regisss/math_qa huggingface dataset:
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 . 3982 . what is the difference between rohan ’ s and sudhir ’ s share in the profit ?
Options: a ) rs . 362 , b ) rs . 383 , c ) rs . 398 , d ) rs . 399 , e ) rs . 400
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 . 3982 × 1 / 11 = rs . 362 . a )"
Answer: a
Problem: how many words , with or without meaning , can be formed using all letters of the word orange using each letter exactly once ?
Options: a ) 700 , b ) 720 , c ) 740 , d ) 760 , e ) 780
Rationale: "the word orange has exactly 6 letters which are all different . therefore the number of words that can be formed = number of permutations of 6 letters taken all at a time . = p ( 6 , 6 ) = 6 ! = 6 × 5 x 4 x 3 x 2 × 1 = 720 answer : b"
Answer: b
Problem: if p is the product of the integers from 1 to 32 , inclusive , what is the greatest integer k for which 3 ^ k is a factor of p ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "32 ! has 3 , 6 , 9 , . . . . 30 as factors , which are 10 multiples of 3 . we need to add 4 more to 10 because of 9 , 18 , and 27 . the answer is c ."
Answer: c
Problem: two kinds of vodka are mixed in the ratio 1 : 5 and 5 : 1 and they are sold fetching the profit 10 % and 20 % respectively . if the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4 / 3 and 5 / 3 times respectively , then the mixture will fetch the profit of
Options: a ) 21 % , b ) 20 % , c ) 21 % 18 % , d ) 23 % , e ) can not be determined
Rationale: "the profit on the first kind of vodka = x % ; the profit on the second kind of vodka = y % . when they are mixed in the ratio 1 : 2 ( total of 3 parts ) the average profit is 10 % : ( x + 2 y ) / 3 = 10 . when they are mixed in the ratio 2 : 1 ( total of 3 parts ) the average profit is 20 % : ( 2 x + y ) / 3 = 20 . solving gives : x = 30 % and y = 0 % . after the individual profit percent on them areincreased by 4 / 3 and 5 / 3 times respectively the profit becomes 40 % and 0 % , on the first and te second kinds of vodka , respectively . if they are mixed in equal ratio ( 1 : 1 ) , then the mixture will fetch the profit of ( 40 + 0 ) / 2 = 20 % . answer : c"
Answer: c
Problem: a salesman sold twice as much pears in the afternoon than in the morning . if he sold $ 360 kilograms of pears that day , how many kilograms did he sell in the morning and how many in the afternoon ?
Options: a ) 120 , b ) 180 , c ) 240 , d ) 280 , e ) 320
Rationale: "let x be the number of kilograms he sold in the morning . then in the afternoon he sold 2 x kilograms . so , the total is x + 2 x = 3 x . this must be equal to 360 . 3 x = 360 x = 3603 x = 120 therefore , the salesman sold 120 kg in the morning and 2 ⋅ 120 = 240 kg in the afternoon . so answer is c ."
Answer: c
Problem: the average of the marks of 25 students in a class is 70 . if the marks of each student are doubled , find the new average ?
Options: a ) 140 , b ) 100 , c ) 85 , d ) 160 , e ) 190
Rationale: "sum of the marks for the 25 students = 25 * 70 = 1750 . the marks of each student are doubled , the sum also will be doubled . the new sum = 1750 * 2 = 3500 . so , the new average = 3500 / 25 = 140 . answer : a"
Answer: a
Problem: a train after traveling for 50 km meets with an accident and then proceeds at 3 / 4 of its former speed and arrives at its destination 35 minutes late . had the accident occurred 24 km farther , it would have reached the destination only 25 minutes late . what is the speed w of the train .
Options: a ) a ) 45 , b ) b ) 33 , c ) c ) 48 , d ) d ) 55 , e ) e ) 61
Rationale: "let y be the balance distance to be covered and x be the former speed . a train after traveling for 50 km meets with an accident and then proceeds at 3 / 4 of its former speed and arrives at its destination 35 minutes late so , y / ( 3 x / 4 ) - y / x = 35 / 60 4 y / 3 x - y / x = 7 / 12 y / x ( 4 / 3 - 1 ) = 7 / 12 y / x * 1 / 3 = 7 / 12 y / x = 7 / 4 4 y - 7 x = 0 . . . . . . . . 1 had the accident occurred 24 km farther , it would have reached the destination only 25 minutes late so , ( y - 24 ) / ( 3 x / 4 ) - ( y - 24 ) / x = 25 / 60 4 ( y - 24 ) / 3 x - ( y - 24 ) / x = 5 / 12 ( y - 24 ) / x ( 4 / 3 - 1 ) = 5 / 12 ( y - 24 ) / x * 1 / 3 = 5 / 12 ( y - 24 ) * 12 = 3 x * 5 ( y - 24 ) * 4 = 5 x 4 y - 5 x = 96 . . . . . . . 2 eq 2 - eq 1 2 x = 96 x = 48 = w ans = c"
Answer: c
Problem: amit and ananthu can do a work in 10 days and 20 days respectively . amit started the work and left after 2 days . ananthu took over and completed the work . in how many days was the total work completed ?
Options: a ) 18 days , b ) 20 days , c ) 23 days , d ) 25 days , e ) 27 days
Rationale: amit ’ s one day ’ s work = 1 / 10 amit ’ s 2 day ’ s work = 1 / 10 * 2 = 1 / 5 work left = 1 - 1 / 5 = 4 / 5 ananthu ’ s one day ’ s work = 1 / 20 ananthu can do work in = 4 / 5 * 20 = 16 days so total days = 16 + 2 = 18 days answer : a
Answer: a
Problem: there are two positive numbers in the ratio 4 : 8 . if the larger number exceeds the smaller by 16 , then find the smaller number ?
Options: a ) 25 , b ) 20 , c ) 77 , d ) 88 , e ) 44
Rationale: "let the two positive numbers be 5 x and 8 x respectively . 8 x - 4 x = 16 4 x = 16 = > x = 4 = > smaller number = 5 x = 20 . answer : b"
Answer: b
Problem: cheese , bologna , and peanut butter sandwiches were made for a picnic in a ratio of 1 to 7 to 8 . if a total of 80 sandwiches were made , how many bologna sandwiches were made ?
Options: a ) 15 , b ) 30 , c ) 35 , d ) 42 , e ) 48
Rationale: for deciding such task we should calculate all parts 1 + 7 + 8 = 16 parts and we should calculate how many sandwiches holds 1 part : 80 / 16 = 5 sandwiches in one part for bologna we have 7 parts so : 7 * 5 = 35 answer is c
Answer: c
Problem: for the past n days , the average ( arithmetic mean ) daily production at a company was 50 units . if today ' s production of 110 units raises the average to 55 units per day , what is the value of n ?
Options: a ) 9 , b ) 11 , c ) 13 , d ) 15 , e ) 17
Rationale: "the daily production was raised by 5 units for n days , which has a weighting of 5 n . 5 n = 110 - 55 = 55 n = 11 the answer is b ."
Answer: b
Problem: a train is 360 meter long is running at a speed of 50 km / hour . in what time will it pass a bridge of 140 meter length ?
