regisss/math_qa huggingface dataset:
Problem: ram , who is half as efficient as krish , will take 27 days to complete a task if he worked alone . if ram and krish worked together , how long will they take to complete the task ?
Options: a ) 16 days , b ) 12 days , c ) 9 days , d ) 6 days , e ) 18 days
Rationale: number of days taken by ram to complete task = 27 since ram is half as efficient as krish , amount of work done by krish in 1 day = amount of work done by ram in 2 days if total work done by ram in 27 days is 27 w amount of work done by ram in 1 day = w amount of work done by krish in 1 day = 2 w total amount of work done by krish and ram in a day = 3 w total amount of time needed by krish and ram to complete task = 27 w / 3 w = 9 days answer c
Answer: c
Problem: what is the compound interest on rs : 60,000 for 4 months at the rate of 5 % per annum
Options: a ) 1058.24 , b ) 2006.24 , c ) 1006.13 , d ) 1015.24 , e ) 1014.24
Rationale: "it is monthly compound rate = 5 / 12 % per month 60000 * ( 1 + 5 / 1200 ) ^ 4 - 60000 = 1006.13 answer : c"
Answer: c
Problem: two persons a and b can complete a piece of work in 40 days and 60 days respectively . if they work together , what part of the work will be completed in 6 days ?
Options: a ) 1 / 8 , b ) 1 / 3 , c ) 1 / 6 , d ) 1 / 2 , e ) 1 / 4
Rationale: "a ' s one day ' s work = 1 / 40 b ' s one day ' s work = 1 / 60 ( a + b ) ' s one day ' s work = 1 / 40 + 1 / 60 = 1 / 24 the part of the work completed in 6 days = 6 ( 1 / 24 ) = 1 / 4 . answer : e"
Answer: e
Problem: at what price must an article costing rs . 95 be marked in order that after deducting 5 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 130 , b ) 125 , c ) 145 , d ) 135 , e ) 144
Rationale: "cp = 95 sp = 47.50 * ( 125 / 100 ) = 118.125 mp * ( 95 / 100 ) = 118.125 mp = 125 answer : b"
Answer: b
Problem: a “ sophie germain ” prime is any positive prime number p for which 2 p + 1 is also prime . the product of all the possible units digits of sophie germain primes greater than 9 is
Options: a ) 3 , b ) 7 , c ) 21 , d ) 189 , e ) 267
Rationale: "in that case , the sophie prime numbers greater than 9 are 11,23 , 47,59 , . . which yields units digit as 1 , 3,7 and 9 product would be 1 x 3 x 7 x 9 = 189 answer should be d"
Answer: d
Problem: a man performs 1 / 2 of the total journey by rail , 1 / 3 by bus and the remaining 3 km on foot . his total journey is
Options: a ) 18 km , b ) 10 km , c ) 12 km , d ) 24 km , e ) 25 km
Rationale: "explanation : let the journey be x km then , 1 x / 2 + 1 x / 3 + 3 = x 5 x + 18 = 6 x x = 18 km answer : option a"
Answer: a
Problem: the sum of all consecutive odd integers from − 27 to 37 , inclusive , is
Options: a ) 110 , b ) 135 , c ) 150 , d ) 165 , e ) 235
Rationale: "the sum of the odd numbers from - 27 to + 27 is 0 . let ' s add the remaining numbers . 29 + 31 + 33 + 35 + 37 = 5 ( 33 ) = 165 the answer is d ."
Answer: d
Problem: if 20 % of a number is equal to one - third of another number , what is the ratio of first number to the second number ?
Options: a ) 2 : 5 , b ) 1 : 4 , c ) 5 : 3 , d ) 6 : 11 , e ) 2 : 3
Rationale: "let 20 % of a = 1 / 3 b then 20 a / 100 = 1 b / 3 a / 5 = b / 3 a / b = 5 / 3 a : b = 5 : 3 answer is c"
Answer: c
Problem: a person travels from p to q a speed of 60 km / hr and returns by increasing his speed by 50 % . what is his average speed for both the trips ?
Options: a ) 33 , b ) 75 , c ) 48 , d ) 99 , e ) 21
Rationale: speed on return trip = 150 % of 60 = 90 km / hr . average speed of trip = 60 + 90 / 2 = 150 / 2 = 75 km / hr answer : b
Answer: b
Problem: ( 1.1 + 1.1 + 1.1 + 1.1 ) x 1.1 x 1.1 = ? = ? x 0.121
Options: a ) 54 , b ) 33 , c ) 44 , d ) 22 , e ) 26
Rationale: "explanation : ? = ( 1.1 + 1.1 + 1.1 + 1.1 ) x 1.1 x 1.1 / 0.121 = ( 4.4 x 1.1 x 1.1 ) / 0.121 = 44 answer : option c"
Answer: c
Problem: how much is 85 % of 40 is greater than 4 / 5 of 25 ?
Options: a ) 22 , b ) 14 , c ) 88 , d ) 12 , e ) 66
Rationale: "( 85 / 100 ) * 40 – ( 4 / 5 ) * 25 = 14 answer : b"
Answer: b
Problem: ( 23341379 x 72 ) = ?
Options: a ) 1680579288 , b ) 1223441288 , c ) 2142579288 , d ) 2142339288 , e ) none of these
Rationale: "explanation : 23341379 x 72 = 23341379 ( 70 + 2 ) = ( 23341379 x 70 ) + ( 23341379 x 2 ) = 1633896530 + 46682758 = 1680579288 . answer : option a"
Answer: a
Problem: in a fuel station the service costs $ 2.10 per vehicle and every liter of fuel costs $ 0.70 . assuming that you fill up 3 mini - vans and 2 trucks , what will be the total cost , if a mini - van ' s tank is 65 liters and a truck ' s tank is 120 % bigger and they are all empty ?
Options: a ) $ 338.50 , b ) $ 341.40 , c ) $ 344.30 , d ) $ 347.20 , e ) $ 350.10
Rationale: the service cost of 3 vans and 2 trucks is 5 * 2.10 $ 10.50 the fuel in 3 vans is 3 * 65 = 195 liters the fuel in 2 trucks is 2 * 65 * 2.2 = 286 liters the total fuel ( vans + trucks ) = 481 liters the total fuel cost is 481 * 0.7 = $ 336.70 the total cost is $ 336.70 + $ 10.50 = $ 347.20 the answer is d .
Answer: d
Problem: following an increase in prices , the price of a candy box was 10 pounds and the price of a can of soda was 15 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 ) 12 . , c ) 13 . , d ) 18 . , e ) 14.5
Rationale: price of candy before price increase = 10 / 1.25 = 8 price of soda before price increase = 15 / 1.5 = 10 total price = 8 + 10 = 18 d is the answer
Answer: d
Problem: the population of a bacteria colony doubles every day . if it was started 9 days ago with 2 bacteria and each bacteria lives for 11 days , how large is the colony today ?
