regisss/math_qa huggingface dataset:
Problem: when positive integer n is divided by 3 , the remainder is 1 . when n is divided by 5 , the remainder is 4 . what is the smallest positive integer p , such that ( n + p ) is a multiple of 11 ?
Options: a ) 1 , b ) 2 , c ) 5 , d ) 7 , e ) 20
Rationale: when positive integer n is divided by 3 , the remainder is 1 i . e . , n = 3 x + 1 values of n can be one of { 1 , 4 , 7 , 10 , 13 , 16 , 19 , 22 . . . . . . . . . . . . . . 49 , 52 , 59 . . . . . . . . . . . . . . . . . . } similarly , when n is divided by 5 , the remainder is 5 . . i . e . , n = 5 y + 4 values of n can be one of { 4 , 9 , 14 , 19 , . . . } combining both the sets we get n = { 4,19 , 52 , . . . . . . . . . . . } what is the smallest positive integer p , such that ( n + p ) is a multiple of 11 or 11 x in case of n = 4 p = 7 so for min value of p , we take min value of n . d is the answer .
Answer: d
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 . 12400 after a year ?
Options: a ) 3630 , b ) 2881 , c ) 3720 , d ) 9977 , e ) 2212
Rationale: "6300 : 4200 : 10500 3 : 2 : 5 3 / 10 * 12400 = 3720 . answer : c"
Answer: c
Problem: two tains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post . if the length of each train be 100 metres , in what time ( in seconds ) will they cross each other travelling in opposite direction ?
Options: a ) 12 , b ) 11.9 , c ) 16 , d ) 20 , e ) 18
Rationale: sol . speed of the first train = [ 100 / 10 ] m / sec = 10 m / sec . speed of the second train = [ 100 / 15 ] m / sec = 6.7 m / sec . relative speed = ( 10 + 6.7 ) = m / sec = 16.7 m / sec . ∴ required time = ( 100 + 100 ) / 16.7 secc = 11.9 sec . answer b
Answer: b
Problem: if 40 % of ( x - y ) = 20 % of ( x + y ) , then what percent of x is y ?
Options: a ) 50.5 % , b ) 44.4 % , c ) 22.2 % , d ) 33.3 % , e ) 25 %
Rationale: "40 % of ( x - y ) = 20 % of ( x + y ) 40 / 100 ( x - y ) = 20 / 100 ( x + y ) x = 3 y required percentage = y / x * 100 = y / 3 y * 100 = 33.3 % answer is d"
Answer: d
Problem: in a 500 m race , the ratio of the speeds of two contestants a and b is 3 : 4 . a has a start of 170 m . then , a wins by :
Options: a ) 60 m , b ) 20 m , c ) 43 m , d ) 20 m , e ) 23 m
Rationale: "to reach the winning post a will have to cover a distance of ( 500 - 170 ) m , i . e . , 330 m . while a covers 3 m , b covers 4 m . while a covers 330 m , b covers 4 x 330 / 3 m = 440 m . thus , when a reaches the winning post , b covers 440 m and therefore remains 60 m behind . a wins by 60 m . answer : a"
Answer: a
Problem: from a pack of cards , two cards are drawn one after the other , with replacement . what is the probability that the first card is a club and the second card is a red king ?
Options: a ) 1 / 13 , b ) 1 / 15 , c ) 1 / 26 , d ) 1 / 52 , e ) 1 / 104
Rationale: p ( club ) = 1 / 4 p ( red king ) = 1 / 26 p ( club then a red king ) = 1 / 4 * 1 / 26 = 1 / 104 the answer is e .
Answer: e
Problem: a cube is painted red on all faces . it is then cut into 27 equal smaller cubes . how many cubes are painted on only 2 faces ?
Options: a ) 12
b ) 8
c ) 6
d ) 10
e ) 16
Rationale: the mini - cubes with 2 painted sides are all on the edge of the cube , in the ` ` middle ' ' of the edge . there are 4 in front , 4 in back and 4 more on the ` ` strip ' ' that runs around the left / top / right / bottom of the cube . 4 + 4 + 4 = 12 . answer a
Answer: a
Problem: in a certain pond , 40 fish were caught , tagged , and returned to the pond . a few days later , 40 fish were caught again , of which 2 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what is the approximate number of fish in the pond ?
Options: a ) 1000 , b ) 625 , c ) 1,250 , d ) 2,500 , e ) 10,000
Rationale: "total fish = x percentage of second catch = ( 2 / 40 ) * 100 = 5 % so , x * 5 % = 50 x = 1000 ans . a"
Answer: a
Problem: a man can do a piece of work in 6 days , but with the help of his son he can do it in 3 days . in what time can the son do it alone ?
Options: a ) 7 days , b ) 6 days , c ) 5 days , d ) 4 days , e ) none of these
Rationale: "explanation : in this type of question , where we have one person work and together work done . then we can easily get the other person work just by subtracting them . as son ' s one day work = ( 1 / 3 − 1 / 6 ) = ( 6 − 3 ) / 18 = 1 / 6 so son will do whole work in 6 days answer : b"
Answer: b
Problem: meena wrote all the numbers from 1 to 59,999 inclusive . how many digits did she write in total ?
Options: a ) 248,889 , b ) 268,889 , c ) 288,889 , d ) 308,889 , e ) 328,889
Rationale: "1 - 9 = > 1 * 9 digits 10 - 99 = > 2 * 90 = 180 ( numbers between 10 - 99 is 90 where each has 2 digits ) 100 - 999 = > 3 * 900 = 2700 1000 - 9999 = > 4 * 9000 = 36,000 10000 - 59999 = > 5 * 50,000 = 250,000 the answer is 288,889 the answer is c ."
Answer: c
Problem: if 3 < x < 6 < y < 9 , then what is the greatest possible positive integer difference of x and y ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "3 < x < 6 < y < 9 ; 3 < x y < 9 3 + y < x + 9 y - x < 6 . positive integer difference is 5 ( for example y = 8.5 and x = 3.5 ) answer : c ."
Answer: c
Problem: if 125 % of j is equal to 25 % of k , 150 % of k is equal to 50 % of l , and 175 % of l is equal to 75 % of m , then 20 % of m is equal to what percent of 150 % of j ?
