5 years . what is the sum ?
Options: a ) 6693.75 , b ) 8032.5 , c ) 4462.5 , d ) 8900 , e ) none of these
Rationale: "let the sums be p . now , 60 % of p = 4016.25 or , p = 6693.75 answer a"
Answer: a
Problem: a man buys 50 pens at marked price of 46 pens from a whole seller . if he sells these pens giving a discount of 1 % , what is the profit percent ?
Options: a ) 5.3 % , b ) 7.6 % , c ) 10.6 % , d ) 12 % , e ) none of these
Rationale: "explanation : let marked price be re . 1 each c . p . of 50 pens = rs . 46 s . p . of 50 pens = 99 % of rs . 50 = rs . 49.50 profit % = ( profit / c . p . ) x 100 profit % = ( 3.50 / 46 ) x 100 = 7.6 % answer b"
Answer: b
Problem: a dog is tied to a tree by a long nylon cord . if the dog runs from the due north side of the tree to the due south side of the tree with the cord extended to its full length at all items , and the dog ran approximately 30 feet , what was the approximate length of the nylon cord w , in feet ?
Options: a ) 30 , b ) 25 , c ) 15 , d ) 10 , e ) 5
Rationale: "because the cord was extended to its full length at all items , the dog ran along a semi - circular path , from north to south . the circumference of a full circle is 2 * pi * r , but since we only care about the length of half the circle , the semi - circle path is pi * r . w = pi * r = 30 . round pi = 3 , then r = 10 . chord is about 10 feet long . d"
Answer: d
Problem: what is the least value of x , so that 2 x 5475 is divisible by 9
Options: a ) 7 , b ) 8 , c ) 4 , d ) 3 , e ) 2
Rationale: "explanation : the sum of the digits of the number is divisible by 9 . then the number is divisible by 9 . 2 + x + 5 + 4 + 7 + 5 = 23 + x least value of x may be ' 4 ' , so that the total 23 + 4 = 27 is divisible by 9 . answer : option c"
Answer: c
Problem: in the rectangular coordinate system , if the line x = 5 y + 5 passes through points ( m , n ) and ( m + 2 , n + p ) , what is the value of p ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 1 / 4 , d ) 2 / 5 , e ) 3 / 7
Rationale: "x = 5 y + 5 , and thus y = x / 5 - 1 the slope is 1 / 5 . the slope of a line through points ( m , n ) and ( m + 2 , n + p ) is ( n + p - n ) / ( m + 2 - m ) = p / 2 p / 2 = 1 / 5 and thus p = 2 / 5 the answer is d ."
Answer: d
Problem: in digging a pond 20 m * 15 m * 5 m the volumes of the soil extracted will be ?
Options: a ) 3387 , b ) 1000 , c ) 2866 , d ) 1500 , e ) 1121
Rationale: "20 * 15 * 5 = 1500 answer : d"
Answer: d
Problem: a train overtakes two persons who are walking in the same direction in which the train is going , at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively . the length of the train is :
Options: a ) 10 , b ) 100 , c ) 50 , d ) 200 , e ) 300
Rationale: 2 kmph = ( 2 x 5 / 18 ) m / sec = 5 / 9 m / sec . 4 kmph = ( 4 x 5 / 18 ) m / sec = 10 / 9 m / sec . let the length of the train be x metres and its speed by y m / sec . then , ( x / y - 5 / 9 ) = 9 and ( x / y - 10 / 9 ) = 10 . 9 y - 5 = x and 10 ( 9 y - 10 ) = 9 x = > 9 y - x = 5 and 90 y - 9 x = 100 . on solving , we get : x = 50 . therefore length of the train is 50 m . answer : c
Answer: c
Problem: the sum of the present ages of two persons a and b is 45 . if the age of a is twice that of b , find the sum of their ages 5 years hence ?
Options: a ) 55 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "a + b = 45 , a = 2 b 2 b + b = 45 = > b = 15 then a = 30 . 5 years , their ages will be 35 and 20 . sum of their ages = 35 + 20 = 55 . answer : a"
Answer: a
Problem: the length of a rectangle is two third of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 4761 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 13 units ?
