regisss/math_qa huggingface dataset:
Problem: in a fuel station the service costs $ 2.05 per car , every liter of fuel costs 0.6 $ . assuming that you fill up 3 mini - vans and 2 trucks , how much money will the fuel cost to all the cars owners total , if a mini - van ' s tank is 70 liters and a truck ' s tank is 120 % bigger and they are all empty - ?
Options: a ) 312.6 $ , b ) 321.05 $ , c ) 343.7 $ , d ) 398.85 $ , e ) 412.12 $
Rationale: "service cost of 3 van and 2 truck = 2.05 * ( 3 + 2 ) = 10.5 fuel in 3 van = 3 * 70 = 210 litre fuel in 2 trucks = 2 * 70 ( 1 + 120 / 100 ) = 308 total fuel ( van + truck ) = 518 litre total fuel cost = 518 * 0.6 = 310.8 total cost = fuel + service = 310.8 + 10.25 = 321.05 answer is b"
Answer: b
Problem: a man two flats for $ 675958 each . on one he gains 16 % while on the other he loses 16 % . how much does he gain or lose in the whole transaction ?
Options: a ) 2 % , b ) 2.56 % , c ) 3.12 % , d ) 4.65 % , e ) 5.12 %
Rationale: "in such a case there is always a loss loss % = ( 16 / 10 ) ^ 2 = 64 / 25 = 2.56 % answer is b"
Answer: b
Problem: in an office , 60 percent of the workers have at least 5 years of service , and a total of 16 workers have at least 10 years of service . if 90 percent of the workers have fewer than 10 years of service , how many of the workers have at least 5 but fewer than 10 years of service ?
Options: a ) 96 , b ) 64 , c ) 50 , d ) 144 , e ) 160
Rationale: "( 10 / 100 ) workers = 16 = > number of workers = 160 ( 60 / 100 ) * workers = x + 16 = > x = 96 answer a"
Answer: a
Problem: a rectangular lawn of dimensions 120 m * 60 m has two roads each 10 m wide running in the middle of the lawn , one parallel to the length and the other parallel to the breadth . what is the cost of traveling the two roads at rs . 3 per sq m ?
Options: a ) s . 5100 , b ) s . 3900 , c ) s . 3228 , d ) s . 3922 , e ) s . 3928
Rationale: "area = ( l + b – d ) d ( 120 + 60 – 10 ) 10 = > 1700 m 2 1700 * 3 = rs . 5100 answer : a"
Answer: a
Problem: the sum of the first 50 positive even integers is 2550 . what is the sum of the even integers from 502 to 600 inclusive ?
Options: a ) 23,550 , b ) 27,550 , c ) 31,550 , d ) 35,550 , e ) 39,550
Rationale: "2 + 4 + 6 + 8 + . . . + 100 = 2550 502 + 504 + . . . + 600 = 50 ( 500 ) + ( 2 + 4 + . . . + 100 ) = 25,000 + 2550 = 27,550 the answer is b ."
Answer: b
Problem: if n is the greatest positive integer for which 2 ^ n is a factor of 8 ! , then n = ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "8 ! = 40320 e . 2 ^ 10 = 512 ( 40320 / 512 ) - this is not a factor of 8 ! d . 2 ^ 8 = 256 ( 40320 / 256 ) - this is not a factor of 8 ! c . 2 ^ 6 = 64 ( 720 / 64 ) - this is a factor of 8 ! c is answer"
Answer: c
Problem: when x is multiplied by 3 , the result is 18 more than the result of subtracting x from 70 . what is the value of x ?
Options: a ) - 4 , b ) - 2 , c ) 11 , d ) 13 , e ) 22
Rationale: "the equation that can be formed is : 3 x - 18 = 70 - x or , 4 x = 88 or , x = 22 . e answer ."
Answer: e
Problem: what is the average of xx , 2 x 2 x , and 66 ?