Options: a ) 87 , b ) 69 , c ) 36 , d ) 72 , e ) 21
Rationale: "speed = 50 km / hr = 50 * ( 5 / 18 ) m / sec = 125 / 9 m / sec total distance = 360 + 140 = 500 meter time = distance / speed = 500 * ( 9 / 125 ) = 36 seconds answer : c"
Answer: c
Problem: the population of locusts in a certain swarm doubles every two hours . if 4 hours ago there were 1,000 locusts in the swarm , in approximately how many hours will the swarm population exceed 128,000 locusts ?
Options: a ) 12 , b ) 8 , c ) 4 , d ) 10 , e ) 16
Rationale: - 4 hours : 1,000 - 2 hours : 2,000 now : 4,000 + 2 hours : 8,000 + 4 hours : 16,000 + 6 hours : 32,000 + 8 hours : 64,000 + 10 hours : 128,000 answer : d
Answer: d
Problem: the cash difference between the selling prices of an book at a profit of 12 % and 20 % is $ 3 . the ratio of the two selling prices is :
Options: a ) 55 : 23 , b ) 52 : 33 , c ) 52 : 53 , d ) 45 : 53 , e ) 14 : 15
Rationale: "let c . p . of the book be $ x . then , required ratio = 112 % of x / 120 % of x = 112 / 120 = 14 / 15 = 14 : 15 e"
Answer: e
Problem: mixture contains alcohol and water in the ratio 4 : 3 . if 5 liters of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture .
Options: a ) 10 , b ) 99 , c ) 27 , d ) 22 , e ) 29
Rationale: "let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 20 x = 4 ( 3 x + 5 ) 8 x = 20 x = 2.5 quantity of alcohol = ( 4 x 2.5 ) litres = 10 litres . answer : a"
Answer: a
Problem: a train 310 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 140 m long ?
Options: a ) 40 , b ) 56 , c ) 41 , d ) 36 , e ) 34
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 310 + 140 = 450 m required time = 450 * 2 / 25 = 36 sec answer : option d"
Answer: d
Problem: a merchant gets a 5 % discount on each meter of fabric he buys after the first 2,000 meters and a 7 % discount on every meter after the next 1,500 meters . the price , before discount , of one meter of fabric is $ 2 , what is the total amount of money the merchant spends on 6,500 meters of fabric ?
Options: a ) $ 11,320 , b ) $ 12,430 , c ) $ 13,540 , d ) $ 14,650 , e ) $ 15,760
Rationale: "for first 2000 meters he does not get any discount . the price is 2 * 2000 = $ 4000 for next 1500 meters , he gets a 5 % discount . the price is 1.9 * 1500 = $ 2850 for the next 1500 meters , he gets a 7 % discount . the price is 1.86 * 3000 = $ 5580 the total price is $ 4000 + $ 2850 + $ 5580 = $ 12,430 the answer is b ."
Answer: b
Problem: two pipes a and b can fill a tank in 36 hours and 46 hours respectively . if both the pipes are opened simultaneously , how much time will be taken to fill the tank ?
Options: a ) 20.195 hrs , b ) 21.195 hrs , c ) 22.195 hrs , d ) 23.195 hrs , e ) 20.495 hrs
Rationale: "a fill in one hour = 1 / 36 b fill in one hour = 1 / 46 both fill in one hour = 1 / 36 + 1 / 46 = 82 / 1656 time taken by both pipes = 1656 / 82 = 20.195 hrs answer : a"
Answer: a
Problem: a grocer has a sale of rs . 5435 , rs . 5927 , rs . 5855 , rs . 6230 and rs . 5562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 5500 ?
Options: a ) 4991 , b ) 5991 , c ) 3991 , d ) 6542 , e ) 6995
Rationale: "total sale for 5 months = rs . ( 5435 + 5927 + 5855 + 6230 + 5562 ) = rs . 29009 . required sale = rs . [ ( 5500 x 6 ) - 29009 ] = rs . ( 33000 - 29009 ) = rs . 3991 answer : option c"
Answer: c
Problem: find the result of equation of the ellipse whose foci are at ( 0 , - 5 ) and ( 0 , 5 ) and the length of its major axis is 14 .
Options: a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1
Rationale: from the coordinates of the foci , c = 5 and the major axis is the y axis . from the length of the major axis , we obtain a = 7 . also b 2 = a 2 - c 2 = 24 . the equation of the ellipse is given by x 2 / 24 + y 2 / 49 = 1 correct answer is e ) 1
Answer: e
Problem: if p represents the product of the first 16 positive integers , then p is not a multiple of
Options: a ) 99 , b ) 84 , c ) 72 , d ) 65 , e ) 51
Rationale: "answer is e . since prime factor of 51 is 3 x 17 . 17 is a prime number and not part of the first 15 positive integers . a ) 9 x 11 b ) 12 x 7 c ) 12 x 6 d ) 13 x 5 e ) 3 x 17"
Answer: e
Problem: if 12 machine can finish a job in 40 days , then how many more machines would be needed to finish the job in one - fourth less time ?
Options: a ) a . 4 , b ) b . 8 , c ) c . 10 , d ) d . 12 , e ) e . 16
Rationale: you might think of this in a management context - we can use the principle of ' person - hours ' to solve any problem where we have identical workers . so , using simpler numbers , suppose you know that 6 identical employees , working simultaneously , would finish a job in 5 hours . then that job requires 6 * 5 = 30 total hours of person - work . if instead you wanted the job done in 3 hours , you ' d assign 30 / 3 = 10 employees to do the job , because you want to get a total of 30 hours of work from the employees . we can solve this problem identically . if 12 machines ( identical ones , i assume ) work simultaneously for 40 days , they will do a total of 12 * 40 machine - days of work . so the job requires 12 * 40 days of machine work in total . we instead want the job done in 1 / 4 less time , so in 30 days . so we ' ll need 12 * 40 / 30 = 16 machines , or 4 additional machines . a
Answer: a
Problem: following an increase in prices , the price of a candy box was 20 pounds and the price of a can of soda was 6 pounds . if the price of a candy box was raised by 25 % , and the price of a can of soda was raised by 50 % . what was the price of a box of candy plus a can of soda before prices were raised ?
Options: a ) 11 . , b ) 20 . , c ) 13 . , d ) 14 . , e ) 14.5
Rationale: "price of candy before price increase = 20 / 1.25 = 16 price of soda before price increase = 6 / 1.5 = 4 total price = 16 + 4 = 20 b is the answer"
Answer: b
Problem: a rectangular farm has to be fenced one long side , one short side and the diagonal . if the cost of fencing is rs . 14 per meter . the area of farm is 1200 m 2 and the short side is 30 m long . how much would the job cost ?
Options: a ) 1276 , b ) 1680 , c ) 2832 , d ) 1299 , e ) 1236
Rationale: "explanation : l * 30 = 1200 è l = 40 40 + 30 + 50 = 120 120 * 14 = 1680 answer : option b"
Answer: b
Problem: . a car covers a distance of 810 km in 5 hours . find its speed ?
