regisss/math_qa huggingface dataset:
Problem: a not - so - good clockmaker has four clocks on display in the window . clock # 1 loses 35 minutes every hour . clock # 2 gains 15 minutes every hour relative to clock # 1 ( i . e . , as clock # 1 moves from 12 : 00 to 1 : 00 , clock # 2 moves from 12 : 00 to 1 : 15 ) . clock # 3 loses 20 minutes every hour relative to clock # 2 . finally , clock # 4 gains 20 minutes every hour relative to clock # 3 . if the clockmaker resets all four clocks to the correct time at 12 noon , what time will clock # 4 display after 6 actual hours ( when it is actually 6 : 00 pm that same day ) ?
Options: a ) 5 : 00 , b ) 5 : 34 , c ) 5 : 42 , d ) 6 : 00 , e ) 6 : 24
Rationale: "c 1 loses 15 minutes every hour . so after 60 minutes have passed , c 1 displays that 60 - 15 = 45 minutes have passed . c 2 gains 15 minutes for every 60 minutes displayed on c 1 . thus , the time displayed on c 2 is 75 / 60 = 5 / 4 the time displayed on c 1 . so after 60 minutes have passed , c 2 displays the passing of ( 5 / 4 * 45 ) minutes . c 3 loses 20 minutes for every 60 minutes displayed on c 2 . thus , the time displayed on c 3 is 40 / 60 = 2 / 3 the time displayed on c 2 . so after 60 minutes have passed , c 3 displays the passing of ( 2 / 3 * 5 / 4 * 45 ) minutes . c 4 gains 20 minutes for every 60 minutes displayed on c 3 . thus , the time displayed on c 4 is 80 / 60 = 4 / 3 the time displayed on clock 3 . so after 60 minutes have passed , c 4 displays the passing of 4 / 3 * 2 / 3 * 5 / 4 * 45 = 50 minutes . c 4 loses 10 minutes every hour . in 6 hours , c 4 will lose 6 * 10 = 60 minutes = 1 hour . since the correct time after 6 hours will be 6 pm , c 4 will show a time of 6 - 1 = 6 : 24 pm . the correct answer is e ."
Answer: e
Problem: if a = 1 , what is the value of – ( a ^ 2 + a ^ 3 + a ^ 4 + a ^ 5 ) ?
Options: a ) - 14 , b ) - 4 , c ) 0 , d ) 4 , e ) 14
Rationale: if a = 1 , then putting values in equation = - [ ( 1 ) ^ 2 + ( 1 ) ^ 3 + ( 1 ^ 4 ) + ( 1 ^ 5 ) ] = - [ 1 + 1 + 1 + 1 ] = - 4 answer = b = - 4
Answer: b
Problem: what profit percent is made by selling an article at a certain price , if by selling at 2 / 3 rd of that price , there would be a loss of 30 % ?
Options: a ) 20 % , b ) 29 % , c ) 70 % , d ) 27 % , e ) 5 %
Rationale: "sp 2 = 2 / 3 sp 1 cp = 100 sp 2 = 70 2 / 3 sp 1 = 70 sp 1 = 105 100 - - - 105 = > 5 % answer : e"
Answer: e
Problem: an astronomer noted that a grouping of red giant stars had an average solar mass of 8 m each , and a grouping of white dwarf stars had an average solar mass of 1.5 m each . if the astronomer calculated the total solar mass of both groupings to be 49 m , what total number of red giant stars and white dwarf stars did the astronomer note ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: we can determine quickly that total number should range between 49 / 8 < = n < = 49 / 1.5 , so ans should be between 6 and 33 . now solving the expression 8 a + 1.5 b = 49 decreasing 49 in multiple of 8 and checking divisibility of that number by 1.5 . this way we get 2 red giants , 22 white dwarfs we get 49 , but 2 + 22 = 24 and 24 is not an option . next we get 5 red giants and 6 white dwarfs to get 49 , 5 * 8 + 6 * 1.5 = 49 hence total number is 5 + 6 = 11 ans b
Answer: b
Problem: village a ’ s population is 300 greater than village b ' s population . if village b ’ s population were reduced by 600 people , then village a ’ s population would be 4 times as large as village b ' s population . what is village b ' s current population ?
Options: a ) 900 , b ) 1000 , c ) 1100 , d ) 1200 , e ) 1300
Rationale: a = b + 300 . a = 4 ( b - 600 ) . 4 ( b - 600 ) = b + 300 . 3 b = 2700 . b = 900 . the answer is a .
Answer: a
Problem: the cost of 2 chairs and 3 tables is rs . 1500 . the cost of 3 chairs and 2 tables is rs . 1200 . the cost of each table is more than that of each chair by ?
Options: a ) 228 , b ) 287 , c ) 277 , d ) 188 , e ) 300
Rationale: "explanation : 2 c + 3 t = 1500 - - - ( 1 ) 3 c + 2 t = 1200 - - - ( 2 ) subtracting 2 nd from 1 st , we get - c + t = 300 = > t - c = 300 answer : e"
Answer: e
Problem: a sum amounts to rs . 4851 in 2 years at the rate of 5 % p . a . if interest was compounded yearly then what was the principal ?
Options: a ) s . 4000 , b ) s . 5000 , c ) s . 4400 , d ) s . 4800 , e ) s . 5800
Rationale: "ci = 4851 , r = 5 , n = 2 ci = p [ 1 + r / 100 ] ^ 2 = p [ 1 + 5 / 100 ] ^ 2 4851 = p [ 21 / 20 ] ^ 2 4851 [ 20 / 21 ] ^ 2 4400 answer : c"
Answer: c
Problem: the average monthly salary of 10 employees in an organisation is rs . 1600 . if the manager ' s salary is added , then the average salary increases by rs . 100 . what is the manager ' s monthly salary ?
Options: a ) rs . 3601 , b ) rs . 3618 , c ) rs . 2700 , d ) rs . 3619 , e ) rs . 3610
Rationale: "manager ' s monthly salary = rs . ( 1700 * 11 - 1600 * 10 ) = rs . 2700 answer : c"
Answer: c
Problem: if a lends rs . 1200 to b at 10 % per annum and b lends the same sum to c at 18 % per annum then the gain of b in a period of 2 years is ?
Options: a ) 190 , b ) 188 , c ) 192 , d ) 145 , e ) 188
Rationale: "( 1200 * 8 * 2 ) / 100 = > 192 answer : c"
Answer: c
Problem: if an integer n is to be chosen at random from the integers 1 to 96 , inclusive , what is the probability that n ( n + 1 ) ( n + 2 ) will be divisible by 6 ?