Options: a ) x + 2 , b ) x + 2 x , c ) x + 2 x + 2 , d ) 2 x + 2 , e ) x + 2 x - 2
Rationale: "by the definition of an average , we get : x + 2 x + 63 = 3 x + 63 x + 2 x + 63 = 3 x + 63 = 3 ( x + 2 ) 3 = x + 2 . = 3 ( x + 2 ) 3 = x + 2 . hence , the answer is x + 2 x + 2 or option c"
Answer: c
Problem: 10 men can complete a work in 7 days . but 10 women need 14 days to complete the same work . how many days will 5 men and 10 women need to complete the work ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 10
Rationale: work done by 10 men in 1 day = 1 / 7 work done by 1 man in 1 day = ( 1 / 7 ) / 10 = 1 / 70 work done by 10 women in 1 day = 1 / 14 work done by 1 woman in 1 day = 1 / 140 work done by 5 men and 10 women in 1 day = 5 × ( 1 / 70 ) + 10 × ( 1 / 140 ) = 5 / 70 + 10 / 140 = 1 / 7 = 5 men and 10 women can complete the work in 7 days answer : option c
Answer: c
Problem: vijay sells a cupboard at 10 % below cost price . had he got rs . 1500 more , he would have made a profit of 10 % . what is the cost price of the cupboard ?
Options: a ) 7450 , b ) 7500 , c ) 7400 , d ) 7500 , e ) none of these
Rationale: "explanation : cost price = 1500 / ( 0.10 + 0.10 ) = 1500 / 0.20 = rs . 7500 answer b"
Answer: b
Problem: there has been successive increases of 20 % and then 10 % in the price of gas from the previous month . by what percentage should a driver reduce gas consumption so that the expenditure does not change ?
Options: a ) 16 % , b ) 20 % , c ) 24 % , d ) 28 % , e ) 32 %
Rationale: "let p be the original price per unit of gas . let x be the original gas consumption . let y be the reduced gas consumption . y * 1.1 * 1.2 * p = x * p y = x / ( 1.1 * 1.2 ) which is about 0.76 x which is a decrease of about 24 % . the answer is c ."
Answer: c
Problem: the length of a rectangle is increased by 35 % and its breadth is decreased by 20 % . what is the effect on its area ?
Options: a ) 10800 , b ) 1299 , c ) 1000 , d ) 10000 , e ) 2887
Rationale: "100 * 100 = 10000 135 * 80 = 10800 answer : a"
Answer: a
Problem: express 25 mps in kmph ?
Options: a ) 23 , b ) 88 , c ) 90 , d ) 27 , e ) 21
Rationale: "25 * 18 / 5 = 90 kmph answer : c"
Answer: c
Problem: a can finish a work in 24 days and b can do the same work in 15 days . b worked for 10 days and left the job . in how many days , a alone can finish the remaining work ?
Options: a ) 6 , b ) 5 , c ) 5.5 , d ) 7 , e ) 8
Rationale: "b ' s 10 day ' s work = ( 1 x 10 ) = 2 . 15 3 remaining work = ( 1 - 2 ) = 1 . 3 3 now , 1 work is done by a in 1 day . 24 therefore 1 work is done by a in ( 24 x 1 ) = 8 days . e"
Answer: e
Problem: a satellite is composed of 30 modular units , each of which is equipped with a set of sensors , some of which have been upgraded . each unit contains the same number of non - upgraded sensors . if the number of non - upgraded sensors on one unit is 1 / 6 the total number of upgraded sensors on the entire satellite , what fraction of the sensors on the satellite have been upgraded ?
Options: a ) 5 / 6 , b ) 1 / 5 , c ) 1 / 6 , d ) 1 / 7 , e ) 1 / 24
Rationale: "let x be the number of upgraded sensors on the satellite . the number of non - upgraded sensors per unit is x / 6 . the number of non - upgraded sensors on the whole satellite is 30 ( x / 6 ) = 5 x . the fraction of sensors which have been upgraded is x / ( x + 5 x ) = x / 6 x = 1 / 6 the answer is c ."
Answer: c
Problem: a certain class of students is being divided into teams . the class can either be divided into 16 teams with an equal number of players on each team or 24 teams with an equal number of players on each team . what is the lowest possible number of students in the class ?
