regisss/math_qa huggingface dataset:
Problem: a gardener wants to plant trees in his garden in such a way that the number of trees in each row should be the same . if there are 6 rows or 4 rows or 8 rows , then no tree will be left . find the least number of trees required
Options: a ) 24 , b ) 60 , c ) 28 , d ) 76 , e ) 21
Rationale: "explanation : the least number of trees that are required = lcm ( 6 , 4,8 ) = 24 answer : a"
Answer: a
Problem: a number is selected at random from the first 30 natural numbers . what is the probability that the number is a multiple of either 2 or 19 ?
Options: a ) 17 / 30 , b ) 2 / 5 , c ) 7 / 15 , d ) 8 / 15 , e ) 11 / 30
Rationale: "number of multiples of 2 from 1 through 30 = 30 / 2 = 15 number of multiples of 19 from 1 through 30 = 30 / 19 = 1 number of multiples of 2 and 19 both from 1 through 30 = number of multiples of 19 * 2 ( = 38 ) = 0 total favourable cases = 15 + 1 - 0 = 16 probability = 16 / 30 = 8 / 15 answer : option d"
Answer: d
Problem: the cash difference between the selling prices of an article at a profit of 6 % and 8 % is rs 3 . the ratio of two selling prices is
Options: a ) 51 : 52 , b ) 52 : 53 , c ) 53 : 54 , d ) 54 : 55 , e ) none of these
Rationale: "explanation : let the cost price of article is rs . x required ratio = ( 106 % of x ) / ( 108 % of x ) = 106 / 108 = 53 / 54 = 53 : 54 . answer : c"
Answer: c
Problem: working simultaneously and independently at an identical constant rate , 30 machines of a certain type can produce a total of x units of product p in 3 days . how many of these machines , working simultaneously and independently at this constant rate , can produce a total of 5 x units of product p in 10 days ?
Options: a ) 41 , b ) 44 , c ) 45 , d ) 47 , e ) 50
Rationale: "the rate of 30 machines is rate = job / time = x / 3 units per day - - > the rate of 1 machine 1 / 30 * ( x / 3 ) = x / 90 units per day ; now , again as { time } * { combined rate } = { job done } then 10 * ( m * x / 90 ) = 5 x - - > m = 45 . answer : c ."
Answer: c
Problem: 30 men shake hands with each other . maximum no of handshakes without cyclic handshakes .
Options: a ) 190 , b ) 200 , c ) 210 , d ) 220 , e ) 435
Rationale: "or , if there are n persons then no . of shakehands = nc 2 = 30 c 2 = 435 answer : e"
Answer: e
Problem: a car traveled 448 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city . if the car traveled 6 fewer miles per gallon in the city than on the highway , how many miles per gallon did the car travel in the city ?
Options: a ) 14 , b ) 18 , c ) 21 , d ) 22 , e ) 27
Rationale: "let the speed in highway be h mpg and in city be c mpg . h = c + 6 h miles are covered in 1 gallon 462 miles will be covered in 462 / h . similarly c miles are covered in 1 gallon 336 miles will be covered in 336 / c . both should be same ( as car ' s fuel capacity does not change with speed ) = > 336 / c = 448 / h = > 336 / c = 448 / ( c + 6 ) = > 336 c + 336 * 6 = 448 c = > c = 336 * 6 / 112 = 18 answer b ."
Answer: b
Problem: at what rate percent on simple interest will rs . 750 amount to rs . 950 in 5 years ?
Options: a ) 3.33 % , b ) 5.93 % , c ) 4.33 % , d ) 5.33 % , e ) 6.33 %
Rationale: "200 = ( 750 * 5 * r ) / 100 r = 5.33 % answer : d"
Answer: d
Problem: from the sale of sleeping bags , a retailer made a gross profit of 15 % of the wholesale cost . if each sleeping bag was sold for $ 28 , what was the wholesale cost per bag ?
Options: a ) 3.0 , b ) 3.36 , c ) 24.34 , d ) 25.0 , e ) 31.36
Rationale: "cost price * 1.15 = selling price - - > cost price * 1.15 = $ 28 - - > cost price = $ 24.34 . answer : c ."
Answer: c
Problem: find 40 % of 240
Options: a ) 96 , b ) 94 , c ) 86 , d ) 74 , e ) 110
Rationale: "we know that r % of m is equal to r / 100 × m . so , we have 40 % of 240 40 / 100 × 240 = 96 answer : a"
Answer: a
Problem: sara bought both german chocolate and swiss chocolate for some cakes she was baking . the swiss chocolate cost $ 3.5 per pound , and german chocolate cost $ 2.5 per pound . if the total the she spent on chocolate was $ 70 and both types of chocolate were purchased in whole number of pounds , how many total pounds of chocolate she purchased ?
Options: a ) 7 , b ) 8 , c ) 10 , d ) 24 , e ) 15
Rationale: if there were all the expensive ones , 3.5 . . . . there would be 70 / 3.5 or 20 of them but since 2.5 $ ones are also there , answer has to be > 20 . . . . if all were 2.5 $ ones , there will be 70 / 2.5 or 28 . . so only 24 is left ans d . .
Answer: d
Problem: two men start from opposite banks of a river . they meet 340 meters away from one of the banks on forward journey . after that they meet at 170 meters from the other bank of the river on their backward journey . what will be the width of the river ( in meters ) ?
Options: a ) 750 , b ) 850 , c ) 900 , d ) 980 , e ) 950
Rationale: let p , q are two persons then their speeds be a , b - > m / hr x - - - - 340 - - - - - - - - - - - - - - - - - - - - - - | - - - ( d - 340 ) - - - - - - - - - y in forward journey time taken by p = 340 / a ; time taken by q = d - 340 / b ; in forward journey , time taken by p = time taken by q so 340 / a = d - 340 / b a / b = 340 / d - 340 - - - - - - - - - - - - ( 1 ) after that they continue their journeyand reach other banks now in backward journey , x - - - - - - - - - - - - - - - ( d - 170 ) - - - - - - - - - - - - - - - - - - - - - - - - - - | - - - - - 170 - - - - - - y distance travelled by p from meet 1 to meet 2 = ( d - 340 ) + 170 distance travelled by p from meet 1 to meet 2 = 340 + ( d - 170 ) now time taken by p = time taken by q ( d - 340 ) + 170 / a = 340 + ( d - 170 ) / b ( d - 340 ) + 170 / 340 + ( d - 170 ) = a / b - - - - - - - - - ( 2 ) from 1 & 2 340 / ( d - 340 ) = ( d - 340 ) + 170 / 340 + ( d - 170 ) 340 / ( d - 340 ) = d - 170 / d + 170 340 d + 57800 = d ^ 2 - 340 d - 170 d + 57800 340 d = d ^ 2 - 510 d d ^ 2 - 850 d = 0 d ( d - 850 ) = 0 d = 0 ord = 850 so width of the river is 850 answer : b
Answer: b
Problem: if the number is decreased by 5 and divided by 7 the result is 7 . what would be the result if 34 is subtracted and divided by 10 ?