Options: a ) 104 , b ) 55 , c ) 162 , d ) 174 , e ) 2761
Rationale: "810 / 5 = 162 kmph answer : c"
Answer: c
Problem: the compounded ratio of ( 2 : 3 ) , ( 6 : 11 ) and ( 11 : 2 ) is
Options: a ) 2 : 0 , b ) 2 : 1 , c ) 2 : 9 , d ) 2 : 2 , e ) 2 : 5
Rationale: answer : b ) 2 : 1
Answer: b
Problem: in a photography exhibition , some photographs were taken by octavia the photographer , and some photographs were framed by jack the framer . jack had framed 24 photographs taken by octavia , and 12 photographs taken by other photographers . if 36 of the photographs in the exhibition were taken by octavia , how many photographs were either framed by jack or taken by octavia ?
Options: a ) 36 , b ) 48 , c ) 72 , d ) 96 , e ) 108
Rationale: the number of photographs either framed by jack or taken by octavia = { jack } + { octavia } - { overlap } = 36 + 36 - 24 = 48 ( { overlap } is green box ) . answer : b
Answer: b
Problem: a train 360 m long is running at a speed of 45 kmph . in what time will it pass a bridge 140 m long ?
Options: a ) 40 sec , b ) 42 sec , c ) 45 sec , d ) 48 sec , e ) 49 sec
Rationale: "speed of the train 45 * 5 / 18 = 25 / 2 m / sec time = ( 360 + 140 ) / 25 / 2 = 500 * 2 / 25 = 40 sec answer : a"
Answer: a
Problem: what is value of ( p + q ) / ( p - q ) if p / q = 7 ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 4 / 3 , d ) 5 / 3 , e ) none of these
Rationale: explanation : ( p + q ) / ( p - q ) = ( p / q + 1 ) / ( p / q - 1 ) = ( 7 + 1 ) / ( 7 - 1 ) = 4 / 3 . answer : c
Answer: c
Problem: find the area of a cuboid of length 8 cm , breadth 6 cm . and height 9 cm .
Options: a ) 400 cm cube , b ) 410 cm cube , c ) 420 cm cube , d ) 432 cm cube , e ) 480 cm cube
Rationale: "area of a cuboid = lxbxh = 8 cm x 6 cm x 9 cm = 432 cm cube answer : d"
Answer: d
Problem: if | 5 x - 20 | = 100 , then find the sum of the values of x ?
Options: a ) 1 , b ) - 2 , c ) 8 , d ) - 3 , e ) 4
Rationale: "| 5 x - 20 | = 100 5 x - 20 = 100 or 5 x - 20 = - 100 5 x = 120 or 5 x = - 80 x = 24 or x = - 16 sum = 24 - 16 = 8 answer is c"
Answer: c
Problem: a windmill is taking advantage of strong air currents in order to produce electrical energy . on a typical day the wind speed is around 20 mph and in that speed the windmill produces 400 kw / h ( kilowatts per hour ) . on a stormy day a windmill produces 20 % more energy . how much kw / h can 3 windmills produce in two hours on a stormy day ?
Options: a ) 2880 . , b ) 4860 . , c ) 5780 , d ) 5760 , e ) 6380 .
Rationale: normal day = 400 kw / h stormy day = 400 * 1.2 = 480 kw / h 3 windmills for 2 hours on stormy day 480 * 3 * 2 = 2880 answer : a
Answer: a
Problem: john has 10 pairs of matched socks . if he loses 13 individual socks , what is the greatest number of pairs of matched socks he can have left ?
Options: a ) 7 , b ) 3 , c ) 5 , d ) 4 , e ) 1
Rationale: "because we have to maximize the pair of matched socks , we will remove 6 pairs ( 12 socks ) out of 10 pairs 1 sock from the 7 th pair . thus the no of matching socks pair remaining = 10 - 7 = 3 answer b"
Answer: b
Problem: arjun started a business with rs . 20,000 and is joined afterwards by anoop with rs . 30 , 000 . after how many months did anoop join if the profits at the end of the year are divided equally ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "suppose anoop joined after 3 months . then , 20000 * 12 = 30000 * ( 12 – x ) = > 120000 = 30000 x = > x = 4 . answer : b"
Answer: b
Problem: the points a ( 0 , 0 ) , b ( 0 , 4 a - 5 ) and c ( 2 a + 1 , 2 a + 5 ) form a triangle . if angle abc = 90 , what is the area of triangle abc ?
Options: a ) 80 , b ) 82.5 , c ) 78.5 , d ) 75.5 , e ) 74
Rationale: "1 / 2 bh = 1 / 2 ( 2 a + 1 ) ( 2 a + 5 ) now 4 a - 5 = 2 a + 5 2 a = 10 , a = 5 therefore , a ( 0,0 ) ; b ( 0,15 ) ; c ( 10,15 ) 1 / 2 * 11 * 15 = 82.5 answer : b"
Answer: b
Problem: ramesh purchased a refrigerator for rs . 12500 after getting a discount of 20 % on the labelled price . he spent rs . 125 on transport and rs . 250 on installation . at what price should it be sold so that the profit earned would be 18 % if no discount was offered ?
Options: a ) 17608 , b ) 17606 , c ) 17604 , d ) 17600 , e ) 18880
Rationale: "price at which the tv set is bought = rs . 12,500 discount offered = 20 % marked price = 12500 * 100 / 80 = rs . 15625 the total amount spent on transport and installation = 125 + 250 = rs . 375 \ total price of tv set = 15625 + 375 = rs . 16000 the price at whichthe tv should be sold to get a profit of 18 % if no discount was offered = 16000 * 118 / 100 = rs . 18880 . answer : e"
Answer: e
Problem: a hall is 15 meters long and 15 meters wide . if the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls , what is the volume of the hall ( in cubic meters ) ?
Options: a ) 975.5 , b ) 1250.5 , c ) 1465.5 , d ) 1687.5 , e ) 1824.5
Rationale: "2 hl + 2 hw = 2 lw h = lw / ( l + w ) volume = lwh = ( lw ) ^ 2 / ( l + w ) = 1687.5 the answer is d ."
Answer: d
Problem: what is the total surface area in square meters of a rectangular solid whose length is 9 meters , width is 8 meters , and depth is 5 meters ?
Options: a ) 152 m 2 , b ) 162 m 2 , c ) 180 m 2 , d ) 300 m 2 , e ) 314 m 2
Rationale: "surface area of a cuboid = 2 ( lb + bh + lh ) = 2 ( 9 * 8 + 8 * 5 + 9 * 5 ) = 2 ( 72 + 40 + 45 ) = 2 * 157 = 314 m 2 answer : e"
Answer: e
Problem: how many multiples of 7 are there between 10 and 100 ( both are inclusive ) ?
Options: a ) 11 , b ) 13 , c ) 15 , d ) 17 , e ) 21
Rationale: "7 multiples are 14 , 21,28 , - - - - - - - - - , 98 it should be mentioned whether 10 and 100 are inclusive . the answer is ( 98 - 14 ) / 7 + 1 = 13 answer is b"
Answer: b
Problem: a car traveling at a certain constant speed takes 4 seconds longer to travel 1 km than it would take to travel 1 km at 80 km / hour . at what speed , in km / hr , is the car traveling ?