Options: a ) 0.35 , b ) 466 , c ) 35 , d ) 350 , e ) 3500
Rationale: "imo answer should be 350 . . . consider j = 10 , then k = 50 , l = 150 and m = 350 . . . . 20 % of 350 , comes out to be 70 . . . . 150 % of 10 is 15 . . . . ( 70 * 100 ) / 15 = 466.66 . . . . ans : b"
Answer: b
Problem: a producer of tea blends two varieties of tea from two tea gardens one costing rs 18 per kg and another rs 20 per kg in the ratio 5 : 3 . if he sells the blended variety at rs 22 per kg , then his gain percent is
Options: a ) 12 % , b ) 13 % , c ) 14 % , d ) 15 % , e ) 17 %
Rationale: "explanation : suppose he bought 5 kg and 3 kg of tea . cost price = rs . ( 5 x 18 + 3 x 20 ) = rs . 150 . selling price = rs . ( 8 x 22 ) = rs . 176 . profit = 176 - 150 = 26 so , profit % = ( 26 / 150 ) * 100 = 17 % option e"
Answer: e
Problem: the cost price of 20 articles is the same as the selling price of x articles . if the profit is 25 % , find out the value of x
Options: a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17
Rationale: "explanation : let the cost price of one article = rs . 1 cp of x articles = rs . x cp of 20 articles = 20 selling price of x articles = 20 profit = 25 % [ given ] ⇒ ( sp − cp / cp ) = 25 / 100 = 1 / 4 ⇒ ( 20 − x ) / x = 1 / 4 ⇒ 80 − 4 x = x ⇒ 5 x = 80 option d ⇒ x = 805 = 16"
Answer: d
Problem: convert the 19 / 36 m / s into kilometers per hour ?
Options: a ) 1.7 , b ) 1.5 , c ) 1.3 , d ) 1.1 , e ) 1.9
Rationale: "19 / 36 m / s = 19 / 36 * 18 / 5 = 19 / 10 = 1.9 kmph . answer : e"
Answer: e
Problem: an error 5 % in excess is made while measuring the side of a square . what is the percentage of error in the calculated area of the square ?
Options: a ) 4.05 % , b ) 4.02 % , c ) 4 % , d ) 10.28 % , e ) 2 %
Rationale: "percentage error in calculated area = ( 5 + 5 + ( 5 ã — 5 ) / 100 ) % = 10.25 % answer : d"
Answer: d
Problem: for a certain art exhibit , a museum sold admission tickets to a group of 30 people every 6 minutes from 9 : 00 in the morning to 6 : 00 in the afternoon , inclusive . the price of a regular admission ticket was $ 10 and the price of a student ticket was $ 6 . if on one day 2 times as many regular admission tickets were sold as student tickets , what was the total revenue from ticket sales that day ?
Options: a ) $ 23400 , b ) $ 25920 , c ) $ 28080 , d ) $ 28500 , e ) $ 29160
Rationale: "from 9 : 00 in the morning to 6 : 00 in the afternoon , inclusive there are 9 * 10 = 90 five - minute intervals , thus total of 54 * 30 tickets were sold . say x student and 2 x regular tickets were sold , then x + 2 x = 90 * 30 - - > x = 30 * 30 and 2 x = 2 * ( 30 * 30 ) = 30 * 60 . therefore , the total revenue from ticket sales that day was 30 * 30 * 6 + 30 * 60 * 10 = $ 23,400 . answer : a ."
Answer: a
Problem: a can give b 100 meters start and c 170 meters start in a kilometer race . how much start can b give c in a kilometer race ?
Options: a ) 11.77 meters , b ) 55.77 meters , c ) 77.77 meters , d ) 113.77 meters , e ) none of these
Rationale: "explanation : a runs 1000 meters while b runs 900 meters and c runs 830 meters . therefore , b runs 900 meters while c runs 830 meters . so , the number of meters that c runs when b runs 1000 meters = ( 1000 x 830 ) / 900 = 922.22 meters thus , b can give c ( 1000 - 922.22 ) = 77.77 meters start answer : c"
Answer: c
Problem: company t produces two kinds of stereos : basic and deluxe . of the stereos produced by company t last month , 2 / 3 were basic and the rest were deluxe . if it takes 7 / 5 as many hours to produce a deluxe stereo as it does to produce a basic stereo , then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos ?
Options: a ) 5 / 17 , b ) 7 / 17 , c ) 4 / 17 , d ) 3 / 17 , e ) 5
Rationale: # of basic stereos was 2 / 3 of total and # of deluxe stereos was 1 / 3 of total , let ' s assume total = 15 , then basic = 10 and deluxe = 5 . now , if time needed to produce one deluxe stereo is 1 unit than time needed to produce one basic stereo would be 7 / 5 units . total time for basic would be 10 * 1 = 10 and total time for deluxe would be 5 * 7 / 5 = 7 - - > total time for both of them would be 10 + 7 = 17 - - > deluxe / total = 7 / 17 . b
Answer: b
Problem: a rectangular block 10 cm by 20 cm by 30 cm is cut into an exact number of equal cubes . find the least possible number of cubes ?
Options: a ) 6 , b ) 10 , c ) 15 , d ) 40 , e ) 22
Rationale: "volume of the block = 10 * 20 * 30 = 6000 cm ^ 3 side of the largest cube = h . c . f of 10 , 20,30 = 10 cm volume of the cube = 10 * 10 * 10 = 1000 cm ^ 3 number of cubes = 6000 / 1000 = 6 answer is a"
Answer: a
Problem: at a certain company , each employee has a salary grade s that is at least 1 and at most 5 . each employee receives an hourly wage p , in dollars , determined by the formula p = 11.50 + 0.25 ( s – 1 ) . an employee with a salary grade of 5 receives how many more dollars per hour than an employee with a salary grade of 1 ?
Options: a ) $ 0.50 , b ) $ 1.00 , c ) $ 1.25 , d ) $ 1.50 , e ) $ 1.75
Rationale: oa is definitely wrong . the answer should be e .
Answer: e
Problem: by selling an article at rs . 800 , a shopkeeper makes a profit of 25 % . at what price should he sell the article so as to make a loss of 45 % ?
Options: a ) s . 429 , b ) s . 352 , c ) s . 429 , d ) s . 128 , e ) s . 419
Rationale: "sp = 800 profit = 25 % cp = ( sp ) * [ 100 / ( 100 + p ) ] = 800 * [ 100 / 125 ] = 640 loss = 45 % = 45 % of 640 = rs . 288 sp = cp - loss = 640 - 288 = rs . 352 answer : b"
Answer: b
Problem: at a tanning salon , customers are charged $ 10 for their first visit in a calendar month and $ 5 for each visit after that in the same calendar month . in the last calendar month , 100 customers visited the salon , of which 30 made a second visit , and 10 made a third visit . all other customers made only one visit . if those visits were the only source of revenue for the salon , what was the revenue for the last calendar month at the salon ?
Options: a ) $ 1220 , b ) $ 1200 , c ) $ 1300 , d ) $ 1340 , e ) $ 1880
Rationale: "i get b . this question seems too straightforward for 600 + . am i missing something ? 100 first - time visits - - > 100 ( 10 ) = $ 1000 30 + 10 = 40 subsequent visits - - > 40 ( 5 ) = $ 200 total revenue : 1000 + 200 = $ 1200 the answer is b ."