Options: a ) 4 , b ) 7 , c ) 8 , d ) 2 , e ) 3
Rationale: "explanation : let the number be x . then , ( x - 5 ) / 7 = 7 = > x - 5 = 49 x = 54 . : ( x - 34 ) / 10 = ( 54 - 34 ) / 10 = 2 answer : option d"
Answer: d
Problem: a 160 meter long train crosses a man standing on the platform in 9 sec . what is the speed of the train ?
Options: a ) 96 kmph , b ) 64 kmph , c ) 52 kmph , d ) 86 kmph , e ) 76 kmph
Rationale: "s = 160 / 9 * 18 / 5 = 64 kmph answer : b"
Answer: b
Problem: the difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4 % per annum is re . 1 . the sum ( in rs . ) is ?
Options: a ) 625 , b ) 827 , c ) 657 , d ) 726 , e ) 634
Rationale: "let the sum be rs . x . then , [ x ( 1 + 4 / 100 ) 2 - x ] = ( 676 / 625 x - x ) = 51 / 625 x s . i . = ( x * 4 * 2 ) / 100 = 2 x / 25 51 x / 625 - 2 x / 25 = 1 or x = 625 . answer : a"
Answer: a
Problem: how many pieces of 0.85 metres can be cut from a rod 42.5 metres long ?
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70
Rationale: "number of pieces = 42.5 / 0.85 = 42.50 / 0.85 = 4250 / 85 = 50 . answer : c"
Answer: c
Problem: 60 % of a number is added to 160 , the result is the same number . find the number ?
Options: a ) 300 , b ) 400 , c ) 266 , d ) 99 , e ) 121
Rationale: ": ( 60 / 100 ) * x + 160 = x 2 x = 800 x = 400 answer : b"
Answer: b
Problem: difference of 2 numbers is 1660 . if 7.5 % of one number is 12.5 % of the other number , find the 2 numbers ?
Options: a ) 125,150 , b ) 5124,4515 , c ) 4150,2490 , d ) 3250,4510 , e ) 1254,3210
Rationale: "let the numbers be x and y 7.5 % of x = 12.5 % of y x = 125 y / 75 = 5 y / 3 x - y = 1660 5 y / 3 - y = 1660 y = 2490 x = 5 y / 3 = 4150 answer is c"
Answer: c
Problem: an optometrist charges $ 150 per pair for soft contact lenses and $ 85 per pair for hard contact lenses . last week she sold 5 more pairs of soft lenses than hard lenses . if her total sales for pairs of contact lenses last week were $ 2,395 , what was the total number of pairs of contact lenses that she sold ?
Options: a ) 11 , b ) 13 , c ) 15 , d ) 17 , e ) 19
Rationale: "( x + 5 ) * 150 + x * 85 = 2395 = > x = 7 total lens = 7 + ( 7 + 5 ) = 19 answer e"
Answer: e
Problem: cole drove from home to work at an average speed of 75 kmh . he then returned home at an average speed of 105 kmh . if the round trip took a total of 1 hours , how many minutes did it take cole to drive to work ?
Options: a ) 35 , b ) 50 , c ) 62 , d ) 75 , e ) 78
Rationale: "first round distance travelled ( say ) = d speed = 75 k / h time taken , t 2 = d / 75 hr second round distance traveled = d ( same distance ) speed = 105 k / h time taken , t 2 = d / 105 hr total time taken = 1 hrs therefore , 1 = d / 75 + d / 105 lcm of 75 and 105 = 525 1 = d / 75 + d / 105 = > 1 = 7 d / 525 + 5 d / 525 = > d = 525 / 12 km therefore , t 1 = d / 75 = > t 1 = 525 / ( 12 x 75 ) = > t 1 = ( 7 x 60 ) / 12 - - in minutes = > t 1 = 35 minutes . a"
Answer: a
Problem: sum of the squares of 3 no . ' s is 179 and the sum of their products taken two at a time is 131 . find the sum ?
Options: a ) 20 , b ) 21 , c ) 26 , d ) 28 , e ) 30
Rationale: "( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 179 + 2 * 131 a + b + c = √ 441 = 21 b"
Answer: b
Problem: if 20 % of 30 is greater than 25 % of a number by 2 , the number is :
Options: a ) 16 , b ) 24 , c ) 20 , d ) 32 , e ) none of these
Rationale: explanation : = > 20 / 100 * 30 - 25 / 100 * x = 2 = > x / 4 = 4 so x = 16 answer : a
Answer: a
Problem: how many positive integers less than 5000 are evenly divisible by neither 15 nor 23 ?
Options: a ) 4,514 , b ) 4,475 , c ) 4,521 , d ) 4,428 , e ) 4,349
Rationale: integers less than 5000 divisible by 15 5000 / 15 = 333 . something , so 333 integers less than 5000 divisible by 23 5000 / 23 = 238 . # # , so 238 we have double counted some , so take lcm of 15 and 23 = 105 and divide by 5000 , we get 47 . so all numbers divisible by 15 and 23 = 333 + 238 - 47 = 524 now subtract that from 4999 . 4999 - 524 = 4521 answer c .
Answer: c
Problem: p alone can complete a job in 12 days . the work done by q alone in one day is equal to one - half of the work done by p alone in one day . in how many days can the work be completed if p and q work together ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "p ' s rate is 1 / 12 q ' s rate is 1 / 24 the combined rate is 1 / 12 + 1 / 24 = 1 / 8 if they work together , the job will take 8 days . the answer is d ."
Answer: d
Problem: suzie ’ s discount footwear sells all pairs of shoes for one price and all pairs of boots for another price . on monday the store sold 22 pairs of shoes and 16 pairs of boots for $ 460 . on tuesday the store sold 8 pairs of shoes and 32 pairs of boots for $ 560 . how much more do pairs of boots cost than pairs of shoes at suzie ’ s discount footwear ?
Options: a ) 15 , b ) 18 , c ) 21 , d ) 23 , e ) 25
Rationale: let x be pair of shoes and y be pair of boots . 22 x + 16 y = 460 . . . eq 1 8 x + 32 y = 560 . . . . eq 2 . now multiply eq 1 by 2 and sub eq 2 . 44 x = 920 8 x = 560 . 36 x = 360 = > x = 10 . sub x in eq 2 . . . . we get 80 + 32 y = 560 . . . then we get 32 y = 480 then y = 25 differenece between x and y is 15 answer : a
Answer: a
Problem: if ( a + b ) = 4 , ( b + c ) = 9 and ( c + d ) = 3 , what is the value of ( a + d ) ?
Options: a ) 16 . , b ) 8 . , c ) 7 , d ) 2 . , e ) - 2
Rationale: "given a + b = 4 = > a = 4 - b - - > eq 1 b + c = 9 c + d = 3 = > d = 3 - c - - > eq 2 then eqs 1 + 2 = > a + d = 4 - b + 3 - c = > 7 - ( b + c ) = > 7 - 9 = - 2 . option e . . ."
