regisss/math_qa huggingface dataset:
Problem: y = x ^ 2 + bx + 128 cuts the x axis at ( h , 0 ) and ( k , 0 ) . if h and k are integers , what is the least value of b ?
Options: a ) - 129 , b ) - 132 , c ) 32 , d ) 64 , e ) 128
Rationale: "as the curve cuts the x - axis at ( h , 0 ) and ( k , 0 ) . therefore h , k are the roots of the quadratic equation . for the quadratic equation is in the form of ax ^ 2 + bx + c = 0 , the product of the roots = c / a = 128 / 1 = 64 and the sum of the roots = - b / a = - b / 1 128 can be expressed as product of two numbers in the following ways : 1 * 128 2 * 64 4 * 32 8 * 16 the sum of the roots is maximum when the roots are 1 and 128 and the maximum sum is 1 + 128 = 129 . the least value possible for b is therefore - 129 . a"
Answer: a
Problem: 3 years ago , the average age of a family of 5 members was 17 . a baby having been born , the average age of the family is the same today . what is the age of the child ?
Options: a ) 3 , b ) 2 , c ) 4 , d ) 1 , e ) 5
Rationale: present age of 5 members = 5 x 17 + 3 x 5 = 100 years also , present ages of 5 members + age of the baby = 6 x 17 = 102 years age of the baby = 102 – 100 = 2 years . answer : b
Answer: b
Problem: car a runs at the speed of 33 km / hr & reaches its destination in 7 hr . car b runs at the speed of 44 km / h & reaches its destination in 5 h . what is the respective ratio of distances covered by car a & car b ?
Options: a ) 20 : 23 , b ) 25 : 27 , c ) 21 : 20 , d ) 29 : 23 , e ) 24 : 25
Rationale: "sol . distance travelled by car a = 33 × 7 = 231 km distance travelled by car b = 44 × 5 = 220 km ratio = 231 / 220 = 21 : 20 c"
Answer: c
Problem: a and b undertake to do a piece of work for $ 120 . a alone can do it in 4 days while b alone can do it in 6 days . with the help of c , they finish it in 2 days . find the share of b ?
Options: a ) $ 150 , b ) $ 100 , c ) $ 200 , d ) $ 50 , e ) $ 40
Rationale: "c ' s 1 day work = ( 1 / 2 ) - ( 1 / 4 + 1 / 6 ) = 1 / 12 a : b : c = 1 / 4 : 1 / 6 : 1 / 12 = 3 : 2 : 1 b ' s share = 120 * 2 / 6 = $ 40 answer is e"
Answer: e
Problem: a , b , and c were to be paid in proportion to the part of work they did while working on the same piece of work . a and b individually can finish the piece of work in 12 days and 15 days respectively . they worked together for 5 days and then c completed the remaining work all alone . if $ 810 was the net sum to be paid for the entire work , what was the average daily wage of b ?
Options: a ) $ 144 , b ) $ 90 , c ) $ 60 , d ) $ 54 , e ) $ 48
Rationale: the correct answer is d .
Answer: d
Problem: an aeroplane covers a certain distance at a speed of 240 kmph in 4 hours . to cover the same distance in 1 2 / 3 hours , it must travel at a speed of :
Options: a ) 520 , b ) 620 , c ) 576 , d ) 740 , e ) 720
Rationale: "distance = ( 240 x 4 ) = 960 km . speed = distance / time speed = 960 / ( 5 / 3 ) km / hr . [ we can write 1 2 / 3 hours as 5 / 3 hours ] required speed = ( 960 x 3 / 5 ) km / hr = 576 km / hr answer c ) 576 km / hr"
Answer: c
Problem: how many numbers from 29 to 79 are exactly divisible by 11 ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 11 , e ) 12
Rationale: "option ' a ' 29 / 11 = 2 and 79 / 11 = 7 = = > 7 - 2 = 5 numbers"
Answer: a
Problem: the racing magic takes 60 seconds to circle the racing track once . the charging bull makes 40 rounds of the track in an hour . if they left the starting point together , how many minutes will it take for them to meet at the starting point for the second time ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: time taken by racing magic to make one circle = 60 seconds time taken bycharging bullto make one circle = 60 mins / 40 = 1.5 mins = 90 seconds lcm of 90 and 60 seconds = 180 seconds time taken for them to meet at the starting point for the second time = 180 * 2 = 360 seconds = 6 mins answer b
Answer: b
Problem: how many liters of water must be evaporated from 50 liters of a 2 - percent sugar solution to get a 10 - percent solution ?
Options: a ) 25 , b ) 30 , c ) 35 , d ) 40 , e ) 45
Rationale: "2 % of a 50 liter solution is 1 l which is 10 % of the solution at the end . the solution at the end must be 1 l . we need to evaporate 40 liters . the answer is d ."
Answer: d
Problem: what is the probability of always having x + y > 0 , where y < 0
Options: a ) 1 / 2 , b ) 1 / 8 , c ) 3 / 4 , d ) 1 / 4 , e ) none
Rationale: "total value of x can be : 1 . x < 0 ; 2 . x = 0 ; 3 . x > 0 but less than y in magnitude 4 . x > 0 as well as | y | so probability of having x + y > 0 would be 1 / 4 answer : d"
Answer: d
Problem: the surface area of a sphere is 4 π r 2 , where r is the radius of the sphere . if the area of the base of a hemisphere is 3 , what is the surface area w of that hemisphere ?
Options: a ) 6 / π , b ) 9 / π , c ) 6 , d ) 9 , e ) 12
Rationale: "given area of the base of a hemisphere is 3 = pi * r ^ 2 thus r = sqrt ( 3 / pi ) . surface area of whole sphere = 4 * pi * r ^ 2 . = 4 * pi * 3 / pi = 12 . since the hemisphere is half of a sphere the surface area of the hemisphere = 12 / 2 = 6 ( curved part , not including the flat rounded base ) . but the total surface area = 6 + area of the base of a hemisphere . = 6 + 3 = 9 . answer is d ! !"
Answer: d
Problem: factory x ' s bulbs work for over 5000 hours in 37 % of cases , whereas factory y ' s bulbs work for over 5000 hours in 75 % of cases . it is known that factory x supplies 40 % of the total bulbs available . what is the chance that a purchased bulb will work for longer than 5000 hours ?
Options: a ) 56.4 % , b ) 58 % , c ) 57.4 % , d ) 55 % , e ) 59.8 %
Rationale: "for x , 40 % of 37 % will work . for y , 60 % of 75 % will work . * 60 % is the rest of the bulb supply in the market . so , the probability that a purchased bulb will work is : 0.40 ( 0.37 ) = . 148 0.60 ( 0.75 ) = 0.45 the combined probability then is 14.8 + 45 = 59.8 % ans e"
Answer: e
Problem: a certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint . if 2 gallons of the mixture is needed and the individual colors can be purchased only in one gallon or half gallon cans , what is the least amount of paint e , in gallons , that must be purchased in order to measure out the portions needed for the mixture ?