Options: a ) 6 , b ) 36 , c ) 48 , d ) 60 , e ) 72
Rationale: "let total no of students in the class be n so , we are told that n is divisible by both 16 24 so , lets find the least common multiple of 16 24 , ie 48 so our answer is ( c ) 48"
Answer: c
Problem: if 5 % more is gained by selling an article for rs . 350 than by selling it for rs . 320 , the cost of the article is
Options: a ) 289 , b ) 231 , c ) 200 , d ) 288 , e ) 600
Rationale: "explanation : let c . p . be rs . x . then , 5 % of x = 350 - 320 = 30 x / 20 = 30 = > x = 600 answer : e"
Answer: e
Problem: a hall 36 m long and 15 m broad is to be paved with stones , each measuring 5 dm by 5 dm . the number of stones required is :
Options: a ) 180 , b ) 1800 , c ) 18 , d ) 2160 , e ) 1.8
Rationale: "area of the hall = 3600 * 1500 area of each stone = ( 50 * 50 ) therefore , number of stones = ( 3600 * 1500 / 50 * 50 ) = 2160 answer : d"
Answer: d
Problem: on the number line , the number p is twice as many units from - 2 as - 2 is from 3 . if p is less than – 2 , what is the value of p ?
Options: a ) – 12 , b ) – 10 , c ) – 6 , d ) 10 , e ) 14
Rationale: "distance between - 2 and 3 = 5 since number p is twice as many units from - 2 as - 2 is from 3 , therefore p can be - 12 since , p is less than - 2 , the value of p = - 12 answer a"
Answer: a
Problem: before leaving home for the town of madison , pete checks a map which shows that madison is 6 inches from his current location , gardensquare . pete arrives in madison 2.5 hours later and drove at an average speed of 60 miles per hour . at what scale , in inches per mile , is the map drawn ?
Options: a ) 1 / 25 , b ) 1 / 30 , c ) 1 / 10 , d ) 2 , e ) 30
Rationale: "pete covered 2.5 * 60 = 150 miles which correspond to 6 inches on the map - - > scale in inches per mile is 6 / 150 = 1 / 25 . answer : a ."
Answer: a
Problem: a person lent a certain sum of money at 5 % per annum at simple interest and in 8 years the interest amounted to $ 480 less than the sum lent . what was the sum lent ?
Options: a ) 700 , b ) 800 , c ) 900 , d ) 1000 , e ) 1100
Rationale: "p - 480 = ( p * 5 * 8 ) / 100 p = 800 the answer is b ."
Answer: b
Problem: all numbers from 1 to 200 ( in decimal system ) are written in base 6 and base 7 systems . how many of the numbers will have a non - zero units digit in both base 6 and base 7 notations ?
Options: a ) 143
b ) 200
c ) 157
d ) 122
e ) 132
Rationale: detailed solution if a number written in base 6 ends with a zero , it should be a multiple of 6 . in other words , the question wants us to find all numbers from 1 to 200 that are not multiples of 6 or 7 . there are 33 multiples of 6 less than 201 . there are 28 multiples of 7 less than 201 . there are 4 multiples of 6 & 7 ( or multiple of 42 ) from 1 to 200 . so , total multiples of 6 or 7 less than 201 = 33 + 28 - 4 = 57 . number of numbers with non - zero units digit = 200 - 57 = 143 . correct answer : a
Answer: a
Problem: two trains are moving in the same direction at 72 kmph and 36 kmph . the faster train crosses a man in the slower train in 25 seconds . find the length of the faster train ?
Options: a ) 270 , b ) 250 , c ) 187 , d ) 257 , e ) 271
Rationale: "relative speed = ( 72 - 36 ) * 5 / 18 = 2 * 5 = 10 mps . distance covered in 25 sec = 25 * 10 = 250 m . the length of the faster train = 250 m . answer : b"
Answer: b
Problem: an urn contains 6 red , 5 blue and 2 green marbles . if 2 marbles are picked at random , what is the probability that both are red ?