Answer: e
Problem: the difference between a 8 digit number and the number formed by reversing its digit is not a multiple of
Options: a ) 3 , b ) 5 , c ) 296297 , d ) 888891 , e ) 2666673
Rationale: "another approach is to test a number . let ' s say the original number is 12000002 so , the reversed number is 20000021 the difference = 20000021 - 12000002 = 8000019 no check the answer choices 8000019 is a multiple of 3,296297 , 888891,2666673 5 is not a multiple of 8000019 answer ; b"
Answer: b
Problem: a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 27 , then how old is b ?
Options: a ) 11 years , b ) 10 years , c ) 18 years , d ) 189 years , e ) 28 years
Rationale: "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 27 5 x = 25 = > x = 5 hence , b ' s age = 2 x = 10 years . answer : b"
Answer: b
Problem: 15 51 216 1100 ? 46452
Options: a ) 6630 , b ) 6650 , c ) 6560 , d ) 6530 , e ) none of these
Rationale: "the format of the series 15 * 3 + 6 = 51 51 * 4 + 12 = 216 216 * 5 + 20 = 1100 1100 * 6 + 30 = 6630 6630 * 7 + 42 = 46452 answer : a"
Answer: a
Problem: if a * b denotes the greatest common divisor of a and b , then ( ( 12 * 15 ) * ( 18 * 24 ) ) = ?
Options: a ) 24 , b ) 12 , c ) 6 , d ) 4 , e ) 3
Rationale: "the greatest common divisor of 12 and 15 is 3 . hence 12 * 15 = 3 ( note that * here denotes the function not multiplication ) . the greatest common divisor of 18 and 24 is 6 . hence 18 * 24 = 6 . hence ( ( 12 * 16 ) * ( 18 * 24 ) ) = 3 * 6 . the greatest common divisor of 3 and 6 is 3 . answer ; e ."
Answer: e
Problem: what annual installment will discharge a debt of rs . 1260 due in 3 years at 12 % simple interest ?
Options: a ) 315 , b ) 345 , c ) 325 , d ) 375 , e ) none of them
Rationale: "let each installment be rs . x then , ( x + ( ( x * 12 * 1 ) / 100 ) ) + ( x + ( ( x * 12 * 2 ) / 100 ) ) + x = 1260 = ( ( 28 x / 25 ) + ( 31 x / 25 ) + x ) = 1260 ï ƒ › ( 28 x + 31 x + 25 x ) = ( 1260 * 25 ) x = ( 1260 * 25 ) / 84 = rs . 375 . therefore , each installment = rs . 375 . answer is d ."
Answer: d
Problem: what is the sum of all even numbers from 1 to 801 ?
Options: a ) 160400 , b ) 281228 , c ) 281199 , d ) 122850 , e ) 128111
Rationale: "explanation : 800 / 2 = 400 400 * 401 = 160400 answer : a"
Answer: a
Problem: there are 225 female managers in a certain company . find the total number of female employees in the company , if 2 / 5 of all the employees are managers and 2 / 5 of all male employees are managers .
Options: a ) 300 , b ) 400 , c ) 562.5 , d ) 600 , e ) none of these
Rationale: as per question stem 2 / 5 m ( portion of men employees who are managers ) + 225 ( portion of female employees who are managers ) = 2 / 5 t ( portion of total number of employees who are managers ) , thus we get that 2 / 5 m + 225 = 2 / 5 t , or 2 / 5 ( t - m ) = 225 , from here we get that t - m = 562.5 , that would be total number of female employees and the answer ( c )
Answer: c
Problem: if a randomly selected non - negative single digit integer is added to { 2 , 3 , 4 , 8 } . what is the probability that the median of the set will increase but the range still remains the same ?
Options: a ) 0.2 , b ) 0.3 , c ) 0.4 , d ) 0.5 , e ) 0.6
Rationale: "we are selecting from non - negative single digit integers , so from { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } . these 10 digits represent the total number of outcomes . hence , the total number of outcomes is 10 . we need to find the probability that the median of the set will increase but the range still remains the same . the median of the set is ( 3 + 4 ) / 2 = 3.5 , thus the number selected must be 4 or greater . for the range to remain the same , the number must be between 2 and 8 inclusive . to satisfy both conditions , the number selected must be 4 , 5 , 6 , 7 , or 8 . the probability is 5 / 10 = 0.5 the answer is d ."
Answer: d
Problem: a school has received 60 % of the amount it needs for a new building by receiving a donation of $ 300 each from people already solicited . people already solicited represent 40 % of the people from whom the school will solicit donations . how much average contribution is requited from the remaining targeted people to complete the fund raising exercise ?
Options: a ) $ 200 , b ) $ 177.78 , c ) $ 100 , d ) $ 277.78 , e ) $ 377.78
Rationale: "let the amount school needs = x let total people school plans to solicit = t school has received 60 % of x = > ( 3 / 5 ) x people already solicited = 40 % of t = > ( 2 / 5 ) t now , as per the information given in the question : ( 3 / 5 ) x = $ 400 . ( 2 / 5 ) . t - - - - - - - - - - - - - - - - - - - - - - - - - - - 1 remaning amount is 40 % i . e ( 2 / 5 ) x - - - - - - because school has already received 60 % and the remaining people are 60 % i . e ( 3 / 5 ) . t - - - - - because 40 % of the people are already solicited so , average contribution required from the remaining targeted people is ( 2 / 5 ) x = ( amount required ) . ( 3 / 5 ) . t - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 2 divide eqn 1 by eqn 2 amount required = $ 177.78 b"
Answer: b
Problem: how many prime numbers are between 15 / 7 and 131 / 6 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "15 / 7 = 3 - 131 / 6 = 22 - prime numbers between 3 and 22 are 5 , 7 , 11 , 13 , 17 , and 19 - sign signifies that the number is marginally less . answer d"
Answer: d
Problem: a can do a job in 18 days and b can do it in 30 days . a and b working together will finish twice the amount of work in days ?
Options: a ) 29 ½ days , b ) 22 ½ days , c ) 92 ½ days , d ) 28 ½ days , e ) 92 ½ days
Rationale: "1 / 18 + 1 / 30 = 8 / 90 = 4 / 45 45 / 4 = 11 ¼ * 2 = 22 ½ days answer : b"
Answer: b
Problem: the cost of manufacturing a popular model car is made up of 3 items : cost of raw material , labour and overheads - in a year the cost of 3 items were in the ration of 4 : 3 : 2 . next year the cost of the raw material rose by 10 % , labour cost increased by 8 % but overhead reduced by 5 % . then % increase int the price of the car ?
Options: a ) 7.67 % , b ) 6 % , c ) 0.54 % , d ) 9.54 % , e ) 8.54 %
Rationale: before increase total cost = 4 + 3 + 2 = 9 , after increasing the cost = 9.54 so increase of . 54 over 9 , equal to 6 % answer : b
Answer: b
Problem: two trains a and b starting from two points and travelling in opposite directions , reach their destinations 9 hours and 4 hours respectively after meeting each other . if the train a travels at 90 kmph , find the rate at which the train b runs .