Options: a ) 2 , b ) 2 1 / 2 , c ) 3 , d ) 3 1 / 2 , e ) 4
Rationale: "given w : b = 3 : 5 that means say 3 gallons of white paint + 5 gallons of black paint = 8 gallons of paint mixture . but we want least amount of whiteblack paints for minimum of 2 gallons of mixture , so lets reduce keeping same ratio , 1.5 : 2.5 gives 1.5 + 2.5 = 4 gallons of mixture , but we want only 2 gallons , lets further reduce 0.75 : 1.25 gives 1 + 1.5 = 2.5 gallons of mixture . this looks ok , but lets reduce further just to be sure 0.375 : 0.625 gives 0.5 + 1 = 1.5 gallons of mixture , thats less than 2 gallons of mixture , so not acceptable . so correct ans is 2.5 gallons . b"
Answer: b
Problem: a and b complete a work in 4 days . a alone can do it in 8 days . if both together can do the work in how many days ?
Options: a ) 3.75 days , b ) 3.99 days , c ) 2.67 days , d ) 2.98 days , e ) 2.44 days
Rationale: "1 / 4 + 1 / 8 = 3 / 8 8 / 3 = 2.67 days answer : c"
Answer: c
Problem: roja and pooja start moving in the opposite directions from a pole . they are moving at the speeds of 8 km / hr and 3 km / hr respectively . after 4 hours what will be the distance between them ?
Options: a ) 22 km , b ) 20 km , c ) 44 km , d ) 18 km , e ) 16 km
Rationale: "distance = relative speed * time = ( 8 + 3 ) * 4 = 44 km [ they are travelling in the opposite direction , relative speed = sum of the speeds ] . answer : c"
Answer: c
Problem: in a company with 48 employees , some part - time and some full - time , exactly ( 1 / 3 ) of the part - time employees and ( 1 / 4 ) of the full - time employees take the subway to work . what is the greatest possible number q of employees who take the subway to work ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: "p / 3 + f / 4 = p / 3 + ( 48 - p ) / 4 = 12 + p / 2 p / 3 + f / 3 = ( p + f ) / 3 = 48 / 3 = 16 p / 4 + f / 4 = 12 p / 3 + f / 3 > p / 3 + f / 4 > p / 4 + f / 4 - - > 16 > 12 + p / 12 > 12 greatest possible q : 12 + p / 12 = 15 - - > p = 36 ( integer - - > good ) 15 or d is the answer"
Answer: d
Problem: how many multiples of 8 are there between 100 and 200 ( both are inclusive ) ?
Options: a ) 27 , b ) 4 , c ) 6 , d ) 13.5 , e ) 8
Rationale: "the answer is ( 200 - 100 ) / 8 + 1 = 13.5 answer is d"
Answer: d
Problem: the salary of a typist was at first raised by 10 % and then the same was reduced by 5 % . if he presently draws rs . 1045 . what was his original salary ?
Options: a ) 1009 , b ) 1018 , c ) 1000 , d ) 1082 , e ) 1029
Rationale: "x * ( 110 / 100 ) * ( 95 / 100 ) = 1045 x * ( 11 / 10 ) * ( 1 / 100 ) = 11 x = 1000 answer : c"
Answer: c
Problem: how many pounds of salt at 50 cents / lb must be mixed with 45 lbs of salt that costs 35 cents / lb so that a merchant will get 20 % profit by selling the mixture at 48 cents / lb ?
Options: a ) 20 , b ) 15 , c ) 40 , d ) 50 , e ) 90
Rationale: "selling price is 48 cents / lb for a 20 % profit , cost price should be 40 cents / lb ( cp * 6 / 5 = 48 ) basically , you need to mix 35 cents / lb ( salt 1 ) with 50 cents / lb ( salt 2 ) to get a mixture costing 45 cents / lb ( salt avg ) weight of salt 1 / weight of salt 2 = ( salt 2 - saltavg ) / ( saltavg - salt 1 ) = ( 50 - 45 ) / ( 45 - 35 ) = 1 / 2 we know that weight of salt 1 is 45 lbs . weight of salt 2 must be 90 lbs . answer ( e )"
Answer: e
Problem: if the sum of a number and its square is 132 , then what is the number ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "explanation : let the number be x . then , x 2 + x = 132 = > x 2 + x - 132 = 0 = > ( x + 12 ) ( x - 11 ) = 0 = > x = 11 answer : option b"
Answer: b
Problem: 0.363 * 0.522 + 0.363 * 0.478 = ?
Options: a ) 0.522 , b ) 0.845 , c ) 0.363 , d ) 0.985 , e ) 0.885
Rationale: "given expression = 0.363 * ( 0.522 + 0.478 ) = 0.363 * 1 = 0.363 answer : c"
Answer: c
Problem: lilly has 10 fish and rosy has 8 fish . in total , how many fish do they have in all ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "10 + 8 = 18 the answer is d ."
Answer: d
Problem: a certain clock marks every hour by striking a number of times equal to the hour , and the time required for a stroke is exactly equal to the time interval between strokes . at 6 : 00 the time lapse between the beginning of the first stroke and the end of the last stroke is 55 seconds . at 12 : 00 , how many seconds elapse between the beginning of the first stroke and the end of the last stroke ?
Options: a ) a . 72 , b ) b . 115 , c ) c . 48 , d ) d . 46 , e ) e . 44
Rationale: "at 6 : 00 it ' ll chime 6 times . if we assume that the time taken to chime is x , then time between chimes is also x . so you have 6 chimes , which is 6 x and 5 time intervals between chimes . this means that 11 x = 55 seconds . thus x = 5 seconds . by a similar logic , at 12 : 00 , there are 12 chimes and 11 intervals so the total time is ( 12 + 11 ) x = 23 x = 115 seconds . answer b"
Answer: b
Problem: two numbers n and 10 have lcm = 36 and gcf = 5 . find n .
Options: a ) 35 , b ) 56 , c ) 76 , d ) 18 , e ) 24
Rationale: "the product of two integers is equal to the product of their lcm and gcf . hence . 10 * n = 36 * 5 n = 36 * 5 / 10 = 18 correct answer d"
Answer: d
Problem: the difference between c . i . and s . i . on an amount of rs . 15,000 for 2 years is rs . 216 . what is the rate of interest per annum ?
Options: a ) 8 , b ) 2 , c ) 9 , d ) 4 , e ) 12
Rationale: "explanation : [ 15000 * ( 1 + r / 100 ) 2 - 15000 ] - ( 15000 * r * 2 ) / 100 = 216 15000 [ ( 1 + r / 100 ) 2 - 1 - 2 r / 100 ] = 216 15000 [ ( 100 + r ) 2 - 10000 - 200 r ] / 10000 = 216 r 2 = ( 216 * 2 ) / 3 = 144 = > r = 12 rate = 12 % answer : option e"
Answer: e
Problem: employees of a certain company are each to receive a unique 7 - digit identification code consisting of the digits 0 , 1 , 2 , 3 , 4 , 5 , and 6 such that no digit is used more than once in any given code . in valid codes , the second digit in the code is exactly twice the first digit . how many valid codes are there ?