Options: a ) 2 / 3 , b ) 3 / 8 , c ) 1 / 2 , d ) 5 / 8 , e ) 3 / 4
Rationale: i get 5 / 8 as well 1 to 96 inclusive means we have 48 odd and 48 even integers e o e / 6 = integer , therefore we have 48 / 96 numbers divisible by 6 o e o / 6 = not integer we can not forget multiples of 6 from 1 to 96 we have 16 numbers that are multiple of 8 therefore , 48 / 96 + 16 / 96 = 64 / 96 = 2 / 3 answer : a
Answer: a
Problem: how many integers from 0 to 50 inclusive have a remainder of 3 when divided by 5 ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "the numbers should be of the form 5 c + 3 . the minimum is 3 when c = 0 . the maximum is 48 when c = 9 . there are 10 such numbers . the answer is e ."
Answer: e
Problem: 6 students wrote science exam . their average marks are 70 . 5 students got 65 , 75 , 55 , 72 and 69 marks respectively . therefore what is the marks of the sixth student ?
Options: a ) 84 , b ) 68 , c ) 85 , d ) 75 , e ) 42
Rationale: explanation total marks of 5 students = ( 65 + 75 + 55 + 72 + 69 ) = 336 required marks = [ ( 70 x 6 ) – 336 ] = ( 420 – 336 ) = 84 answer a
Answer: a
Problem: two trains of length 100 m and 200 m are 100 m apart . they start moving towards each other on parallel tracks , at speeds 54 kmph and 90 kmph . in how much time will the trains cross each other ?
Options: a ) 10 sec , b ) 11 sec , c ) 12 sec , d ) 60 / 7 sec , e ) 90 / 7 sec
Rationale: "a relative speed = ( 54 + 90 ) * 5 / 18 = 8 * 5 = 40 mps . the time required = d / s = ( 100 + 100 + 200 ) / 35 = 400 / 40 = 10 sec ."
Answer: a
Problem: a bowl was filled with 10 ounces of water , and 0.010 ounce of the water evaporated each day during a 50 - day period . what percent of the original amount of water evaporated during this period ?
Options: a ) 0.004 % , b ) 0.04 % , c ) 0.40 % , d ) 5 % , e ) 40 %
Rationale: "total amount of water evaporated each day during a 50 - day period = . 008 * 50 = . 010 * 100 / 2 = 1.0 / 2 = . 5 percent of the original amount of water evaporated during this period = ( . 5 / 10 ) * 100 % = 5 % answer d"
Answer: d
Problem: what is the prime factors ’ number of 28 ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "prime factors ’ number , as i assume , for a number x = a ^ n * b ^ m * c ^ o * d ^ p . . . is = n + m + o + p . . . so , 28 = 2 ^ 2 * 7 ^ 1 prime factors ’ number will be 2 + 1 = 3 . hence , answer is b ."
Answer: b
Problem: the sum of 7 th and 23 rd term of a . p . is equal to the sum of 8 th , 15 th and 13 th term . find the term which is 0
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: t 7 + t 23 = t 8 + t 15 + t 13 = > a + 6 d + a + 22 d = a + 7 d + a + 14 d + a + 12 d = > a + 5 d = 0 = > t 6 = 0 i . e . 6 th term is zero . answer : a
Answer: a
Problem: the cost of registration at a professional association meeting was $ 50 per person ; a lunch for registrants only was available for an additional $ 22 per person . if the number of registrants who paid for lunch was 30 more than the number who did not , and if receipts for registration and lunch totaled $ 75,360 , how many people paid just for registration at the meeting ?
Options: a ) 700 , b ) 800 , c ) 600 , d ) 1,500 , e ) 1,800
Rationale: "hope this might be useful to you . let the number of people who have opted only to register = x now since the registration cost is 50 $ per person , the total amount sums to = 50 x $ as per the information given in the question , the number of registrants who paid for lunch was 30 more than the number who did not . that means , total number of people who registered and paid for lunch = 30 + x . for the people who registered for lunch the cost is 50 $ ( for the event registration ) + 22 $ ( for lunch ) = 72 $ . total amount in this case sums to = 72 ( 30 + x ) = 2160 + 72 x now , total amount received was 75360 . thus , from the above data , 50 x + 2160 + 72 x = 75360 122 x = 75360 - 2160 122 x = 73200 x = 600 . hence the correct ans is c"
Answer: c
Problem: what is the perimeter of a rectangular field whose diagonal is 5 m and length is 4 m ?
Options: a ) 20 m , b ) 15 m , c ) 14 m , d ) 10 m , e ) 25 m
Rationale: "sol : breadth of the rectangular plot is = 5 ^ 2 - 4 ^ 2 = 3 m therefore , perimeter of the rectangular plot = 2 ( 4 + 3 ) = 14 m c ) 14 m"
Answer: c
Problem: the least number which must be subtracted from 709 to make it exactly divisible by 9 is :
Options: a ) a ) 2 , b ) b ) 3 , c ) c ) 7 , d ) d ) 5 , e ) e ) 6
Rationale: "on dividing 709 by 9 , we get remainder = 7 therefore , required number to be subtracted = 7 answer : c"
Answer: c
Problem: let c be defined as the sum of all prime numbers between 0 and 35 . what is c / 3
Options: a ) 155 , b ) 129 , c ) 64.3 , d ) 47 , e ) 43
Rationale: prime numbers between 0 and 30 - 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 33 sum , c = 193 c / 3 = 64.3 answer c
Answer: c
Problem: the speed of a boat in still water in 22 km / hr and the rate of current is 5 km / hr . the distance travelled downstream in 24 minutes is :
Options: a ) 10.6 , b ) 10.2 , c ) 10.8 , d ) 10.4 , e ) 10.0
Rationale: speed downstream = ( 22 + 5 ) = 27 kmph time = 24 minutes = 24 / 60 hour = 2 / 5 hour distance travelled = time × speed = 2 / 5 × 27 = 10.8 km answer is c .
Answer: c
Problem: a boat having a length 3 m and breadth 3 m is floating on a lake . the boat sinks by 1 cm when a man gets on it . the mass of the man is :
Options: a ) 100 kg , b ) 120 kg , c ) 89 kg , d ) 90 kg , e ) 110 kg
Rationale: "volume of water displaced = ( 3 x 3 x 0.01 ) m 3 = 0.09 m 3 . mass of man = volume of water displaced x density of water = ( 0.09 x 1000 ) kg = 90 kg . answer : d"
Answer: d
Problem: by selling 12 pencils for a rupee a man loses 20 % . how many for a rupee should he sell in order to gain 20 % ?
Options: a ) 8 , b ) 76 , c ) 17 , d ) 7 , e ) 77
Rationale: "80 % - - - 12 120 % - - - ? 80 / 120 * 12 = 8 answer : a"
Answer: a
Problem: due to construction , the speed limit along an 10 - mile section of highway is reduced from 55 miles per hour to 35 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) 6.24 , b ) 8 , c ) 10 , d ) 15 , e ) 24
Rationale: "old time in minutes to cross 10 miles stretch = 10 * 60 / 55 = 10 * 12 / 11 = 10.9 new time in minutes to cross 10 miles stretch = 10 * 60 / 35 = 10 * 12 / 7 = 17.14 time difference = 6.24 ans : a"
Answer: a
Problem: walking with 4 / 5 of my usual speed , i miss the bus by 7 minutes . what is my usual time ?