Options: a ) 40 , b ) 60 , c ) 135 , d ) 80 , e ) 100
Rationale: "if two objects a and b start simultaneously from opposite points and , after meeting , reach their destinations in ‘ a ’ and ‘ b ’ hours respectively ( i . e . a takes ‘ a hrs ’ to travel from the meeting point to his destination and b takes ‘ b hrs ’ to travel from the meeting point to his destination ) , then the ratio of their speeds is given by : sa / sb = √ ( b / a ) i . e . ratio of speeds is given by the square root of the inverse ratio of time taken . sa / sb = √ ( 4 / 9 ) = 2 / 3 this gives us that the ratio of the speed of a : speed of b as 2 : 3 . since speed of a is 80 kmph , speed of b must be 80 * ( 3 / 2 ) = 135 kmph c"
Answer: c
Problem: a vessel of capacity 90 litres is fully filled with pure milk . nine litres of milk is removed from the vessel and replaced with water . nine litres of the solution thus formed is removed and replaced with water . find the quantity of pure milk in the final milk solution ?
Options: a ) 73.9 , b ) 72.9 , c ) 73.0 , d ) 73.5 , e ) 92.2
Rationale: "let the initial quantity of milk in vessel be t litres . let us say y litres of the mixture is taken out and replaced by water for n times , alternatively . quantity of milk finally in the vessel is then given by [ ( t - y ) / t ] n * t for the given problem , t = 90 , y = 9 and n = 2 . hence , quantity of milk finally in the vessel = [ ( 90 - 9 ) / 90 ] 2 ( 90 ) = 72.9 litres . answer : option b"
Answer: b
Problem: 377 ÷ 13 ÷ 29 × 1 / 4 ÷ 2 = ?
Options: a ) 1 / 6 , b ) 1 / 8 , c ) 1 / 10 , d ) 1 / 12 , e ) 1 / 15
Rationale: explanation : 377 ÷ 13 ÷ 29 × 1 / 4 ÷ 2 = ? = > ? = ( 337 / ( 13 × 29 × 4 × 2 ) ) = 1 / 8 answer : option b
Answer: b
Problem: if x = 2 ^ 8 and x ^ x = 2 ^ k , what is k ?
Options: a ) 2 ^ 15 , b ) 2 ^ 14 , c ) 2 ^ 13 , d ) 2 ^ 12 , e ) 2 ^ 11
Rationale: "solution : we know that x = 2 ^ 8 which implies x ^ x = ( 2 ^ 8 ) ^ ( 2 ^ 8 ) = 2 ^ ( 8 * 2 ^ 8 ) [ because ( x ^ y ) ^ z = x ^ ( y * z ) ) ] so 2 ^ ( 2 ^ 3 * 2 ^ 8 ) = 2 ^ ( 2 ^ ( 3 + 8 ) ) [ because x ^ a * x ^ b = x ^ ( a + b ) ] therefore x ^ x = 2 ^ ( 2 ^ 11 ) given that x ^ x = 2 ^ k so 2 ^ ( 2 ^ 11 ) = 2 ^ k since the base is same the exponent will also be same therefore k = 2 ^ 11 answer : e"
Answer: e
Problem: if 11.25 m of a uniform steel rod weighs 42.75 kg . what will be the weight of 6 m of the same rod ?
Options: a ) 22.8 kg , b ) 25.6 kg , c ) 28 kg , d ) 26.5 kg , e ) none of these
Rationale: "explanation : let the required weight be x kg . then , less length , less weight ( direct proportion ) = > 11.25 : 6 : : 42.75 : x = > 11.25 x x = 6 x 42.75 = > x = ( 6 x 42.75 ) / 11.25 = > x = 22.8 answer : a"
Answer: a
Problem: david obtained 70 , 60 , 78 , 60 and 65 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology what are his average marks ?
Options: a ) 75 , b ) 27.6 , c ) 66.6 , d ) 16.5 , e ) 11
Rationale: "explanation : average = ( 70 + 60 + 78 + 60 + 65 ) / 5 = 333 / 5 = 66.6 . answer : c"
Answer: c
Problem: a car drives 60 miles on local roads at 30 mph , and 65 miles on the highway at 65 mph , what is the average speed of the entire trip ?
Options: a ) 36 mph , b ) 40 mph , c ) 44 mph , d ) 42 mph , e ) 58 mph
Rationale: "so the answer is plainly d . . . . we have a general relation for speed , time and distance : v ( velocity ) * t ( time ) = d ( distance ) for first part we have d = 60 miles , and v = 30 mph so we can obtain time : 30 * t = 60 or t = 60 / 30 = 2 hours the needed time to cover 60 miles in the same way we should divide 65 by 65 to find the needed time to cover 65 miles , so t = 1 hours so the total time for covering total distance would be 2 + 1 = 3 hours and total distance is 60 + 65 = 125 miles final stage : average speed is total distance divide to total time : 125 / 3 = 41.6 miles per hour that rounds up to 42 . . . ."
Answer: d
Problem: set a consists of the integers from 4 to 15 , inclusive , while set b consists of the integers from 7 to 20 , inclusive . how many distinct integers do belong to the both sets at the same time ?
Options: a ) 5 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "a = { 4 , 5,6 , 7,8 , 9,10 , 11,12 } b = { 6 , 7,8 , 9,10 , 11,12 . . . } thus we see that there are 9 distinct integers that are common to both . d is the correct answer ."
Answer: d
Problem: the length of the bridge , which a train 120 metres long and travelling at 45 km / hr can cross in 30 seconds , is :
Options: a ) 230 , b ) 240 , c ) 245 , d ) 255 , e ) 260
Rationale: "speed = [ 45 x 5 / 18 ] m / sec = [ 25 / 2 ] m / sec time = 30 sec let the length of bridge be x metres . then , ( 120 + x ) / 30 = 25 / 2 = > 2 ( 120 + x ) = 750 = > x = 255 m . answer : option d"
Answer: d
Problem: the length of a rectangle is halved while its width is also halved . what is the % change in area ?
Options: a ) 25 % , b ) 30 % , c ) 50 % , d ) 65 % , e ) 75 %
Rationale: "the original area is l * w the new area is 0.5 l * 0.5 w = 0.25 * l * w = l * w - 0.75 * l * w the area decreased by 75 % . the answer is e ."
Answer: e
Problem: the floor of a rectangular room is 15 m long and 12 m wide . the room is surrounded by a verandah of width 2 m on all its sides . the area of the verandah is :
Options: a ) 124 m 2
b ) 120 m 2
c ) 108 m 2
d ) 58 m 2
e ) none of these
Rationale: area of the outer rectangle = 19 × 16 = 304 m 2 area of the inner rectangle = 15 × 12 = 180 m 2 required area = ( 304 – 180 ) = 124 m 2 answer a
Answer: a
Problem: a , band c enter into partnership . a invests 3 times as much as b and b invests two - third of what c invests . at the end of the year , the profit earned is rs . 6600 . what is the share of b ?