Options: a ) 6 / 13 , b ) 5 / 26 , c ) 6 / 26 , d ) 9 / 26 , e ) 10 / 27
Rationale: option ( b ) is correct p ( both are red ) , 6 c 2 / 13 c 2 = 5 / 26 answer b
Answer: b
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 30 % of m is equal to what percent of 200 % of j ?
Options: a ) 0.35 , b ) 3.5 , c ) 525 , d ) 350 , e ) 3500
Rationale: "imo answer should be 350 . . . consider j = 10 , then k = 50 , l = 150 and m = 350 . . . . 30 % of 350 , comes out to be 105 . . . . 200 % of 10 is 20 . . . . ( 105 * 100 ) / 20 = 525 . . . . ans : c"
Answer: c
Problem: solve below question 2 x + 1 = - 15
Options: a ) - 8 , b ) - 9 , c ) 9 , d ) 8 , e ) - 7
Rationale: "2 x + 1 = - 15 x = - 8 a"
Answer: a
Problem: a salesman ' s income consists of a commission and a base salary of $ 350 per week . over the past 5 weeks , his weekly income totals have been $ 556 , $ 413 , $ 420 , $ 436 and $ 395 . what must his average ( arithmetic mean ) commission be per week over the next two weeks so that his average weekly income is $ 500 over the 7 - week period ?
Options: a ) $ 150 , b ) $ 290 , c ) $ 365 , d ) $ 715 , e ) $ 730
Rationale: "total weekly income over 5 weeks = $ 556 + $ 413 + $ 420 + $ 436 + $ 395 = $ 2220 for avg weekly income to be $ 500 over 7 weeks , we need total weekly income over 7 weeks = $ 3500 now , $ 3500 - $ 2220 = $ 1280 from this , we subtract base salary for 2 weeks i . e $ 350 * 2 = $ 700 therefore , commission = $ 1280 - $ 700 = $ 580 for 2 weeks avg weekly commission = $ 290 answer b"
Answer: b
Problem: a man can row 4.8 km / hr in still water . it takes him twice as long to row upstream as to row downstream . what is the rate of the current ?
Options: a ) 1.9 , b ) 1.7 , c ) 1.2 , d ) 1.5 , e ) 1.6
Rationale: "speed of boat in still water ( b ) = 4.8 km / hr . speed of boat with stream ( down stream ) , d = b + u speed of boat against stream ( up stream ) , u = b – u it is given upstream time is twice to that of down stream . ⇒ downstream speed is twice to that of upstream . so b + u = 2 ( b – u ) ⇒ u = b / 3 = 1.6 km / hr . answer : e"
Answer: e
Problem: 125 liters of a mixture of milk and water contains in the ratio 3 : 2 . how much water should now be added so that the ratio of milk and water becomes 3 : 4 ?
Options: a ) 12 liters , b ) 32 liters , c ) 41 liters , d ) 50 liters , e ) 34 liters
Rationale: "milk = 3 / 5 * 125 = 75 liters water = 50 liters 75 : ( 50 + p ) = 3 : 4 150 + 3 p = 400 = > p = 50 50 liters of water are to be added for the ratio become 3 : 4 . answer : d"
Answer: d
Problem: a pupil ' s marks were wrongly entered as 35 instead of 23 . due to that the average marks for the class got increased by half . the number of pupils in the class is :
Options: a ) 30 , b ) 80 , c ) 20 , d ) 25 , e ) 24
Rationale: let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 . x / 2 = ( 35 - 23 ) = > x / 2 = 12 = > x = 24 . answer : e
Answer: e
Problem: there are 6 baskets numbered from 1 to 6 and filled with apples . 10 children are asked to pick apples one by one from each basket such that the number of apples picked by each child from each basket is equal to the number marked on the basket . if there were 1000 apples in total and the baskets were filled in such a way that none of the basket became empty in the process , how many apples were left in the end ?