Options: a ) 512 , b ) 768 , c ) 4096 , d ) 2048 , e ) 1024
Rationale: "9 days ago - 2 8 days ago - 4 7 days ago - 8 6 days ago - 16 5 days ago - 32 4 days ago - 64 3 days ago - 128 2 days ago - 256 yesterday - 512 today - 1024 ans : e"
Answer: e
Problem: in how many ways can an answer key for a quiz be written if the quiz contains 4 true - false questions followed by 2 multiples - choice questions with 4 answer choices each , if the correct answers to all true - false questions can not be the same ?
Options: a ) 120 , b ) 190 , c ) 224 , d ) 298 , e ) 256
Rationale: "there are 2 ^ 4 = 16 possibilities for the true - false answers . however we need to remove two cases for tttt and ffff . there are 4 * 4 = 16 possibilities for the multiple choice questions . the total number of possibilities is 14 * 16 = 224 . the answer is c ."
Answer: c
Problem: in what time will a train 135 m long cross an electric pole , it its speed be 140 km / hr ?
Options: a ) 3.5 , b ) 2.7 , c ) 2.9 , d ) 2.3 , e ) 2.1
Rationale: "speed = 140 * 5 / 18 = 38.8 m / sec time taken = 135 / 38.8 = 3.5 sec . answer : a"
Answer: a
Problem: a man buys a cycle for rs . 1200 and sells it at a loss of 10 % . what is the selling price of the cycle ?
Options: a ) s . 1080 , b ) s . 1140 , c ) s . 1090 , d ) s . 1202 , e ) s . 1092
Rationale: "s . p . = 90 % of rs . 1200 = rs . 90 x 1200 / 100 = rs . 1080 answer : option a"
Answer: a
Problem: the average age of 30 students in a class is 14 years . if the age of teacher is also included , the average becomes 15 years , find the age of the teacher .
Options: a ) 43 , b ) 44 , c ) 45 , d ) 47 , e ) 48
Rationale: explanation : if teacher ' s age is 14 years , there is no change in the average . but teacher has contributed 1 year to all the students along with maintaining his age at 15 . age of teacher = average age of all + total increase in age = 15 + ( 1 x 30 ) = 45 years answer : c
Answer: c
Problem: john and lewis leave city a for city b simultaneously at 6 a . m in the morning driving in two cars at speeds of 40 mph and 60 mph respectively . as soon as lewis reaches city b , he returns back to city a along the same route and meets john on the way back . if the distance between the two cities is 240 miles , how far from city a did john and lewis meet ?
Options: a ) 150 miles , b ) 160 miles , c ) 140 miles , d ) 170 miles , e ) 200 miles
Rationale: time taken by lewis to reach city b = 240 / 60 = 4 hours in 4 hours , john travels 40 * 4 = 160 miles so distance at which they meet should be greater than 160 miles . only b satisfies . answer is b .
Answer: b
Problem: a salesman â € ™ s terms were changed from a flat commission of 5 % on all his sales to a fixed salary of rs . 1000 plus 2.5 % commission on all sales exceeding rs . 4000 . if his remuneration as per new scheme was rs . 700 more than that by the previous schema , his sales were worth ?
Options: a ) s . 8,000 , b ) s . 9,000 , c ) s . 20,000 , d ) s . 10,000 , e ) s . 50,000
Rationale: [ 1000 + ( x - 4000 ) * ( 2.5 / 100 ) ] - x * ( 5 / 100 ) = 700 x = 8000 answer a
Answer: a
Problem: the average weight of 8 persons increases by 3 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?
Options: a ) 75 kg , b ) 65 kg , c ) 55 kg , d ) 89 kg , e ) 25 kg
Rationale: total weight increased = ( 8 x 3 ) kg = 24 kg . weight of new person = ( 65 + 24 ) kg = 89 kg . answer : d
Answer: d
Problem: in a village of 100 households , 85 have at least one dvd player , 90 have at least one cell phone , and 55 have at least one mp 3 player . if x and y are respectively the greatest and lowest possible number of households that have all 3 of these devices , x – y is :
Options: a ) 65 , b ) 55 , c ) 45 , d ) 35 , e ) 25
Rationale: am i missing something here ? ? ? it seems straightforward . . . . . . the obvious maximum that have all 3 is 55 , because you are limited by the smallest number . the minimum is simply the sum of the max of each people who dont have the product , so : 100 - 90 = 10 do n ' t have cell 100 - 85 = 15 do n ' t have dvd and 100 - 55 = 45 do n ' t have mp 3 so a total of 10 + 15 + 45 = 70 combined who might not have some combination of the 3 products . so subtract that from 100 , to give you the minimum of the people who could have all 3 and you get 100 - 70 = 30 . 55 - 30 = 25 e
Answer: e
Problem: of the diplomats attending a summit conference , 14 speak french , 32 do not speak russian , and 20 % of the diplomats speak neither french nor russian . if 10 % of the diplomats speak both languages , then how many diplomats attended the conference ?
Options: a ) 72 , b ) 96 , c ) 108 , d ) 120 , e ) 180
Rationale: { total } = { french } + { russian } - { both } + { neither } { total } = 14 + ( { total } - 32 ) - ( 0.1 * { total } ) + 0.2 * { total } solving gives { total } = 180 . answer : e .
Answer: e
Problem: in a certain pond , 80 fish were caught , tagged , and returned to the pond . a few days later , 80 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 ` s the approximate number of fish in the pond ?
Options: a ) 400 , b ) 625 , c ) 1250 , d ) 3200 , e ) 10 000
Rationale: "the percent of tagged fish in the second catch is 2 / 80 * 100 = 2.5 % . we are told that 2.5 % approximates the percent of tagged fish in the pond . since there are 80 tagged fish , then we have 0.025 x = 80 - - > x = 3,200 . answer : d ."
Answer: d
Problem: the cost price of an article is 25 % of the marked price . calculate the gain percent after allowing a discount of 50 % .
Options: a ) 25 % , b ) 50 % , c ) 100 % , d ) 150 % , e ) none
Rationale: "sol . let marked price = rs . 100 . then , c . p . = rs . 25 . s . p = rs . 50 . â ˆ ´ gain % = [ 25 / 25 * 100 ] % = 100.0 % . answer c"
Answer: c
Problem: the total marks obtained by a student in mathematics and physics is 40 and his score in chemistry is 20 marks more than that in physics . find the average marks scored in mathamatics and chemistry together .
Options: a ) 40 , b ) 26 , c ) 27 , d ) 28 , e ) 30
Rationale: "let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 40 and c - p = 20 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 40 + 20 ) / 2 = 30 . answer : e"
Answer: e
Problem: anup manages to draw 7 circles of equal radii with their centres on the diagonal of a square such that two extreme circles touch two sides of the square and each middle circle touches two circles on either side . find the ratio of radius of the circles to the side of the square .