Options: a ) 598 sq . units
b ) 556 sq . units
c ) 589 sq . units
d ) 958 sq . units
e ) 985 sq . units
Rationale: given that the area of the square = 4761 sq . units = > side of square = â ˆ š 4761 = 69 units the radius of the circle = side of the square = 69 units length of the rectangle = 2 / 3 * 69 = 46 units given that breadth = 13 units area of the rectangle = lb = 46 * 13 = 598 sq . units answer : a
Answer: a
Problem: a car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 90 kilometers per hour . at what speed , in kilometers per hour , is the car traveling ?
Options: a ) 71.5 , b ) 72 , c ) 72.5 , d ) 73 , e ) 85.7
Rationale: "many approaches are possible , one of them : let the distance be 1 kilometer . time to cover this distance at 90 kilometers per hour is 1 / 90 hours = 3,600 / 90 seconds = 40 seconds ; time to cover this distance at regular speed is 40 + 2 = 42 seconds = 42 / 3,600 hours = 7 / 600 hours ; so , we get that to cover 1 kilometer 1 / ( 7 / 600 ) hours is needed - - > regular speed 85.7 kilometers per hour ( rate is a reciprocal of time or rate = distance / time ) . answer : e ."
Answer: e
Problem: a searchlight on top of the watchtower makes 2 revolutions per minute . what is the probability that a man appearing near the tower will stay in the dark for at least 5 seconds ?
Options: a ) 5 / 6 , b ) 5 / 12 , c ) 7 / 12 , d ) 11 / 12 , e ) 11 / 15
Rationale: "the searchlight completes one revolution every 30 seconds . the probability that the man ' s area will be lit up is 5 / 30 = 1 / 6 . the probability that he will stay in the dark is 1 - 1 / 6 = 5 / 6 the answer is a ."
Answer: a
Problem: on a map , 1 inch represents 28 miles . how many v inches would be necessary to represent a distance of 383.6 miles ?
Options: a ) 5.2 , b ) 7.4 , c ) 13.7 , d ) 21.2 , e ) 28.7
Rationale: "v inches necessary to represent a distance of 383.6 miles = 383.6 / 28 = 13.7 answer c"
Answer: c
Problem: 36 welders work at a constant rate they complete an order in 5 days . if after the first day , 12 welders start to work on the other project , how many more days the remaining welders will need to complete the rest of the order ?
Options: a ) 5 , b ) 2 , c ) 8 , d ) 4 , e ) 6
Rationale: "1 . we need to find out the time taken by 24 workers after day 1 . 2 . total no . of wokers * total time taken = time taken by 1 worker 3 . time taken by 1 worker = 36 * 5 = 180 days 4 . but on day 1 thirty - six workers had already worked finishing 1 / 5 of the job . so 24 workers have to finish only 4 / 5 of the job . 5 . total time taken by 24 workers can be got from formula used at ( 2 ) . i . e . , 24 * total time taken = 180 . total time taken by 6 workers to finish the complete job is 180 / 24 = 7.5 days . 6 . time taken by 24 workers to finish 4 / 5 of the job is 4 / 5 * 7.5 = 6 days . the answer is choice e"
Answer: e
Problem: there are 23 students in a class . in how many different ways can a committee of 3 students be formed ?
Options: a ) 1254 , b ) 1482 , c ) 1771 , d ) 1875 , e ) 1923
Rationale: "23 c 3 = 23 * 22 * 21 / 6 = 1771 the answer is c ."
Answer: c
Problem: the volume of the sphere qq is ( dfrac { 37 } { 64 } % ) less than thevolume of sphere pp and the volume of sphere rr is ( dfrac { 19 } { 27 } % ) less than that of sphere qq . by what is the surface areaof sphere rr less than the surfacearea of sphere pp ?