Options: a ) 90 , b ) 91 , c ) 210 , d ) 790 , e ) 910
Rationale: "total number of apples in the basket initially = 1000 each child picks up = 1 + 2 + 3 + 4 + 5 + 6 = 6 * 7 / 2 = 21 total number of apples picked up by 10 children = 21 * 10 = 210 number of apples left in the end = 1000 - 210 = 790 answer is d"
Answer: d
Problem: in a lottery there are 100 prizes and 300 blanks . a lottery is drawn at random . what is the probability of getting a prize ?
Options: a ) 1 / 2 , b ) 5 / 400 , c ) 1 / 5 , d ) 1 / 3 , e ) 1 / 4
Rationale: "total draws = prizes + blanks = 100 + 300 = 400 probability of getting a prize = 100 / 400 = 1 / 4 correct option is e"
Answer: e
Problem: the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 400 resolutions ?
Options: a ) 708 m , b ) 704 m , c ) 774 m , d ) 714 m , e ) 563.2 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 500 resolutions . = 400 * 2 * 22 / 7 * 22.4 = 56320 cm = 563.2 m answer : e"
Answer: e
Problem: q is as much younger than r as he is older than t . if the sum of the ages of r and t is 50 years , what is definitely the difference between r and q ' s age ?
Options: a ) 23 , b ) 28 , c ) 25 , d ) 19 , e ) 11
Rationale: explanation : given r – q = q – t and r + t = 50 which gives q = 25 as the difference between r & q and q & t is same so answer is 25 years answer : c
Answer: c
Problem: if x and y are integers , what is the least positive number of 24 x + 21 y ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: "24 x + 21 y = 3 ( 8 x + 7 y ) which will be a minimum positive number when 8 x + 7 y = 1 . 8 ( 1 ) + 7 ( - 1 ) = 1 then 3 ( 8 x + 7 y ) can have a minimum positive value of 3 . the answer is a ."
Answer: a
Problem: the average of runs of a cricket player of 20 innings was 32 . how many runs must he make in his next innings so as to increase his average of runs by 3 ?
Options: a ) 95 , b ) 106 , c ) 122 , d ) 116 , e ) 122
Rationale: "average = total runs / no . of innings = 32 so , total = average x no . of innings = 32 * 20 = 640 now increase in avg = 4 runs . so , new avg = 32 + 3 = 35 runs total runs = new avg x new no . of innings = 35 * 21 = 735 runs made in the 11 th inning = 735 - 640 = 95 answer : a"
Answer: a
Problem: a sum of money deposited at c . i . amounts to rs . 500 in 3 years and to rs . 650 in 4 years . find the rate percent ?
Options: a ) 25 % , b ) 30 % , c ) 35 % , d ) 40 % , e ) 45 %
Rationale: "500 - - - 150 100 - - - ? = > 30 % answer : b"
Answer: b
Problem: joan took out a mortgage from hel local bank . each monthly mortgage payment she makes must be triple the amount of the previous month ' s payment . if her first payment is $ 100 , and the total amount she must pay back is $ 36400 , how many months will it take joan to pay back her mortgage ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 11 , e ) 13
Rationale: "joan starts off with 100 $ . . which is to be tripled every month her monthly payments look like this : 100 , 300 , 900 , 2700 . . . . . . . . . upto 36400 this can be re written as : 100 x 1 , 100 x 3 , 100 x 9 , 100 x 27 . . . . . . 100 x 364 so we have 1 , 3 , 9 , 27 . . . . . 36400 in gp we know that a = 1 , and r = 3 ( its easy to figure it out by looking at the question , but regardless of it being mentioned in the question we can still compute the value of r using the formula tn = a 3 ^ n - 1 . . . ) therefore to find the sum of n terms of a gp we use this formula : sn = a ( 1 - r ^ n ) / 1 - r using this and plugging in the information we get . . . 364 = 1 - 3 ^ n / 1 - 3 ; 1 - 3 ^ n / - 2 cross multiplying we get 364 x - 2 = 1 - 3 ^ n - 728 = 1 - 3 ^ n - 729 = - 3 ^ n 729 = 3 ^ n ( negatives cancel out ) 729 can also be re written as 3 ^ 6 therefore ; 3 ^ 6 = 3 ^ n thus n = 6 ( a )"
Answer: a
Problem: the average of first five multiples of 6 is
Options: a ) 3 , b ) 18 , c ) 9 , d ) 12 , e ) 15
Rationale: "solution average = 6 ( 1 + 2 + 3 + 4 + 5 ) / 5 = 90 / 5 . = 18 answer b"
Answer: b
Problem: a big container is 35 % full with water . if 16 liters of water is added , the container becomes 3 / 4 full . what is the capacity of the big container in liters ?