Options: a ) 1 : ( 2 + 6 ^ ( 1 / 2 ) )
b ) 1 : ( 4 + 7 ^ ( 1 / 3 ) )
c ) ( 2 + 7 ^ ( 1 / 2 ) ) : 1
d ) ( 2 + 7 ^ ( 1 / 2 ) ) : 2
e ) none of these
Rationale: diagonal of square = ( 2 * r ) * 7 + ( 2 ^ ( 1 / 2 ) * r - r ) * 2 diagonal has 7 squares diameters length + little distance between extreme squares to the end point [ form a square of side r from center of extreme circle to the extreme end to find distance ] distance = 2 ^ ( 1 / 2 ) * r - r d = a * 2 ^ ( 1 / 2 ) a = 2 ^ ( 1 / 2 ) * [ 6 * r + 2 ^ ( 1 / 2 ) * r ] r / a = 1 : [ 2 + 6 * 2 ^ ( 1 / 2 ) ] answer is none of the above answer : e
Answer: e
Problem: a light flashes every 20 seconds , how many times will it flash in ? of an hour ?
Options: a ) 550 , b ) 600 , c ) 650 , d ) 180 , e ) 750
Rationale: "1 flash = 20 sec for 1 min = 3 flashes so for 1 hour = 3 * 60 = 180 flashes . answer : d"
Answer: d
Problem: the cost of 3 pens and 5 pencils is rs . 240 . also the cost of one pen and one pencil is in the ratio of 5 : 1 respectively . what is the cost of one dozen pens ?
Options: a ) rs . 200 , b ) rs . 720 , c ) rs . 300 , d ) rs . 150 , e ) none of these
Rationale: "explanation : let the cost of one pen is ‘ 5 x ’ and pencil is ‘ x ’ 3 x 5 x + 5 x = rs . 240 15 x + 5 x = rs . 240 x = 240 / 20 = 12 : . cost of 1 pen = 5 x = 5 x 12 = 60 : . cost of 12 pens , i . e . ( one dozen ) = 60 x 12 = rs . 720 answer : option b"
Answer: b
Problem: the regular price per can of a certain brand of soda is $ 0.55 . if the regular price per can is discounted 25 percent when the soda is purchased in 24 - can cases , what is the price of 70 cans of this brand of soda purchased in 24 - can cases ?
Options: a ) $ 16.32 , b ) $ 18.00 , c ) $ 21.60 , d ) $ 24.48 , e ) $ 28.87
Rationale: "the discounted price of one can of soda is ( 0.75 ) ( $ 0.55 ) , or $ 0.4125 therefore , the price of 70 cans of soda at the discounted price would be ( 70 ) ( $ 0.4125 ) = 28.875 answer : e"
Answer: e
Problem: the ratio between the number of sheep and the number of horses at the stewart farm is 2 to 7 , if each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day , what is the number of sheep in the farm ?
Options: a ) 18 , b ) 16 , c ) 32 , d ) 56 , e ) 60
Rationale: "let the number of sheeps and horses be 4 x and 7 x . now total number of horses = total consumption of horse food / consumption per horse = 12880 / 230 = 56 , which is equal to 7 x . = > x = 8 sheeps = 2 x = 2 * 8 = 16 . hence b"
Answer: b
Problem: the average monthly salary of 20 employees in an organisation is rs . 1500 . 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 ) 2988 , c ) 2789 , d ) 2887 , e ) 1297
Rationale: "manager ' s monthly salary rs . ( 1600 * 21 - 1500 * 20 ) = rs . 3600 . answer : a"
Answer: a
Problem: a call center has two teams . each member of team a was able to process 6 / 5 calls as compared to each member of team b . if team a has 5 / 8 as many number of call center agents as team b , what fraction of the total calls was processed by team b ?
Options: a ) 3 / 2 , b ) 3 / 4 , c ) 4 / 7 , d ) 1 / 2 , e ) 1 / 5
Rationale: "let team b has 8 agents , so team a has 5 agents let each agent of team b picked up 5 calls , so total calls by team b = 40 so , each agent in team a picked up 6 calls , so total calls for team a = 30 fraction for team b = 40 / ( 40 + 30 ) = 4 / 7 = answer = c"
Answer: c
Problem: after decreasing 24 % in the price of an article costs rs . 1064 . find the actual cost of an article ?
Options: a ) 1667 , b ) 6789 , c ) 1200 , d ) 6151 , e ) 1400
Rationale: "cp * ( 76 / 100 ) = 1064 cp = 14 * 100 = > cp = 1400 answer : e"
Answer: e
Problem: a metallic sheet is of rectangular shape with dimensions 48 m x 36 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 8 m , the volume of the box ( in m 3 ) is :
Options: a ) 4830 , b ) 5120 , c ) 6420 , d ) 8960 , e ) none
Rationale: "explanation clearly , l = ( 48 – 16 ) m = 32 m , b = ( 36 - 16 ) m = 20 m , h = 8 m . volume of the box = ( 32 x 20 x 8 ) m 3 = 5120 m 3 . answer b"
Answer: b
Problem: 300 × ? + ( 12 + 4 ) × 1 / 8 = 602
Options: a ) a ) 4 , b ) b ) 3 , c ) c ) 5 , d ) d ) 2 , e ) e ) 8
Rationale: explanation : = > 300 × ? + ( 12 + 4 ) × 1 / 8 = 602 = > 300 × ? = 602 - ( 12 + 4 ) × 1 / 8 = > 300 × ? = 602 - 2 = 600 = > ? = 600 / 300 = 2 answer : option d
Answer: d
Problem: if 2 / z = 2 / ( z + 1 ) + 2 / ( z + 36 ) which of these integers could be the value of z ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 6
Rationale: "solving for z algebraically in this problem would not be easy . instead , we can follow the hint in the question ( “ which of these integers … ” ) and test each answer choice : a . 2 / 0 = 2 / 1 + 2 / 36 incorrect ( division by zero ) b . 2 / 1 = 2 / 2 + 2 / 37 incorrect c . 2 / 2 = 2 / 3 + 2 / 38 incorrect d . 2 / 3 = 2 / 4 + 2 / 39 incorrect e . 2 / 4 = 2 / 5 + 2 / 40 correct the correct answer is e , because it contains the only value that makes the equation work . notice how quickly this strategy worked in this case"
Answer: e
Problem: girl and boy together can complete a piece of work in 35 days while girl alone can complete the same work in 60 days . boy alone will be able to complete the same working in :
Options: a ) 72 , b ) 75 , c ) 84 , d ) 88 , e ) 90
Rationale: subtraction of fraction ab − cd = ad − cbbd girl and boy finish one work with company = 35 days ( girl + boy ) ′ s one day ’ s work = 135 girl alone finish the same work = 60 days girl ′ s one day ’ s work = 160 b ′ s one day ’ s work = ( a + b ) ′ s one day ’ s work - a ′ s one day ’ s work 135 − 160 = 184 hence b alone can complete the work in 84 days
Answer: b
Problem: what is 15 percent of 34
Options: a ) 5.1 , b ) 4.1 , c ) 3.1 , d ) 2.1 , e ) none of these
Rationale: "explanation : it will be 15 % of 34 = ( 15 / 100 ) * 34 = 5.10 answer : option a"
Answer: a
Problem: rs . 2500 is divided into two parts such that if one part be put out at 5 % simple interest and the other at 6 % , the yearly annual income may be rs . 140 . how much was lent at 5 % ?