Answer: b
Problem: pat , kate , and mark charged a total of 126 hours to a certain project . if pat charged twice as much time to the project as kate and 1 / 3 as much time as mark , how many more hours did mark charge to the project than kate ?
Options: a ) 18 , b ) 36 , c ) 72 , d ) 70 , e ) 108
Rationale: "70 all u do is do 2 : 1 : 6 = > 2 x + x + 6 x = 126 = > x = 14 28 : 14 : 84 84 - 14 = 70 answer d"
Answer: d
Problem: calculate the area of a triangle , if the sides of are 52 cm , 48 cm and 20 cm , what is its area ?
Options: a ) 480 cm 2 , b ) 580 cm 2 , c ) 380 cm 2 , d ) 180 cm 2 , e ) 280 cm 2
Rationale: "the triangle with sides 52 cm , 48 cm and 20 cm is right angled , where the hypotenuse is 52 cm . area of the triangle = 1 / 2 * 48 * 20 = 480 cm 2 answer : a"
Answer: a
Problem: employees of a certain company are each to receive a unique 9 - digit identification code consisting of the digits 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , and 8 such that no digit is used more than once in any given code . in valid codes , the second digit in the code is exactly twice the first digit . how many valid codes are there ?
Options: a ) 14,720 , b ) 16,240 , c ) 18,320 , d ) 20,160 , e ) 22,480
Rationale: "there are 7 ! ways to make codes starting with 12 . there are 7 ! ways to make codes starting with 24 . there are 7 ! ways to make codes starting with 36 . there are 7 ! ways to make codes starting with 48 . the number of codes is 4 * 7 ! = 20,160 . the answer is d ."
Answer: d
Problem: the amount of time that three people worked on a special project was in the ratio of 2 to 4 to 6 . if the project took 144 hours , how many more hours did the hardest working person work than the person who worked the least ?
Options: a ) 47 hours , b ) 45 hours , c ) 48 hours , d ) 49 hours , e ) 50 hours
Rationale: let the persons be a , b , c . hours worked : a = 2 * 144 / 12 = 24 hours b = 4 * 144 / 12 = 48 hours c = 6 * 144 / 12 = 72 hours c is the hardest worker and a worked for the least number of hours . so the difference is 72 - 24 = 48 hours . answer : c
Answer: c
Problem: how many positive integers less than 50 have a reminder 5 when divided by 7 ?
Options: a ) 3 , b ) 7 , c ) 4 , d ) 5 , e ) 6
Rationale: "take the multiples of 7 and add 5 0 x 7 + 5 = 5 . . . . 6 x 7 + 5 = 47 there are 7 numbers answer b"
Answer: b
Problem: a car is purchased on hire - purchase . the cash price is $ 24 000 and the terms are a deposit of 10 % of the price , then the balance to be paid off over 60 equal monthly installments . interest is charged at 12 % p . a . what is the monthly installment ?
Options: a ) $ 503 , b ) $ 504 , c ) $ 555 , d ) $ 576 , e ) $ 587
Rationale: "explanation : cash price = $ 24 000 deposit = 10 % ã — $ 24 000 = $ 2400 loan amount = $ 24000 â ˆ ’ $ 2400 number of payments = 60 = $ 21600 i = p * r * t / 100 i = 12960 total amount = 21600 + 12960 = $ 34560 regular payment = total amount / number of payments = 576 answer : d"
Answer: d
Problem: a truck covers a distance of 550 metres in 1 minute whereas a train covers a distance of 33 kms in 45 minutes . what is the ratio of their speed ?
Options: a ) 3 : 7 , b ) 4 : 7 , c ) 1 : 4 , d ) 3 : 4 , e ) 2 : 5
Rationale: "explanation : speed of the truck = distance / time = 550 / 1 = 550 meters / minute speed of the train = distance / time = 33 / 45 km / minute = 33000 / 45 meters / minut speed of the truck / speed of the train = 550 / ( 33000 / 45 ) = ( 550 × 45 ) / 33000 = ( 55 × 45 ) / 3300 = ( 11 × 45 ) / 660 = ( 11 × 9 ) / 132 = 9 / 12 = 34 hence , speed of the truck : speed of the train = 3 : 4 answer : option d"
Answer: d
Problem: a sum of money is distributed among a , b , c , d in the proportion of 6 : 4 : 8 : 5 . if c gets $ 3000 more than d , what is the b ' s share ?
Options: a ) $ 2000 , b ) $ 6000 , c ) $ 1000 , d ) $ 4000 , e ) $ 5000
Rationale: "let the shares of a , b , c , d are 6 x , 4 x , 8 x , 5 x 8 x - 5 x = 3000 3 x = 3000 , x = 1000 b ' s share = 4 x = $ 4000 answer is d"
Answer: d
Problem: on the independence day , bananas were be equally distributed among the children in a school so that each child would get two bananas . on the particular day 380 children were absent and as a result each child got two extra bananas . find the actual number of children in the school ?
Options: a ) 237 , b ) 287 , c ) 760 , d ) 287 , e ) 720
Rationale: "explanation : let the number of children in the school be x . since each child gets 2 bananas , total number of bananas = 2 x . 2 x / ( x - 380 ) = 2 + 2 ( extra ) = > 2 x - 760 = x = > x = 760 . answer : c"
Answer: c
Problem: in town p , 70 percent of the population are employed , and 42 percent of the population are employed males . what percent of the employed people in town p are females ?
Options: a ) 25 % , b ) 30 % , c ) 35 % , d ) 40 % , e ) 45 %
Rationale: "the percent of the population who are employed females is 70 - 42 = 28 % the percent of employed people who are female is 28 % / 70 % = 40 % . the answer is d ."
Answer: d
Problem: at 15 : 00 there were 20 students in the computer lab . at 15 : 03 and every three minutes after that , 3 students entered the lab . if at 15 : 10 and every ten minutes after that 9 students left the lab , how many students were in the computer lab at 15 : 44 ?
Options: a ) 7 , b ) 14 , c ) 25 , d ) 27 , e ) 30
Rationale: "initial no of students + 3 * ( 1 + no of possible 3 minute intervals between 15 : 03 and 15 : 44 ) - 8 * ( 1 + no of possible 10 minute intervals between 15 : 10 and 15 : 44 ) 20 + 3 * 14 - 8 * 4 = 25 c"
Answer: c
Problem: the toll for crossing a certain bridge is $ 0.65 each crossing . drivers who frequently use the bridge may instead purchase a sticker each month for $ 13.00 and then pay only $ 0.30 each crossing during that month . if a particular driver will cross the bridge twice on each of x days next month and will not cross the bridge on any other day , what is the least value of x for which this driver can save money by using the sticker ?