Options: a ) 16 min , b ) 26 min , c ) 28 min , d ) 20 min , e ) 12 min
Rationale: "speed ratio = 1 : 4 / 5 = 5 : 4 time ratio = 4 : 51 - - - - - - - - 7 4 - - - - - - - - - ? è 28 answer : c"
Answer: c
Problem: if difference between compound interest and simple interest on a sum at 10 % p . a . for 2 years is rs . 150 then sum is
Options: a ) s . 15000 , b ) s . 15100 , c ) s . 15800 , d ) s . 16000 , e ) s . 16200
Rationale: "p ( r / 100 ) ^ 2 = c . i - s . i p ( 10 / 100 ) ^ 2 = 150 15000 answer : a"
Answer: a
Problem: in one hour , a boat goes 8 km along the stream and 2 km against the stream . the sped of the boat in still water ( in km / hr ) is :
Options: a ) 3 , b ) 5 , c ) 8 , d ) 9 , e ) 10
Rationale: "solution speed in still water = 1 / 2 ( 8 + 2 ) km / hr = 5 kmph . answer b"
Answer: b
Problem: coconuts were purchased at 150 per 100 and sold at 2 per coconut . if 2000 coconuts were sold , what was the total profit made ?
Options: a ) 500 , b ) 1000 , c ) 1500 , d ) 2000 , e ) none of these
Rationale: c . p . for one coconut = 150 ⁄ 100 = 3 ⁄ 2 s . p . for one coconut = 2 profit on one coconut = 2 - 3 ⁄ 2 = 1 ⁄ 2 ∴ profit on 2000 coconut = 1 ⁄ 2 × 2000 = 1000 answer b
Answer: b
Problem: what is the factorial of 5 ?
Options: a ) 1 , b ) 60 , c ) 120 , d ) 130 , e ) 180
Rationale: "c 120 120 ( 5 x 4 x 3 x 2 x 1 ) ."
Answer: c
Problem: when working alone , painter w can paint a room in 2 hours , and working alone , painter x can paint the same room in e hours . when the two painters work together and independently , they can paint the room in 3 / 4 of an hour . what is the value of e ?
Options: a ) 3 / 4 , b ) 1 [ 1 / 5 ] , c ) 1 [ 2 / 5 ] , d ) 1 [ 3 / 4 ] , e ) 2
Rationale: "rate * time = work let painter w ' s rate be w and painter x ' s rate be x r * t = work w * 2 = 1 ( if the work done is same throughout the question then the work done can be taken as 1 ) = > w = 1 / 2 x * e = 1 = > x = 1 / e when they both work together then their rates get added up combined rate = ( w + x ) r * t = work ( w + x ) * 3 / 4 = 1 = > w + x = 4 / 3 = > 1 / 2 + 1 / e = 4 / 3 = > 1 / e = ( 8 - 3 ) / 6 = 5 / 6 = > e = 6 / 5 = 1 [ 1 / 5 ] answer b"
Answer: b
Problem: a train is 435 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length
Options: a ) 20 seconds , b ) 30 seconds , c ) 46 seconds , d ) 50 seconds , e ) none of these
Rationale: "explanation : speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 435 + 140 = 575 meter time = distance / speed = 575 ∗ 2 / 25 = 46 seconds option c"
Answer: c
Problem: if the l . c . m of two numbers is 450 and their product is 22500 , find the h . c . f of the numbers .
Options: a ) 50 , b ) 30 , c ) 125 , d ) 25 , e ) none of these
Rationale: "h . c . f = ( product of the numbers ) / ( their l . c . m ) = 22500 / 450 = 50 . answer : a"
Answer: a
Problem: the area of a parallelogram is 72 cm ^ 2 and its altitude is twice the corresponding base . what is the length of the base ?
Options: a ) 1 cm
b ) 3 cm
c ) 6 cm
d ) 4 cm
e ) 2 cm
Rationale: let base = x cm height = 2 x cm area = x ã — 2 x = 2 x ^ 2 area = x ã — 2 x = 2 x ^ 2 area is given as 72 cm ^ 2 2 x ^ 2 = 72 x ^ 2 = 36 x = 6 cm answer : c
Answer: c
Problem: martin buys a pencil and a notebook for 80 cents . at the same store , gloria buys a notebook and an eraser for $ 1.15 cents , and zachary buys a pencil and an eraser for 75 cents . how many cents would it cost to buy 3 pencils , 3 notebooks , and 3 erasers ? ( assume that there is no volume discount . )
Options: a ) 325 , b ) 345 , c ) 365 , d ) 385 , e ) 405
Rationale: pencil + notebook = 80 notebook + eraser = 115 pencil + eraser = 75 let ' s add all three equations . 2 pencils + 2 notebooks + 2 erasers = 270 cents the cost to buy 3 of each would be ( 3 / 2 ) ( 270 ) = 405 the answer is e .
Answer: e
Problem: when 200 is divided by positive integer x , the remainder is 3 . what is the remainder when 297 is divided by x ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: "f 200 / x leaves a reminder 3 then ( 200 - 3 ) i . e . 197 is divisible by x so ( 200 + 197 ) / x leaves a reminder rem ( 200 / x ) + rem ( 197 / x ) = > 3 + 0 = 3 answer : b"
Answer: b
Problem: if a fast song has 160 beats per minute , and a slow song has 90 beats per minute , how many minutes total would you play a fast and a slow song to have a stream of music that had a total of 1020 beats ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: we can determine quickly that total number should range between 1020 / 160 < = n < = 1020 / 90 , so ans should be between 6 and 12 . now solving the expression 160 a + 90 b = 1020 decreasing 1020 by multiples of 160 and checking divisibility of that number by 9 , we get fast song plays for 3 minutes and slow somg plays for 6 minutes , 3 * 160 + 6 * 90 = 1020 hence total number of minutes stream of music plays is 3 + 6 = 9 minutes ans d
Answer: d
Problem: in a party every person shakes hands with every other person . if there were a total of 190 handshakes in the party then what is the number of persons present in the party ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 20
Rationale: "explanation : let the number of persons be n â ˆ ´ total handshakes = nc 2 = 190 n ( n - 1 ) / 2 = 190 â ˆ ´ n = 20 answer : option e"
Answer: e
Problem: a cube of edge 7 cm is cut into cubes each of edge 1 cm . the ratio of the total surface area of one of the small cubes to that of the large cube is equal to :
Options: a ) 1 : 25 , b ) 1 : 49 , c ) 1 : 52 , d ) 1 : 522 , e ) none
Rationale: "sol . required ratio = 6 * 1 * 1 / 6 * 7 * 7 = 1 / 49 = 1 : 49 . answer b"
Answer: b
Problem: ratio between rahul and deepak is 4 : 3 , after 6 years rahul age will be 30 years . what is deepak present age ?