Options: a ) 40 %
b ) 50 %
c ) 75 %
d ) 80 %
e ) 90 %
Rationale: let the volume of sphere pp be 64 parts . therefore volume of sphere qq = 64 − 3764 % = 64 − 3764 % of 6464 = 64 − 37 = 27 = 64 − 37 = 27 parts . the volume of rr = 27 − 1927 × 27 = 27 − 1927 × 27 = 27 − 19 = 8 = 27 − 19 = 8 parts . volume ratio : = p : q : r = 64 : 27 : 8 = p : q : r = 64 : 27 : 8 radius ratio : = p : q : r = 4 : 3 : 2 = p : q : r = 4 : 3 : 2 the surface area will be 16 : 9 : 516 : 9 : 5 surface area of rr is less than the surface area of sphere pp 16 k − 4 k = 12 k 16 k − 4 k = 12 k now , = 12 k 16 k × 100 = 12 k 16 k × 100 = 75 % = 75 % thus surface area of sphere rr is less than the surface area of sphere p by 75 % c
Answer: c
Problem: the length of the bridge , which a train 150 meters long and travelling at 45 km / hr can cross in 30 seconds , is :
Options: a ) 230 , b ) 225 , c ) 245 , d ) 238 , e ) 236
Rationale: "speed = ( 45 * 5 / 18 ) m / sec = ( 25 / 2 ) m / sec . time = 30 sec . let the length of bridge be x meters . then , ( 150 + x ) / 30 = 25 / 2 = = > 2 ( 150 + x ) = 750 = = > x = 225 m . answer : option b"
Answer: b
Problem: speed of a boat in standing water is 7 kmph and speed of the stream is 1.5 kmph . a man can rows to a place at a distance of 105 km and comes back to the starting point . the total time taken by him is ?
Options: a ) 32.44 hours , b ) 31.44 hours , c ) 30.44 hours , d ) 29.44 hours , e ) 28.44 hours
Rationale: "speed upstream = 5.5 kmph speed downstream = 8.5 kmph total time taken = 105 / 5.5 + 105 / 8.5 = 31.44 hours answer is b"
Answer: b
Problem: excluding stoppages , the speed of a train is 45 kmph and including stoppages it is 37 kmph . of how many minutes does the train stop per hour ?
Options: a ) 73 , b ) 83 , c ) 12 , d ) 83 , e ) 11
Rationale: "explanation : t = 8 / 45 * 60 = 11 answer : option e"
Answer: e
Problem: a man traveled a total distance of 1800 km . he traveled one - third of the whole trip by plane and the distance traveled by train is one - half of the distance traveled by bus . if he traveled by train , plane and bus , how many kilometers did he travel by bus ?
Options: a ) 700 , b ) 800 , c ) 900 , d ) 1000 , e ) 1100
Rationale: "total distance traveled = 1800 km . distance traveled by plane = 600 km . distance traveled by bus = x distance traveled by train = x / 2 x + x / 2 + 600 = 1800 3 x / 2 = 1200 x = 800 km the answer is b ."
Answer: b
Problem: the jogging track in a sports complex is 726 m in circumference . suresh and his wife start from the same point and walk in opposite direction at 4.5 km / hr and 3.75 km / hr respectively . they will meet for the first time in :
Options: a ) 5.5 min . , b ) 6 min . , c ) 4.9 min . , d ) 5.28 min . , e ) 5 min .
Rationale: "let both of them meet after t min 4500 m are covered by suresh in 60 m . in t min he will cover 4500 t / 60 likewise , in t min suresh ' s wife will cover 3750 t / 60 given , ( 4500 t / 60 ) + ( 3750 t / 60 ) = 726 t = 5.28 minutes answer : d"
Answer: d
Problem: a and b have monthly incomes in the ratio 5 : 6 and monthly expenditures in the ratio 3 : 4 . if they save rs . 1800 and rs . 1600 respectively , find the monthly income of b
Options: a ) rs . 3400 , b ) rs . 2700 , c ) rs . 1720 , d ) rs . 7200 , e ) rs . 8200
Rationale: explanation : incomes of a and b = 5 x and 6 x and expenses of a and b = 3 y and 4 y then , savings of a = 5 x - 3 y = 1800 — ? ( 1 ) savings of b = 6 x - 4 y = 1600 — ? ( 2 ) by solving equations ( 1 ) and ( 2 ) y = 1400 monthly income of b = expenses of b + savings of b = 4 y + 1600 = 4 ( 1400 ) + 1600 = rs . 7200 answer : d
Answer: d
Problem: mr . kramer , the losing candidate in a two - candidate election , received 942,568 votes , which was exactly 40 percent of all votes cast . approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast ?