Options: a ) 2288 , b ) 27669 , c ) 1766 , d ) 1000 , e ) 2871
Rationale: "( x * 5 * 1 ) / 100 + [ ( 2500 - x ) * 6 * 1 ] / 100 = 140 x = 1000 answer : d"
Answer: d
Problem: the difference between the local value and the face value of 7 in the numeral 32675149 is ?
Options: a ) 75142 , b ) 64851 , c ) 5149 , d ) 69993 , e ) none of these
Rationale: "( local value of 7 ) - ( face value of 7 ) = ( 70000 - 7 ) = 69993 d )"
Answer: d
Problem: the average ( arithmetic mean ) of the 5 positive integers k , m , r , s , and t is 16 , and k < m < r < s < t . if t is 42 , what is the greatest possible value of the median of the 5 integers ?
Options: a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 22
Rationale: we need to find the median which is the third value when the numbers are in increasing order . since k < m < r < s < t , the median would be r . the average of the positive integers is 16 which means that in effect , all numbers are equal to 16 . if the largest number is 42 , it is 26 more than 16 . we need r to be maximum so k and m should be as small as possible to get the average of 16 . since all the numbers are positive integers , k and m can not be less than 1 and 2 respectively . 1 is 15 less than 16 and 2 is 14 less than 16 which means k and m combined are 29 less than the average . 42 is already 26 more than 16 and hence we only have 29 - 26 = 3 extra to distribute between r and s . since s must be greater than r , r can be 16 + 1 = 17 and s can be 16 + 2 = 18 . so r is 17 . answer ( a )
Answer: a
Problem: a rectangular field has a length 10 meters more than it is width . if the area of the field is 231 , what is the length ( in meters ) of the rectangular field ?
Options: a ) 21 , b ) 23 , c ) 25 , d ) 27 , e ) 29
Rationale: "area = l * w = ( l ) * ( l - 10 ) = 231 trial and error : 20 * 10 = 200 ( too low ) 21 * 11 = 231 the length is 21 meters . the answer is a ."
Answer: a
Problem: a cycle is bought for rs . 600 and sold for rs . 1080 , find the gain percent ?
Options: a ) 22 , b ) 20 , c ) 90 , d ) 80 , e ) 11
Rationale: "600 - - - - 180 100 - - - - ? = > 80 % answer : d"
Answer: d
Problem: how many integers are between 3 and 86 / 7 , inclusive ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "86 / 7 = 12 . xx we are not concerned about the exact value of 86 / 7 as we just need the integers . since the values are small , we can write down the integers . the different integers between 3 and 86 / 7 would be 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 total number of integers = 10 option c if we need to find the number of integers between two numbers n and m , where m > n the number of integers = m - n + 1 in the given question , the number of integers = 12 - 3 + 1 = 10 answer : c"
Answer: c
Problem: a man goes downstream at 15 kmph , and upstream 8 kmph . the speed of the stream is
Options: a ) 0 kmph , b ) 3.5 kmph , c ) 16 kmph , d ) 2.5 kmph , e ) 26 kmph
Rationale: "speed of the stream = 1 / 2 ( 15 - 8 ) kmph = 3.5 kmph . correct option : b"
Answer: b
Problem: if 12 people contributed a total of $ 20.00 toward a gift and each of them contributed at least $ 1.00 , then the maximum possible amount any one person could have contributed is
Options: a ) $ 1.00 , b ) $ 1.25 , c ) $ 5.00 , d ) $ 9.00 , e ) $ 20.00
Rationale: d for me 11 people with 1 $ each - > maximum = 9
Answer: d
Problem: the diagonals of a rhombus are 12 cm and 20 cm . find its area ?
Options: a ) 329 , b ) 288 , c ) 120 , d ) 238 , e ) 31
Rationale: "1 / 2 * 12 * 20 = 120 answer : c"
Answer: c
Problem: the majority owner of a business received 25 % of the profit , with each of 4 partners receiving 25 % of the remaining profit . if the majority owner and two of the owners combined to receive $ 76,875 , how much profit did the business make ?
Options: a ) $ 98,000 , b ) $ 106,000 , c ) $ 112,000 , d ) $ 118,000 , e ) $ 123,000
Rationale: "let p be the total profit . p / 4 + 1 / 2 * ( 3 p / 4 ) = p / 4 + 3 p / 8 = 5 p / 8 = $ 76,875 p = $ 123,000 the answer is e ."
Answer: e
Problem: a and b can do a piece of work in 40 days and 40 days respectively . they work together for 10 days and b leaves . in how many days the whole work is completed ?
Options: a ) 30 days , b ) 35 days , c ) 40 days , d ) 45 days , e ) 50 days
Rationale: "explanation : ( a + b ) ’ s 10 days work = 10 [ 1 / 40 + 1 / 40 ] = 10 [ 1 + 1 / 40 ] = 1 / 2 a complete remaining work in 1 / 2 * 40 = 20 total work = 10 + 20 = 30 days answer : option a"
Answer: a
Problem: in the first 10 overs of a cricket game , the run rate was only 3.2 . what should be the run rate in the remaining 20 overs to reach the target of 282 runs ?
Options: a ) 6.25 , b ) 5.5 , c ) 7.4 , d ) 5 , e ) 12.5
Rationale: "explanation : runs scored in the first 10 overs = 10 × 3.2 = 32 total runs = 282 remaining runs to be scored = 282 - 32 = 250 remaining overs = 20 run rate needed = 250 / 20 = 12.5 answer : option e"
Answer: e
Problem: a car dealership has 40 cars on the lot , 30 % of which are silver . if the dealership receives a new shipment of 80 cars , 40 % of which are not silver , what percentage of total number of cars are silver ?
Options: a ) 35 % , b ) 37.5 % , c ) 45 % , d ) 47.5 % , e ) 50 %
Rationale: "number of silver cars before shipment = 30 % of 40 = 12 number of silver cars after shipment = 60 % of 80 = 48 total number of silver cars out of 120 = 48 + 12 = 60 , which is 50 % e is my answer ."
Answer: e
Problem: a person walks at a speed of 4 km / hr and runs at a speed of 8 km / hr . how many hours will the person require to cover a distance of 12 km , if the person completes half of the distance by walking and the other half by running ?
Options: a ) 1.25 , b ) 1.75 , c ) 2.25 , d ) 2.75 , e ) 3.25
Rationale: "time = 6 / 4 + 6 / 8 = 18 / 8 = 2.25 hours the answer is c ."
Answer: c
Problem: the total number of plums that grow during each year on a certain plum tree is equal to the number of plums that grew during the previous year , less the age of the tree in years ( rounded down to the nearest integer ) . during its 5 th year , the plum tree grew 50 plums . if this trend continues , how many plums will it grow during its 6 th year ?
Options: a ) 40 , b ) 42 , c ) 45 , d ) 48 , e ) 54
Rationale: "1 st year : 0 - 1 ( age ) , we take age = 0 ( as the question says that we have to ( rounded down to the nearest integer ) ) 2 ndyear : 1 - 2 ( age ) , we take age = 1 3 rd year : 2 - 3 ( age ) , we take age = 2 4 th year : 3 - 4 ( age ) , we take age = 3 5 th year : 4 - 5 ( age ) , we take age = 4 6 th year : 5 - 6 ( age ) , we take age = 5 thus for the 5 th year = 50 , 6 th year = 50 - 5 = 45 . the correct answer is c ."