Options: a ) 18 , b ) 15 , c ) 77 , d ) 266 , e ) 182
Rationale: "present age is 4 x and 3 x , = > 4 x + 6 = 30 = > x = 6 so deepak age is = 3 ( 6 ) = 18 answer : a"
Answer: a
Problem: a , b and c rents a pasture for rs . 480 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should c pay ?
Options: a ) 270 , b ) 199 , c ) 676 , d ) 149 , e ) 122
Rationale: "12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 9 / 29 * 480 = 149 answer : d"
Answer: d
Problem: what is remainder of the division ( 1525 * 1527 * 1529 ) / 12 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "remainder will be number / 100 here as the divisor is two digit number = 12 . hence checking for the last two digits = 5 * 7 * 9 = 15 thus remainder = 3 . answer : d"
Answer: d
Problem: a pharmaceutical company received $ 5 million in royalties on the first $ 20 million in sales of the generic equivalent of one of its products and then $ 9 million in royalties on the next $ 108 million in sales . by approximately what percent did the ratio of royalties to sales decrease from the first $ 20 million in sales to the next $ 108 million in sales ?
Options: a ) 8 % , b ) 15 % , c ) 45 % , d ) 52 % , e ) 67 %
Rationale: solution : this is a percent decrease problem . we will use the formula : percent change = ( new – old ) / old x 100 to calculate the final answer . we first set up the ratios of royalties to sales . the first ratio will be for the first 20 million in sales , and the second ratio will be for the next 108 million in sales . because all of the sales are in millions , we do not have to express all the trailing zeros in our ratios . first 20 million royalties / sales = 5 / 20 = 1 / 4 next 108 million royalties / sales = 9 / 108 = 1 / 12 because each ratio is not an easy number to use , we can simplify each one by multiplying each by the lcm of the two denominators , which is 60 . keep in mind that we are able to do this only because our answer choices are expressed in percents . first 20 million royalties / sales = ( 5 / 20 ) x 12 = 3 next 108 million royalties / sales = 9 / 108 = ( 1 / 12 ) x 12 = 1 we can plug 15 and 5 into our percent change formula : ( new – old ) / old x 100 [ ( 1 – 3 ) / 3 ] x 100 - 200 / 3 x 100 at this point we can stop and consider the answer choices . since we know that 200 / 3 is just a bit less than ½ , we know that - 200 / 3 x 100 is about a 67 % decrease . answer e .
Answer: e
Problem: in the first 10 overs of a cricket game , the run rate was only 5.2 . what should be the run rate in the remaining 40 overs to reach the target of 282 runs ?
Options: a ) 6.25 , b ) 6.5 , c ) 6.75 , d ) 5.75 , e ) 8
Rationale: "10 overs - run rate = 5.2 runs scored in first 10 overs = 52 remaining overs 40 total runs to be scored = 282 52 runs already scored 282 - 52 = 230 230 runs to be scored in 40 overs let required runrate be x 40 * x = 230 x = 230 / 40 x = 5.75 the required runrate is 5.75 answer : d"
Answer: d
Problem: of the diplomats attending a summit conference , 30 speak french , 32 do not speak russian , and 20 % of the diplomats speak neither french nor russian . if 10 % of the diplomats speak both languages , then how many diplomats attended the conference ?
Options: a ) 20 , b ) 96 , c ) 108 , d ) 120 , e ) 150
Rationale: "{ total } = { french } + { russian } - { both } + { neither } { total } = 30 + ( { total } - 32 ) - ( 0.1 * { total } ) + 0.2 * { total } solving gives { total } = 20 . answer : a ."
Answer: a
Problem: during the second quarter of 1984 , a total of 3 , 976000 domestic cars were sold . if this was 32 % greater than the number sold during the first quarter of 1984 , how many were sold during the first quarter ?
Options: a ) 714,240 , b ) 2 , 261,760 , c ) 2 , 400,000 , d ) 3 , 012,121 , e ) 3 , 915,790
Rationale: let number of cars sold in 1 st quarter = x number of cars sold in 2 nd quarter = 32 % greater than the number sold during the first quarter = ( 1 + 32 / 100 ) x = 1.32 x 1.32 x = 3 , 976,000 = > x = 3 , 012,121 so , answer will be d
Answer: d
Problem: if 0.2 of a number is equal to 0.08 of another number , the ratio of the numbers is :
Options: a ) 2 : 3 , b ) 3 : 4 , c ) 2 : 5 , d ) 20 : 3 , e ) 30 : 7
Rationale: "0.2 a = 0.08 b - > a / b = 0.08 / 0.20 = 8 / 20 = 2 / 5 : . a : b = 2 : 5 answer : c"
Answer: c
Problem: a man covered a certain distance at some speed . had he moved 3 kmph faster , he would have taken 40 minutes less . if he had moved 2 kmph slower , he would have taken 40 minutes more . the distance ( in km ) is
Options: a ) 27 , b ) 87 , c ) 40 , d ) 18 , e ) 17
Rationale: explanation : let distance = x km and usual rate = y kmph . then , x / y - x / ( y + 3 ) = 40 / 60 - - > 2 y ( y + 3 ) = 9 x - - - - - ( i ) also , x / ( y - 2 ) - x / y = 40 / 60 - - > y ( y - 2 ) = 3 x - - - - - - - - ( ii ) on dividing ( i ) by ( ii ) , we get : x = 40 km . answer : c
Answer: c
Problem: if the average of w , b , c , 14 and 15 is 12 . what is the average value of w , b , c and 29
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: w + b + c + 14 + 15 = 12 * 5 = 60 = > w + b + c = 60 - 29 = 31 w + b + c + 29 = 31 + 29 = 60 average = 60 / 4 = 15 answer d
Answer: d
Problem: set a of 8 positive integers may have the same element and have 40 . and set b of 8 positive integers must have different elements and have 40 . when m and n are the greatest possible differences between 40 and other elements ’ sums in set a and set b , respectively , m - n = ?
Options: a ) 21 , b ) 29 , c ) 23 , d ) 25 , e ) 26
Rationale: this is maximum - minimum . hence , 40 - ( 1 + 1 + 1 + 1 + 1 + 1 + 1 ) = 32 and 40 - ( 1 + 2 + 3 + 4 + 5 + 6 + 7 ) = 11 . so , 32 - 11 = 21 . the correct answer is a .
Answer: a
Problem: after 6 games , team b had an average of 65 points per game . if it got only 47 points in game 7 , how many more points does it need to score to get its total above 500 ?
Options: a ) 85 , b ) 74 , c ) 67 , d ) 63 , e ) 28
Rationale: "( 6 * 65 ) + 47 + x > 500 390 + 47 + x > 500 437 + x > 500 = > x > 63 option d"
Answer: d
Problem: on thursday mabel handled 90 transactions . anthony handled 10 % more transactions than mabel , cal handled 2 / 3 rds of the transactions that anthony handled , and jade handled 16 more transactions than cal . how much transactions did jade handled ?