Options: a ) 10 % , b ) 12 % , c ) 15 % , d ) 17 % , e ) 20 %
Rationale: "lets assume that candidate got 40 % votes and total votes is 100 . candidate won = 40 remaining = 60 to get 50 % , candidate requires 10 votes from 100 which is 10 % and 10 votes from 60 . 10 / 60 = 1 / 6 = . 166 = 16.67 % which is approx 17 % . hence the answer is d"
Answer: d
Problem: a certain manufacturer of cake , muffin , and bread mixes has 100 buyers , of whom 50 purchases cake mix , 40 purchase muffin mix , and 16 purchase both cake mix and muffin mix . if a buyer is to be selected at random from the 100 buyers , what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix ?
Options: a ) 1 / 10 , b ) 13 / 50 , c ) 1 / 2 , d ) 7 / 10 , e ) 9 / 10
Rationale: "c + m + b - cm - mb - cb - 2 cmb = 100 c - cake buyers , m - muffin and b - bread buyers . cm , mb , cb and cmb are intersecting regions . the question asks for people who have bought only bread mixes = b - cb - mb - 2 cmb has to be found out . 50 + 40 + b - cb - mb - 16 - 2 cmb = 100 b - cb - mb - 2 cmb = 26 hence the probability = 26 / 100 = 13 / 50 . b"
Answer: b
Problem: if it is 5 : 14 in the evening on a certain day , what time in the morning was it exactly 2 , 880702 minutes earlier ? ( assume standard time in one location . )
Options: a ) 5 : 32 , b ) 5 : 36 , c ) 5 : 48 , d ) 5 : 54 , e ) 5 : 58
Rationale: 5 : 14 minus 2 , 880,702 must end with 2 , the only answer choice which ends with 2 is a . answer : a .
Answer: a
Problem: a man can row 6 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and back . how far is the place ?
Options: a ) 2.29 , b ) 2.88 , c ) 2.2 , d ) 2.12 , e ) 2.14
Rationale: "m = 6 s = 1.2 ds = 6 + 1.2 = 7.2 us = 6 - 1.2 = 4.8 x / 7.2 + x / 4.8 = 1 x = 2.88 answer : b"
Answer: b
Problem: when positive integer n is divided by 3 , the remainder is 2 . when n is divided by 6 , the remainder is 5 . how many values less than 100 can n take ?
Options: a ) 0 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "a quick approac to this q is . . the equation we can form is . . 3 x + 2 = 7 y + 5 . . 3 x - 3 = 7 y . . . 3 ( x - 1 ) = 7 y . . . so ( x - 1 ) has to be a multiple of 7 as y then will take values of multiple of 3 . . here we can see x can be 1 , 8,15 , 22,29 so 5 values till 100 is reached as ( 29 - 1 ) * 3 = 84 and next multiple of 7 will be 84 + 21 > 100 . . ans 4 . . d"
Answer: d
Problem: a sports equipment store sold ping pong rackets for a total of $ 539 . if the average ( arithmetic mean ) price of a pair of rackets is $ 9.8 , how many pairs were sold ?
Options: a ) 55 , b ) 100 , c ) 490 , d ) 500 , e ) 980
Rationale: "average price for a pair of rackets = $ 9.8 total cost = $ 9.8 * x = $ 539 x = 55 pairs were sold . answer : a"
Answer: a
Problem: a retailer bought a machine at a wholesale price of $ 80 and later on sold it after a 20 % discount of the retail price . if the retailer made a profit equivalent to 20 % of the wholesale price , what is the retail price of the machine ?
Options: a ) $ 80 , b ) $ 100 , c ) $ 120 , d ) 135 , e ) 160
Rationale: "the price after the discount was 1.2 * 80 = $ 96 let x be the retail price . 0.8 x = $ 96 x = 96 / 0.8 = $ 120 the answer is c ."