Answer: c
Problem: in what ratio must rice of rs . 32 per kg be mixed with rice of rs . 42 per kg so that cost of mixture is rs . 20 per kg ?
Options: a ) 13 : 6 , b ) 13 : 5 , c ) 11 : 6 , d ) 11 : 5 , e ) 12 : 5
Rationale: "( 20 - 42 ) / ( 32 - 20 ) = 22 / 12 = 11 : 6 answer : c"
Answer: c
Problem: in a lottery there are 10 prizes and 25 blanks . a lottery is drawn at random . what is the probability of getting a prize ?
Options: a ) 1 / 5 , b ) 2 / 7 , c ) 2 / 5 , d ) 1 / 7 , e ) 3 / 5
Rationale: "total draws = prizes + blanks = 10 + 25 = 35 probability of getting a prize = 10 / 35 = 2 / 7 correct option is b"
Answer: b
Problem: if the number is divided by 3 , it reduced by 48 . the number is
Options: a ) a ) 51 , b ) b ) 50 , c ) c ) 45 , d ) d ) 72 , e ) e ) 36
Rationale: "explanation : let the number be x . then , x - ( x / 3 ) = 48 = > 2 x / 3 = 48 = > x = 72 answer : option d"
Answer: d
Problem: an equilateral triangle t 2 is formed by joining the mid points of the sides of another equilateral triangle t 1 . a third equilateral triangle t 3 is formed by joining the mid - points of t 2 and this process is continued indefinitely . if each side of t 1 is 80 cm , find the sum of the perimeters of all the triangles .
Options: a ) 180 cm , b ) 220 cm , c ) 240 cm , d ) 270 cm , e ) 480 cm
Rationale: "we have 80 for first triangle , when we join mid - points of first triangle we get the second equilateral triangle then the length of second one is 40 and continues . so we have 80 , 40,20 , . . . we have ratio = 1 / 2 , and it is gp type . sum of infinite triangle is a / 1 - r = 80 / 1 - ( 1 / 2 ) = 160 equilateral triangle perimeter is 3 a = 3 * 160 = 480 . so option e ."
Answer: e
Problem: if 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n = 4 ^ 26 , then n =
Options: a ) 3 , b ) 6 , c ) 12 , d ) 23 , e ) 25
Rationale: "2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n = 4 ^ 26 = > 4 x 2 ^ 2 n = 4 ^ 26 = 2 ^ 52 = > 2 ^ 2 x 2 ^ 2 n = 2 ^ 52 = > 2 ^ ( 2 n + 2 ) = 2 ^ 52 = > 2 n + 2 = 52 = > n = 25 so . answer will be e"
Answer: e
Problem: if a - b = 5 and a 2 + b 2 = 34 , find the value of ab .
Options: a ) a ) 4.5 , b ) b ) 12 , c ) c ) 15 , d ) d ) 18 , e ) e ) 20
Rationale: "explanation : 2 ab = ( a 2 + b 2 ) - ( a - b ) 2 = 34 - 25 = 9 ab = 4.5 . answer : a"
Answer: a
Problem: john makes $ 60 a week from his job . he earns a raise and now makes $ 110 a week . what is the % increase ?
Options: a ) 16 % , b ) 83.33 % , c ) 17 % , d ) 17.61 % , e ) 17.56 %
Rationale: "increase = ( 50 / 60 ) * 100 = ( 5 / 6 ) * 100 = 83.33 % . b"
Answer: b
Problem: a certain number of workers can do a work in 35 days . if there were 10 workers more it could be finished in 10 days less . how many workers are there ?
Options: a ) 25 , b ) 30 , c ) 28 , d ) 24 , e ) 32
Rationale: "number of workers = 10 * ( 35 - 10 ) / 10 = 25 answer is a"
Answer: a
Problem: in the formula a = ( 2 r ) ^ 3 , if r is halved , then a is multiplied by ?
Options: a ) 64 , b ) 1 / 8 , c ) 1 , d ) 8 , e ) 1 / 64
Rationale: say r = 2 = > a 1 = 64 when r = 1 ; v 2 = 8 v 2 = 1 / 8 * v 1 . answer : b
Answer: b
Problem: the value of a machine depreciates at 20 % per annum . if its present value is rs . 1 , 50,000 , at what price should it be sold after two years such that a profit of rs . 22,000 is made ?
Options: a ) 328897 , b ) 120000 , c ) 118000 , d ) 277768 , e ) 188871
Rationale: the value of the machine after two years = 0.8 * 0.8 * 1 , 50,000 = rs . 96,000 sp such that a profit of rs . 22,000 is made = 96,000 + 24,000 = rs . 1 , 18,000 answer : c
Answer: c
Problem: a cycle is bought for rs . 900 and sold for rs . 1180 , find the gain percent ?
Options: a ) 11 , b ) 31 , c ) 99 , d ) 77 , e ) 18
Rationale: "900 - - - - 280 100 - - - - ? = > 31 % answer : b"
Answer: b
Problem: all the students of class are told to sit in circle shape . here the boy at the 8 th position is exactly opposite to 33 th boy . total number of boys in the class ?
Options: a ) 40 , b ) 50 , c ) 28 , d ) 38 , e ) 48
Rationale: "as half the circle shape consist of 33 - 8 = 25 boys , so total number of boys in full circle = 2 * 25 = 50 answer : b"
Answer: b
Problem: 45 girls and 60 boys are present at a party . there are 17 girl - boy are in relationship among them . if a girl and a boy is selected at random , what is the probability that they will be not a couple ?
Options: a ) 17 / 2900 , b ) 2683 / 2700 , c ) 2496 / 2700 , d ) 2369 / 2700 , e ) 198 / 270
Rationale: in how many ways we can select a girl and a boy from 45 lady and 60 gentlemen ? in 45 * 60 = 2,700 ways . we have a total of 17 couples so , the probability of selecting a couple is 17 / 2,700 = 17 / 2700 . probability of there will not be a couple = 1 - ( 17 / 2700 ) = 2683 / 2700 ans - b
Answer: b
Problem: if p ( a ) = 2 / 15 , p ( b ) = 4 / 15 , and p ( a â ˆ ª b ) = 11 / 15 find p ( a | b )
Options: a ) 11 / 4 , b ) 2 / 3 , c ) 3 / 2 , d ) 4 / 5 , e ) 4 / 7
Rationale: "p ( a | b ) = p ( a â ˆ ª b ) / p ( b ) p ( a | b ) = ( 11 / 15 ) / ( 4 / 15 ) = 11 / 4 . a"
Answer: a
Problem: how long does a train 110 m long running at the speed of 72 km / hr takes to cross a bridge 134 m length ?
Options: a ) 82.1 sec . , b ) 12.2 sec , c ) 19.1 sec . , d ) 17.1 sec . , e ) 42.1 sec .