Options: a ) 80 , b ) 81 , c ) 82 , d ) 83 , e ) 84
Rationale: "solution : mabel handled 90 transactions anthony handled 10 % more transactions than mabel anthony = 90 + 90 × 10 % = 90 + 90 × 0.10 = 90 + 9 = 99 cal handled 2 / 3 rds of the transactions than anthony handled cal = 2 / 3 × 99 = 66 jade handled 16 more transactions than cal . jade = 66 + 16 = 82 jade handled = 82 transactions . answer : c"
Answer: c
Problem: a man buys an article for $ 100 . and sells it for $ 125 . find the gain percent ?
Options: a ) 10 % , b ) 15 % , c ) 25 % , d ) 20 % , e ) 30 %
Rationale: "c . p . = $ 100 s . p . = $ 125 gain = $ 25 gain % = 25 / 100 * 100 = 25 % answer is c"
Answer: c
Problem: what is 35 % of 4 / 13 of 780 ?
Options: a ) 62 , b ) 73 , c ) 84 , d ) 95 , e ) 106
Rationale: "this problem can be solved easily if we just use approximation : 35 % is a little over 1 / 3 , while 4 / 13 is a little less than 4 / 12 , which is 1 / 3 . thus , the answer is about 1 / 3 of 1 / 3 of 780 , or 1 / 9 of 780 . since the first 1 / 3 is a slight underestimate and the second 1 / 3 is a slight overestimate , the errors will partially cancel each other out . our estimate will be relatively accurate . the number 780 is between 720 and 810 , so ( 1 / 9 ) * 780 will be between 80 and 90 . keeping track not only of your current estimate , but also of the degree to which you have overestimated or underestimated , can help you pinpoint the correct answer more confidently . the closest answer is 84 , so this is the answer to choose . the answer is c ."
Answer: c
Problem: two pipes can fill a tank in 20 minutes and 12 minutes . an outlet pipe can empty the tank in 10 minutes . if all the pipes are opened when the tank is empty , then how many minutes will it take to fill the tank ?
Options: a ) 24 , b ) 26 , c ) 28 , d ) 30 , e ) 32
Rationale: "let v be the volume of the tank . the rate per minute at which the tank is filled is : v / 20 + v / 12 - v / 10 = v / 30 per minute the tank will be filled in 30 minutes . the answer is d ."
Answer: d
Problem: the radius of a wheel is 20 cm . what is the distance covered by the wheel in making 500 resolutions ?
Options: a ) 708 m , b ) 704 m , c ) 314.3 m , d ) 714 m , e ) 744 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 500 resolutions . = 500 * 2 * 22 / 7 * 20 = 31428.5 cm = 314.3 m answer : c"
Answer: c
Problem: list a consists of 12 consecutive integers . if - 4 is the least integer in list a , what is the range of positive integers in list a ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 11 , e ) 12
Rationale: since - 4 is the least integer in list a , then 7 is the largest integer in that list . thus the range of the positive integers in the list is 7 - 1 = 6 . answer : b .
Answer: b
Problem: joe needs to paint all the airplane hangars at the airport , so he buys 360 gallons of paint to do the job . during the first week , he uses 1 / 2 of all the paint . during the second week , he uses 1 / 5 of the remaining paint . how many gallons of paint has joe used ?
Options: a ) 18 , b ) 144 , c ) 175 , d ) 216 , e ) 250
Rationale: "total paint initially = 360 gallons paint used in the first week = ( 1 / 2 ) * 360 = 180 gallons . remaning paint = 180 gallons paint used in the second week = ( 1 / 5 ) * 180 = 36 gallons total paint used = 216 gallons . option d"
Answer: d
Problem: convert 100 miles into inches ?
Options: a ) 6336000 , b ) 6542000 , c ) 5462300 , d ) 6213000 , e ) 6120330
Rationale: "1 feet = 12 inches 1 mile = 5280 feet 100 mile = 5280 * 12 * 100 = 6336000 ans : a"
Answer: a
Problem: how many digits will be there to the right of the decimal point in the product of 95.75 and . 02554 ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "sum of decimal places = 7 . since the last digit to the extreme right will be zero ( since 5 x 4 = 20 ) so there will be 6 significant digits to the right of the decimal point . answer is e ."
Answer: e
Problem: if an integer n is to be chosen at random from the integers 1 to 96 , inclusive , what is the probability that n ( n + 1 ) ( n + 2 ) will be divisible by 4 ?
Options: a ) 1 / 4 , b ) 3 / 8 , c ) 1 / 2 , d ) 5 / 8 , e ) 3 / 4
Rationale: "i get 5 / 8 as well 1 to 96 inclusive means we have 48 odd and 48 even integers e o e / 4 = integer , therefore we have 48 / 96 numbers divisible by 8 o e o / 4 = not integer we can not forget multiples of 8 from 1 to 96 we have 24 numbers that are multiple of 4 therefore , 48 / 96 + 24 / 96 = 72 / 96 = 3 / 4 answer : e"
Answer: e
Problem: in township k each property is taxed at 12 percent of its assessed value . if the assessed value of a property in township k is increased from $ 20,000 to $ 24,000 , by how much will the property tax increase ?
Options: a ) $ 32 , b ) $ 50 , c ) $ 320 , d ) $ 400 , e ) $ 480
Rationale: "increase in house value = $ 24,000 - $ 20,000 = $ 4000 so , tax increase = 12 % of $ 4000 = $ 480 answer : e"
Answer: e
Problem: when y is divided by 288 , the remainder is 44 . what is the remainder when the same y is divided by 24 ?
Options: a ) 20 , b ) 21 , c ) 23 , d ) 25 , e ) 26
Rationale: y = 288 * a + 44 = ( 24 * 12 ) * a + 24 + 20 the answer is a .
Answer: a
Problem: a certain university will select 1 of 5 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidates are there to fill the 3 positions ?
Options: a ) 42 , b ) 70 , c ) 140 , d ) 165 , e ) 225
Rationale: "1 of 5 will be chosen for the math 2 of 10 will be chosen for the computer none of the 3 chosen people can be in more than one departments . we can choose any of the 5 candidates for the math dep . , which gives as 5 selections . we can choose 2 of the 10 candidates for the computer dep . , which gives us 2 selections and 8 rejections . so , the way to find how many different selections of 2 candidates we can have for the computer dep . , we do : 10 ! / 2 ! * 8 ! = ( 9 * 10 ) / 2 = 90 / 2 = 45 . we are multiplying our individual selections : 5 * 45 = 225 in the bolded part , we do n ' t have to multiply all of the numbers , as those in 8 ! are included in 10 ! , so we simplify instead . ans e"
Answer: e
Problem: the cross - section of a cannel is a trapezium in shape . if the cannel is 14 m wide at the top and 4 m wide at the bottom and the area of cross - section is 380 sq m , the depth of cannel is ?
Options: a ) 39 , b ) 28 , c ) 27 , d ) 42 , e ) 71
Rationale: "1 / 2 * d ( 14 + 4 ) = 380 d = 42 answer : d"
Answer: d
Problem: after decreasing 24 % in the price of an article costs rs . 1140 . find the actual cost of an article ?