Answer: c
Problem: there are 7 teams in a certain league and each team plays each of the other teams exactly twice . if each game is played by 2 teams , what is the total number of games played ?
Options: a ) 15 , b ) 16 , c ) 28 , d ) 42 , e ) 64
Rationale: "every team plays with 6 teams . . . so total no of matches = 7 x 6 = 42 . now , each match is played twice = > 42 x 2 but 2 teams play a match = > 42 x 2 / 2 = 42 . answer : d"
Answer: d
Problem: in expressing a length of 61.472 km as nearly as possible with the 3 significant digits , find the percentage error ?
Options: a ) 0.35 % , b ) 0.4 % , c ) 0.045 % , d ) 0.6 % , e ) none of these
Rationale: explanation : error = ( 61.5 - 61.472 ) = 0.028 required percentage = 0.028 / 61.472100 = 0.045 answer : c
Answer: c
Problem: if x + y + z = 1 . then xy + yz + zx is
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) 1 / 6
Rationale: 1 / 2 + 1 / 2 + 0 = 1 xy = 1 / 2 * 1 / 2 = 1 / 4 answer : c
Answer: c
Problem: in the storage room of a certain bakery , the ratio of sugar to flour is 5 to 2 , and the ratio of flour to baking soda is 10 to 1 . if there were 60 more pounds of baking soda in the room , the ratio of flour to baking soda would be 8 to 1 . how many pounds of sugar are stored in the room ?
Options: a ) 600 , b ) 1200 , c ) 1500 , d ) 3600 , e ) 6000
Rationale: "sugar : flour = 5 : 2 = 25 : 10 ; flour : soda = 10 : 1 = 10 : 1 ; thus we have that sugar : flour : soda = 25 x : 10 x : 1 x . also given that 10 x / ( 1 x + 60 ) = 8 / 1 - - > x = 240 - - > sugar = 25 x = 6000 answer : e ."
Answer: e
Problem: machine a can process 6000 envelopes in 3 hours . machines b and c working together but independently can process the same number of envelopes in 2.5 hours . if machines a and c working together but independently process 3000 envelopes in 1 hour , then how many hours would it take machine b to process 9800 envelopes .
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 7
Rationale: "you can either take the amount of work done as the same as karishma has done or take the work done by each in the same time . i will do the latter 1 . work done in 1 hr by a is 2000 envelopes 2 . work done in 1 hr by a and c is 3000 envelopes 3 . so work done in 1 hr by c is 1000 envelopes 4 . work done in 1 hr by b and c is 2400 envelopes 5 . so work done in 1 hr by b is 1400 envelopes 6 . so to process 9800 envelopes b will take 9800 / 1400 hrs = 7 hrs so the answer is choice e"
Answer: e
Problem: difference between two numbers is 5 , 6 times of the smaller lacks by 8 from the 4 times of the greater . find the numbers ?
Options: a ) 5,1 , b ) 7,3 , c ) 9,8 , d ) 11,6 , e ) 13,7
Rationale: explanation : x – y = 5 4 x – 6 y = 8 x = 11 y = 6 d )
Answer: d
Problem: angelina walked 600 meters from her home to the grocery at a constant speed . she then walked 480 meters to the gym at double the speed . she spent 40 seconds less on her way from the grocery to the gym than on her way from home to the grocery . what was angelina ' s speed , in meters per second , from the grocery to the gym ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 9 , e ) 12
Rationale: "let the speed be x . . . so time taken from home to grocery = 600 / x . . the speed to gym = 2 x . . so time taken = 480 / 2 x = 240 / x . . its given 600 / x - 240 / x = 40 . . 360 / x = 40 . . x = 9 m / secs . . so grocery to gym = 2 * 9 = 18 m / s . . . d"
Answer: d
Problem: a train running at the speed of 180 km / hr crosses a pole in 36 seconds . what is the length of the train ?
Options: a ) 450 m , b ) 500 m , c ) 550 m , d ) 600 m , e ) 650 m
Rationale: "speed = ( 180 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec length of the train = ( speed x time ) = ( 50 / 3 * 36 ) m = 600 m . answer : d"
Answer: d
Problem: two brothers took the gmat exam , the higher score is x and the lower one is y . if the difference between the two scores 1 / 4 , what is the value of y / x ?