Options: a ) 70 , b ) 72 , c ) 74 , d ) 75 , e ) 78
Rationale: "time to cover 1 kilometer at 80 kilometers per hour is 1 / 80 hours = 3,600 / 80 seconds = 45 seconds ; time to cover 1 kilometer at regular speed is 45 + 4 = 49 seconds = 49 / 3,600 hours = 1 / 74 hours ; so , we get that to cover 1 kilometer 1 / 74 hours is needed - - > regular speed 74 kilometers per hour ( rate is a reciprocal of time or rate = distance / time ) . answer : c"
Answer: c
Problem: a , b and c invested rs . 6300 , rs . 4200 and rs . 10500 respectively , in a partnership business . find the share of a in profit of rs . 12500 after a year ?
Options: a ) 3630 , b ) 2881 , c ) 2887 , d ) 3750 , e ) 2212
Rationale: 6300 : 4200 : 10500 3 : 2 : 5 3 / 10 * 12100 = 3750 . answer : d
Answer: d
Problem: two numbers are in the ratio of 2 : 3 . if 20 be subtracted from each , they are in the ratio of 10 : 17 . find the numbers ?
Options: a ) 70,105 , b ) 60,88 , c ) 80,120 , d ) 60,84 , e ) 60,81
Rationale: "( 2 x - 20 ) : ( 3 x - 20 ) = 10 : 17 x = 35 = > 70,105 answer : a"
Answer: a
Problem: a student needs 30 % of the marks on a test to pass the test . if the student gets 80 marks and fails the test by 100 marks , find the maximum marks set for the test .
Options: a ) 400 , b ) 600 , c ) 800 , d ) 1000 , e ) 1200
Rationale: "30 % = 180 marks 1 % = 6 marks 100 % = 600 marks the answer is b ."
Answer: b
Problem: to asphalt 1 km road , 30 men spent 12 days working 8 hours per day . how many days , 20 men will spend to asphalt a road of 2 km working 8 hours a day ?
Options: a ) 40 , b ) 36 , c ) 42 , d ) 44 , e ) 46
Rationale: "man - hours required to asphalt 1 km road = 30 * 12 * 8 = 2880 man - hours required to asphalt 2 km road = 2880 * 2 = 5760 man - hours available per day = 20 * 8 = 160 therefore number of days = 5760 / 240 = 36 days ans = b"
Answer: b
Problem: if x and j are integers and 2 x – j = 11 , then 4 x + j can not be
Options: a ) – 5 , b ) 1 , c ) 13 , d ) 17 , e ) 551
Rationale: 2 x - j = 11 . . . . j = 2 x - 11 4 x + j = 4 x + 2 x - 11 = 6 x - 11 6 x - 11 = - 5 . . . x = 1 6 x - 11 = 1 . . . x = 2 6 x - 11 = 13 . . . x = 4 6 x - 11 = 17 . . x is not integer 6 x - 11 = 551 . . x is not integer i think the choice e is 55 not 551 . otherwise both de can not be solution = d
Answer: d
Problem: 15.06 * 0.001 = ?
Options: a ) 15060000 , b ) 0.001506 , c ) 0.01506 , d ) 0.1506 , e ) none of these
Rationale: "explanation : clearly after decimal 5 digits should be there . option c"
Answer: c
Problem: a small table has a length of 12 inches and a breadth of b inches . cubes are placed on the surface of the table so as to cover the entire surface . the maximum side of such cubes is found to be 4 inches . also , a few such tables are arranged to form a square . the minimum length of side possible for such a square is 48 inches . find b .
Options: a ) 8 , b ) 16 , c ) 24 , d ) 32 , e ) 48
Rationale: "from the info that the maximum sides of the cubes is 4 , we know that the gcf of 12 ( = 2 ^ 2 * 3 ) and ` ` b ' ' is 4 ( = 2 ^ 2 ) , so ` ` b ' ' = 2 ^ x , where x > = 2 . from the second premise , we know that the lcm of 12 ( 2 ^ 2 * 3 ) and ` ` b ' ' is 48 ( 2 ^ 4 * 3 ) , so ` ` b ' ' = 2 ^ 4 or 2 ^ 4 * 3 ( 16 or 48 ) . combining 2 premises shows the answer is b ( 16 ) ."
Answer: b
Problem: an investment yields an interest payment of $ 228 each month . if the simple annual interest rate is 9 % , what is the amount of the investment ?
Options: a ) $ 28,300 , b ) $ 30,400 , c ) $ 31,300 , d ) $ 32,500 , e ) $ 35,100
Rationale: "let the principal amount = p simple annual interest = 9 % simple monthly interest = ( 9 / 12 ) = ( 3 / 4 ) % ( 3 / 4 ) * ( p / 100 ) = 228 = > p = ( 228 * 4 * 10 ^ 2 ) / 3 = 76 * 4 * 10 ^ 2 = 304 * 10 ^ 2 answer b"
Answer: b
Problem: on a certain road 10 % of the motorists exceed the posted speed limit and receive speeding tickets , but 24 % of the motorists who exceed the posted speed limit do not receive speeding tickets . what percent of the motorists on the road exceed the posted speed limit ?
Options: a ) 10.5 % , b ) 13.2 % , c ) 15 % , d ) 22 % , e ) 30 %
Rationale: "answer is b . this question is in the og and thus well explained by ets . those who exceed : x so x = 10 % + 0,24 x id est x = 13.2 %"
Answer: b
Problem: joe ’ s average ( arithmetic mean ) test score across 4 equally weighted tests was 45 . he was allowed to drop his lowest score . after doing so , his average test score improved to 50 . what is the lowest test score that was dropped ?
Options: a ) 20 , b ) 30 , c ) 55 , d ) 65 , e ) 80
Rationale: "the arithmetic mean of 4 equally weighted tests was 45 . so what we can assume is that we have 4 test scores , each 45 . he dropped his lowest score and the avg went to 50 . this means that the lowest score was not 45 and other three scores had given the lowest score 5 each to make it up to 45 too . when the lowest score was removed , the other 3 scores got their 5 back . so the lowest score was 3 * 5 = 15 less than 45 . so the lowest score = 45 - 15 = 30 answer ( b )"
Answer: b
Problem: if y > 0 , ( 4 y ) / 20 + ( 3 y ) / 10 is what percent of y ?
Options: a ) 40 % , b ) 50 % , c ) 60 % , d ) 70 % , e ) 80 %
Rationale: "can be reduced to 2 y / 10 + 3 y / 10 = y / 2 = 50 % answer b"
Answer: b
Problem: in how many years rs 100 will produce the same interest at 5 % as rs . 600 produce in 4 years at 10 %
Options: a ) 44 , b ) 52 , c ) 50 , d ) 46 , e ) 48
Rationale: "explanation : clue : firstly we need to calculate the si with prinical 600 , time 4 years and rate 10 % , it will be rs . 240 then we can get the time as time = ( 100 * 240 ) / ( 100 * 5 ) = 48 option e"
Answer: e
Problem: in the number 10,0 ab , a and b represent the tens and units digits , respectively . if 11,0 ab is divisible by 55 , what is the greatest possible value of b × a ?