Rationale: "speed = 72 * 5 / 18 = 20 m / sec total distance covered = 110 + 134 = 244 m . required time = 244 / 20 = 12.2 sec . answer : b"
Answer: b
Problem: what percent is 70 of 280 ?
Options: a ) 12 % , b ) 25 % , c ) 26 % , d ) 27 % , e ) 28 %
Rationale: "70 / 280 = 1 / 4 1 / 4 × 100 = 25 % b"
Answer: b
Problem: ifaequals the sum of the even integers from 2 to 40 , inclusive , andbequals the sum of the odd integers from 1 to 39 , inclusive , what is the value of a - b ?
Options: a ) 1 , b ) 10 , c ) 19 , d ) 20 , e ) 21
Rationale: this is a solution from beatthegmat : even numbers : ( 40 - 2 ) / 2 + 1 = 20 even integers . ( 40 + 2 ) / 2 = 21 is the average of the even set . sum = avg * ( # of elements ) = 21 * 20 = 420 = a odd numbers : ( 39 - 1 ) / 2 + 1 = 20 odd integers . ( 39 + 1 ) / 2 = 20 is the average of the odd set . sum = avg * ( # of elements ) = 20 * 20 = 400 = b a - b = 420 - 400 = 20 . answer : d
Answer: d
Problem: a train running at the speed of 90 km / hr crosses a pole in 12 seconds . find the length of the train ?
Options: a ) 150 , b ) 872 , c ) 287 , d ) 288 , e ) 300
Rationale: "speed = 90 * ( 5 / 18 ) m / sec = 75 / 3 m / sec length of train ( distance ) = speed * time ( 75 / 3 ) * 12 = 300 meter answer : e"
Answer: e
Problem: two cars , car 1 and car 2 move towards each other from e and y respectively with respective speeds of 20 m / s and 15 m / s . after meeting each other car 1 reaches y in 10 seconds . in how many seconds does car 2 reach e starting from y ?
Options: a ) 15.5 sec , b ) 8.4 sec , c ) 33.6 sec , d ) 31.11 sec , e ) 16.8 sec
Rationale: e - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | - - - - - - - - - - - - - - - - - - - - - - - - - - - - y car a ( 20 mps ) - - - - - - - - - - - - - - - - - - - - - - - - - > p < - - - - - - - - - - - - - - - car b ( 15 mps ) let 2 cars meet each other at point p in t seconds . car 1 covers distance = 20 t . car 2 covers distance = 15 t . so , total distance ey = 35 t . from p , car 1 reaches onto y in 10 secs . so it covers 15 t further . so , 15 t / 20 = 10 so t = 40 / 3 sec and total distance = ( 35 * 40 ) / 3 hence car 2 will cover total distance in ( 35 * 40 ) / ( 3 * 15 ) = 31.11 sec approx . answer d
Answer: d
Problem: the radius of a semicircular plot is 25 . what is the approximate perimeter of the plot ?
Options: a ) 114
b ) 150
c ) 129
d ) 25
e ) 57
Rationale: perimeter of a circle = 2 pi * r perimeter of a semicircle = pi * r + 2 r aprox perimiter = 3.14 * 25 + 2 * 25 = 128.50 approximately 129 answer c
Answer: c
Problem: how many two - digit whole numbers yield a remainder of 3 when divided by 10 and also yield a remainder of 3 when divided by 4 ? options :
Options: a ) one , b ) two , c ) three , d ) four , e ) five
Rationale: numbers giving remainder 3 when divided by 10 = 13,23 , 33,43 , 53,63 , 73,83 , 93 numbers giving remainder 3 when divided by 4 = alternate numbers ( coloured in red ) = 4 correct option : d
Answer: d
Problem: on a race track a maximum of 5 horses can race together at a time . there are a total of 25 horses . there is no way of timing the races . what is the minimum number t of races we need to conduct to get the top 3 fastest horses ?
Options: a ) 5 , b ) 7 , c ) 8 , d ) 10 , e ) 11
Rationale: "t = 7 is the correct answer . good solution buneul . b"
Answer: b
Problem: from the beginning to the end of 2007 , the price of a stock rose 20 percent . in 2008 , it dropped 25 percent . in 2009 , it rose 30 percent . what percent of the stock â € ™ s 2007 starting price was the price of the stock at the end of 2009 ?
Options: a ) 80 , b ) 117 , c ) 95 , d ) 100 , e ) 108
Rationale: "assume a value at the beginning of 2007 . as this is a % question , assume p = 100 . at the end of 2007 it becmae = 1.2 * 100 = 120 at the end of 2008 it decreased by 25 % = 120 * . 75 = 90 at the end of 2009 it increased by 30 % = 90 * 1.3 = 117 thus ratio = 117 / 100 = 1.17 ( in % terms = 117 % ) . thus b is the correct answer ."
Answer: b
Problem: a rectangular tiled patio is composed of 40 square tiles . the rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles . after the change in layout , the patio will still have 40 tiles , and it will still be rectangular . how many rows are in the tile patio before the change in layout ?
Options: a ) 5 , b ) 6 , c ) 10 , d ) 13 , e ) 28
Rationale: "r * c = 70 and ( 6 + 4 ) ( c - 2 ) = 70 - - > r = 6 and c = 6 . answer : b ."
Answer: b
Problem: set s consists of integers { 6 , 7 , 10 , 12 , 15 } . if integer n is included in the set , the average ( arithmetic mean ) of set s will increase by 40 % . what is the value of integer n ?
Options: a ) 26 , b ) 30 , c ) 34 , d ) 38 , e ) 42
Rationale: "the average of the numbers in set s is 10 . if we increase the mean by 40 % , the new mean is 14 . thus , on average , 5 numbers increase by 4 . therefore n = 14 + 20 = 34 the answer is c ."
Answer: c
Problem: a girl was asked to multiply a certain number by 43 . she multiplied it by 34 and got his answer less than the correct one by 1224 . find the number to be multiplied .
Options: a ) 130 , b ) 132 , c ) 134 , d ) 136 , e ) 138
Rationale: "let the required number be x . then , 43 x – 34 x = 1224 or 9 x = 1224 or x = 136 . required number = 136 . answer : d"
Answer: d
Problem: what will be the difference between simple and compound interest @ 20 % per annum on a sum of $ 500 after 2 years ?
Options: a ) $ 10 , b ) $ 20 , c ) $ 25 , d ) $ 30 , e ) $ 40
Rationale: "s . i . = 500 * 20 * 2 / 100 = $ 200 c . i . = 500 * ( 1 + 20 / 100 ) ^ 2 - 500 = $ 220 difference = 220 - 200 = $ 20 answer is b"
Answer: b
Problem: martins made a part payment of $ 650 toward buying a brand new washing machine , which represents 15 % of the total cost of the washing machine , how much remains to be paid ?
Options: a ) $ 1116.3 , b ) $ 3583.3 , c ) $ 3283.3 , d ) $ 3683.3 , e ) $ 2683.3
Rationale: explanation : let ' s start with what the total price of the washing machine would be . if 15 % is equal to $ 650 then 100 % equals $ x . we just have to multiply $ 650 by 6.67 to get total amount = $ 4333.3 . out of this amount we then need to deduct the amount already paid which was $ 650 so we have $ 4333.3 - $ 650 = $ 3683.3 answer : option d
Answer: d
Problem: a small , rectangular park has a perimeter of 560 feet and a diagonal measurement of 300 feet . what is its area , in square feet ?