Options: a ) 14 , b ) 15 , c ) 16 , d ) 28 , e ) 29
Rationale: "option # 1 : $ 0.75 / crossing . . . . cross twice a day = $ 1.5 / day option # 2 : $ 0.30 / crossing . . . . cross twice a day = $ 0.6 / day + $ 13 one time charge . if we go down the list of possible answers , you can quickly see that 14 days will not be worth purchasing the sticker . 1.5 x 14 ( 21 ) is cheaper than 0.6 x 14 + 13 ( 21.4 ) . . . it ' s pretty close so let ' s see if one more day will make it worth it . . . if we raise the number of days to 15 , the sticker option looks like a better deal . . . 1.5 x 15 ( 22.5 ) vs 0.6 x 15 + 13 ( 22 ) . answer : c"
Answer: c
Problem: a cubical tank is filled with water to a level of 3 feet . if the water in the tank occupies 75 cubic feet , to what fraction of its capacity is the tank filled with water ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 2 / 5 , e ) 3 / 5
Rationale: "the volume of water in the tank is h * l * b = 75 cubic feet . since h = 3 , then l * b = 25 and l = b = 5 . since the tank is cubical , the capacity of the tank is 5 * 5 * 5 = 125 . the ratio of the water in the tank to the capacity is 75 / 125 = 3 / 5 the answer is e ."
Answer: e
Problem: andy solves problems 74 to 135 inclusive in a math exercise . how many problems does he solve ?
Options: a ) 53 , b ) 62 , c ) 51 , d ) 50 , e ) 49
Rationale: "135 - 74 + 1 = 62 ' b ' is the answer"
Answer: b
Problem: 9.009 / 1.001
Options: a ) 0.009 , b ) 0.09 , c ) 0.9 , d ) 9 , e ) 90
Rationale: "answer is 9 , move the decimal forward three places for both numerator and denominator or just multiply both by a thousand . the result is 9009 / 1001 = 9 answer d"
Answer: d
Problem: a number increased by 25 % gives 520 . the number is ?
Options: a ) 216 , b ) 316 , c ) 616 , d ) 516 , e ) 416
Rationale: "formula = total = 100 % , increase = ` ` + ' ' decrease = ` ` - ' ' a number means = 100 % that same number increased by 25 % = 125 % 125 % - - - - - - - > 520 ( 120 ã — 4.16 = 520 ) 100 % - - - - - - - > 416 ( 100 ã — 4.16 = 416 ) option ' e '"
Answer: e
Problem: a , b and c can do a piece of work in 14 , 30 and 40 days respectively . they start the work together but c leaves 4 days before the completion of the work . in how many days is the work done ?
Options: a ) 7.6 days , b ) 7.7 days , c ) 6.7 days , d ) 5.7 days , e ) 8.7 days
Rationale: "x / 14 + x / 30 + x / 40 = 1 x = 7.7 days answer : b"
Answer: b
Problem: joe drives 240 miles at 60 miles per hour , and then he drives the next 120 miles at 40 miles per hour . what is his average speed for the entire trip in miles per hour ?
Options: a ) 42 , b ) 51 , c ) 50 , d ) 54 , e ) 56
Rationale: "t 1 = 240 / 60 = 4 hours t 2 = 120 / 40 = 3 hours t = t 1 + t 2 = 7 hours avg speed = total distance / t = 360 / 7 = 51 mph = b"
Answer: b
Problem: what is the sum of the multiples of 4 between 38 and 127 inclusive ?
Options: a ) 1804 , b ) 1816 , c ) 1824 , d ) 1828 , e ) 1832
Rationale: "the fastest way in an ap is to find the average and multiply with total integers . . between 38 and 127 , the smallest multiple of 4 is 40 and largest = 124 . . average = ( 40 + 124 ) / 2 = 164 / 2 = 82 . . total numbers = ( 124 - 40 ) / 4 + 1 = = 84 / 4 + 1 = 27 + 1 = 22 . . sum = 82 * 22 = 1804 ans a"
Answer: a
Problem: a certain car traveled twice as many miles from town a to town b as it did from town b to town c . from town a to town b , the car averaged 10 miles per gallon , and from town b to town c , the car averaged 18 miles per gallon . what is the average miles per gallon that the car achieved on its trip from town a through town b to town c ?
Options: a ) 13 , b ) 13.5 , c ) 14 , d ) 14.5 , e ) 15
Rationale: "ans is d given d _ ab = 2 * d _ bc let d _ ab = d and d _ bc = x so d = 2 x for average miles per gallon = ( d + x ) / ( ( d / 10 ) + ( x / 18 ) ) = 14.5 ( formula avg speed = total distance / total time )"
Answer: d
Problem: a train 110 m long is running with a speed of 30 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 7 sec , b ) 6 sec , c ) 8 sec , d ) 11 sec , e ) 2 sec
Rationale: "speed of train relative to man = 30 + 6 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . time taken to pass the men = 110 / 10 = 11 sec . answer : d"
Answer: d
Problem: there are 50 boys in a class . their average weight is 45 kg . when one boy leaves the class , the average reduces by 100 g . find the weight of the boy who left the class .
Options: a ) 40.9 kg , b ) 42.9 kg , c ) 49.9 kg , d ) 39.9 kg , e ) none of these
Rationale: here one boy is excluded and final average of the group decreases . ∴ change in average is ( – ) ve = – 0.1 kg . using the formula sum of the quantities excluded = ( changein no . ofquantities × origina laverage ) + ( changeinaverage × final no . ofquantities ) ⇒ weight of the boy who left = ( 1 × 45 ) – ( – 0.1 × 49 ) = 49.9 kg answer c
Answer: c
Problem: two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 20 kmph and 21 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ?
Options: a ) 288 , b ) 492 , c ) 877 , d ) 278 , e ) 178
Rationale: "1 h - - - - - 5 ? - - - - - - 60 12 h rs = 20 + 21 = 41 t = 12 d = 41 * 12 = 492 answer : b"
Answer: b
Problem: how many positive integers less than 240 are multiple of 4 but not multiples of 6 ?
Options: a ) 40 , b ) 31 , c ) 42 , d ) 53 , e ) 64
Rationale: from here , it might be easier to go up in bounds of 60 , so we know that 61 - 120 gives 10 more numbers . 121 - 180 and 181 - 240 as well . this brings us up to 240 with 40 numbers . a cursory glance at the answer choices should confirm that it must be 42 , as all the other choices are very far away . answer choice a is correct here .
Answer: a
Problem: if w / x = 1 / 3 and w / y = 4 / 15 , then ( x + y ) / y =
Options: a ) 4 / 5 , b ) 6 / 5 , c ) 7 / 5 , d ) 8 / 5 , e ) 9 / 5
Rationale: "w / x = 1 / 3 = > x = 3 w and w / y = 4 / 15 = > y = 15 / 4 w ( x + y ) / y = ( 3 w + 15 / 4 w ) / ( 15 / 4 w ) = ( 27 / 4 w ) / ( 15 / 4 w ) = 9 / 5 correct option : e"
Answer: e
Problem: tickets to a certain concert sell for $ 20 each . the first 10 people to show up at the ticket booth received a 40 % discount , and the next 20 received a 15 % discount . if 52 people bought tickets to the concert , what was the total revenue from ticket sales ?