Options: a ) 0 , b ) 5 , c ) 10 , d ) 15 , e ) 25
Rationale: you should notice that 55 * 2 = 110 so 11,000 is divisible by 55 : 55 * 200 = 11,000 ( or you can notice that 11,000 is obviously divisible by both 5 and 11 so by 55 ) - - > b * a = 0 * 0 = 0 . next number divisible by 55 is 11,000 + 55 = 11,055 : b * a = 5 * 5 = 15 ( next number wo n ' t have 110 as the first 3 digits so we have only two options 0 and 25 ) . answer : e . ! please post ps questions in the ps subforum : gmat - problem - solving - ps - 140 / please post ds questions in the ds subforum : gmat - data - sufficiency - ds - 141 / no posting of ps / ds questions is allowed in the mainmath forum . d
Answer: d
Problem: a clock shows the time as 7 a . m . if the minute hand gains 5 minutes every hour , how many minutes will the clock gain by 6 p . m . ?
Options: a ) 45 minutes , b ) 55 minutes , c ) 35 minutes , d ) 25 minutes , e ) 40 minutes
Rationale: "there are 11 hours in between 7 a . m . to 6 p . m . 11 * 5 = 55 minutes . answer : b"
Answer: b
Problem: if mn ≠ 0 and 25 percent of n equals 37 1 / 2 percent of m , what is the value of 12 n / m ?
Options: a ) 18 , b ) 323323 , c ) 8 , d ) 3 , e ) 98
Rationale: given : 25 percent of n equals 37 ( 1 / 2 ) percent of m = > ( 25 / 100 ) * n = ( 75 / 200 ) * m = > 2 n = 3 m . 12 n / m = 6 * 2 n / m = 6 * 3 m / m = 18 . hence a .
Answer: a
Problem: if the cost price of 18 articles is equal to the selling price of 16 articles , what is the percentage of profit or loss that the merchant makes ?
Options: a ) 20 % loss , b ) 12.5 % profit , c ) 33.33 % loss , d ) 30.33 % loss , e ) none of these
Rationale: "explanation : let cost price of 1 article be re . 1 . therefore , cost price of 18 articles = rs . 18 . selling price of 16 articles = rs . 18 therefore , selling price of 18 articles is : - = > 18 / 16 ã — 18 = > 20.25 . therefore , profit = selling price - cost price . = > 20.25 â ˆ ’ 18 = 2.25 . hence , the percentage of profit = profit x 100 / c . p . = > 2.25 / 18 ã — 100 . = > 12.5 % profit . answer : b"
Answer: b
Problem: the average age of 15 students of a class is 16 years . out of these , the average age of 5 students is 14 years and that of the other 9 students is 16 years . tee age of the 15 th student is ?
Options: a ) 22 years , b ) 24 years , c ) 26 years , d ) 28 years , e ) 30 years
Rationale: "age of the 15 th student = [ 15 * 16 - ( 14 * 5 + 16 * 9 ) ] = ( 240 - 214 ) = 26 years . answer : c"
Answer: c
Problem: if the length of an edge of cube p is thrice the length of an edge of cube q , what is the ratio of the volume of cube q to the volume of cube p ?
Options: a ) 1 / 4
b ) 1 / 5
c ) 1 / 6
d ) 1 / 27
e ) 1 / 9
Rationale: the length of cube q = 1 ; the length of cube p = 3 ; the ratio of the volume of cube q to the volume of cube p = 1 ^ 3 / 3 ^ 3 = 1 / 27 answer : d
Answer: d
Problem: si on a certain sum of money for 3 yrs at 8 percent / annum is 1 / 2 the ci on rs . 4000 for 2 yrs at 10 percent / annum . the sum placed on si is ?
Options: a ) rs . 1700 , b ) rs . 1720 , c ) rs . 1750 , d ) rs . 1850 , e ) rs . 2000
Rationale: c . i . = rs . 4000 x 1 + 10 2 - 4000 100 = rs . 4000 x 11 x 11 - 4000 10 10 = rs . 840 . sum = rs . 420 x 100 = rs . 1750 . 3 x 8 c
Answer: c
Problem: bag a contains red , white and blue marbles such that the red to white marble ratio is 1 : 3 and the white to blue marble ratio is 2 : 3 . bag b contains red and white marbles in the ratio of 1 : 4 . together , the two bags contain 22 white marbles . how many red marbles could be in bag a ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 2 , e ) 8
Rationale: "# of red marbles in bag a can be either 2 or 6 . no 2 in the choices , so 6 . d . bag a : r : w : b = 2 : 6 : 9 bag b r : w = 1 : 4 6 x + 4 y = 22 i . e 3 x + 2 y = 11 x has to be odd to make an odd sum from the eq . x = 1 , y = 4 or x = 3 , y = 1 so r can be 2 x i . e 2 or 6 . answer d"
Answer: d
Problem: what is the sum of the first 23 natural numbers ( starting from 1 ) ?
Options: a ) 256 , b ) 266 , c ) 276 , d ) 286 , e ) 296
Rationale: the sum of n natural numbers = n * ( n + 1 ) / 2 = 23 * 24 / 2 = 276 the answer is c .
Answer: c
Problem: in a garden , 26 trees are planted at equal distances along a yard 700 metres long , one tree being at each end of the yard . what is the distance between two consecutive trees ?
Options: a ) 10 , b ) 28 , c ) 12 , d ) 14 , e ) 16
Rationale: "26 trees have 25 gaps between them . length of each gap = 700 / 25 = 28 i . e . , distance between two consecutive trees = 28 answer is b ."
Answer: b
Problem: a , b and c started a business with a total investment of rs . 72000 . a invests rs . 6000 more than b and b invests rs . 3000 less than c . if the total profit at the end of a year is rs . 8640 , find b ' s share .
Options: a ) rs . 3240 , b ) rs . 2520 , c ) rs . 2880 , d ) rs . 3360 , e ) none of these
Rationale: "explanation : let c ' s investment = rs . x b ' s investment = rs . ( x - 3000 ) a ' s investment = rs . ( x - 3000 + 6000 ) = rs . ( x + 3000 ) now , ( a + b + c ) ' s investment = rs . 72000 = > x + ( x - 3000 ) + ( x + 3000 ) = 72000 = > 3 x = 72000 = > x = 24000 hence , a ' s investment = rs . 27000 b ' s investment = rs . 21000 c ' s investment = rs . 24000 ratio of the capitals of a , b and c = 27000 : 21000 : 24000 = 9 : 7 : 8 a ' s share = rs . [ ( 7 / 24 ) ã — 8640 ] = rs . 2520 answer : option b"
Answer: b
Problem: what will be the percentage increase in the area of the cube ' s surface if each of the cube ' s edges grows by 20 % ?
Options: a ) 33 % , b ) 44 % , c ) 55 % , d ) 56 % , e ) 73 %
Rationale: "the question is very easy . my logic is the following : a surface = 6 * a ^ 2 after 20 % increase a surface = 6 * ( ( 1.2 a ) ^ 2 ) = 6 * 1.44 * a ^ 2 the increase in the surface area = ( 6 * 1.44 * a ^ 2 - 6 * a ^ 2 ) / 6 * a ^ 2 = ( 6 * a ^ 2 ( 1.44 - 1 ) ) / ( 6 * a ^ 2 ) = 1.44 - 1 = 0.44 = 44 % answer : b"
Answer: b
Problem: two pipes a and b can separately fill a tank in 12 and 15 minutes respectively . a third pipe c can drain off 45 liters of water per minute . if all the pipes are opened , the tank can be filled in 15 minutes . what is the capacity of the tank ?