Options: a ) 42 , b ) 120 , c ) 210 , d ) 360 , e ) 840
Rationale: "one can use slot method to solve this . 7 digit identification code has 7 slots to fill . for the first slot there are three possible options . ( 1,2 and 3 because first digit has to be half of second ) for the second slot there are three possible options . ( 2,4 and 6 because second digit has to be twice the second ) to fill the first two slots there are only three possible ways . because if the , if the first is 1 the second has to be 2 ( only 1 way ) if the first is 2 the second has to be 4 ( only 1 way ) if the first is 3 the second has to be 6 ( only 1 way ) . so total ways to fill first two slots = 3 ways you are now left with 5 digits and 5 slots to fill , which can be filled in 5 ! ways i . e . 120 ways . total no : of valid codes will be therefore : 120 * 3 = 360 ways . answer : d"
Answer: d
Problem: it is the new year and mandy has made a resolution to lose weight this year . she plans to exercise and do yoga . for exercise she plans to workout at the gym and ride her bicycle in the ratio of 2 : 3 everyday . she will also do yoga in the ratio , yoga : exercise = 2 : 3 . if she rides her bike for 20 minutes , how much time will she spend doing yoga ? ( rounded to minutes )
Options: a ) 10 min . , b ) 33 min . , c ) 17 min . , d ) 23 min . , e ) 25 min .
Rationale: "the ratio is 2 : 3 = gym : ride , so ( 20 ) ( 3 / 2 ) = 30 minutes at the gym , and 30 + 20 = 50 minutes exercise , so ( 2 / 3 ) ( 50 ) = 33 minutes yoga . answer : b"
Answer: b
Problem: two whales are moving in the same direction at 18 mps and 15 mps . the faster whale crosses the slow whale in 15 seconds . what is the length of the slower whale in meters ?
Options: a ) 45 m , b ) 56 m , c ) 39 m , d ) 33 m , e ) 62 m
Rationale: relative speed = ( 18 - 15 ) = 3 mps . distance covered in 15 sec = 15 * 3 = 45 m . the length of the faster train = 45 m . answer : a
Answer: a
Problem: a circular path of 16 m radius has marginal walk 3 m wide all round it . find the cost of leveling the walk at rs . 2 per m 2 ?
Options: a ) rs . 660
b ) rs . 40
c ) rs . 44
d ) rs . 42
e ) rs . 43
Rationale: explanation : π ( 19 ^ 2 - 16 ^ 2 ) = 22 / 7 * ( 361 - 256 ) = 330 330 * 2 = rs . 660 answer : option a
Answer: a
Problem: speed of a boat in standing water is 14 kmph and the speed of the stream is 1.2 kmph . a man rows to a place at a distance of 4864 km and comes back to the starting point . the total time taken by him is
Options: a ) 700 hours , b ) 350 hours , c ) 1400 hours , d ) 1010 hours , e ) none of these
Rationale: explanation : speed downstream = ( 14 + 1.2 ) = 15.2 kmph speed upstream = ( 14 - 1.2 ) = 12.8 kmph total time taken = ( 4864 / 15.2 ) + ( 4864 / 12.8 ) = 320 + 380 = 700 hours . answer : option a
Answer: a
Problem: the avearge score of a cricketer for 10 matches is 38.9 runs . if the average for the first 6 matches is 41 . then find the average for the last 4 matches ?
Options: a ) 33.25 , b ) 35.75 , c ) 34.25 , d ) 35 , e ) none
Rationale: solution required average = ( 38.9 x 10 ) - ( 41 x 6 ) / 4 = 143 / 4 . = 35.75 answer b
Answer: b
Problem: noelle walks from point a to point b at an average speed of 6 kilometers per hour . at what speed , in kilometers per hour , must noelle walk from point b to point a so that her average speed for the entire trip is 7 kilometers per hour ?
Options: a ) 6.75 , b ) 7 , c ) 7.25 , d ) 7.5 , e ) 8.4
Rationale: "let ' s suppose that speed while returning was xkm / h since the distance is same , we can apply the formula of avg speed avg speed = 2 s 1 s 2 / s 1 + s 2 7 = 2 * 6 * x / 6 + x x = 8.4 e is the answer"
Answer: e
Problem: 6 x 0.6 x 0.06 x 0.006 x 60 = ?
Options: a ) 77.76 , b ) 7.776 , c ) 0.7776 , d ) 0.07776 , e ) none otf these
Rationale: "explanation : ? = 6 x 6 / 10 x 6 / 100 x 6 / 1000 x 60 = 77760 / 1000000 = 7776 / 100000 = 0.07776 answer : option d"
Answer: d
Problem: 0.009 / x = 0.02 . find the value of x
Options: a ) 0.045 , b ) 0.09 , c ) 0.9 , d ) 9 , e ) 90
Rationale: "x = 0.009 / 0.045 = 0.9 answer : a"
Answer: a
Problem: if two projectiles are launched at the same moment from 2520 km apart and travel directly towards each other at 432 km per hour and 576 km per hour respectively , how many minutes will it take for them to meet ?
Options: a ) 130 , b ) 135 , c ) 140 , d ) 145 , e ) 150
Rationale: "the projectiles travel a total of 1008 km per hour . the time to meet is 2520 / 1008 = 2.5 hours = 150 minutes the answer is e ."
Answer: e
Problem: what is the smallest number by which 3600 be divided to make it a perfect cube ?
Options: a ) 9
b ) 50
c ) 300
d ) 450
e ) 550
Rationale: solution 3600 = 23 * 52 * 32 * 2 . to make it a perfect cube , it must be divided by 52 * 32 * 2 i . e . , 450 . answer d
Answer: d
Problem: radius of a circle is 5 cm , if we draw a rectangle of maximum size , what is the area of rectangle ?
Options: a ) 30
b ) 40
c ) 50
d ) 60
e ) 70
Rationale: area of rectangle of max size inside circle will be a square with diagonal equal to 10 cms . then side of square = root ( 100 / 2 ) = root 50 area of square = root 50 * root 50 = 50 sq cms . answer : c
Answer: c
Problem: each week , harry is paid x dollars per hour for the first 30 hours and 1.5 x dollars for each additional hour worked that week . each week , james is paid x dollars per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week james worked a total of 47 hours . if harry and james were paid the same amount last week , how many hours did harry work last week ?
Options: a ) 35 , b ) 36 , c ) 37 , d ) 38 , e ) 46
Rationale: "amount earned by james = 40 * x + 7 * 2 x = 54 x therefore , amount earned by harry = 54 x but we know the amount harry earned assuming working y hours ( y > 30 ) is 30 * x + ( y - 30 ) * 1.5 x [ [ we know y > 30 because in 30 h the most harry could earn is 30 x , but he has earned 54 x ] ] so x * ( 1.5 y - 45 + 30 ) = 54 x or x * ( 1.5 y - 15 ) = 54 x so 1.5 y - 15 = 54 so 1.5 y = 69 so y = 46 answer is e"
Answer: e
Problem: the greatest number that divides 60 and 190 leaving remainder 6 and 10 respectively is :
Options: a ) 15 , b ) 18 , c ) 19 , d ) 22 , e ) 23
Rationale: explanation : 60 - 6 = 54 , 190 - 10 = 180 highest number that divides 54 and 180 is hcf of numbers hcf of 54 nad 180 = 18 answer : b
Answer: b
Problem: 5 bells begin to toll together at 12 : 00 noon and toll respectively at intervals of 3 , 4 , 5 , 6 , and 7 seconds . not including the toll at 12 : 00 noon , how many more times will all 5 bells toll together before 1 : 00 pm ( i . e . one hour later ) ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: the least common multiple is 2 * 2 * 3 * 5 * 7 = 420 . 3600 seconds / 420 = 8 + remainder . the answer is b .