Options: a ) $ 600 , b ) $ 740 , c ) $ 850 , d ) $ 900 , e ) $ 1,140
Rationale: "price of 1 ticket = 20 $ revenue generated from sales of first 10 tickets = 10 * ( 60 / 100 * 20 ) = 10 * 12 = 120 revenue generated from sales of next 20 tickets = 20 * ( 85 / 100 * 20 ) = 20 * 17 = 340 revenue generated from sales of last 22 tickets = 20 * 22 = 440 revenue generated from sales of 52 tickets = 120 + 340 + 440 = 900 $ answer d"
Answer: d
Problem: a bowl of nuts is prepared for a party . brand p mixed nuts are 20 % almonds and brand q ' s deluxe nuts are 25 % almonds . if a bowl contains a total of 64 ounces of nuts , representing a mixture of both brands , and 14 ounces of the mixture are almonds , how many ounces of brand q ' s deluxe mixed nuts are used ?
Options: a ) 14 , b ) 20 , c ) 32 , d ) 44 , e ) 48
Rationale: "lets say x ounces of p is mixed with q . = > 64 - x ounces of q is present in the mixture ( as the total = 64 ounces ) given total almond weight = 14 ounces ( 20 x / 100 ) + ( 25 / 100 ) ( 64 - x ) = 14 = > x = 40 = > 64 - 40 = 14 ounces of q is present in the mixture . answer is a ."
Answer: a
Problem: a policeman noticed a criminal from a distance of 265 km . the criminal starts running and the policeman chases him . the criminal and the policeman run at the rate of 8 km and 9 km per hour respectively . what is the distance between them after 3 minutes ?
Options: a ) 100 m , b ) 120 m , c ) 130 m , d ) 150 m , e ) none of these
Rationale: "explanation : solution : relative speed = ( 9 - 8 ) = 1 km / hr . distance covered in 3 minutes = ( 1 * 3 / 60 ) km = 1 / 20 km = 50 m . . ' . distance between the criminal and policeman = ( 265 - 50 ) m = 215 m . answer : e"
Answer: e
Problem: a university cafeteria offers 6 flavors of pizza - pork , gobi - manjurian , pepperoni , chicken , hawaiian and vegetarian . if a customer has an option ( but not the obligation ) to add extra cheese , mushrooms or both to any kind of pizza , how many different pizza varieties are available ?
Options: a ) 4 , b ) 8 , c ) 12 , d ) 36 , e ) 32
Rationale: 6 flavours * 6 choices = 6 c 1 * 6 c 1 = 6 * 6 = 36 = d
Answer: d
Problem: the sum of three consecutive multiples of 3 is 117 . what is the largest number ?
Options: a ) 45 , b ) 48 , c ) 51 , d ) 42 , e ) 54
Rationale: "let the numbers be 3 x , 3 x + 3 and 3 x + 6 . then , 3 x + ( 3 x + 3 ) + ( 3 x + 6 ) = 117 9 x = 108 x = 12 largest number = 3 x + 6 = 42 answer : d"
Answer: d
Problem: in a zoo , the ratio of the number of cheetahs to the number 4 then what is the increase in the number of pandas ?
Options: a ) 2 , b ) 12 , c ) 5 , d ) 10 , e ) 15
Rationale: one short cut to solve the problem is c : p = 1 : 3 c increased to 5 = > 1 : 3 = 5 : x = > x = 15 = > p increased by 12 b is the answer
Answer: b
Problem: a train 250 m long running at 72 kmph crosses a platform in 50 sec . what is the length of the platform ?
Options: a ) 150 m , b ) 200 m , c ) 250 m , d ) 750 m , e ) 300 m
Rationale: "d = 72 * 5 / 18 = 50 = 1000 â € “ 250 = 750 m answer : d"
Answer: d
Problem: how many multiples of 3 are there between 5 and 59 , 5 and 59 inclusive ?
Options: a ) 16 , b ) 22 , c ) 18 , d ) 11 , e ) 9
Rationale: "3 multiples are . . . 6,9 , 12,15 , 18,21 , 24,27 , 30,33 , 36,39 , 42,45 , 48,51 , 54,57 , . . . , the answer is = 18 answer is c"
Answer: c
Problem: in a mixture of 45 litres the ratio of milk to water is 4 : 1 . additional 12 litres of water is added to the mixture . find the ratio of milk to water in the resulting mixture .
Options: a ) 12 / 7 , b ) 4 / 1 , c ) 2 / 3 , d ) 3 / 4 , e ) 3 / 2
Rationale: "given that milk / water = 4 x / x and 4 x + x = 45 - - > x = 9 . thus milk = 4 x = 36 liters and water = x = 9 liters . new ratio = 36 / ( 9 + 12 ) = 36 / 21 = 12 / 7 . answer : a ."
Answer: a
Problem: in 1979 approximately 1 / 3 of the 32.3 million airline passengers traveling to or from the united states used kennedy airport . if the number of such passengers that used miami airport was 1 / 2 the number that used kennedy airport and 4 times the number that used logan airport , approximately how many millions of these passengers used logan airport that year ?
Options: a ) 18.6 , b ) 9.3 , c ) 6.2 , d ) 1.33 , e ) 1.6
Rationale: "number of passengers using kennedy airport = 32 / 3 = ~ 10.67 passengers using miami airport = 10.67 / 2 = ~ 5.34 passengers using logan airport = 5.34 / 4 = ~ 1.33 so d"
Answer: d
Problem: what is the greater of the two numbers whose product is 2496 , given that the sum of the two numbers exceeds their difference by 64 ?
Options: a ) a ) 96 , b ) b ) 108 , c ) c ) 110 , d ) d ) 78 , e ) of these
Rationale: "let the greater and the smaller number be g and s respectively . gs = 2496 g + s exceeds g - s by 64 i . e . , g + s - ( g - s ) = 64 i . e . , 2 s = 64 = > s = 32 . g = 2496 / s = 78 . answer : d"
Answer: d
Problem: rs . 6490 is divided so that 4 times the first share , six times the 2 nd share and twice the third share amount to the same . what is the value of the first share ?
Options: a ) s 6490 , b ) s 1880 , c ) s 1660 , d ) s 1550 , e ) s 1770
Rationale: "a + b + c = 6490 4 a = 6 b = 2 c = x a : b : c = 1 / 4 : 1 / 6 : 1 / 2 = 3 : 2 : 6 3 / 11 * 6490 = rs 1770 answer : e"
Answer: e
Problem: of the goose eggs laid at a certain pond , 2 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year . if 125 geese survived the first year and if no more than one goose hatched from each egg , how many goose eggs were laid at the pond ?