Options: a ) 1100 , b ) 800 , c ) 1400 , d ) 1200 , e ) none of them
Rationale: "let c ' s capital = rs . x . then , b ' s capital = rs . ( 2 / 3 ) x a ’ s capital = rs . ( 3 x ( 2 / 3 ) . x ) = rs . 2 x . ratio of their capitals = 2 x : ( 2 / 3 ) x : x = 6 : 2 : 3 . hence , b ' s share = rs . ( 6600 x ( 2 / 11 ) ) = rs . 1200 . answer is d ."
Answer: d
Problem: a reduction of 40 % in the price of apples would enable a man to obtain 64 more for rs . 40 , what is reduced price per dozen ?
Options: a ) 1 , b ) 3 , c ) 6 , d ) 7 , e ) 10
Rationale: "b 40 * ( 40 / 100 ) = 16 - - - 64 ? - - - 12 = > rs . 3"
Answer: b
Problem: a , b , c , d and e are 5 consecutive points on a straight line . if bc = 3 cd , de = 7 , ab = 5 and ac = 11 , what is the length of ae ?
Options: a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: ac = 11 and ab = 5 , so bc = 6 . bc = 3 cd so cd = 2 . the length of ae is ab + bc + cd + de = 5 + 6 + 2 + 7 = 20 the answer is c .
Answer: c
Problem: a tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume . if 3,000 gallons of water evaporate from the tank , the remaining solution will be approximately what percent sodium chloride ?
Options: a ) 6.28 % , b ) 7.14 % , c ) 7.86 % , d ) 8.25 % , e ) 8.63 %
Rationale: "the amount of sodium chloride is 0.05 * 10,000 = 500 gallons 500 / 7000 = 1 / 14 which is about 7.14 % the answer is b ."
Answer: b
Problem: if a : b : : 3 : 7 , then what is ( 5 a + 6 b ) : ( a - 4 b ) ?
Options: a ) 57 : 11 , b ) - 57 : 11 , c ) 11 : 10 , d ) - 57 : 25 , e ) - 1 : 10
Rationale: "a / b = 3 / 7 dividing numerator & denominator of ' ( 5 a + 6 b ) / ( a - 2 b ) ' by b , [ 5 ( a / b ) + 6 ] / [ ( a / b ) - 4 ] = [ 5 * ( 3 / 7 ) + 6 ] / [ ( 3 / 7 ) - 4 ] = - 57 / 25 answer : d"
Answer: d
Problem: of 3 numbers , the third is 4 times the second and the second is two times the first . if their average is 165 , the second number of the 3 numbers is :
Options: a ) 18 , b ) 100 , c ) 90 , d ) 45 , e ) 120
Rationale: explanation : let first number be x . so , 2 nd no . = 2 x & 3 rd no . = 8 x . so , x + 2 x + 8 x = 165 × 3 = 495 11 x = 495 / 11 x = 495 / 11 hence , first number is x = 45 so , second number is = 2 x 45 = 90 answer : c
Answer: c
Problem: the side of a rhombus is 20 m and length of one of its diagonals is 16 m . the area of the rhombus is ?
Options: a ) 223.28 , b ) 293.28 , c ) 293.78 , d ) 291.28 , e ) 193.28
Rationale: "area of the rhombus = 1 / 2 * p * √ 4 ( a ) 2 - ( p ) 2 a = 20 ; p = 16 a = 1 / 2 * 16 * √ 4 ( 20 ) 2 - ( 16 ) 2 = 1 / 2 * 16 * √ 1600 - 256 = 1 / 2 * 16 * √ 1344 a = 293.28 answer : b"
Answer: b
Problem: in a certain company , a third of the workers do not have a retirement plan . 20 % of the workers who do not have a retirement plan are women , and 50 % of the workers who do have a retirement plan are men . if 120 of the workers of that company are men , how many of the workers are women ?
Options: a ) 80 , b ) 95 , c ) 105 , d ) 120 , e ) 210
Rationale: "20 % of the workerswithoutretirement plan are women , this means 80 % of the workerswithoutretirement plan are men right ? makes 100 % = no retirement plan . then 40 % of those wo have a retirement plan are men , which means 60 % of those who have a retirement plan are women . these percentages are always refering to the subgroupsretirement plan = yesandno retirement plan . make the total workers equal x and work from there and it should be fine > x / 3 have no retirement plan at all . i struggled with the question a lot , it was hard for me although usually i have no problems with sets questions like this . i believe it must be a 700 + question . yes , you are right . i read the question incorrectly ! i glazed overnotfor some reason . if 20 % of the workers who do not have a retirement plan are women , 80 % who do not have retirement plan are men . also 40 % who do have retirement plan are men . since 1 / 3 do not have retirement plan and 2 / 3 do have , it becomes a simple weighted average question . cavg = ( 80 * 1 + 50 * 2 ) / 3 = 60 % are men total = 120 * 100 / 60 = 200 no . of women = 200 - 120 = 80 a"
Answer: a
Problem: how many seconds will a train 70 meters long take to cross a bridge 80 meters long if the speed of the train is 36 kmph ?
Options: a ) 22 sec , b ) 27 sec , c ) 25 sec , d ) 15 sec , e ) 11 sec
Rationale: "explanation : d = 70 + 80 = 150 s = 36 * 5 / 18 = 10 mps t = 150 / 10 = 15 sec answer : option d"
Answer: d
Problem: for the past n days , the average ( arithmetic mean ) daily production at a company was 30 units . if today ' s production of 90 units raises the average to 35 units per day , what is the value of n ?
Options: a ) 30 , b ) 18 , c ) 10 , d ) 9 , e ) 3
Rationale: "( average production for n days ) * n = ( total production for n days ) - - > 30 n = ( total production for n days ) ; ( total production for n days ) + 90 = ( average production for n + 1 days ) * ( n + 1 ) - - > 30 n + 90 = 35 * ( n + 1 ) - - > n = 3 . answer : e ."
Answer: e
Problem: how many unique positive odd integers less than 80 are equal to the product of a positive multiple of 5 and an odd number ?
Options: a ) 4 , b ) 8 , c ) 11 , d ) 12 , e ) 15
Rationale: "the question basically asks how many positive odd integers less than 80 are odd multiples of 5 so we have 5,15 , 25,35 , 45,55 , 65,75 = 8 b"
Answer: b
Problem: there were two candidates in an election . winner candidate received 70 % of votes and won the election by 280 votes . find the number of votes casted to the winning candidate ?
Options: a ) 228 , b ) 744 , c ) 490 , d ) 199 , e ) 231
Rationale: "w = 70 % l = 30 % 70 % - 30 % = 40 % 40 % - - - - - - - - 280 70 % - - - - - - - - ? = > 280 / 40 * 70 = 490 answer : c"
Answer: c
Problem: add 16 % of 36 and 13 % of 45 .
Options: a ) 9.5 , b ) 8.5 , c ) 7.2 , d ) 7 , e ) 8
Rationale: "16 % of 36 + 13 % of 45 36 * 16 / 100 + 45 * 13 / 100 5.8 + 1.4 = 7.2 answer c"
Answer: c
Problem: a is 30 % more efficient than b . how much time will they , working together , take to complete a job which a alone could have done in 23 days ?