Answer: b
Problem: 9 students bought burgers for $ 143 dollars . if the bill has to be divided among these students , how much amount should be added to the amound to make it divided amoung them equally in dollars ( in whole number of dollars )
Options: a ) $ 1 , b ) $ 2 , c ) $ 3 , d ) $ 4 , e ) $ 5
Rationale: in order to divide the sum in 9 parts , the amount must be divisible by 9 divisibility rule of 9 : the sum of the digits must be divisible by 9 sum of digits of 143 = 8 and 9 is divisible by 9 . hence , we need to add 1 to this number for it to be divisible by 9 correct option : a
Answer: a
Problem: amit and ananthu can do a work in 15 days and 25 days respectively . amit started the work and left after 3 days . ananthu took over and completed the work . in how many days was the total work completed ?
Options: a ) 28 days , b ) 20 days , c ) 23 days , d ) 25 days , e ) 27 days
Rationale: "amit ’ s one day ’ s work = 1 / 15 amit ’ s 3 day ’ s work = 1 / 15 * 3 = 1 / 5 work left = 1 - 1 / 5 = 4 / 5 ananthu ’ s one day ’ s work = 1 / 25 ananthu can do work in = 4 / 5 * 25 = 20 / 1 days so total days = 25 + 3 = 28 days answer : a"
Answer: a
Problem: b alone can do piece of work in 10 days . a alone can do it in 15 days . if the total wages for the work is rs 5000 , how much should b be paid if they work together for the entire duration of the work ?
Options: a ) 267 , b ) 7 , c ) 76 , d ) 8 , e ) 82
Rationale: answer : a
Answer: a
Problem: a , b and c , each working alone can complete a job in 6 , 8 and 12 days respectively . if all three of them work together to complete a job and earn $ 1170 , what will be c ' s share of the earnings ?
Options: a ) $ 1100 , b ) $ 260 , c ) $ 1080 , d ) $ 1170 , e ) $ 630
Rationale: "explanatory answer a , b and c will share the amount of $ 1170 in the ratio of the amounts of work done by them . as a takes 6 days to complete the job , if a works alone , a will be able to complete 1 / 6 th of the work in a day . similarly , b will complete 1 / 8 th and c will complete 1 / 12 th of the work . so , the ratio of the work done by a : b : c when they work together will be equal to 1 / 6 : 1 / 8 : 1 / 12 multiplying the numerator of all 3 fractions by 24 , the lcm of 6 , 8 and 12 will not change the relative values of the three values . we get 24 / 6 : 24 / 8 : 24 / 12 = 4 : 3 : 2 . i . e . , the ratio in which a : b : c will share $ 1170 will be 4 : 3 : 2 . hence , c ' s share will be 2 * 1170 / 9 = 260 correct choice is ( b )"
Answer: b
Problem: express a speed of 180 kmph in meters per second ?
Options: a ) 10 mps , b ) 05 mps , c ) 50 mps , d ) 12 mps , e ) 11 mps
Rationale: "c 50 mps 180 * 5 / 18 = 50 mps"
Answer: c
Problem: sum of two numbers is 25 . two times of the first exceeds by 5 from the three times of the other . then the numbers will be ?
Options: a ) a ) 5 , b ) b ) 9 , c ) c ) 11 , d ) d ) 13 , e ) e ) 15
Rationale: "explanation : x + y = 25 2 x – 3 y = 5 x = 16 y = 9 b )"
Answer: b
Problem: rs . 1300 is divided so that 4 times the first share , thrice the 2 nd share and twice the third share amount to the same . what is the value of the third share ?
Options: a ) s . 528 , b ) s . 600 , c ) s . 528 , d ) s . 540 , e ) s . 549
Rationale: "a + b + c = 1300 4 a = 3 b = 2 c = x a : b : c = 1 / 4 : 1 / 3 : 1 / 2 = 3 : 4 : 6 6 / 13 * 1300 = rs . 600 answer : b"
Answer: b
Problem: joe went on a diet 4 months ago when he weighed 212 pounds . if he now weighs 188 pounds and continues to lose at the same average monthly rate , in approximately how many months will he weigh 160 pounds ?
Options: a ) 3 , b ) 3.5 , c ) 4 , d ) 4.5 , e ) 5
Rationale: "212 - 188 = 24 pounds lost in 4 months 24 / 4 = 6 , so joe is losing weight at a rate of 6 pounds per month . . . . in approximately how many months will he weigh 160 pounds ? a simple approach is to just list the weights . now : 188 lbs in 1 month : 182 lbs in 2 months : 176 lbs in 3 months : 170 lbs in 4 months : 164 lbs in 5 months : 158 lbs since 160 pounds is halfway between 164 and 158 , the correct answer must be 4.5 months . answer : d"
Answer: d
Problem: each day a man meets his wife at the train station after work , and then she drives him home . she always arrives exactly on time to pick him up . one day he catches an earlier train and arrives at the station an hour early . he immediately begins walking home along the same route the wife drives . eventually his wife sees him on her way to the station and drives him the rest of the way home . when they arrive home the man notices that they arrived 12 minutes earlier than usual . how much time did the man spend walking ?
Options: a ) 45 minutes , b ) 50 minutes , c ) 40 minutes , d ) 54 minutes , e ) 35 minutes
Rationale: "as they arrived 12 minutes earlier than usual , they saved 12 minutes on round trip from home to station ( home - station - home ) - - > 6 minutes in each direction ( home - station ) - - > wife meets husband 6 minutes earlier the usual meeting time - - > husband arrived an hour earlier the usual meeting time , so he must have spent waking the rest of the time before their meeting , which is hour - 6 minutes = 54 minutes . answer : d"
Answer: d
Problem: how many numbers from 29 to 79 are exactly divisible by 11
Options: a ) 5 , b ) 7 , c ) 8 , d ) 9 , e ) 11
Rationale: "29 / 11 = 2 and 79 / 11 = 7 = = > 7 - 2 = 5 numbers option ' a '"
Answer: a
Problem: calculate the time it will take for a train that is 200 meter long to pass a bridge of 180 meter length , if the speed of the train is 65 km / hour ?