Options: a ) 3 . , b ) 2 . , c ) 1 / 5 , d ) 1 / 3 . , e ) there is n ' t enough data to answer the question .
Rationale: "answer is c : 1 / 5 x - y = ( x + y ) / 4 solving for y / x = 1 / 5"
Answer: c
Problem: walking 3 / 2 of his usual rate , a boy reaches his school 4 min early . find his usual time to reach the school ?
Options: a ) 12 , b ) 99 , c ) 27 , d ) 28 , e ) 20
Rationale: "speed ratio = 1 : 3 / 2 = 2 : 3 time ratio = 3 : 2 1 - - - - - - - - 3 4 - - - - - - - - - ? 12 m . answer : a"
Answer: a
Problem: when 5 is added to half of one - third of one - fifth of a number , the result is one - fifteenth of the number . find the number ?
Options: a ) 32 , b ) 150 , c ) 60 , d ) 27 , e ) 11
Rationale: "explanation : let the number be 5 + 1 / 2 [ 1 / 3 ( a / 5 ) ] = a / 15 = > 5 = a / 30 = > a = 150 answer : b"
Answer: b
Problem: in a certain game , a large bag is filled with blue , green , purple and red chips worth 1 , 5 , x and 11 points each , respectively . the purple chips are worth more than the green chips , but less than the red chips . a certain number of chips are then selected from the bag . if the product of the point values of the selected chips is 440 , how many purple chips were selected ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "440 = 1 * 5 * 8 * 11 the factor of 8 must come from the purple point value , so there is 1 purple chip . the answer is a ."
Answer: a
Problem: 9 business executives and 7 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ?
Options: a ) 144 , b ) 131 , c ) 99 , d ) 90 , e ) 45
Rationale: there are 9 business exec and in each handshake 2 business execs are involved . hence 9 c 2 = 36 also , each of 9 exec will shake hand with every 7 other chairmen for total of 63 handshake . total = 36 + 63 = 99 ans : c
Answer: c
Problem: from a pack of cards , two cards are drawn one after the other , with replacement . what is the probability that the first card is a club and the second card is a king or queen ?
Options: a ) 2 / 13 , b ) 3 / 13 , c ) 1 / 26 , d ) 1 / 52 , e ) 3 / 52
Rationale: "p ( club ) = 1 / 4 p ( king or queen ) = 2 / 13 p ( club then a king / queen ) = 1 / 4 * 2 / 13 = 1 / 26 the answer is c ."
Answer: c
Problem: a container has 40 l milk . 4 l milk is taken out and replaced with water , the process done 3 times . what is the amount of milk now left ?
Options: a ) 29.16 l , b ) 29.19 l , c ) 29.12 l , d ) 29.11 l , e ) 29.14 l
Rationale: explanation : in regard to the problem let after n times liquid in the container is x and liquid removed is y = > liquid in container = x = > liquid removed = y after one trial , quantity of pure liquid = x - ( 1 - y / x ) after n trials quantity of pure liquid = x - ( 1 - y / x ) n therefore , putting the values ( x = 40 l y = 4 l n = 3 ) and solving = > 40 - ( 1 - 4 / 40 ) 3 = 29.16 l answer : a
Answer: a
Problem: if the length of rectangle is three times of its breadth . if the area of rectangle is 6075 sq . m , then calculate the length ?
Options: a ) 145
b ) 135
c ) 75
d ) 140
e ) none of these
Rationale: let breadth = x , length = 3 x . area of rectangle = length * breadth = 3 x ^ 2 = 6075 x ^ 2 = 2025 , x = √ 2025 = 45 m length = 135 m answer b
Answer: b
Problem: the average of 9 observations was 9 , that of the 1 st of 4 being 10 and that of the last 4 being 8 . what was the 5 th observation ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "1 to 9 = 9 * 9 = 81 1 to 4 = 4 * 10 = 40 4 to 9 = 6 * 8 = 48 5 th = 48 + 40 = 88 – 81 = 7 answer : d"
Answer: d
Problem: how much water must be added to 48 litres of milk at 1 1 ⁄ 2 litres for 20 so as to have a mixture worth 10 2 ⁄ 3 a litre ?