Options: a ) 11 days , b ) 13 days , c ) 20 3 / 17 days , d ) 21 days , e ) none of these
Rationale: "explanation : ratio of times taken by a and b = 100 : 130 = 10 : 13 suppose b takes x days to do the work . x = ( 23 * 13 ) / 10 = 299 / 10 a ' s 1 day work = 1 / 23 ; b ' s 1 day work = 10 / 299 ( a + b ) ' s 1 day work = ( 1 / 23 + 10 / 299 ) = 1 / 13 a and b together can complete the job in 13 days . answer is b"
Answer: b
Problem: suresh started a business , investing rs . 18000 . after 3 months and 4 months respectively , rohan and sudhir joined him with capitals of 12000 and 9000 . at the end of the year the total profit was rs . 3850 . what is the difference between rohan ’ s and sudhir ’ s share in the profit ?
Options: a ) s . 345 , b ) s . 350 , c ) s . 352 , d ) s . 362 , e ) s . 368
Rationale: suresh : rohan : sudhir ratio of their investments = 18000 × 12 : 12000 × 9 : 9000 × 8 = 6 : 3 : 2 the difference between rohan ’ s and sudhir ’ s share = 1 share : . i . e . = rs . 3850 × 1 / 11 = rs . 350 . b
Answer: b
Problem: a train passes a station platform in 36 sec and a man standing on the platform in 20 sec . if the speed of the train is 72 km / hr . what is the length of the platform ?
Options: a ) 229 , b ) 240 , c ) 288 , d ) 277 , e ) 320
Rationale: "speed = 72 * 5 / 18 = 20 m / sec . length of the train = 20 * 20 = 400 m . let the length of the platform be x m . then , ( x + 400 ) / 36 = 20 = > x = 320 m . answer : e"
Answer: e
Problem: in a certain city , 60 percent of the registered voters are democrats and the rest are republicans . in a mayoral race , if 75 percent of the registered voters who are democrats and 20 percent of the registered voters who are republicans are expected to vote for candidate a , what percent of the registered voters are expected to vote for candidate a ?
Options: a ) 50 % , b ) 53 % , c ) 54 % , d ) 55 % , e ) 57 %
Rationale: "registered voters = 100 d = 60 r = 40 75 % of d ( 60 ) = 45 20 % of r ( 40 ) = 8 total voter % of registered voters = 53 / 100 53 % answer : b"
Answer: b
Problem: a jogger running at 9 km / hr along side a railway track is 200 m ahead of the engine of a 210 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?
Options: a ) 89 , b ) 20 , c ) 36 , d ) 41 , e ) 34
Rationale: "speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 200 + 210 = 410 m . time taken = 410 / 10 = 41 sec . answer : option d"
Answer: d
Problem: if 4 / p = 8 & 6 / q = 18 then p - q = ?
Options: a ) 5 / 24 , b ) 6 / 24 , c ) 7 / 24 , d ) 1 / 6 , e ) 9 / 24
Rationale: "p = 4 / 8 , q = 6 / 18 = > q = 1 / 3 therefore p - q = ( 1 / 2 ) - ( 1 / 3 ) = 1 / 6 answer : d"
Answer: d
Problem: a box contain the number of balls which is as much greater than 20 is less than 30 . the number of balls is ?
Options: a ) 40 , b ) 25 , c ) 30 , d ) 50 , e ) 35
Rationale: "answer let the number be x . then , x - 20 = 30 - x â ‡ ’ 2 x = 30 + 20 = 50 â ‡ ’ 2 x = 50 â ˆ ´ x = 25 correct option : b"
Answer: b
Problem: if 10 typists can type 30 letters in 30 minutes , then how many letters will 40 typists working at the same rate complete in 1 hour ?
Options: a ) 200 , b ) 210 , c ) 205 , d ) 225 , e ) 240
Rationale: "no . of letters typing by 10 typists in 30 minutes = 30 no . of letters typing by 10 typists in 60 minutes = 30 * 2 = 60 no . of letters typing by 40 typists in 60 minutes = 60 / 10 * 40 = 240 answer : e"
Answer: e
Problem: a car going at 20 miles per hour set out on an 80 - mile trip at 9 : 00 a . m . exactly 10 minutes later , a second car left from the same place and followed the same route . how fast , in miles per hour , was the second car going if it caught up with the first car at 10 : 30 a . m . ?
Options: a ) 40 , b ) 50 , c ) 53 , d ) 55 , e ) 60
Rationale: "let car a = car that starts at 9 am car b = car that starts at 9 : 10 am time for which car a travels at speed of 20 m per hour = 1.5 hours distance travelled by car a = 20 * 1.5 = 30 miles since car b catches up car a at 10 : 30 , time = 80 mins = 4 / 3 hour speed of car b = 30 / ( 4 / 3 ) = 40 miles per hour answer a"
Answer: a
Problem: the ratio of number of boys and girls in a school is 1 : 2 . if there are 90 students in the school , find the number of girls in the school ?
Options: a ) 45 , b ) 50 , c ) 60 , d ) 75 , e ) 90
Rationale: let the number of boys and girls be x and 2 x total students = 100 number of girls in the school = 2 * 90 / 3 = 60 answer is c
Answer: c
Problem: an amount of rs . 1638 was divided among a , b and c , in the ratio 1 / 2 : 1 / 3 : 1 / 4 . find the share of c ?
Options: a ) 386 , b ) 378 , c ) 396 , d ) 395 , e ) 394
Rationale: "let the shares of a , b and c be a , b and c respectively . a : b : c = 1 / 2 : 1 / 3 : 1 / 4 let us express each term with a common denominator which is the last number divisible by the denominators of each term i . e . , 12 . a : b : c = 6 / 12 : 4 / 12 : 3 / 12 = 6 : 4 : 3 . share of c = 3 / 13 * 1638 = rs . 378 answer : b"
Answer: b
Problem: a group of 3 investors and 3 clients recently frequented the chinese luyang restaurant . the total bill for the meal , including 20 % gratuity , came to $ 720 . on average , how much did the meal of each individual cost before gratuity ?
Options: a ) $ 160 , b ) $ 96 , c ) $ 90 , d ) $ 80 , e ) $ 100
Rationale: 3 investors and 3 clients - so total 6 people the bill $ 720 includes 20 % gratuity . . . so the actual cost of dinner was $ 600 now , the cost per person will be $ 600 / 6 which is $ 100 option e
Answer: e
Problem: a man can row a distance of 5 km in 60 min with the help of the tide . the direction of the tide reverses with the same speed . now he travels a further 30 km in 10 hours . how much time he would have saved if the direction of tide has not changed ?
Options: a ) 2 , b ) 8 , c ) 4 , d ) 6 , e ) 5
Rationale: "explanation : he covered 5 km in 1 hour , so he might cover 30 km in 6 hours . but he took 10 hours . he would have saved 10 â € “ 6 = 4 hours . answer : c"
Answer: c
Problem: a man cycling along the road noticed that every 10 minutes a bus overtakes him and every 4 minutes he meets an oncoming bus . if all buses and the cyclist move at a constant speed , what is the time interval between consecutive buses ?