Options: a ) 280 , b ) 400 , c ) 540 , d ) 625 , e ) 840
Rationale: of the goose eggs laid at a certain pond , 2 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month : 2 / 3 * 3 / 4 = 1 / 2 survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year : ( 1 - 3 / 5 ) * 1 / 2 = 1 / 5 survived the first year . 120 geese survived the first year : 1 / 5 * ( total ) = 125 - - > ( total ) = 625 . answer : d .
Answer: d
Problem: the average salary per month of 55 employees in a company is rs 8500 . if the managers salary is added , the average salary increases to rs 8800 , what is the salary of the manager ?
Options: a ) 10000 , b ) 12000 , c ) 23000 , d ) 25300 , e ) 45000
Rationale: explanation : salary of the manager = ( 56 * 8800 - 55 * 8500 ) = 25300 answer : d
Answer: d
Problem: there are 24 students in a seventh grade class . they decided to plant birches and roses at the school ' s backyard . while each girl planted 3 roses , every three boys planted 1 birch . by the end of the day they planted 2424 plants . how many birches were planted ?
Options: a ) 2 , b ) 5 , c ) 8 , d ) 6 , e ) 4
Rationale: "let x be the number of roses . then the number of birches is 24 − x , and the number of boys is 3 × ( 24 − x ) . if each girl planted 3 roses , there are x 3 girls in the class . we know that there are 24 students in the class . therefore x 3 + 3 ( 24 − x ) = 24 x + 9 ( 24 − x ) = 3 ⋅ 24 x + 216 − 9 x = 72 216 − 72 = 8 x 1448 = x 1 x = 18 so , students planted 18 roses and 24 - x = 24 - 18 = 6 birches . correct answer is d ) 6"
Answer: d
Problem: how many of the positive factors of 10 , 16 and how many common factors are there in numbers ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "factors of 12 - 1 , 2 , 3 , 4 , 6 , and 12 factors of 16 - 1 , 2 , 4 , 8 and 16 comparing both , we have three common factors of 45,16 - 3 answer c"
Answer: c
Problem: in a simultaneous throw of pair of dice . find the probability of getting the total more than 7
Options: a ) 5 / 7 , b ) 4 / 7 , c ) 5 / 12 , d ) 4 / 7 , e ) 1 / 6
Rationale: here n ( s ) = ( 6 * 6 ) = 36 let e = event of getting a total more than 7 = { ( 2,6 ) , ( 3,5 ) , ( 3,6 ) , ( 4,4 ) , ( 4,5 ) , ( 4,6 ) , ( 5,3 ) , ( 5,4 ) , ( 5,5 ) , ( 5,6 ) , ( 6,2 ) , ( 6,3 ) , ( 6,4 ) , ( 6,5 ) , ( 6,6 ) } p ( e ) = n ( e ) / n ( s ) = 15 / 36 = 5 / 12 option c
Answer: c
Problem: calculate the largest 6 digit number which is exactly divisible by 99 ?
Options: a ) 999991 , b ) 999965 , c ) 999912 , d ) 999936 , e ) 999930
Rationale: "largest 4 digit number is 999999 after doing 999999 ÷ 96 we get remainder 55 hence largest 4 digit number exactly divisible by 88 = 9999 - 55 = 9944 answer : d"
Answer: d
Problem: a green grocer received a boxful of tomatoes and on opening the box found that several had gone bad . he then counted them up so that he could make a formal complaint and found that 68 were mouldy , which was 16 per cent of the total contents of the box . how many tomatoes were in the box ?
Options: a ) 336 , b ) 425 , c ) 275 , d ) 235 , e ) 689
Rationale: b 425 ( 68 ã · 16 ) ã — 100
Answer: b
Problem: the water level in a reservoir has been dropping at the rate of 12 inches per day . exactly 5 days ago , the water level was at w inches . what will be the water level exactly 4 days from now if the rate at which the level is dropping remains the same ?
Options: a ) w − 108 , b ) w − 56 , c ) w − 14 , d ) w + 14 , e ) w + 126
Rationale: drop = 12 inches / day 5 days ago = w , means now it ' s equal w - 60 and in 4 days = w - 60 - 48 = w - 108 answer a
Answer: a
Problem: how many boxes do we need if we have to carry 250 apples into boxes that each hold 25 apples ?
Options: a ) a ) 9 , b ) b ) 5 , c ) c ) 7 , d ) d ) 10 , e ) e ) none of the above
Rationale: sol . apples 250 each carries 25 = 250 / 25 = 10 answer : d
Answer: d
Problem: how many seconds does sandy take to cover a distance of 600 meters , if sandy runs at a speed of 15 km / hr ?
Options: a ) 128 , b ) 136 , c ) 144 , d ) 152 , e ) 160
Rationale: "15 km / hr = 15000 m / 3600 s = ( 150 / 36 ) m / s = ( 25 / 6 ) m / s time = 600 / ( 25 / 6 ) = 144 seconds the answer is c ."
Answer: c
Problem: if shares of two persons in profits are rs . 600 and rs . 300 then ratio of their capitals is
Options: a ) 3 : 4 , b ) 2 : 3 , c ) 4 : 3 , d ) 1 : 3 , e ) 2 : 1
Rationale: "total profit = 1000 ratio = 600 / 300 = 2 : 1 answer : e"
Answer: e
Problem: the mean of 50 observations was 36 . it was found later that an observation 48 was wrongly taken as 23 . the corrected new mean is :
Options: a ) 36.5 , b ) 35 , c ) 34 , d ) 33 , e ) 32.5
Rationale: "correct sum = ( 36 * 50 + 48 - 23 ) = 1825 . correct mean = 1825 / 50 = 36.5 answer a"
Answer: a
Problem: a school has received 60 % of the amount it needs for a new building by receiving a donation of $ 500 each from people already solicited . people already solicited represent 50 % of the people from whom the school will solicit donations . how much average contribution is requited from the remaining targeted people to complete the fund raising exercise ?
Options: a ) $ 200 , b ) $ 333.33 , c ) $ 100.25 , d ) $ 277.78 , e ) $ 377.00
Rationale: "let us suppose there are 100 people . 50 % of them donated $ 25000 ( 500 * 50 ) $ 25000 is 60 % of total amount . so total amount = 25000 * 100 / 60 remaining amount is 40 % of total amount . 40 % of total amount = 25000 * ( 100 / 60 ) * ( 40 / 100 ) = 50000 / 3 this amount has to be divided by 50 ( remaining people are 50 ) so per head amount is 50000 / 3 / 50 = 32000 / 180 = 333.33 ; answer : b"
Answer: b
Problem: a certain bacteria colony doubles in size every day for 19 days , at which point it reaches the limit of its habitat and can no longer grow . if two bacteria colonies start growing simultaneously , how many days will it take them to reach the habitat ’ s limit ?