Options: a ) 10 litres , b ) 12 litres , c ) 15 litres , d ) 18 litres , e ) none of these
Rationale: "c . p . of 1 litre of milk = ( 20 × 2 ⁄ 3 ) = 40 ⁄ 3 ∴ ratio of water and milk = 8 ⁄ 3 : 32 ⁄ 3 = 8 : 32 = 1 : 4 ∴ quantity of water to be added to 48 litres of milk = ( 1 ⁄ 4 × 48 ) litres = 12 litres . answer b"
Answer: b
Problem: a salesman â € ™ s terms were changed from a flat commission of 5 % on all his sales to a fixed salary of rs . 1000 plus 2.5 % commission on all sales exceeding rs . 4,000 . if his remuneration as per new scheme was rs . 100 more than that by the previous schema , his sales were worth ?
Options: a ) s . 14,000 , b ) s . 12,000 , c ) s . 32,000 , d ) s . 40,000 , e ) s . 50,000
Rationale: "[ 1000 + ( x - 4000 ) * ( 2.5 / 100 ) ] - x * ( 5 / 100 ) = 100 x = 32000 answer : c"
Answer: c
Problem: two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 24 seconds . the ratio of their speeds is ?
Options: a ) 3 / 6 , b ) 3 / 2 , c ) 7 / 3 , d ) 3 / 5 , e ) 5 / 2
Rationale: "let the speeds of the two trains be x m / sec and y m / sec respectively . then , length of the first train = 27 x meters , and length of the second train = 17 y meters . ( 27 x + 17 y ) / ( x + y ) = 24 = = > 27 x + 17 y = 24 x + 24 y = = > 3 x = 7 y = = > x / y = 7 / 3 . answer : c"
Answer: c
Problem: 32 % of employees are women with fair hair . 40 % of fair - haired employees are women . what percent of employees have fair hair ?
Options: a ) 25 , b ) 30 , c ) 50 , d ) 55 , e ) 80
Rationale: "i came up with ( e ) 80 think of 100 people total : from the first fact , 32 of these are women with fair hair . from the second fact , these 30 women make up 40 % of the total fair haired population . we can then make a ratio of 60 : 40 fair haired men to fair haired women . this means that ( 60 / 40 ) * 32 equals the number of fair haired men , which is 48 men with fair hair . add this 48 to the 32 women and get 80 fair haired men and women out of 100 total men and women . 80 % e"
Answer: e
Problem: while visiting a small town in the united states , i lost my overcoat in a bus . when i reported the matter to the bus company i was asked the number of the bus . though i did not remember the exact number i did remember that the bus number bad a certain peculiarity about it . the number plate showed the bus number as a perfect square and also if the plate was turned upside down . ? the number would still be a perfect square — of course it was not ? i came to know from the bus company they had only 5 100 buses numbered from 1 to 500 . from this i was able to deduce the bus number . can you tell what was the other number .
Options: a ) 127 , b ) 196 , c ) 116 , d ) 140 , e ) 234
Rationale: b 196 the only numbers that can be turned upside down and still read as a number are 0 , 1 , 6 , 8 and 9 . the numbers 0 , 1 and 8 remain 0 , 1 and 8 when turned over , but 6 becomes 9 and 9 becomes 6 . therefore the possible numbers on the bus were 9 , 16 , 81 , 100 , 169 or 196 . however , the number 196 is the only number which becomes a perfect square when turned over because 961 is the perfect square of 31 . therefore 196 is the correct answer .
Answer: b
Problem: a car traveled from san diego to san francisco at an average speed of 51 miles per hour . if the journey back took twice as long , what was the average speed of the trip ?
Options: a ) 24 . , b ) 34 . , c ) 36 . , d ) 42 . , e ) 44 .
Rationale: "let the time taken be = x one way distance = 51 x total distance traveled = 2 * 51 x = 102 x total time taken = x + 2 x = 3 x average speed = 102 x / 3 x = 34 answer : b"
Answer: b