Options: a ) 43,200 , b ) 19,600 , c ) 20,000 , d ) 20,400 , e ) 20,800
Rationale: "you can avoid a lot of work in this problem by recognizing that , with the info provided , the diagonal forms a triangle inside the rectangle with sides that have a 3 : 4 : 5 ratio . diagonal = 200 2 x + 2 y = 560 , or x + y = 280 a ^ 2 + b ^ 2 = c ^ 2 for each the sides of the triangle using the ratio 3 : 4 : 5 for sides , and knowing c = 300 , you can deduce the following a = 180 b = 240 180 x 240 = 43,200 a is the answer ."
Answer: a
Problem: in the storage room of a certain bakery , the ratio of sugar to flour is 5 to 6 , and the ratio of flour to baking soda is 10 to 1 . if there were 60 more pounds of baking soda in the room , the ratio of flour to baking soda would be 8 to 1 . how many pounds of sugar are stored in the room ?
Options: a ) 600 , b ) 1200 , c ) 1500 , d ) 1600 , e ) 2000
Rationale: "sugar : flour = 5 : 6 = 25 : 30 ; flour : soda = 10 : 1 = 30 : 3 ; thus we have that sugar : flour : soda = 25 x : 30 x : 3 x . also given that 30 x / ( 3 x + 60 ) = 8 / 1 - - > x = 80 - - > sugar = 25 x = 2,000 . answer : e ."
Answer: e
Problem: the h . c . f of two numbers is 19 and their l . c . m is 4263 . if one of the numbers is 399 , then the other is ?
Options: a ) 202 , b ) 203 , c ) 204 , d ) 205 , e ) 206
Rationale: "other number = ( 19 * 4263 ) / 399 = 203 . answer : b"
Answer: b
Problem: in a restaurant , the profit is 110 % of the cost . if the cost increases by 12 % but the selling price remains constant , approximately what percentage of the selling price is the profit ?
Options: a ) 30 % , b ) 47 % , c ) 90 % , d ) 100 % , e ) none of these
Rationale: explanation : let c . p . = rs . 100 . then , profit = rs . 110 , s . p . = rs . 210 . new c . p . = 112 % of rs . 100 = rs . 112 new s . p . = rs . 210 . profit = rs . ( 210 - 112 ) = rs . 98 . required percentage = ( 98 / 210 * 100 ) % = 47 % appox answer : b
Answer: b
Problem: at a loading dock , each worker on the night crew loaded 3 / 4 as many boxes as each worker on the day crew . if the night crew has 3 / 4 as many workers as the day crew , what fraction of all the boxes loaded by the two crews did the day crew load ?
Options: a ) 3 / 5 , b ) 4 / 5 , c ) 11 / 15 , d ) 16 / 25 , e ) 19 / 25
Rationale: "let x be the number of workers on the day crew . let y be the number of boxes loaded by each member of the day crew . then the number of boxes loaded by the day crew is xy . the number of boxes loaded by the night crew is ( 3 x / 4 ) ( 3 y / 4 ) = 9 xy / 16 the total number of boxes is xy + 9 xy / 16 = 25 xy / 16 the fraction loaded by the day crew is xy / ( 25 xy / 16 ) = 16 / 25 the answer is d ."
Answer: d
Problem: walking 6 / 5 of his usual rate , a boy reaches his school 4 min early . find his usual time to reach the school ?
Options: a ) 22 , b ) 99 , c ) 27 , d ) 24 , e ) 20
Rationale: "speed ratio = 1 : 6 / 5 = 5 : 6 time ratio = 6 : 5 1 - - - - - - - - 6 4 - - - - - - - - - ? 24 m . answer : d"
Answer: d
Problem: how many seconds will a 500 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 66 km / hr ?
Options: a ) 11 , b ) 30 , c ) 29 , d ) 88 , e ) 61
Rationale: "speed of train relative to man = 66 - 3 = 63 km / hr . = 63 * 5 / 18 = 35 / 2 m / sec . time taken to pass the man = 500 * 2 / 35 = 28.57 sec . approx . 29 sec answer : c"
Answer: c
Problem: what number times ( 1 ⁄ 4 ) ^ 2 will give the value of 4 ^ 3 ?
Options: a ) 4 , b ) 16 , c ) 64 , d ) 256 , e ) 1024
Rationale: "x * ( 1 / 4 ) ^ 2 = 4 ^ 3 x = 4 ^ 2 * 4 ^ 3 = 4 ^ 5 = 1024 the answer is e ."
Answer: e
Problem: a vendor bought toffees at 6 for a rupee . how many for a rupee must he sell to gain 25 % ?
Options: a ) 2 , b ) 9 , c ) 6 , d ) 3 , e ) 5
Rationale: "c . p . of 6 toffees = re . 1 s . p . of 6 toffees = 150 % of re . 1 = rs . 3 / 2 for rs . 3 / 2 , toffees sold = 6 . for re . 1 , toffees sold = 6 x 3 / 2 = 9 . answer b"
Answer: b
Problem: one night 19 percent of the female officers on a police force were on duty . if 152 police officers were on duty that night and half of these were female officers , how many female officers were on the police force ?
Options: a ) 300 , b ) 350 , c ) 400 , d ) 450 , e ) 500
Rationale: "let x be the number of female police officers on the police force . the number of female police officers on duty was 76 . 0.19 x = 76 x = 400 the answer is c ."
Answer: c
Problem: a car ferry can hold up to 70 tons of cargo . what is the greatest number of vehicles that the ferry can carry if half the vehicles are cars with an average ( arithmetic mean ) weight of 0.75 tons and half of the vehicles are trucks with an average ( arithmetic mean ) weight of 6 tons ?
Options: a ) 20 , b ) 24 , c ) 28 , d ) 32 , e ) 36
Rationale: "the weight of one car and one truck is 6.75 tons . 70 / 6.75 = 10 plus a remainder the ferry could carry 10 cars and 10 trucks for a total of 20 vehicles . the answer is a ."
Answer: a
Problem: a train passes a platform in 35 seconds . the same train passes a man standing on the platform in 20 seconds . if the speed of the train is 54 km / hr , the length of the platform is
Options: a ) 280 meter , b ) 240 meter , c ) 225 meter , d ) 200 meter , e ) none of these
Rationale: "explanation : speed of the train = 54 km / hr = ( 54 × 10 ) / 35 m / s = 15 m / s length of the train = speed × time taken to cross the man = 15 × 20 = 300 m let the length of the platform = l time taken to cross the platform = ( 300 + l ) / 15 = > ( 300 + l ) / 15 = 35 = > 300 + l = 15 × 35 = 525 = > l = 525 - 300 = 225 meter answer : option c"
Answer: c
Problem: a grocer has 400 pounds of coffee in stock , 20 percent of which is decaffeinated . if the grocer buys another 100 pounds of coffee of which 50 percent is decaffeinated , what percent , by weight , of the grocer ’ s stock of coffee is decaffeinated ?