Options: a ) 6.33 , b ) 7.5 , c ) 10 , d ) 18 , e ) 19
Rationale: "if there is one bacteria colony , then it will reach the limit of its habitat in 20 days . if there are two bacteria colonies , then in order to reach the limit of habitat they would need to double one time less than in case with one colony . thus colonies need to double 18 times . answer : d . similar questions to practice : hope it helps ."
Answer: d
Problem: the diameter of a circle is 4 / π . find the circumference of the circle .
Options: a ) 8
b ) 4 π
c ) 4
d ) 6
e ) 5
Rationale: circumference = 2 * pi * r = 2 * pi * 4 / pi = > 8 a
Answer: a
Problem: simplify : 0.3 * 0.3 + 0.3 * 0.3
Options: a ) 0.52 , b ) 0.42 , c ) 0.18 , d ) 0.64 , e ) 0.46
Rationale: "given exp . = 0.3 * 0.3 + ( 0.3 * 0.3 ) = 0.09 + 0.09 = 0.18 answer is c ."
Answer: c
Problem: how many prime numbers exist between 260 and 280 ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: straight a way lets exclude all the even numbers between 260 and 280 . so now the number starts from 261 to 279 ( only odd ) 261 is a divisible of 3 and next odd divisible by 3 will be 261 + 6 = 267 + 6 = 273 + 6 = 279 . also we can eliminate numbers ending with ' 5 ' so in odd , the excluded numbers are 261 , 265,267 , 273,279 , which leave us with 263,269 , 271,277 . checked the above listed four numbers are divisible by any numbers till 20 . answer : e
Answer: e
Problem: one robot builds a robot in 1 hour , another one builds a robot in 2 hours . the 2 robots work together and when a new robot is complete , it joins the others , working at a constant rate of one robot in 2 hours . how much time will it take until there are 8 robots altogether , if the robots build only one robot at a time ?
Options: a ) 70 min , b ) 94 min , c ) 110 min , d ) 131 1 / 7 min , e ) 146 1 / 7 min
Rationale: "first the 2 robots work at the rate of 1 + 1 / 2 = 3 / 2 so they complete one robot in 2 / 3 rd of an hour = 40 minutes - ( 1 ) now the 3 robots work together at the rate of 1 + 1 / 2 + 1 / 2 = 4 / 2 = 2 / 1 so they complete one robot in 1 / 2 an hour , i . e 30 minutes - ( 2 ) now the 4 robots work together at the rate of 1 + 1 / 2 + 1 / 2 + 1 / 2 = 5 / 2 so they complete one robot in 2 / 5 th of an hour - ( 3 ) now the 5 robots work together at the rate of 1 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 = 3 so they complete one robot in 1 / 3 th of an hour - ( 4 ) now the 6 robots work together at the rate of 1 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 = 7 / 2 so they complete one robot in 2 / 7 th of an hour - ( 5 ) now the 7 robots work together at the rate of 1 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 = 9 / 2 so they complete one robot in 2 / 9 th of an hour - ( 6 ) and now we have 8 robots so total = ( 1 ) + ( 2 ) + ( 3 ) + ( 4 ) + ( 5 ) + ( 6 ) = 146 1 / 7 minutes answer - e"
Answer: e
Problem: { - 10 , - 6 , - 5 , - 4 , - 2.5 , - 1 , 0 , 2.5 , 4 , 6 , 7 , 10 } a number is to be selected at random from the set above . what is the probability that the number will be a solution to the equation ( x - 4 ) ( x + 9 ) ( 2 x + 5 ) = 0 ?
Options: a ) 1 / 12 , b ) 1 / 6 , c ) 1 / 4 , d ) 1 / 3 , e ) 1 / 2
Rationale: x = - 2.5 prob = 1 / 12 answer - a
Answer: a
Problem: a crow leaves its nest , and flies back and forth from its nest to a nearby ditch to gather worms . the distance between the nest and the ditch is 300 meters . in one and a half hours , the crow manages to bring worms to its nest 15 times . what is the speed of the crow in kilometers per hour ?
Options: a ) 1 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "the distance between the nest and the ditch is 300 meters . 15 times mean = a crow leaves its nest , and flies back ( going and coming back ) i . e . 2 times we get total 30 rounds . so the distance is 30 * 300 = 9000 . d = st 9000 / 1.5 = t , i think we can take 9000 meters as 9 km , then only we get t = 6 . ( 1000 meters = 1 km ) d )"
Answer: d
Problem: a and b are two multiples of 36 , and q is the set of consecutive integers between a and b , inclusive . if q contains 9 multiples of 9 , how many multiples of 4 are there in q ?
Options: a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: "now given that q is set the consecutive integers between a and b . and q contains 9 multiples of 9 let take a as 36 . then 36 45 54 63 72 81 90 99 108 . . . so b will 108 . now let ' s check the multiples of 4 among this set 108 - 36 / 4 + 1 = > 18 + 1 = > 19 ans option b ."
Answer: b
Problem: find the value of ( 20 c 18 ) * ( 20 c 20 )
Options: a ) 400 , b ) 380 , c ) 360 , d ) 350 , e ) 330
Rationale: "20 c 20 = 1 ( 20 c 2 ) * ( 20 c 20 ) = 20 ! * 1 / 18 ! = 20 * 19 * 18 ! / 18 ! = 20 * 19 * 1 = 380 answer : b"
Answer: b
Problem: if 30 % of a class averages 95 % on a test , 50 % of the class averages 79 % on the test , and the remainder of the class averages 60 % on the test , what is the overall class average ? ( round final answer to the nearest percent ) .
Options: a ) 76 % , b ) 77 % , c ) 78 % , d ) 79 % , e ) 80 %
Rationale: "this question is a weighted average question with a series of dependent variables . the remaining portion of the class represents 100 % - 30 % - 50 % = 20 % of the class converting the portions of the class population to decimal weights , we find : class average = 0.30 x 95 + 0.50 x 79 + 0.20 x 60 = 80 the class average ( rounded ) is 80 % final answer e ) 80 %"
Answer: e
Problem: two kinds of vodka are mixed in the ratio 2 : 6 and 6 : 3 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 ) 20 % , b ) 40 % , c ) 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 : a"
Answer: a
Problem: if the tens digit of positive integers m , y are 6 , how many values of the tens digit of 2 ( m + y ) can be there ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: if the tens digit of positive integers m , y are 6 , how many values of the tens digit of 2 ( m + y ) can be there ? a . 2 b . 3 c . 4 d . 5 e . 6 - > if m = y = 60 , 2 ( m + y ) = 240 is derived . if m = y = 69 , 2 ( m + y ) = 276 is derived , which makes 4,5 , 6,7 possible for the tens digit . therefore , the answer is c .