Options: a ) 20 seconds , b ) 4 seconds , c ) 31.04 seconds , d ) 11.04 seconds , e ) 21.04 seconds
Rationale: "speed = 65 km / hr = 65 * ( 5 / 18 ) m / sec = 18.06 m / sec total distance = 200 + 180 = 380 meter time = distance / speed = 380 * ( 100 / 1806 ) = 21.04 seconds answer : e"
Answer: e
Problem: if z is a multiple of 8902 , what is the remainder when z ^ 2 is divided by 4 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) it depends on z .
Rationale: "2 is a factor of 8902 , so 2 is a factor of z . then 2 ^ 2 = 4 is a factor of z ^ 2 . then the remainder when z ^ 2 is divided by 4 is 0 . the answer is a ."
Answer: a
Problem: a person travels from p to q a speed of 50 km / hr and returns by increasing his speed by 50 % . what is his average speed for both the trips ?
Options: a ) 62.5 , b ) 77 , c ) 48 , d ) 99 , e ) 21
Rationale: "speed on return trip = 150 % of 50 = 75 km / hr . average speed of trip = 50 + 75 / 2 = 125 / 2 = 62.5 km / hr answer : a"
Answer: a
Problem: the ratio of incomes of two person p 1 and p 2 is 5 : 4 and the ratio of their expenditures is 3 : 2 . if at the end of the year , each saves rs . 1600 , then what is the income of p 1 ?
Options: a ) rs . 800 , b ) rs . 2400 , c ) rs . 4000 , d ) rs . 3200 , e ) rs . 4200
Rationale: let the income of p 1 and p 2 be rs . 5 x and rs . 4 x respectively and let their expenditures be rs . 3 y and 2 y respectively . then , 5 x – 3 y = 1600 … ( i ) and 4 x – 2 y = 1600 … … . . ( ii ) on multiplying ( i ) by 2 , ( ii ) by 3 and subtracting , we get : 2 x = 1600 - > x = 800 p 1 ’ s income = rs 5 * 800 = rs . 4000 answer : c
Answer: c
Problem: what is the area of a square field whose diagonal of length 40 m ?
Options: a ) 287 , b ) 269 , c ) 750 , d ) 200 , e ) 800
Rationale: "d 2 / 2 = ( 40 * 40 ) / 2 = 800 answer : e"
Answer: e
Problem: find the area of a rhombus one side of which measures 20 cm and one diagonal is 28 cm .
Options: a ) 200 cm 2
b ) 300 cm 2
c ) 400 cm 2
d ) 448 cm 2
e ) 100 cm 2
Rationale: explanation : let other diagonal = 2 x cm . since diagonals of a rhombus bisect each other at right angles , we have : ( 20 ) 2 = ( 12 ) 2 + ( x ) 2 = > x = √ ( 20 ) 2 – ( 12 ) 2 = √ 256 = 16 cm . _ i so , other diagonal = 32 cm . area of rhombus = ( 1 / 2 ) x ( product of diagonals ) = ( 1 / 2 × 28 x 32 ) cm 2 = 448 cm 2 answer : option d
Answer: d
Problem: find the greatest number which is such that when 794 , 858 and 1351 are divided by it , the remainders are all same .
Options: a ) 1 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: given , the remainders are same i . e . differences of that numbers are exactly divisible . hence , you have to find hcf ( x – y , y – z , z – x ) . 858 – 794 = 64 ; 1351 – 794 = 557 ; 1351 – 858 = 493 . hcf of ( 64 , 557 , 493 ) = 1 . answer : a
Answer: a
Problem: a man spend 1 / 5 of his salary on food , 1 / 10 of his salary on house rent and 3 / 5 salary on clothes . he still has $ 14000 left with him . find salary . .
Options: a ) $ 10400 , b ) $ 14000 , c ) $ 144000 , d ) $ 1800 , e ) $ 140000
Rationale: "[ 1 / ( x 1 / y 1 + x 2 / y 2 + x 3 / y 3 ) ] * total amount = balance amount [ 1 - ( 1 / 5 + 1 / 10 + 3 / 5 ) } * total salary = $ 14000 , = [ 1 - 9 / 10 ] * total salary = $ 14000 , total salary = $ 14000 * 10 = $ 140000 , correct answer ( e )"
Answer: e
Problem: the equal amounts of money are deposited in two banks each at 15 % per annum for 3.5 years and 10 years respectively . if the difference between their interests is rs . 144 , find the each sum ?
Options: a ) rs . 117.69 , b ) rs . 147.69 , c ) rs . 137.69 , d ) rs . 157.69 , e ) rs . 127.69
Rationale: "( p * 10 * 15 ) / 100 - ( p * 3.5 * 15 ) / 100 = 144 = > p = rs . 147.69 answer : b"
Answer: b
Problem: in traveling from a dormitory to a certain city , a student went 1 / 5 of the way by foot , 2 / 3 of the way by bus , and the remaining 12 kilometers by car . what is the distance , in kilometers , from the dormitory to the city ?
Options: a ) 30 , b ) 45 , c ) 60 , d ) 90 , e ) 120
Rationale: whole trip = distance by foot + distance by bus + distance by car x = 1 / 5 x + 2 / 3 x + 12 x - 13 / 15 x = 12 2 / 15 x = 12 = > so x = ( 15 / 2 ) * 12 = 90 km answer d
Answer: d
Problem: an error 3 % in excess is made while measuring the side of a square . the percentage of error in the calculated area of the square is :
Options: a ) 6.05 , b ) 6.09 , c ) 6.03 , d ) 6.02 , e ) 6.01
Rationale: "explanation : 100 cm is read as 103 cm . a 1 = ( 100 × 100 ) cm 2 = 10000 and a 2 = ( 103 × 103 ) cm 2 = 10609 ( a 2 - a 1 ) = 10609 - 10000 = 609 = > 609 / 10000 * 100 = 6.09 answer : b"
Answer: b
Problem: what is the sum of the first 30 odd natural numbers
Options: a ) 300 , b ) 400 , c ) 900 , d ) 600 , e ) 700
Rationale: sum of first n odd natural nuber is = n ^ 2 so sum of the first 30 odd natural numbers = ( 30 ) ^ 2 = 900 ans 900 answer : c
Answer: c
Problem: the l . c . m . of 2 numbers is 54 . the numbers are in the ratio 2 : 3 . find their sum ?
Options: a ) 36 , b ) 40 , c ) 45 , d ) 32 , e ) 56
Rationale: "let the numbers be 2 x and 3 x l . c . m . = 6 x 6 x = 54 x = 9 the numbers are = 18 and 27 required sum = 18 + 27 = 45 answer is c"
Answer: c
Problem: the ratio of investments of two partners p and q is 7 : 5 and the ratio of their profits is 7 : 10 . if p invested the money for 7 months , find for how much time did q invest the money ?