Options: a ) 5 minutes , b ) 6 minutes , c ) 8 minutes , d ) 9 minutes , e ) 48 / 7 minutes
Rationale: "let ' s say the distance between the buses is d . we want to determine interval = \ frac { d } { b } , where b is the speed of bus . let the speed of cyclist be c . every 10 minutes a bus overtakes cyclist : \ frac { d } { b - c } = 10 , d = 10 b - 10 c ; every 4 minutes cyclist meets an oncoming bus : \ frac { d } { b + c } = 4 , d = 4 b + 4 c ; d = 10 b - 10 c = 4 b + 4 c , - - > b = 7 c / 3 , - - > d = 12 b - 12 b * 3 / 7 = 48 / 7 b . interval = \ frac { d } { b } = \ frac { 48 / 7 b } { b } = 48 / 7 answer : e ( 48 / 7 minutes ) ."
Answer: e
Problem: the simple form of the ratio 4 / 2 : 2 / 5 is ?
Options: a ) 10 : 6 , b ) 5 : 1 , c ) 15 : 3 , d ) 25 : 3 , e ) 30 : 3
Rationale: "4 / 2 : 2 / 5 = 20 : 4 = 5 : 1 answer : b"
Answer: b
Problem: the average score of 35 students in a class is 37 . if every student is given 3 grace marks , the new average of the class is :
Options: a ) 33 , b ) 21 , c ) 38 , d ) 40 , e ) 92
Rationale: explanation : average score = 37 grace mark 3 is given to 35 student then its average will be 3 . hence new average = 37 + 3 = 40 answer : d
Answer: d
Problem: chris mixed 3 pounds of raisins with 4 pounds of nuts . if a pound of nuts costs 2 times as much as a pound of raisins , then the total cost of the raisins was what fraction of the total cost of the mixture ?
Options: a ) 1 / 7 , b ) 1 / 5 , c ) 1 / 4 , d ) 1 / 3 , e ) 3 / 11
Rationale: 1 lbs of raisin = $ 1 3 lbs of raisin = $ 3 1 lbs of nuts = $ 2 4 lbs of nuts = $ 8 total value of mixture = 8 + 3 = 11 fraction of the value of raisin = 3 / 11 ans : e
Answer: e
Problem: 82 * 83 * 84 * . . 89 what is the digit in units place ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "in the product 82 * 83 * 84 * 85 * 86 . . . . . . * 89 last ( unit ) digit will be zero as 82 * 85 will give zero as last ( unit ) digit and further multiplication with any number will also give zero at unit place . answer : a"
Answer: a
Problem: a bag contains 20 red jellybeans and 20 blue jellybeans . if 3 jellybeans are removed one at a time , at random and are not replaced , what is the probability that all 3 jellybeans removed from the bag are blue ?
Options: a ) 9 / 100 , b ) 2 / 19 , c ) 1 / 8 , d ) 3 / 20 , e ) 3 / 10
Rationale: "method - 1 10 red jellybeans and 10 blue jellybeans total outcomes = no . of ways to choose 3 jelly bean at random out of a total 20 jellybeans = 20 c 3 = 1140 favourable outcomes = no . of ways to choose 3 jelly bean such that they are all blue out of 10 blue = 10 c 3 = 120 probability = favourable outcomes / total outcomes = 10 c 3 / 20 c 3 probability = 120 / 1140 = 2 / 19 answer : option b method - 2 probability of first jelly bean to be blue = 10 / 20 [ total 10 blue out of total 20 jellybeans ] probability of second jelly bean to be blue = 9 / 19 [ total 9 blue remaining out of total 19 jellybeans remaining ] probability of third jelly bean to be blue = 8 / 18 [ total 8 blue remaining out of total 18 jellybeans remaining ] required probability = ( 10 / 20 ) * ( 9 / 19 ) * ( 8 / 18 ) = 3 / 20 answer : option d"
Answer: d
Problem: a man spends 2 / 5 of his salary on house rent , 3 / 10 of his salary on food and 1 / 8 of his salary on conveyence . if he has rs . 1400 left with him , find his expenditure on food and conveyence .
Options: a ) 800 , b ) 900 , c ) 100 , d ) 700 , e ) 500
Rationale: "let the salary be x , therefore house rent = 2 x / 5 , food = 3 x / 10 , conveyence = x / 8 . it is given that left over salary is 1400 / - so , x - ( 2 x / 5 + 3 x / 10 + x / 10 ) = 1400 by solving x = 8000 expenditure on food = 3200 and conveyence = 1000 answer : c"
Answer: c
Problem: there are 17 students in a certain class . on the day the test was given , taqeesha was absent . the other 16 students took the test , and their average was 77 . the next day , taqeesha took the test , and with her grade included , the new average is 78 . what is taqeesha ’ s grade on the test ?
Options: a ) 78 , b ) 80 , c ) 87 , d ) 91 , e ) 94
Rationale: explanations 1 ) the average of the first 16 students is 77 . this means , the sum of these 16 scores is sum = ( average ) * ( number of scores ) = 77 * 16 = 1232 once taqeesha takes her test , the average of all 17 scores is 78 . this means , the sum of these 17 scores is : sum = ( average ) * ( number of scores ) = 78 * 17 = 1326 once we had the sum of the 16 scores , all we had to do was add taqeesha ’ s score to that total to get the sum of all 17 . therefore , the difference in these two sums is taqeesha ’ s score . 1326 – 1232 = 94 . answer : e .
Answer: e
Problem: from january 1 , 1991 , to january 1 , 1993 , the number of people enrolled in health maintenance organizations increased by 15 percent . the enrollment on january 1 , 1993 , was 60 million . how many million people , to the nearest million , were enrolled in health maintenance organizations on january 1 , 1991 ?
Options: a ) 38 , b ) 39 , c ) 40 , d ) 41 , e ) 52
Rationale: "1.15 x = 60 - - > 23 / 20 * x = 60 - - > x = 60 * 20 / 23 = 1200 / 23 = ~ 52 . answer : e ."
Answer: e
Problem: a reduction of 30 % in the price of oil enables a house wife to obtain 5 kgs more for rs . 800 , what is the reduced price for kg ?
Options: a ) 46 , b ) 47 , c ) 48 , d ) 49 , e ) 50
Rationale: "800 * ( 30 / 100 ) = 240 - - - - 5 ? - - - - 1 = > rs . 48 answer : c"
Answer: c
Problem: a , b , c and d are 4 consecutive numbers . if the sum of a and dis 109 , what is the product of b and c ?
Options: a ) 2652 , b ) 2578 , c ) 2970 , d ) 3354 , e ) 4234
Rationale: c 2970 here d = a + 3 a + a + 3 = 109 2 a = 106 a = 53 so , numbers are 53 , 54 , 55 and 56 ∴ b × c = 54 × 55 = 2970
Answer: c
Problem: jane makes toy bears . when she works with an assistant , she makes 80 percent more bears per week and works 10 percent fewer hours each week . having an assistant increases jane ’ s output of toy bears per hour by what percent q ?