Options: a ) 32 , b ) 40 , c ) 48 , d ) 54 , e ) 60
Rationale: "16 liters is 40 % of the capacity c . 16 = 0.4 c c = 16 / 0.4 = 40 liters . the answer is b ."
Answer: b
Problem: in objective test a correct ans score 4 marks and on a wrong ans 2 marks are - - - . a student score 480 marks from 150 question . how many ans were correct ?
Options: a ) 120 , b ) 130 , c ) 110 , d ) 150 , e ) 180
Rationale: let x be the correct answer and y be the wrong answer so the total number of questions is ( x + y ) = 150 = > 4 x - 2 y = 480 = > 6 x = 780 hence x = 130 answer : b
Answer: b
Problem: a number when divided by a certain divisor left remainder 251 , when twice the number was divided by the same divisor , the remainder was 112 . find the divisor ?
Options: a ) 370 , b ) 365 , c ) 390 , d ) 456 , e ) 460
Rationale: "easy solution : n = dq 1 + 251 2 n = 2 dq 1 + 502 - ( 1 ) 2 n = dq 2 + 112 - ( 2 ) as ( 1 ) = ( 2 ) = 2 n d * ( q 2 - 2 q 1 ) = 390 d * some integer = 390 checking all options only ( c ) syncs with it . answer c"
Answer: c
Problem: excluding stoppages , the average speed of a bus is 120 km / hr and including stoppages , the average speed of the bus is 40 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 15 min , b ) 18 min , c ) 16 min , d ) 20 min , e ) 40 min
Rationale: "in 1 hr , the bus covers 120 km without stoppages and 40 km with stoppages . stoppage time = time take to travel ( 120 - 40 ) km i . e 80 km at 120 km / hr . stoppage time = 80 / 120 hrs = 40 min answer : e"
Answer: e
Problem: the units digit of ( 10 ) ^ ( 87 ) + ( 93 ) ^ ( 46 ) is :
Options: a ) 9 , b ) 4 , c ) 6 , d ) 8 , e ) 0
Rationale: "first part will be zero always 2 nd part with power of three therefore , the second term has a units digit of 9 . of course 0 + 9 = 9 , a"
Answer: a
Problem: consider a lady took a loan from a bank at the rate of 12 % p . a . simple interest . after 3 years she had to pay rs . 9900 interest only for the period . the principal amount borrowed by her was
Options: a ) rs . 2000 , b ) rs . 27500 , c ) rs . 15000 , d ) rs . 20000 , e ) none of these
Rationale: "explanation : principal = rs . ( 100 × 9900 / 12 × 3 ) = > rs . 27500 . answer : b"
Answer: b
Problem: if the cost price is 96 % of the selling price , then what is the profit percent ?
Options: a ) 4.17 % , b ) 5 % , c ) 6.12 % , d ) 3.25 % , e ) 5.75 %
Rationale: "let s . p . = $ 100 c . p . = $ 96 profit = $ 4 profit % = 4 / 96 * 100 = 25 / 6 = 4.17 % answer is a"
Answer: a
Problem: how many multiples of 5 are there between 70 and 358 ?
Options: a ) 54 , b ) 55 , c ) 56 , d ) 57 , e ) 58
Rationale: "5 * 14 = 70 5 * 71 = 355 total no of multiples = ( 71 - 14 ) + 1 = 57 + 1 = 58 answer is e ."
Answer: e
Problem: a , b and c invests rs . 6000 , rs . 5000 and rs . 3000 in a business . after one year c removed his money ; a and b continued the business for two more year . if the net profit after 3 years be rs . 4206 , then c ' s share in the profit is ?