Options: a ) 11 , b ) 10 , c ) 18 , d ) 16 , e ) 14
Rationale: "7 * 5 : 7 * x = 7 : 10 x = 14 answer : e"
Answer: e
Problem: if x ^ 2 + 1 / x ^ 2 = √ 12 , what is the value of x ^ 4 + 1 / x ^ 4 ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "important : i notice that if we square x ² , we get x ⁴ , and if we square 1 / x ² , we get 1 / x ⁴ , so let ' s see what happens if we take the equation x ² + 1 / x ² = √ 12 andsquareboth sides : ( x ² + 1 / x ² ) ² = 12 so , ( x ² + 1 / x ² ) ( x ² + 1 / x ² ) = 12 expand to get : x ⁴ + 1 + 1 + 1 / x ⁴ = 12 simplify : x ⁴ + 1 / x ⁴ = 10 answer : a"
Answer: a
Problem: the ratio of 3 numbers is 5 : 3 : 4 and their sum is 108 . the second number of the 3 numbers is ?
Options: a ) 23 , b ) 27 , c ) 30 , d ) 32 , e ) 34
Rationale: 5 : 3 : 4 total parts = 12 12 parts - - > 108 1 part - - - - > 9 the second number of the three numbers is = 3 3 parts - - - - > 27 b )
Answer: b
Problem: a group of 55 adults and 70 children go for trekking . if there is meal for either 70 adults or 90 children and if 42 adults have their meal , find the total number of children that can be catered with the remaining food .
Options: a ) 33 , b ) 54 , c ) 36 , d ) 17 , e ) 01
Rationale: explanation : as there is meal for 70 adults and 42 have their meal , the meal left can be catered to 28 adults . now , 70 adults = 90 children 7 adults = 9 children therefore , 28 adults = 36 children hence , the meal can be catered to 36 children . answer : c
Answer: c
Problem: tom and john traveled in the same direction along the equal route at their constant speed rates of 15 km per hour and 10 km per hour , respectively . after 15 minutes tom passed john , tom reaches a certain gas station , how many w minutes it takes john to reach the station ?
Options: a ) 5 min , b ) 6 min , c ) 7 and 1 / 2 min , d ) 8 min , e ) 10 min
Rationale: since the question states “ after 15 minutes ” , we can say tom traveled 15 / 4 km for 15 minutes as he can travel 15 km per hour . hence , using the same logic , we can say john traveled 10 / 4 km as he travels 10 km per hour . so , john has to travel ( 15 / 4 ) - ( 10 / 4 ) km = 5 / 4 km more . since john ’ s speed is 10 km / hour , which means 1 km / 6 minutes . as he has to travel 5 / 4 km more , it is going to take him 6 ( 5 / 4 ) minutes . hence , w = 6 ( 5 / 4 ) = 15 / 2 minutes . the correct answer is c .
Answer: c
Problem: if 40 % of a number is equal to 2 / 3 of another number , what is the ratio of first number to the second number ?
Options: a ) 5 / 3 , b ) 3 / 5 , c ) 3 / 7 , d ) 5 / 7 , e ) 7 / 9
Rationale: "let 40 % of a = 2 / 3 b then , 40 * a / 100 = 2 * b / 3 a / b = 5 / 3 ans - a"
Answer: a
Problem: pipe a fills a tank in 20 minutes . pipe b can fill the same tank 4 times as fast as pipe a . if both the pipes are kept open when the tank is empty , how many minutes will it take to fill the tank ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "a ' s rate is 1 / 20 and b ' s rate is 1 / 5 . the combined rate is 1 / 20 + 1 / 5 = 1 / 4 the pipes will fill the tank in 4 minutes . the answer is c ."
Answer: c
Problem: in one alloy there is 12 % chromium while in another alloy it is 8 % . 20 kg of the first alloy was melted together with 35 kg of the second one to form a third alloy . find the percentage of chromium in the new alloy .
Options: a ) 9.45 % , b ) 10 % , c ) 15 % , d ) 20 % , e ) 25 %
Rationale: "the amount of chromium in the new 20 + 35 = 55 kg alloy is 0.12 * 20 + 0.08 * 35 = 5.2 kg , so the percentage is 5.2 / 55 * 100 = 9.2 % . answer : a ."
Answer: a
Problem: the number which exceeds 16 % of it by 42 is ?
Options: a ) 50 , b ) 25 , c ) 52 , d ) 58 , e ) 60
Rationale: "let the number be x . then , x - 16 % of x = 42 . x - 16 / 100 x = 42 x = ( 42 * 25 ) / 21 = 50 answer : a"
Answer: a
Problem: the units digit of ( 35 ) ^ ( 87 ) + ( 93 ) ^ ( 53 ) is :
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 0
Rationale: the units digit of powers of 3 , cycles in a group of 4 : { 3 , 9 , 7 , 1 } 53 has the form 4 k + 1 , so the units digit of 93 ^ 53 is 3 . the units digit of powers of 5 is always 5 . 3 + 5 = 8 , so the units digit is 8 . the answer is d .
Answer: d
Problem: in a graduating class , 40 percent of the students are male . in this class , 40 percent of the male students and 30 percent of the female students are 25 years old or older . if one student in the class is randomly selected , approximately what is the probability that he or she will be less than 25 years old ?
Options: a ) 0.66 , b ) 0.72 , c ) 0.78 , d ) 0.84 , e ) 0.9
Rationale: "let x be the total number of students . the number students who are younger than 25 is 0.6 * 0.4 x + 0.7 * 0.6 x = 0.66 x the answer is a ."
Answer: a
Problem: a number is doubled and 13 is added . if resultant is trebled , it becomes 93 . what is that number
Options: a ) 8 , b ) 9 , c ) 12 , d ) 14 , e ) 16
Rationale: "explanation : = > 3 ( 2 x + 13 ) = 93 = > 2 x + 13 = 31 = > x = 9 option b"
Answer: b
Problem: we define that k @ j is the product of j number from k in increasing order for positive integers k , j . for example , 6 @ 4 = 6 * 7 * 8 * 9 . if a = 2020 and b = 2120 , what is the value t of the ratio a / b ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 2 / 3 , d ) 1 / 4 , e ) 1 / 5
Rationale: "t - > a / b = 20 * 21 * … … * 39 / 21 * 22 * … . * 39 * 40 = 20 / 40 = 1 / 2 . therefore , the answer is a ."
Answer: a
Problem: a type of extra - large suv averages 12.2 miles per gallon ( mpg ) on the highway , but only 7.6 mpg in the city . what is the maximum distance , in miles , that this suv could be driven on 22 gallons of gasoline ?
Options: a ) 190 , b ) 284.6 , c ) 300 , d ) 268 , e ) 312
Rationale: "so 12.2 * 22 = 268 . . imo option d is correct answer . ."
Answer: d
Problem: a library has an average of 1000 visitors on sundays and 700 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is :
Options: a ) 740 , b ) 750 , c ) 760 , d ) 770 , e ) 775
Rationale: "explanation : since the month begins with a sunday , so there will be five sundays in the month , required average = ( 1000 * 5 + 700 * 25 ) / 30 = 22500 / 30 = 750 answer : b ) 750"
Answer: b
Problem: a man can row upstream at 12 kmph and downstream at 38 kmph , and then find the speed of the man in still water ?
Options: a ) 11 , b ) 25 , c ) 30 , d ) 88 , e ) 34
Rationale: "us = 12 ds = 38 m = ( 12 + 38 ) / 2 = 25 answer : b"
Answer: b
Problem: in a college the ratio of the numbers of boys to the girls is 8 : 5 . if there are 120 girls , the total number of students in the college is ?