Options: a ) 20 % , b ) 80 % , c ) 100 % , d ) 180 % , e ) 200 %
Rationale: "c . let ' s assume just jane 40 bears per 40 / hrs a week , so that is 1 bear / hr . with an assistant she makes 72 bears per 36 hours a week or 2 bears / hr ( [ 40 bears * 1.8 ] / [ 40 hrs * . 90 ] ) . q = [ ( 2 - 1 ) / 1 ] * 100 % = 100 %"
Answer: c
Problem: a student traveled 25 percent of the distance of the trip alone , continued another 40 miles with a friend , and then finished the last half of the trip alone . how many miles long was the trip ?
Options: a ) 120 , b ) 140 , c ) 160 , d ) 180 , e ) 200
Rationale: "let x be the total length of the trip . 0.25 x + 40 miles + 0.5 x = x 40 miles = 0.25 x x = 160 miles the answer is c ."
Answer: c
Problem: of all the students in a certain dormitory , 1 / 2 are first - year students and the rest are second - year students . if 4 / 5 of the first - year students have not declared a major and if the fraction of second - year students who have declared a major is 4 times the fraction of first - year students who have declared a major , what fraction of all the students in the dormitory are second - year students who have not declared a major ?
Options: a ) 1 / 15 , b ) 4 / 5 , c ) 4 / 15 , d ) 1 / 5 , e ) 2 / 5
Rationale: tot students = x 1 st year student = x / 2 - - - - > non majaor = 4 / 5 ( x / 2 ) - - - - - > maj = 1 / 5 ( x / 2 ) 2 nd year student = x / 2 - - - - > maj = 4 ( 1 / 5 ( x / 2 ) ) = 2 / 5 ( x ) - - - > non major = x / 2 - 2 / 5 ( x ) = 1 / 5 ( x ) hence 1 / 5 d
Answer: d
Problem: if the personal income tax rate is lowered from 42 % to 28 % , what is the differential savings for a tax payer having an annual income before tax to the tune of $ 34500 ?
Options: a ) $ 3500 , b ) $ 5000 , c ) $ 4830 , d ) $ 7000 , e ) $ 10000
Rationale: "saving = ( 42 - 28 ) % of 34500 = 4830 . answer : c"
Answer: c
Problem: solve the equation for x : 5 x - 14 + 3 x = 4 + 9 - x
Options: a ) 4 , b ) 5 , c ) 7 , d ) 9 , e ) 3
Rationale: "e 3 8 x + x = 13 + 14 9 x = 27 = > x = 3"
Answer: e
Problem: the positive integers a and b leave remainders of 2 and 3 , respectively , when divided by 6 . a > b . what is the remainder when a – b is divided by 6 ?
Options: a ) 4 , b ) 3 , c ) 5 , d ) 2 , e ) 1
Rationale: let ' s test out some values of m and n that satisfy the given information . a leaves are remainder of 2 when divided by 6 so , a could equal 8 b leaves are remainder of 3 when divided by 6 so , b could equal 3 what is the remainder when a – b is divided by 6 ? so , a - b = 8 - 3 = 5 , and when we divide 5 by 6 , we get 0 with remainder 5 answer : c
Answer: c
Problem: john left home and drove at the rate of 35 mph for 2 hours . he stopped for lunch then drove for another 3 hours at the rate of 55 mph to reach his destination . how many miles did john drive ?
Options: a ) 235 miles . , b ) 245 miles . , c ) 255 miles . , d ) 265 miles . , e ) 275 miles .
Rationale: "the total distance d traveled by john is given by d = 35 * 2 + 3 * 55 = 235 miles . answer a"
Answer: a
Problem: a team won 40 percent of its first 30 games in a particular season , and 80 percent of its remaining games . if the team won a total of 70 percent of its games that season , what was the total number of games that the team played ?
Options: a ) 60 , b ) 90 , c ) 120 , d ) 150 , e ) 180
Rationale: "70 % is 30 % - points above 40 % and 10 % - points below 80 % . thus the ratio of ` ` the first 30 games ' ' to ` ` remaining games ' ' is 1 : 3 . so the team played a total of 30 + 90 = 120 games . the answer is c ."
Answer: c
Problem: mangoes , oranges and apples in a fruit shop are in the ratio of 10 : 2 : 3 . if there are 120 mangoes , the number of apples in the shop is : .
Options: a ) 36 , b ) 42 , c ) 72 , d ) 400 , e ) 56
Rationale: explanation : let mangoes = 10 x , oranges = 2 x & apples = 3 x . now , 10 x = 120 hence x = 12 . number of apples = 3 x = 36 . answer : a
Answer: a
Problem: the average ( arithmetic mean ) of 20 , 40 , and 60 is 9 more than the average of 10 , 70 , and what number ?
Options: a ) 15 , b ) 25 , c ) 35 , d ) 13 , e ) 55
Rationale: "a 1 = 120 / 3 = 40 a 2 = a 1 - 9 = 31 sum of second list = 31 * 3 = 93 therefore the number = 93 - 80 = 13 answer : d"
Answer: d
Problem: if 4 xz + yw = 3 and xw + yz = 6 , what is the value of the expression ( 2 x + y ) ( 2 z + w ) ?
Options: a ) 9 . , b ) 12 . , c ) 15 . , d ) 16 , e ) 18 .
Rationale: "expand this to get : ( 2 x + y ) ( 2 z + w ) = 4 xz + 2 xw + 2 yz + yw = 4 xz + yw + 2 xw + 2 yz [ i rearranged the terms ] = 3 + 2 xw + 2 yz [ replaced 4 xz + yw with 3 ] = 3 + 2 ( xw + yz ) factored out a 2 = 3 + 2 ( 6 ) = 3 + 12 = 15 answer : c"
Answer: c
Problem: the sum of three consecutive even numbers is 42 . find the middle number of the three ?
Options: a ) 14 , b ) 66 , c ) 88 , d ) 99 , e ) 12
Rationale: "three consecutive even numbers ( 2 p - 2 ) , 2 p , ( 2 p + 2 ) . ( 2 p - 2 ) + 2 p + ( 2 p + 2 ) = 42 6 p = 42 = > p = 7 . the middle number is : 2 p = 14 . answer : a"
Answer: a
Problem: in may mrs lee ' s earnings were 60 percent of the lee family ' s total income . in june mrs lee earned 20 percent more than in may . if the rest of the family ' s income was the same both months , then , in june , mrs lee ' s earnings were approximately what percent of the lee family ' s total income ?
Options: a ) 64 % , b ) 68 % , c ) 72 % , d ) 76 % , e ) 80 %
Rationale: "say may income = 100 l ' s income = 60 and rest of the family = 40 in june l ' s income = 60 * 120 / 100 = 72 so 72 / 72 + 40 = 64 % answer : a"
Answer: a
Problem: two cars start at the same time from opposite ends of a highway that is 105 miles long . one car is riding at 15 mph and the second car is riding at 20 mph . how long after they begin will they meet ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "as cars are moving in opposite directions their speeds will be added . so their relative speeds : 20 + 15 = 35 mph total distance to be covered = 105 miles . time taken would be : 105 miles / 35 mph = 3 hours c is the answer ."
Answer: c