Options: a ) 26 % , b ) 30 % , c ) 32 % , d ) 34 % , e ) 40 %
Rationale: "1 . 20 % of 400 = 80 pounds of decaffeinated coffee 2 . 50 % of 100 = 50 pounds of decaffeinated coffee 3 . wt have 130 pounds of decaffeinated out of 500 pounds , that means 130 / 500 * 100 % = 26 % . the correct answer is a ."
Answer: a
Problem: praveen starts business with rs . 3220 and after 5 months , hari joins with praveen as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is hari ’ s contribution in the capital ?
Options: a ) s . 7500 , b ) s . 8000 , c ) s . 8280 , d ) s . 9000 , e ) s . 6000
Rationale: "let hari ’ s capital be rs . x . then , 3220 * 12 / 7 x = 2 / 3 = > 14 x = 115920 = > x = 8280 . answer : c"
Answer: c
Problem: how many integers from 22 to 160 , inclusive , are divisible by 3 but not divisible by 7 ?
Options: a ) 30 , b ) 35 , c ) 40 , d ) 50 , e ) 60
Rationale: "we should find # of integers divisible by 3 but not by 3 * 7 = 21 . # of multiples of 21 in the range from 22 to 160 , inclusive is ( 147 - 42 ) / 21 + 1 = 6 ; 46 - 6 = 40 . answer : c ."
Answer: c
Problem: 8 identical machines , working alone and at their constant rates , take 6 hours to complete a job lot . how long would it take for 4 such machines to perform the same job ?
Options: a ) 2.25 hours , b ) 8.75 hours , c ) 12 hours , d ) 14.25 hours , e ) 16 hours
Rationale: let each machine do 1 unit of work for 1 hour 8 machines - - > 8 units of work in 1 hour for 6 hours = 8 * 6 = 48 units of total work is done . now this 48 units of total work must be done by 4 machines 4 units of work ( 4 machines ) - - - > 1 hour for 48 units of work 4 * 12 - - - > 1 * 12 hours c 12 hours
Answer: c
Problem: a candidate got 35 % of the votes and lost to the rival by 2100 votes . how many votes were cast ?
Options: a ) 7000 , b ) 7200 , c ) 7400 , d ) 7600 , e ) 7800
Rationale: "35 % - - - - - - - - - - - l 65 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 30 % = 2100 10 % = 700 100 % of the votes = 7000 answer : a"
Answer: a
Problem: if you write down all the numbers from 1 to 25 , then how many times do you write 3 ?
Options: a ) a ) 11 , b ) b ) 3 , c ) c ) 2 , d ) d ) 1 , e ) e ) 6
Rationale: "explanation : explanation : clearly , from 1 to 25 , there are ten numbers with 3 as the unit ' s digit - 3 , 13 , 23 so , required number = 3 answer : b"
Answer: b
Problem: what is the square root of 81 , divided by 3 ?
Options: a ) 9 , b ) 36 , c ) 122 , d ) 3 , e ) 1
Rationale: "square root is a number times itself square root of 81 = 6 , 9 / 3 = 3 ( d ) 3"
Answer: d
Problem: the mean of 30 values was 250 . it was detected on rechecking that one value 165 was wrongly copied as 135 for the computation of the mean . find the correct mean .
Options: a ) 151 , b ) 149 , c ) 152 , d ) 251 , e ) none of the above
Rationale: "corrected mean = 250 × 30 − 135 + 165 / 30 = 7500 − 135 + 165 / 30 = 7530 / 30 = 251 answer d"
Answer: d
Problem: a cyclist rides a bicycle 9 km at an average speed of 11 km / hr and again travels 11 km at an average speed of 9 km / hr . what is the average speed for the entire trip ?
Options: a ) 9.3 , b ) 9.6 , c ) 9.8 , d ) 10.1 , e ) 10.3
Rationale: "distance = 20 km time = 9 / 11 + 11 / 9 = ( 81 + 121 ) / 99 = 202 / 99 hours average speed = ( 20 * 99 ) / 202 = 9.8 km / h the answer is c ."
Answer: c
Problem: a man can row upstream at 26 kmph and downstream at 30 kmph , and then find the speed of the man in still water ?
Options: a ) 29 , b ) 28 , c ) 30 , d ) 32 , e ) 23
Rationale: "us = 26 ds = 30 m = ( 30 + 26 ) / 2 = 28 answer : b"
Answer: b
Problem: in a group of 60 people , 35 have visited iceland and 23 have visited norway . if 31 people have visited both iceland and norway , how many people have visited neither country ?
Options: a ) 30 , b ) 31 , c ) 32 , d ) 33 , e ) 34
Rationale: this is an example of a standard overlapping sets question . it has no ' twists ' to it , so you ' ll likely find using the overlapping sets formula to be a fairly easy approach . if you ' re not familiar with it , then here is the formula : 60 = 35 + 23 - 31 + ( # in neither group ) = 33 the prompt gives you all of the numbers you need to get to the correct answer . just plug in and solve . d
Answer: d
Problem: a reduction of 5 % in the price of oil enables a house wife to obtain 10 kgs more for rs . 5000 , what is the reduced price for kg ?
Options: a ) 23 , b ) 27 , c ) 25 , d ) 35 , e ) 15
Rationale: "5000 * ( 5 / 100 ) = 250 - - - - 10 ? - - - - 1 = > rs . 25 answer : c"
Answer: c
Problem: if a 2 - b 2 = 10 and a * b = 8 , find a 4 + b 4 .
Options: a ) 200 , b ) 228 , c ) 182 , d ) 102 , e ) 128
Rationale: "a 2 - b 2 = 10 : given a 4 + b 4 - 2 a 2 b 2 = 102 : square both sides and expand . a * b = 8 : given a 2 b 2 = 82 : square both sides . a 4 + b 4 - 2 ( 64 ) = 100 : substitute a 4 + b 4 = 228 correct answer b"
Answer: b
Problem: find the sum of first 80 odd numbers
Options: a ) 6400 , b ) 8000 , c ) 5000 , d ) 4980 , e ) 4960
Rationale: "explanation : n 2 = 802 = 6400 answer : option a"
Answer: a
Problem: of 58 players on a cricket team , 37 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?
Options: a ) 51 , b ) 55 , c ) 59 , d ) 71 , e ) 92
Rationale: total = 58 thrower = 37 rest = 58 - 37 = 21 left handed = 21 / 3 = 7 right handed = 14 if all thrower are right handed then total right handed is 37 + 14 = 51 so a . 51 is the right answer
Answer: a
Problem: the amount of principal rs . 8000 at compound interest at the ratio of 5 % p . a . for 6 years is
Options: a ) s . 9621 , b ) s . 6921 , c ) s . 10721 , d ) s . 6261 , e ) s . 6361
Rationale: "c . i = p ( 1 + r / 100 ) ^ n = 8000 ( 1 + 5 / 100 ) ^ 6 = rs 10721 answer : c"
Answer: c