Options: a ) 1500 , b ) 6789 , c ) 1200 , d ) 6151 , e ) 1421
Rationale: "cp * ( 76 / 100 ) = 1140 cp = 15 * 100 = > cp = 1500 answer : a"
Answer: a
Problem: in a class of 60 students , 20 did not opt for math . 15 did not opt for science and 5 did not opt for either . how many students of the class opted for both math and science ?
Options: a ) 23 , b ) 25 , c ) 27 , d ) 30 , e ) 48
Rationale: "60 students total 20 did not opt for math 15 did not opt for science 5 did not opt for either total of 40 students in math and 10 did not opt for sci but did for math 40 - 10 = 30 30 students of the class opted for both math and science answer : d . 30"
Answer: d
Problem: a jeep takes 6 hours to cover a distance of 540 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 48 kmph , b ) 52 kmph , c ) 6 o kmph , d ) 63 kmph , e ) 65 kmph
Rationale: "time = 6 distance = 540 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 540 / 9 = 60 kmph c )"
Answer: c
Problem: a room 5 m 44 cm long and 3 m 74 cm broad needs to be paved with square tiles . what will be the least number of square tiles required to cover the floor ?
Options: a ) 176 , b ) 124 , c ) 224 , d ) 186 , e ) 190
Rationale: "length = 5 m 44 cm = 544 cm breadth = 3 m 74 cm = 374 cm area = 544 * 374 hcf = 34 area of square = 34 * 34 cm 2 no of tiles req = 544 * 374 / 34 * 34 = 16 * 11 = 176 answer a"
Answer: a
Problem: the ratio of 2 numbers is 2 : 3 and their h . c . f . is 10 . their l . c . m . is ?
Options: a ) 30 , b ) 60 , c ) 20 , d ) 10 , e ) 40
Rationale: "let the numbers be 2 x and 3 x their h . c . f . = 10 so the numbers are 2 * 10 , 3 * 10 = 20,30 l . c . m . = 60 answer is b"
Answer: b
Problem: what is the remainder when 1250 * 1090 * 1045 * 1055 is divided by 18 ?
Options: a ) 34 , b ) 19 , c ) 16 , d ) 14 , e ) 10
Rationale: "oa is ' c ' . oe : take the remainder from each of 1250 / 18 , 1090 / 18 and so on . . 1250 / 18 gives remainder = 8 1090 / 18 gives remainder = 10 1045 / 18 gives remainder = 1 1055 / 18 gives remainder = 11 the net remainder is the product of above individual remainders . i . e = 8 * 10 * 1 * 11 break them into pairs 8 * 10 / 18 gives remainder 8 and 1 * 11 / 18 gives remainder 11 so 8 * 11 / 18 gives remainder 16 . answer : c"
Answer: c
Problem: the least number , which when divided by 12 , 15 , 20 and 54 leaves in each case a remainder of 8 , is :
Options: a ) 504 , b ) 536 , c ) 544 , d ) 548 , e ) none of these
Rationale: "explanation : required number = ( l . c . m . of 12 , 15 , 20 , 54 ) + 8 = 540 + 8 = 548 . answer : option d"
Answer: d
Problem: if 7 a - 3 b = 10 b + 50 = - 12 b - 2 a , what is the value of 9 a + 9 b ?
Options: a ) - 9 , b ) - 6 , c ) 0 , d ) 6 , e ) 9
Rationale: "( i ) 7 a - 13 b = 50 ( ii ) 2 a + 22 b = - 50 adding ( i ) and ( ii ) : 9 a + 9 b = 0 the answer is c ."
Answer: c
Problem: suppose 10 monkeys take 20 minutes to eat 10 bananas . how many monkeys would it take to eat 80 bananas in 80 minutes ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 20 , e ) 13
Rationale: "one monkey takes 20 min to eat 1 banana , so in 80 mins 1 monkey will eat 4 bananas , so for 80 bananas in 80 min we need 80 / 4 = 20 monkeys answer : d"
Answer: d
Problem: if x + | x | + y = 4 and x + | y | - y = 6 what is x + y = ?
Options: a ) 11 , b ) - 1 , c ) 3 , d ) 5 , e ) 13
Rationale: "if x < 0 and y < 0 , then we ' ll have x - x + y = 7 and x - y - y = 6 . from the first equation y = 7 , so we can discard this case since y is not less than 0 . if x > = 0 and y < 0 , then we ' ll have x + x + y = 7 and x - y - y = 6 . solving gives x = 4 > 0 and y = - 1 < 0 - - > x + y = 3 . since in ps questions only one answer choice can be correct , then the answer is c ( so , we can stop here and not even consider other two cases ) . answer : c . adding both eqn we get 2 x + ixi + iyi = 13 now considering x < 0 and y > 0 2 x - x + y = 13 we get x + y = 11 hence answer should be a"
Answer: a
Problem: if 3 x + y = 40 , 2 x - y = 20 , for integers of x and y , 4 y ^ 2 = ?
Options: a ) 2 , b ) 4 , c ) 0 , d ) 10 , e ) 64
Rationale: "3 x + y = 40 2 x - y = 20 5 x = 60 x = 12 y = 4 4 y ^ 2 = 4 * 16 = 64 answer is e"
Answer: e
Problem: jonathan can type a 30 page document in 40 minutes , susan can type it in 30 minutes , and jack can type it in 24 minutes . working together , how much time will it take them to type the same document ?
Options: a ) 5 minutes , b ) 10 minutes , c ) 15 minutes , d ) 18 minutes , e ) 20 minutes
Rationale: "you may set up common equation like this : job / a + job / b + job / c = job / x memorize this universal formula , you will need it definitely for gmat . and find x from this equation in this specific case , the equation will look like this : 30 / 40 + 30 / 30 + 30 / 24 = 30 / x if you solve this equation , you get the same answer b ( 10 )"
Answer: b
Problem: the measure of the side of a square is multiplied by 7 . if x represents the perimeter of the original square , what is the value of the new perimeter ?
Options: a ) 3 x , b ) 4 x , c ) 7 x , d ) 12 x , e ) 27 x
Rationale: "original perimeter = x hence original side = x / 4 new side = 7 x / 4 new perimeter = 4 * 7 x / 4 = 7 x correct option : c"
Answer: c
Problem: a box contains 10 tablets of medicine a and 17 tablets of medicine b . what is the least number of tablets that should be taken from the box to ensure that at least two tablets of each kind are among the extracted .
Options: a ) 12 , b ) 15 , c ) 17 , d ) 19 , e ) 21
Rationale: "the worst case scenario will be if we remove all 17 tablets of medicine b first . the next 2 tablets we remove have to be of medicine a , so to guarantee that at least two tablets of each kind will be taken we should remove minimum of 17 + 2 = 19 tablets . answer : d ."