Options: a ) 399 , b ) 540 , c ) 772 , d ) 272 , e ) 121
Rationale: "1 / 12 + 1 / 15 - 1 / x = 1 / 15 x = 12 12 * 45 = 540 answer : b"
Answer: b
Problem: what is the diagonal of a square field whose perimeter is 64 m ?
Options: a ) 15 m , b ) 16 √ 2 m , c ) 20 m , d ) 25 m , e ) 18 m
Rationale: "sol : let the side of the square be xm . therefore , 4 x = 64 x = 16 diagonal of the square is = √ 2 * ( 16 ) ^ 2 = 16 √ 2 answer : b"
Answer: b
Problem: the difference between simple interest and compound interest on rs . 1400 for one year at 20 % per annum reckoned half - yearly is :
Options: a ) $ 185.63 , b ) $ 852.36 , c ) $ 875.5 , d ) $ 989.9 , e ) $ 875.8
Rationale: "s . i = [ ( 1400 * 20 * 1 ) / 100 ] = $ 280 . c . i = [ 1400 * ( 1 + ( 5 / 100 ) ^ 2 ) - 1400 ] = $ 1269.8 . difference = ( 1269.8 - 280 ) = $ 989.8 answer ( d )"
Answer: d
Problem: a semicircular shaped window has diameter of 63 cm . its perimeter equals
Options: a ) 162
b ) 766
c ) 298
d ) 277
e ) 198
Rationale: explanation : perimeter of window = { \ color { blue } \ pi } r + 2 r = [ { ( 22 / 7 ) * ( 63 / 2 ) } + 63 ] = 99 + 63 = 162 cm answer : a ) 162
Answer: a
Problem: by selling 100 pens , a trader gains the cost of 30 pens . find his gain percentage ?
Options: a ) 30 % , b ) 33 % , c ) 31 % , d ) 32 % , e ) 34 %
Rationale: "let the cp of each pen be rs . 1 . cp of 100 pens = rs . 100 profit = cost of 30 pens = rs . 30 profit % = 30 / 100 * 100 = 30 % answer : a"
Answer: a
Problem: out of 3 consecutive odd numbers 11 times the first number is equal to addition of thrice the third number and adding 16 to 4 times the second . what is the first number ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: description : = > 11 x = 4 ( x + 2 ) + 16 + 3 ( x + 4 ) = > 11 x = 7 x + 36 = > 4 x = 36 x = 9 answer e
Answer: e
Problem: working together at their respective constant rates , machine a and machine b can produce 1600 units in 8 hours . working alone , machine b would complete that same output in 50 % more time . if machine a were to work on its own for an 8 - hour shift , what percent of the 1600 unit total would it produce ?
Options: a ) 25 , b ) 33 , c ) 50 , d ) 67 , e ) 75
Rationale: 1 / a + 1 / b = 1 / t 1 / a + 1 / 12 = 1 / 8 ( 50 % more of 8 is 12 ) 1 / a = 1 / 24 machine a can produce 1600 units in 24 hrs , so it can produce 1600 * 8 / 24 = 533.33 units is 8 hrs . 533.33 is 33.33 % of 1600 . b is the answer
Answer: b
Problem: according to the formula f = 9 / 5 ( c ) + 32 , if the temperature in degrees farenheit ( f ) increases by 26 , by how much does the temperature in degrees celsius ( c ) increase ?
Options: a ) 9 , b ) 14.44 , c ) 47 , d ) 48 3 / 5 , e ) 59
Rationale: "you can plug in values . c = 5 / 9 * ( f - 32 ) f = 32 - - > c = 0 ; f = 32 + 26 = 58 - - > c = 5 / 9 * 26 = 14.44 . increase = 14.44 degrees . answer : b ."
Answer: b
Problem: if price of t . v set is reduced by 20 % , then its sale increases by 80 % , find net effect on sale value
Options: a ) 44 , b ) 45 , c ) 46 , d ) 47 , e ) 48
Rationale: "- a + b + ( ( - a ) ( b ) / 100 ) = - 20 + 80 + ( - 20 * 80 ) / 100 = - 20 + 80 - 16 = 44 answer : a"
Answer: a
Problem: 9 . on level farmland , two runners leave at the same time from the intersection of two country roads . one runner jogs due north at a constant rate of 8 miles per hour while the second runner jogs due east at a constant rate that is 8 miles per hour faster than the first runner ' s rate . how far apart , to the nearest mile , will they be after 1 / 2 hour ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 12 , e ) 9
Rationale: "if runner 1 is going north and runner 2 is going east they are like two sides of a 90 degree triangle . side 1 = 8 m / h - - > 4 m in 1 / 2 hr side 2 = 16 m / h - - > 8 m in 1 / 2 hr to complete this right angle triangle d ^ 2 = 4 ^ 2 + 8 ^ 2 d ^ 2 = 80 = ~ 9 answer option e"
Answer: e
Problem: the captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average of the team ?
Options: a ) 23 , b ) 25 , c ) 30 , d ) 22 , e ) 40
Rationale: "let the average of the whole team be x years . 11 x - ( 26 + 29 ) = 9 ( x - 1 ) = 11 x - 9 x = 46 = 2 x = 46 = > x = 23 so , average age of the team is 23 years . answer a"
Answer: a
Problem: tom and marry each have a bag of marbles , each of which contains 4 red marbles , 10 blue marbles , and 6 yellow marbles . if tom and marry each select one marble from their respective bags , what is the probability that either tom or marry select a blue marble ?
Options: a ) 1 / 7 , b ) 2 / 4 , c ) 3 / 4 , d ) 1 / 8 , e ) 1 / 16
Rationale: probability that either selects a red marble , p ( either ) = 1 - probability that neither selects a blue marble , p ( neither ) probability that tom selects non blue = 10 c 1 / 20 c 1 = 1 / 2 probability that marry selects non blue = 10 c 1 / 20 c 1 = 1 / 2 = > p ( either ) = 1 - ( 1 / 2 * 1 / 2 ) = 1 - 1 / 4 = 3 / 4 . c )
Answer: c
Problem: if 7 cats can kill 7 rats in 7 minutes , how long will it take 100 cats to kill 100 rats ?
Options: a ) 5 minutes , b ) 6 minutes , c ) 7 minutes , d ) 8 minutes , e ) 9 minutes
Rationale: "it will take 7 minutes for 100 cats to kill 100 rats . 1 cat can kill 1 rat in 7 minutes , so 100 cats can kill 100 rats in 7 minutes answer c"
Answer: c
Problem: at the wholesale store you can buy an 8 - pack of hot dogs for $ 1.55 , a 20 - pack for $ 3.05 , and a 250 - pack for $ 20.95 . what is the greatest number of hot dogs you can buy at this store with $ 300 ?