Options: a ) 312 , b ) 356 , c ) 452 , d ) 416 , e ) 512
Rationale: let the number of boys and girls be 8 x and 5 x then , 5 x = 120 x = 24 total number of students = 13 x = 13 * 24 = 312 answer is a
Answer: a
Problem: there are 20 poles with a constant distance between each pole . a car takes 21 second to reach the 12 th pole . how much will it take to reach the last pole .
Options: a ) 36.4543 , b ) 36.2727 , c ) 31.45128 , d ) 36.41288 , e ) 31.41222
Rationale: "assuming the car starts at the first pole . to reach the 12 th pole , the car need to travel 11 poles ( the first pole does n ' t count , as the car is already there ) . 11 poles 21 seconds 1 pole ( 21 / 11 ) seconds to reach the last ( 20 th ) pole , the car needs to travel 19 poles . 19 pole 19 x ( 21 / 11 ) seconds = 36.2727 seconds answer : b"
Answer: b
Problem: noelle walks from point a to point b at an average speed of 3 kilometers per hour . at what speed , in kilometers per hour , must noelle walk from point b to point a so that her average speed for the entire trip is 5 kilometers per hour ?
Options: a ) 15 , b ) 12.5 , c ) 10 , d ) 8 , e ) 7.75
Rationale: let ' s suppose that speed while returning was xkm / h since the distance is same , we can apply the formula of avg speed avg speed = 2 s 1 s 2 / s 1 + s 2 5 = 2 * 3 * x / 3 + x x = 15 a is the answer
Answer: a
Problem: if 75 percent of a class answered the first question on a certain test correctly , 65 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ?
Options: a ) 10 % , b ) ( 8 ) 20 % , c ) 30 % , d ) 50 % , e ) 60 %
Rationale: "{ total } = { first } + { second } - { both } + { neither } 100 % = 75 % + 65 % - { both } + 20 % - - > { both } = 60 % . answer : e ."
Answer: e
Problem: two trains of equal lengths take 10 sec and 12 sec respectively to cross a telegraph post . if the length of each train be 120 m , in what time will they cross other travelling in opposite direction ?
Options: a ) 11 , b ) 12 , c ) 10.9 , d ) 14 , e ) 15
Rationale: "speed of the first train = 120 / 10 = 12 m / sec . speed of the second train = 120 / 12 = 10 m / sec . relative speed = 12 + 10 = 22 m / sec . required time = ( 120 + 120 ) / 22 = 10.9 sec . answer : option c"
Answer: c
Problem: the area of a triangle will be when a = 1 m , b = 1 m , c = 2 m , a , b , c being lengths of respective sides ?
Options: a ) 2 , b ) 7 , c ) 5 , d ) 3 , e ) 4
Rationale: "s = ( 1 + 1 + 2 ) / 2 = 2 answer : a"
Answer: a
Problem: the average weight of 19 students is 15 kg . by the admission of a new student the average weight is reduced to 14.6 kg . the weight of the new student is ?
Options: a ) 10.6 kg , b ) 10.8 kg , c ) 7 kg , d ) 14.9 kg , e ) none
Rationale: "answer weight of new student = total weight of all 20 students - total weight of initial 19 students = ( 20 x 14.6 - 19 x 15 ) kg = 7 kg . correct option : c"
Answer: c
Problem: how many two digit numbers are there such that the product of their digits after reducing it to the smallest form is a prime number ? for example if we take 98 then 9 * 8 = 72 , 72 = 7 * 2 = 14 , 14 = 1 * 4 = 4 . consider only 4 prime no . s ( 23 , 57 )
Options: a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 20
Rationale: we know prime no . are 2 , 3 , 5 , 7 mulply by 1 is prime no 2 = 21 ( 2 * 1 ) = 73 ( 7 * 3 ) 2 = 21 ( 2 * 1 ) = 37 ( 3 * 7 ) 2 = 12 ( 1 * 2 ) = 43 ( 4 * 3 ) or 34 ( 3 * 4 ) or 26 ( 2 * 6 ) or 62 ( 6 * 2 ) . . . similarly for all prime no then u will got it . . . . 12,13 , 15,17 , 21,26 , 31,34 , 35,37 , 43,51 , 53,57 , 62,71 , 73,75 ans is 18 answer : c
Answer: c
Problem: each of the integers from 1 to 16 is written on the a seperate index card and placed in a box . if the cards are drawn from the box at random without replecement , how many cards must be drawn to ensure that the product of all the integers drawn is even ?
Options: a ) 9 , b ) 12 , c ) 11 , d ) 10 , e ) 3
Rationale: "out of the 16 integers : 8 are odd and 8 are even . if we need to make sure that the product of all the integers withdrawn is even then we need to make sure that we have at least one even number . in the worst case : 1 . we will end up picking odd numbers one by one , so we will pick all 8 odd numbers first 2 . 9 th number will be the first even number so we need to withdraw at least 9 numbers to make sure that we get one even number and the product of all the integers picked is even . so , answer will be 9 . ( a )"
Answer: a
Problem: a taxi owner buys diesel at rs . 8.50 , rs . 9 and rs . 9.50 per litre for 3 successive years . what approximately is the average cost per litre of diesel if he spends rs . 5000 each year ?
Options: a ) 7.98 , b ) 8.98 , c ) 9.98 , d ) 6.98 , e ) 8.12
Rationale: total cost = 5000 × 3 = 15000 total diesel used = 5000 / 8.50 + 5000 / 9 + 5000 / 9.50 = 588 + 555 + 527 = 1670 average cost per litre of diesel = 15000 / 1670 = 8.98 answer : b
Answer: b
Problem: a man invests rs . 5,000 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 . 2500 , d ) rs . 2000 , e ) none of these
Rationale: "explanation : interest on rs . 5000 at 5 % per annum = ( 5000 × 5 × 1 ) / 100 = rs . 250 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 = ( 5000 + x ) × 6 × 1 / 100 . = > 250 + 2 x / 25 = ( 5000 + x ) × 6 × 1 / 100 . = > 25000 + 8 x = ( 5000 + x ) × 6 . = > 25000 + 8 x = 30000 + 6 x . = > 2 x = 5000 . = > x = 2500 . answer : c"
Answer: c
Problem: an ant walks an average of 500 meters in 12 minutes . a beetle walks 15 % less distance at the same time on the average . assuming the beetle walks at her regular rate , what is its speed in km / h ?
Options: a ) 2.215 , b ) 2.5 . , c ) 2.775 , d ) 3.2 , e ) 3.5
Rationale: "the ant walks an average of 500 meters in 12 minutes or , 500 meters in 1 / 5 hours the beetle walks 15 % less distance = 500 - 75 = 425 meters in 12 minutes or , 0.425 km in 12 / 60 = 1 / 5 hours speed = 0.425 * 5 = 2.125 km / h ans should be 2.125 answer : a"
Answer: a
Problem: when 1 / 10 percent of 5,000 is subtracted from 1 / 10 of 5,000 , the difference is
Options: a ) 0 , b ) 50 , c ) 450 , d ) 495 , e ) 500
Rationale: "1 / 10 of 5,000 is 500 ; 1 / 10 percent of 5,000 is 100 times smaller than the above , so it ' s 5 ; thus the difference is 500 - 5 = 495 . answer : d ."