Answer: c
Problem: the maximum number of students among them 848 pens and 630 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils ?
Options: a ) 10 , b ) 4 , c ) 2 , d ) 14 , e ) 16
Rationale: "number of pens = 848 number of pencils = 630 required number of students = h . c . f . of 848 and 630 = 2 answer is c"
Answer: c
Problem: find the ratio of the curved surfaces of two cylinders of same heights if their radii are in the ratio 1 : 2 ?
Options: a ) 1 : 2
b ) 2 : 3
c ) 2 : 9
d ) 2 : 1
e ) 2 : 2
Rationale: 1 : 2 answer : a
Answer: a
Problem: n and m are each 3 - digit integers . each of the numbers 1 , 2 , 3 , 7 , 8 and 9 is a digit of either n or m . what is the smallest possible positive difference between n and m ?
Options: a ) 19 , b ) 49 , c ) 58 , d ) 113 , e ) 131
Rationale: "you have 6 digits : 1 , 2 , 3 , 7 , 8 , 9 each digit needs to be used to make two 3 digit numbers . this means that we will use each of the digits only once and in only one of the numbers . the numbers need to be as close to each other as possible . the numbers can not be equal so the greater number needs to be as small as possible and the smaller number needs to be as large as possible to be close to each other . the first digit ( hundreds digit ) of both numbers should be consecutive integers now let ' s think about the next digit ( the tens digit ) . to minimize the difference between the numbers , the tens digit of the greater number should be as small as possible and the tens digit of the smaller number should be as large as possible . so let ' s not use 1 and 9 in the hundreds places and reserve them for the tens places . now what are the options ? try and make a pair with ( 2 * * and 3 * * ) . make the 2 * * number as large as possible and make the 3 * * number as small as possible . 298 and 317 ( difference is 19 ) or try and make a pair with ( 7 * * and 8 * * ) . make the 7 * * number as large as possible and make the 8 * * number as small as possible . we get 793 and 812 ( difference is 19 ) a"
Answer: a
Problem: the captain of a cricket team of 11 members is 29 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 age of the team ?
Options: a ) 20 years , b ) 21 years , c ) 22 years , d ) 23 years , e ) 26 years
Rationale: "explanation : let the average age of the whole team by x years . 11 x â € “ ( 29 + 32 ) = 9 ( x - 1 ) 11 x â € “ 9 x = 52 2 x = 52 x = 26 . so , average age of the team is 26 years . answer e"
Answer: e
Problem: if the sides of a triangle are 31 cm , 29 cm and 15 cm , what is its area ?
Options: a ) 220.75 cm 2 , b ) 258 cm 2 , c ) 225.50 cm 2 , d ) 222.25 cm 2 , e ) 217.5 cm 2
Rationale: "the triangle with sides 31 cm , 29 cm and 15 cm is right angled , where the hypotenuse is 31 cm . area of the triangle = 1 / 2 * 29 * 15 = 217.5 cm 2 answer : e"
Answer: e
Problem: in what ratio should a variety of rice costing rs . 6.5 per kg be mixed with another variety of rice costing rs . 8.75 per kg to obtain a mixture costing rs . 7.50 per kg ?
Options: a ) 5 / 6 , b ) 5 / 9 , c ) 5 / 4 , d ) 5 / 3 , e ) 7 / 6
Rationale: "let us say the ratio of the quantities of cheaper and dearer varieties = x : y by the rule of allegation , x / y = ( 8.75 - 7.50 ) / ( 7.50 - 6.5 ) = 5 / 4 answer : c"
Answer: c
Problem: a bag contains 7 green and 8 white balls . if two balls are drawn simultaneously , the probability that both are of the same colour is
Options: a ) 7 / 16 , b ) 7 / 12 , c ) 7 / 19 , d ) 7 / 12 , e ) 7 / 15
Rationale: "drawing two balls of same color from seven green balls can be done in ⁷ c ₂ ways . similarly from eight white balls two can be drawn in ⁸ c ₂ ways . p = ⁷ c ₂ / ¹ ⁵ c ₂ + ⁸ c ₂ / ¹ ⁵ c ₂ = 7 / 15 answer : e"
Answer: e
Problem: the average monthly salary of 20 employees in an organisation is rs . 1400 . if the manager ' s salary is added , then the average salary increases by rs . 100 . what is the manager ' s monthly salary ?
Options: a ) 3600 , b ) 3890 , c ) 88798 , d ) 2789 , e ) 3500
Rationale: "explanation : manager ' s monthly salary rs . ( 1500 * 21 - 1400 * 20 ) = rs . 3500 . answer : e"
Answer: e
Problem: 4 men and 6 women can complete a work in 8 days , while 3 men and 7 women can complete it in 10 days . in how many days will 10 women complete it ?
Options: a ) 21 days , b ) 40 days , c ) 27 days , d ) 18 days , e ) 17 days
Rationale: "let 1 man ' s 1 day work = x and 1 woman ' s 1 day work = y . then , 4 x + 6 y = 1 / 8 and 3 x + 7 y = 1 / 10 solving these two equations , we get : x = 11 / 400 and y = 1 / 400 1 woman ' s 1 day work = ( 1 / 400 * 10 ) = 1 / 40 . hence , 10 women will complete the work in 40 days . answer : b"
Answer: b
Problem: a furniture dealer purchased a desk for $ 180 and then set the selling price equal to the purchase price plus a markup that was 40 % of the selling price . if the dealer sold the desk at the selling price , what was the amount of the dealer ' s gross profit from the purchase and the sale of the desk ?
Options: a ) $ 40 , b ) $ 60 , c ) $ 80 , d ) $ 120 , e ) $ 100
Rationale: "purchase price = 180 selling price = x 180 + 0.4 * x = x 0.6 * x = 180 x = 300 profit = 300 - 180 = 120 answer : d"
Answer: d
Problem: a train 400 m long can cross an electric pole in 10 sec and then find the speed of the train ?
Options: a ) 165 kmph , b ) 144 kmph , c ) 172 kmph , d ) 175 kmph , e ) 178 kmph
Rationale: "length = speed * time speed = l / t s = 400 / 10 s = 40 m / sec speed = 40 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 144 kmph answer : b"
Answer: b
Problem: a man can row his boat with the stream at 30 km / h and against the stream in 14 km / h . the man ' s rate is ?
Options: a ) 1 kmph , b ) 4 kmph , c ) 5 kmph , d ) 7 kmph , e ) 8 kmph
Rationale: "ds = 30 us = 14 s = ? s = ( 30 - 14 ) / 2 = 8 kmph answer : e"
Answer: e