Options: a ) 3,108 , b ) 3,100 , c ) 3,108 , d ) 3,540 , e ) 3,256
Rationale: to maximize number of hot dogs with 300 $ total number of hot dogs bought in 250 - pack = 20.95 * 14 = 293.30 $ amount remaining = 300 - 293.30 = 6.7 $ total number of hot dogs bought in 20 - pack = 3.05 * 2 = 6.10 $ amount remaining = 6.70 - 6.10 = 0.6 $ this amount is too less to buy any 8 - pack . greatest number of hot dogs one can buy with 300 $ = 250 * 14 + 20 * 2 = 3,540 answer d
Answer: d
Problem: a person spends 1 / 3 rd of the money with him on clothes , 1 / 5 th of the remaining on food and 1 / 4 th of the remaining on travel . now , he is left with rs 200 . how much did he have with him in the beginning ?
Options: a ) s 200 , b ) s 500 , c ) s 300 , d ) s 450 , e ) s 550
Rationale: suppose the amount in the beginning was rs ’ x ’ money spent on clothes = rs 1 x / 3 balance = rs 2 x / 3 money spent on food = 1 / 5 of 2 x / 3 = rs 2 x / 15 balance = 2 x / 3 - 2 x / 15 = rs 8 x / 15 money spent on travel = 1 / 4 of 8 x / 15 = rs 2 x / 15 = 8 x / 15 - 2 x / 15 = 6 x / 15 = rs 2 x / 5 therefore 2 x / 5 = 200 = 500 answer : b
Answer: b
Problem: the shopkeeper increased the price of a product by 25 % so that customer finds it difficult to purchase the required amount . but somehow the customer managed to purchase only 76 % of the required amount . what is the net difference in the expenditure on that product ?
Options: a ) 12.5 % , b ) 13 % , c ) 5 % , d ) 17 % , e ) 19 %
Rationale: quantity x rate = price 1 x 1 = 1 0.76 x 1.25 = 0.95 decrease in price = ( 0.05 / 1 ) × 100 = 5 % c )
Answer: c
Problem: if a number n is chosen at random from the set of two - digit integers whose digits are both prime numbers , what is the probability r that n is divisible by 3 ?
Options: a ) 1 / 3 , b ) ¼ , c ) 9 / 25 , d ) 5 / 16 , e ) 0
Rationale: "prime digits are : 2 , 3 , 5 , 7 total number of 2 digit # s with both digits prime are : 4 * 4 = 16 out of these numbers divisible by 3 = 33 , 27 , 57 , 72 and 75 . i had to find the numbers manually using the 4 numbers above . = > prob = 5 / 16 . ans d . took me 3 : 20 mins ."
Answer: d
Problem: 0 - - - : - | - - - : - - | - : - - : - | - - : - - - | - : - - - - 1 on the number line above , the segment from 0 to 1 has been divided into fifths , as indicated by the large tick marks , and also into sevenths , as indicated by the small tick marks . what is the least possible distance x between any two of the tick marks ?
Options: a ) 1 / 70 , b ) 1 / 35 , c ) 2 / 35 , d ) 1 / 12 , e ) 1 / 7
Rationale: divisions are 0 1 / 7 2 / 7 3 / 7 4 / 7 5 / 7 6 / 7 1 1 / 5 2 / 5 3 / 5 4 / 5 5 / 5 expressing the same in terms of the lcm of 57 , i . e 35 0 7 / 35 14 / 35 21 / 35 28 / 35 35 / 35 5 / 35 10 / 35 15 / 35 20 / 35 25 / 35 30 / 35 by comparing the divisions with each other we can see 1 / 35 is the shortest possible distance between any two selected divisions . x = 1 / 35 answer is b .
Answer: b
Problem: find the area of a parallelogram with base 21 cm and height 11 cm ?
Options: a ) 231 cm 2 , b ) 384 cm 2 , c ) 672 cm 2 , d ) 267 cm 2 , e ) 286 cm 2
Rationale: "area of a parallelogram = base * height = 21 * 11 = 231 cm 2 answer : a"
Answer: a
Problem: a cycle is bought for rs . 1120 and sold for rs . 1200 , find the gain percent ?
Options: a ) 7 % , b ) 2 % , c ) 6 % , d ) 1 % , e ) 8 %
Rationale: "explanation : 1120 - - - - 80 100 - - - - ? = > 7 % answer : a"
Answer: a
Problem: a trader bought a car at 20 % discount on its original price . he sold it at a 70 % increase on the price he bought it . what percent of profit did he make on the original price ?
Options: a ) 17 % , b ) 72 % , c ) 12 % , d ) 82 % , e ) 36 %
Rationale: "original price = 100 cp = 80 s = 80 * ( 170 / 100 ) = 136 100 - 136 = 36 % answer : e"
Answer: e
Problem: a boat having a length 9 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 ) 189 kg , d ) 180 kg , e ) 270 kg
Rationale: "volume of water displaced = ( 9 x 3 x 0.01 ) m 3 = 0.27 m 3 . mass of man = volume of water displaced x density of water = ( 0.27 x 1000 ) kg = 270 kg . answer : e"
Answer: e
Problem: what annual payment will discharge a debt of rs . 1030 due in 2 years at the rate of 5 % compound interest ?
Options: a ) 553.94 , b ) 551.25 , c ) 534.33 , d ) 543.33 , e ) 646.33
Rationale: "explanation : let each installment be rs . x . then , x / ( 1 + 5 / 100 ) + x / ( 1 + 5 / 100 ) 2 = 1030 820 x + 1030 * 441 x = 553.94 so , value of each installment = rs . 553.94 answer : option a"
Answer: a
Problem: in a factory , there are 90 % technicians and 10 % non - technicians . if the 90 % of the technicians and 10 % of non - technicians are permanent employees , then the percentage of workers who are temporary is ?
Options: a ) 62 % , b ) 57 % , c ) 52 % , d ) 82 % , e ) 42 %
Rationale: "total = 100 t = 90 nt = 10 90 * ( 10 / 100 ) = 910 * ( 90 / 100 ) = 9 9 + 9 = 18 = > 100 - 18 = 82 % answer : d"
Answer: d
Problem: how many seconds will a 450 metre long train take to cross a man running with a speed of 6 km / hr in the direction of the moving train if the speed of the train is 60 km / hr ?
Options: a ) 25 , b ) 30 , c ) 40 , d ) 45 , e ) 60
Rationale: explanation : speed of train relatively to man = ( 60 - 6 ) km / hr = 54 km / hr = ( 54 x 5 / 18 ) m / sec = 15 m / sec time taken to pass the man = ( 450 / 15 ) sec = 30 sec . answer : b
Answer: b
Problem: of the total amount that jill spent on a shopping trip , excluding taxes , she spent 60 percent on clothing , 20 percent on food , and 20 percent on other items . if jill paid a 10 percent tax on the clothing , no tax on the food , and an 10 percent tax on all other items , then the total tax that she paid was what percent of the total amount that she spent , excluding taxes ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 25 , e ) 15
Rationale: "assume she has $ 200 to spend . tax clothing = 60 % = $ 120 = $ 12.00 food = 20 % = $ 40 = $ 0.00 items = 20 % = $ 40 = $ 8.00 total tax = $ 20.00 % of total amount = 20 / 200 * 100 = 10 % answer a"
Answer: a
Problem: 90 kg of an alloy a is mixed with 140 kg of alloy b . if alloy a has lead and tin in the ratio 3 : 4 and alloy b has tin and copper in the ratio 2 : 5 , then the amount of tin in the new alloy is ?