Answer: d
Problem: what will be the fraction of 75 %
Options: a ) 3 / 4 , b ) 1 / 5 , c ) 1 / 10 , d ) 1 / 11 , e ) none of above
Rationale: "explanation : it will 75 * 1 / 100 = 3 / 4 option a"
Answer: a
Problem: what is the least number which should be added to 2782 so that the sum is exactly divisible by 5 , 6 , 4 , and 3 ?
Options: a ) 26 , b ) 32 , c ) 38 , d ) 46 , e ) 52
Rationale: "l . c . m . of 5 , 6 , 4 and 3 = 60 . when dividing 2782 by 60 , the remainder is 22 . the number to be added = 60 - 22 = 38 . the answer is c ."
Answer: c
Problem: how much is 35 % of 40 is greater than 4 / 5 of 25 ?
Options: a ) 29 , b ) 776 , c ) 66 , d ) 14 , e ) 99
Rationale: "( 80 / 100 ) * 40 – ( 4 / 5 ) * 25 35 - 20 = 14 answer : d"
Answer: d
Problem: two cyclist start from the same places in opposite directions . one is going towards north at 10 kmph and the other is going towards south 10 kmph . what time will they take to be 50 km apart ?
Options: a ) 1.2 hr , b ) 2.5 hrs , c ) 3 hrs , d ) 5.2 hrs , e ) 6 hrs
Rationale: "to be ( 10 + 10 ) km apart , they take 1 hour to be 50 km apart , they take 1 / 20 * 50 = 2.5 hrs answer is b"
Answer: b
Problem: the value of ( 0.2 × 0.2 + 0.01 ) ( 0.1 × 0.1 + 0.02 ) - 1 is equal to
Options: a ) 5 / 3 , b ) 9 / 5 , c ) 41 / 4 , d ) 41 / 12 , e ) none
Rationale: "solution given expression ( 0.2 × 0.2 + 0.01 ) / ( 0.1 × 0.1 × + 0.02 ) = 0.04 + 0.01 / 0.01 + 0.02 = 0.05 / 0.03 = 5 / 3 . answer a"
Answer: a
Problem: a person buys an article at rs . 620 . at what price should he sell the article so as to make a profit of 25 % ?
Options: a ) 600 , b ) 882 , c ) 775 , d ) 662 , e ) 521
Rationale: "cost price = rs . 620 profit = 25 % of 620 = rs . 155 selling price = cost price + profit = 620 + 155 = 775 answer : c"
Answer: c
Problem: the average of 10 numbers is 7 . if each number is multiplied by 10 , then what is the average of the new set of numbers ?
Options: a ) 7 , b ) 17 , c ) 70 , d ) 100 , e ) 107
Rationale: the sum of the ten numbers is 7 * 10 = 70 if each number is multiplied by 10 , the new sum is 10 * ( 70 ) . the average is then 10 * 7 = 70 the answer is c .
Answer: c
Problem: if xy = 25 , x / y = 36 , for positive numbers x and y , y = ?
Options: a ) 1 / 2 , b ) 2 , c ) 1 / 3 , d ) 3 , e ) 5 / 6
Rationale: "very easy question . 2 variables and 2 easy equations . xy = 25 - - - > x = 25 / y - ( i ) x / y = 36 - - - > replacing ( i ) here - - - > 25 / ( y ^ 2 ) = 36 - - - > y ^ 2 = 25 / 36 - - - > y = 5 / 6 or - 5 / 6 the question states that x and y are positive integers . therefore , y = 5 / 6 is the answer . answer e ."
Answer: e
Problem: there is a 20 % chance sandy will visit china this year , while there is a 70 % chance that she will visit malaysia this year . what is the probability that sandy will visit either china or malaysia this year , but not both ?
Options: a ) 44 % , b ) 48 % , c ) 54 % , d ) 62 % , e ) 70 %
Rationale: "p ( china and not malaysia ) = 0.2 * 0.3 = 0.06 p ( malaysia and not china ) = 0.7 * 0.8 = 0.56 total probability = 0.06 + 0.56 = 0.62 = 62 % the answer is d ."
Answer: d
Problem: if 80 percent of the test takers taking an old paper and pencil gmat exam answered the first question on a given math section correctly , and 75 percent of the test takers answered the second question correctly , and 5 percent of the test takers answered neither question correctly , what percent answered both correctly ?
Options: a ) 60 % , b ) 65 % , c ) 70 % , d ) 75 % , e ) 80 %
Rationale: "{ total } = { first correctly } + { second correctly } - { both correctly } + { neither correctly } 100 = 80 + 75 - { both correctly } + 5 { both correctly } = 60 . answer : a ."
Answer: a
Problem: dacid obtained 70 , 63 , 80 , 63 and 65 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 67 , b ) 26 , c ) 87 , d ) 26 , e ) 68
Rationale: "average = ( 70 + 63 + 80 + 63 + 65 ) / 5 = 341 / 5 = 68.2 . answer : e"
Answer: e
Problem: the jogging track in a sports complex is 1000 meters in circumference . deepak and his wife start from the same point and walk in opposite directions at 20 km / hr and 13 km / hr respectively . they will meet for the first time in ?
Options: a ) 50 min , b ) 33 min , c ) 35 min , d ) 25 min , e ) 20 min
Rationale: "clearly , the two will meet when they are 1000 m apart to be 20 + 13 = 33 km apart , they take 1 hour to be 1000 m apart , they take 33 * 1000 / 1000 = 33 min . answer is b"
Answer: b
Problem: at a recent small town election for mayor a total of 979 votes were cast for the 4 candidates , the winner exceeding his opponents by 53 , 79 and 105 votes , respectively . how many votes were cast for the candidate in fourth place ?
Options: a ) 134 , b ) 178 , c ) 199 , d ) 166 , e ) 194
Rationale: the number of votes the winning candidate received was 979 + 53 + 79 + 105 / 4 = 304 . the second received 304 – 53 = 251 the fourth place received 304 – 105 = 199 . c
Answer: c
Problem: a train 100 meters long completely crosses a 300 meters long bridge in 30 seconds . what is the speed of the train is ?
Options: a ) 32 kmph , b ) 48 kmph , c ) 34 kmph , d ) 43 kmph , e ) 40 kmph
Rationale: "s = ( 100 + 300 ) / 30 = 400 / 30 * 18 / 5 = 48 answer : b"
Answer: b
Problem: a man buys a cycle for rs . 1600 and sells it at a loss of 10 % . what is the selling price of the cycle ?
Options: a ) 1410 , b ) 1420 , c ) 1430 , d ) 1440 , e ) 1540
Rationale: "s . p . = 90 % of rs . 1600 = 90 / 100 x 1600 = rs . 1440 answer : d"
Answer: d