Answer: d
Problem: the milk level in a rectangular box measuring 60 feet by 25 feet is to be lowered by 6 inches . how many gallons of milk must be removed ? ( 1 cu ft = 7.5 gallons )
Options: a ) 100 , b ) 250 , c ) 750 , d ) 5625 , e ) 5635
Rationale: "6 inches = 1 / 2 feet ( there are 12 inches in a foot . ) , so 60 * 25 * 1 / 2 = 750 feet ^ 3 of milk must be removed , which equals to 750 * 7.5 = 5625 gallons . answer : d ."
Answer: d
Problem: from a group of 4 boys and 4 girls , 2 children are to be randomly selected . what is the probability that 1 boy and 1 girl will be selected ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 5 , d ) 4 / 7 , e ) 5 / 9
Rationale: "the total number of ways to choose 2 children from 8 is 8 c 2 = 28 the number of ways to choose 1 boy and 1 girl is 4 * 4 = 16 p ( 1 boy and 1 girl ) = 16 / 28 = 4 / 7 the answer is d ."
Answer: d
Problem: rhonda picked 2 pen from the table , if there were 7 pens on the table and 5 belongs to jill , what is the probability that the 2 pen she picked does not belong to jill ? .
Options: a ) 5 / 42 , b ) 2 / 42 , c ) 7 / 42 , d ) 2 / 7 , e ) 5 / 7
Rationale: since jill owns 5 of the pen , the subset from which the 2 pens hould be chosen are the 2 pens not owned by jill fom the universe of 7 . the first pen can be one of the 2 from the 7 with probability 2 / 7 . the second pen can be one of the 1 from the 6 remaining with probability 1 / 6 , the total probability will be 2 / 7 × 1 / 6 . on cancellation , this comes to 2 / 42 . thus , the answer is b - 2 / 42 .
Answer: b
Problem: a merchant sells an item at a 20 % discount , but still makes a gross profit of 20 percent of the cost . what percent w of the cost would the gross profit on the item have been if it had been sold without the discount ?
Options: a ) 20 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 75 %
Rationale: "let the market price of the product is mp . let the original cost price of the product is cp . selling price ( discounted price ) = 100 % of mp - 20 % mp = 80 % of mp . - - - - - - - - - - - - - - - - ( 1 ) profit made by selling at discounted price = 20 % of cp - - - - - - - - - - - - - - ( 2 ) apply the formula : profit w = selling price - original cost price = > 20 % of cp = 80 % of mp - 100 % cp = > mp = 120 cp / 80 = 3 / 2 ( cp ) now if product is sold without any discount , then , profit = selling price ( without discount ) - original cost price = market price - original cost price = mp - cp = 3 / 2 cp - cp = 1 / 2 cp = 50 % of cp thus , answer should bec ."
Answer: c
Problem: country x taxes each of its citizens an amount equal to 13 percent of the first $ 40,000 of income , plus 20 percent of all income in excess of $ 40,000 . if a citizen of country x is taxed a total of $ 8,000 , what is her income ?
Options: a ) $ 54,000 , b ) $ 56,000 , c ) $ 64,000 , d ) $ 66,667 , e ) $ 80,000
Rationale: "equation is correct , so math must be a problem . 0.13 * 40,000 + 0.2 * ( x - 40,000 ) = 8,000 - - > 5,200 + 0.2 x - 8,000 = 8,000 - - > 0.2 x = 10,800 - - > x = 54,000 . answer : a ."
Answer: a
Problem: a number when divided by 4 , gives 40 as quotient and 0 as remainder . what will be the remainder when dividing the same number by 3
Options: a ) a ) 1 , b ) b ) 3 , c ) c ) 4 , d ) d ) 6 , e ) e ) 7
Rationale: "explanation : p ÷ 4 = 40 = > p = 40 * 4 = 160 p / 3 = 160 / 3 = 53 , remainder = 1 answer : option a"
Answer: a
Problem: the surface of a cube is 294 sq cm . find its volume ?
Options: a ) 8 cc , b ) 9 cc , c ) 2 cc , d ) 343 cc , e ) 6 cc
Rationale: "6 a 2 = 294 = 6 * 49 a = 7 = > a 3 = 343 cc answer : d"
Answer: d
Problem: of 30 applicants for a job , 16 had at least 4 years ' experience , 21 had degrees , and 5 had less than 4 years ' experience and did not have a degree . how many of the applicants had at least 4 years ' experience and a degree ?
Options: a ) 12 , b ) 10 , c ) 9 , d ) 7 , e ) 5
Rationale: "set a : people with more than 4 years exp set b : people with degree aub = total - ( less than 4 exp and no degree ) aub = 30 - 5 = 25 aub = a + b - aib aib = 21 + 16 - 25 = 12 answer a"
Answer: a
Problem: the average marks of 20 students in a class is 100 . but a student mark is wrongly noted as 50 instead of 10 then find the correct average marks ?
Options: a ) 78 , b ) 82 , c ) 98 , d ) 91 , e ) 85
Rationale: "correct avg marks = 100 + ( 10 - 50 ) / 20 avg = 100 - 2 = 98 answer is c"
Answer: c
Problem: a parking garage rents parking spaces for $ 10 per week or $ 20 per month . how much does a person save in a year by renting by the month rather than by the week ?
Options: a ) $ 140 , b ) $ 160 , c ) $ 220 , d ) $ 240 , e ) $ 280
Rationale: "10 $ per week ! an year has 52 weeks . annual charges per year = 52 * 10 = 520 $ 30 $ per month ! an year has 12 months . annual charges per year = 12 * 20 = 240 $ 520 - 240 = 280 ans e"
Answer: e
Problem: jerry travels 8 miles at an average speed of 40 miles per hour , stops for 14 minutes , and then travels another 20 miles at an average speed of 60 miles per hour . what is jerry ’ s average speed , in miles per hour , for this trip ?
Options: a ) 36 , b ) 42.5 , c ) 44 , d ) 50 , e ) 52.5
Rationale: "total time taken by jerry = ( 8 / 40 ) * 60 minutes + 14 minutes + ( 20 / 60 ) * 60 minutes = 46 minutes average speed = total distance / total time = ( 8 + 20 ) miles / ( 46 / 60 ) hours = 28 * 60 / 46 = 36 miles per hour answer : option a"
Answer: a
Problem: the total surface area of a cuboid length 12 m , breadth 10 m and height 8 m .
Options: a ) 576
b ) 566
c ) 596
d ) 556
e ) 586
Rationale: total surface area of cuboid = 2 ( lb + bh + lh ) = 2 ( 120 + 80 + 96 ) = 2 ( 296 ) = > 596 m ( power 2 ) answer is c .
Answer: c
Problem: the average salary per head of the entire staff of an office including the officers and clerks is rs . 90 . the average salary of officers is rs . 500 and that of the clerks is rs . 84 . if the number of officers is 2 , find the number of officers in the office ?
Options: a ) 620 , b ) 720 , c ) 820 , d ) 920 , e ) 1020
Rationale: "500 84 \ / 90 / \ 6 410 3 : 205 3 - > 12 205 - > ? 820 answer : c"
Answer: c
Problem: what is the least integer greater than – 4 + 0.5 ?