Options: a ) 100.6 kg , b ) 95.4 kg , c ) 117.5 kg , d ) 91.4 kg , e ) 92 kg
Rationale: "quantity of tin in 90 kg of a = 90 * 4 / 7 = 51.4 kg quantity of tin in 140 kg of b = 140 * 2 / 7 = 40 kg quantity of tin in the new alloy = 51.4 + 40 = 91.4 kg answer is d"
Answer: d
Problem: a rectangular garden is to be twice as long as it is wide . if 180 yards of fencing , including the gate , will completely enclose the garden , what will be the length of the garden , in yards ?
Options: a ) 60 , b ) 70 , c ) 80 , d ) 90 , e ) 100
Rationale: "alternate approach backsolving ( using answer options to reach the correct answer ) can work wonders here if one is fast in calculations . given perimeter is 180 so , 2 ( l + b ) = 180 or , l + b = 90 now use the answer options ( given length ; breath will be half the length ) ( a ) 60 l = 60 ; b = 30 l + b = 90 ( b ) 70 l = 70 ; b = 35 l + b = 105 ( c ) 80 l = 80 ; b = 40 l + b = 120 ( d ) 90 l = 90 ; b = 45 l + b = 135 ( e ) 100 l = 100 ; b = 50 l + b = 150 thus you see no , need of any calculations , u can reach the correct option only by checking options ; correct answer will be ( a )"
Answer: a
Problem: what is the value of 3 x ^ 2 − 1.8 x + 0.3 for x = 0.6 ?
Options: a ) − 0.3 , b ) 0 , c ) 0.3 , d ) 1.08 , e ) 2.46
Rationale: "3 x ^ 2 - 1.8 x + 0.3 for x = 0.6 = 3 ( 0.6 * 0.6 ) - 3 * 0.6 * ( 0.6 ) + 0.3 = 0 + 0.3 = 0.3 answer : c"
Answer: c
Problem: three pipes , a , b , & c are attached to a tank . a & b can fill it in 20 & 30 minutes respectively while c can empty it in 20 minutes . if a , b & c are kept open successively for 1.5 minute each , how soon will the tank be filled ?
Options: a ) 2 hours , b ) 4 hours , c ) 5 hours , d ) 2 hours 15 min , e ) 3 hours
Rationale: "in three minute 1 / 20 + 1 / 30 - 1 / 20 = 2 / 60 = 1 / 30 part is filled 4.5 min - - - - - - - - 1 / 30 parts x min - - - - - - - - - 1 part ( full ) x = 135 min = 2 hours 15 min answer : d"
Answer: d
Problem: a train passes a station platform in 30 sec and a man standing on the platform in 20 sec . if the speed of the train is 54 km / hr . what is the length of the platform ?
Options: a ) 120 m , b ) 240 m , c ) 168 m , d ) 75 m , e ) 60 m
Rationale: "speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 20 = 300 m . let the length of the platform be x m . then , ( x + 300 ) / 30 = 15 = > x = 60 m answer : e"
Answer: e
Problem: if the sides of a cube are in the ratio 9 : 7 . what is the ratio of their diagonals ?
Options: a ) 4 : 3 , b ) 16 : 9 , c ) 9 : 7 , d ) 3 : 4 , e ) 3 : 8
Rationale: "explanation : diagonal of a cube = a √ 3 where a is side a 1 : a 2 = 9 : 7 d 1 : d 2 = 9 : 7 where √ 3 cancelled both side answer : c"
Answer: c
Problem: last year elaine spent 20 % of her annual earnings on rent . this year she earned 20 % more than last year and she spent 30 % of her annual earnings on rent . the amount she spent on rent this year is what percent of the amount spent on rent last year ?
Options: a ) 185.5 , b ) 180.0 , c ) 167.5 , d ) 172.5 , e ) 177.5
Rationale: "for this it is easiest to use simple numbers . let ' s assume that elaine ' s annual earnings last year were $ 100 . she would ' ve spent $ 20 of this on rent . this year she earned 20 % more , or $ 120 she would ' ve spent 30 % of this on rent , or $ 36 do $ 36 / $ 20 this will give you 180 % b is the correct answer ."
Answer: b
Problem: a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets $ 500 more than d , what is c ' s share ?
Options: a ) $ 1200 , b ) $ 1600 , c ) $ 1800 , d ) $ 2000 , e ) $ 2400
Rationale: "let the shares of a , b , c and d be 5 x , 2 x , 4 x and 3 x respectively . then , 4 x - 3 x = 500 x = $ 500 c ' s share = 4 x = 4 * $ 500 = $ 2000 the answer is d ."
Answer: d
Problem: two bullet train s 140 m and 200 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time ( in seconds ) which they take to cross each other , is :
Options: a ) 15.8 sec . , b ) 12.24 sec . , c ) 11.8 sec . , d ) 10.8 sec . , e ) 08.8 sec .
Rationale: relative speed = ( 60 + 40 ) km / hr = 100 x 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = ( 140 + 200 ) m = 340 m . required time = 340 x 9 / 250 = 54 / 5 = 12.24 sec . answer b
Answer: b
Problem: in 1950 , richard was 4 times as old as robert . in 1955 , richard was 3 times as old as robert . in which year was richard 1.5 times as old as robert ?
Options: a ) 1960 , b ) 1965 , c ) 1970 , d ) 1975 , e ) 2000
Rationale: "in 1950 : ri = 4 ro - - - - - - - - - - - - - - eq 1 in 1955 : ri + 5 = 3 ( ro + 5 ) - - - - - - - - - eq 2 thus in 1950 , solving eq 1 and eq 2 ro = 10 , ri = 40 now for each year we can calculate : 2000 : ri = 60 , ro = 90 thus ans : e"
Answer: e
Problem: the population of a bacteria culture doubles every 2 minutes . approximately how many minutes will it take for the population to grow from 1,000 to 300,000 bacteria
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "the question basically asks how many minutes it takes for a population to increase by factor 300 ( 300,000 / 1,000 = 300 ) . now you know that every two minutes the population doubles , i . e . is multiplied by 2 . so the equation becomes : 2 ^ x > = 300 , where x represents the number of times the population doubles . a lot of people remember that 2 ^ 10 = 1,024 . hence , 2 ^ 8 = 256 , i . e . the population has to double 8 times . since it takes the population 2 minutes to double once it takes 8 * 2 minutes = 16 minutes to double 8 times . thus , solution d = 16 is correct ."
Answer: d
Problem: in what ratio must tea at rs . 60 per kg be mixed with tea at rs . 70 per kg so that the mixture must be worth rs . 67.5 per kg ?
Options: a ) 3 : 1 , b ) 3 : 2 , c ) 4 : 3 , d ) 1 : 3 , e ) none
Rationale: "required ratio = 250 : 750 = 1 : 3 answer d"
Answer: d