Options: a ) – 3 , b ) – 1 , c ) 0 , d ) 1 , e ) 2
Rationale: "this question is just about doing careful arithmetic and remembering what makes a numberbiggerorsmallercompared to another number . first , let ' s take care of the arithmetic : ( - 4 ) + ( 0.5 ) = - 3.5 on a number line , since we ' re adding + . 5 to a number , the total moves to the right ( so we ' re moving from - 4 to - 3.5 ) . next , the question asks for the least integer that is greater than - 3.5 again , we can use a number line . numbers become greater as you move to the right . the first integer to the right of - 3.5 is - 3 . final answer : a"
Answer: a
Problem: if â € œ * â €  is called â € œ + â €  , â € œ / â €  is called â € œ * â €  , â € œ - â €  is called â € œ / â €  , â € œ + â €  is called â € œ - â €  . 240 / 80 â € “ 60 * 40 - 10 = ?
Options: a ) 355 , b ) 341 , c ) 323.2 , d ) 425.6 , e ) 225.7
Rationale: "explanation : given : 240 / 80 â € “ 60 * 40 - 10 = ? substituting the coded symbols for mathematical operations , we get , 240 * 80 / 60 + 40 / 10 = ? 240 * 1.33 + 4 = ? 319.2 + 4 = 323.2 answer : c"
Answer: c
Problem: 60 boys can complete a work in 24 days . how many men need to complete twice the work in 20 days
Options: a ) 144 , b ) 170 , c ) 180 , d ) 190 , e ) 200
Rationale: "one man can complete the work in 24 * 60 = 1440 days = one time work to complete the work twice it will be completed in let m be the no . of worker assign for this therefore the eqn becomes m * 20 = 2 * 1440 m = 144 workers answer : a"
Answer: a
Problem: jill has 21 gallons of water stored in quart , half - gallon , and one gallon jars . she has equal numbers of each size jar holding the liquid . what is the total number of water filled jars ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 36 , e ) 14
Rationale: let the number of each size of jar = wthen 1 / 4 w + 1 / 2 w + w = 21 1 3 / 4 w = 21 w = 12 the total number of jars = 3 w = 36 answer : d
Answer: d
Problem: jacob is 12 years old . he is 3 times as old as his brother . how old will jacob be when he is twice as old ?
Options: a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17
Rationale: "j = 12 ; j = 3 b ; b = 12 / 3 = 4 ; twice as old so b = 4 ( now ) + ( 4 ) = 8 ; jacob is 12 + 4 = 16 answer : d"
Answer: d
Problem: if two integers x , y ( x > y ) are selected from - 10 to 1 ( inclusive ) , how many possible cases are there ?
Options: a ) 150 , b ) 66 , c ) 190 , d ) 210 , e ) 240
Rationale: "if two integers x , y ( x > y ) are selected from - 10 to 9 ( inclusive ) , how many possible cases are there ? a . 150 b . 180 c . 190 d . 210 e . 240 - - > 12 c 2 = 12 * 11 / 2 = 66 . therefore , the answer is b ."
Answer: b
Problem: a trader sells 40 metres of cloth for rs . 8200 at a profit of rs . 20 per metre of cloth . how much profit will the trder earn on 40 metres of cloth ?
Options: a ) rs . 800 , b ) rs . 1500 , c ) rs . 1000 , d ) rs . 1200 , e ) none of these
Rationale: "explanation : sp of 1 metre cloth = 8200 / 40 = rs . 205 . cp of 1 metre cloth = rs . 205 – 20 = rs . 185 cp on 40 metres = 185 x 40 = rs . 7400 profit earned on 40 metres cloth = rs . 8200 – rs . 7400 = rs . 800 . answer : option a"
Answer: a
Problem: what least value must be given to * so that the number 451 * 603 is exactly divisible by 9 ?
Options: a ) 2 , b ) 5 , c ) 7 , d ) 8 , e ) 9
Rationale: sum of digits = ( 4 + 5 + 1 + x + 6 + 0 + 3 ) = 19 + x divisible by 9 clearly x = 9 answer e 9
Answer: e
Problem: 24 machines can do a work in 10 days . how many machines are needed to complete the work in 40 days ?
Options: a ) 10 , b ) 6 , c ) 4 , d ) 7 , e ) 5
Rationale: "required number of machines = 24 * 10 / 40 = 6 answer is b"
Answer: b
Problem: in a company of 170 employees , 110 are females . a total of 80 employees have advanced degrees and the rest have a college degree only . if 25 employees are males with college degree only , how many employees are females with advanced degrees ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 60
Rationale: the number of males is 170 - 110 = 60 . the number of males with advanced degrees is 60 - 25 = 35 . the number of females with advanced degrees is 80 - 35 = 45 . the answer is b .
Answer: b
Problem: at a particular graduation party with 300 guests , 70 % of the guests brought gifts , and 40 % of the female guests brought gifts . if 36 males did not bring gifts to the party , how many females did bring gifts ?
Options: a ) 18 , b ) 36 , c ) 42 , d ) 68 , e ) 70
Rationale: "the correct method total = 300 . . 70 % of 300 = 210 got gifts . . 90 did not get gift , out of which 48 are males , so remaining 90 - 36 = 54 are females . . but 40 % females brought gift , so 60 % did not get it . . so 60 % = 54 , 100 % = 54 * 100 / 60 = 90 . . ans 40 % of 90 = 36 b"
Answer: b
Problem: if 8 a = 9 b and ab ≠ 0 , what is the ratio of a / 9 to b / 8 ?
Options: a ) 64 / 81 , b ) 8 / 9 , c ) 1 , d ) 9 / 8 , e ) 81 / 64
Rationale: "if ab ≠ 0 then a and b has two integer sets of pair if a = 9 then b = 8 and if a = - 9 then b = - 8 also in fraction if a = 1 / 8 then b = 1 / 9 any of the pair we check the ratio 8 a / 9 b = 1 answer : c"
Answer: c
Problem: in a theater , the first row has 17 seats and each row has 3 more seats than previous row . if the last row has 44 seats , what is the total number of seats in the theater ?
Options: a ) 265 , b ) 275 , c ) 285 , d ) 295 , e ) 305
Rationale: "the number of seats in the theater is 17 + ( 17 + 3 ) + . . . + ( 17 + 27 ) = 10 ( 17 ) + 3 ( 1 + 2 + . . . + 9 ) = 10 ( 17 ) + 3 ( 9 ) ( 10 ) / 2 = 170 + 135 = 305 the answer is e ."
Answer: e
Problem: the list price of an article is rs . 69 . a customer pays rs . 56.16 for it . he was given two successive discounts , one of them being 10 % . the other discount is ?
Options: a ) 9.33 % , b ) 9.44 % , c ) 9.45 % , d ) 9.56 % , e ) 9.67 %
Rationale: "69 * ( 90 / 100 ) * ( ( 100 - x ) / 100 ) = 56.16 x = 9.56 % answer : d"
Answer: d