Options: a ) 276 , b ) 289 , c ) 400 , d ) 350.5 , e ) 300
Rationale: "6 * 36 : 5 * 36 : 3 * 12 6 : 5 : 1 1 / 12 * 4206 = 350.50 answer : d"
Answer: d
Problem: a sum of money deposited at c . i . amounts to rs . 5000 in 5 years and to rs . 5750 in 6 years . find the rate percent ?
Options: a ) 1 % , b ) 5 % , c ) 10 % , d ) 15 % , e ) 20 %
Rationale: 5000 - - - 750 100 - - - ? = > 15 % answer : d
Answer: d
Problem: renu can do a piece of work in 6 days , but with the help of her friend suma , she can do it in 5 days . in what time suma can do it alone ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 15 , e ) 30
Rationale: renu â € ™ s one day â € ™ s work = 1 / 6 suma â € ™ s one day â € ™ s work = 1 / 5 - 1 / 6 = 1 / 30 suma can do it alone in 30 days . answer : e
Answer: e
Problem: if 5 machines can produce 20 units in 10 hours , how long would it take 20 machines to produce 160 units ?
Options: a ) 50 hours , b ) 40 hours , c ) 20 hours , d ) 12 hours , e ) 8 hours
Rationale: "here , we ' re told that 5 machines can produce 20 units in 10 hours . . . . that means that each machine works for 10 hours apiece . since there are 5 machines ( and we ' re meant to assume that each machine does the same amount of work ) , then the 5 machines equally created the 20 units . 20 units / 5 machines = 4 units are made by each machine every 10 hours now that we know how long it takes each machine to make 4 units , we can break this down further if we choose to . . . 10 hours / 4 units = 2.5 hours per unit when 1 machine is working . the prompt asks us how long would it take 20 machines to produce 160 units . if 20 machines each work for 2.5 hours , then we ' ll have 20 units . since 160 units is ' 8 times ' 20 , we need ' 8 times ' more time . ( 2.5 hours ) ( 8 times ) = 20 hours final answer : [ reveal ] spoiler : c"
Answer: c
Problem: a policeman noticed a criminal from a distance of 200 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 = ( 200 - 50 ) m = 150 m . answer : d"
Answer: d
Problem: the average of 6 no . ' s is 3.95 . the average of 2 of them is 4 , while the average of theother 2 is 3.85 . what is the average of the remaining 2 no ' s ?
Options: a ) 4.2 , b ) 4.4 , c ) 4.6 , d ) 5.6 , e ) 4
Rationale: "sum of the remaining two numbers = ( 3.95 * 6 ) - [ ( 4 * 2 ) + ( 3.85 * 2 ) ] = 8 required average = ( 8 / 2 ) = 4 e"
Answer: e
Problem: the population of a town increased from 50000 to 80000 in a decade . the average percent increase of population per year is :
Options: a ) 4.37 % , b ) 5 % , c ) 6 % , d ) 8.75 % , e ) none of these
Rationale: solution increase in 10 year = ( 80000 - 50000 ) = 30000 . increase % = ( 30000 / 50000 x 100 ) % = 60 % â ˆ ´ required average = ( 60 / 10 ) % = 6 % answer c
Answer: c
Problem: calculate the speed of a boat in still water ( in km / hr ) if in one hour , the boat goes 13 km / hr downstream and 10 km / hr upstream .
Options: a ) 3 kmph , b ) 9 kmph , c ) 4 kmph , d ) 8 kmph , e ) 6 kmph
Rationale: "speed in still water = ( 13 + 5 ) 1 / 2 kmph = 9 kmph . answer : b"
Answer: b
Problem: in a single throw of a die , what is the probability of getting a number greater than 2 ?
Options: a ) 1 / 2 , b ) 2 / 5 , c ) 1 / 3 , d ) 2 / 7 , e ) 2 / 3
Rationale: "s = { 1,2 , 3,4 , 5,6 } e = { 3,4 , 5,6 } probability = 4 / 6 = 2 / 3 answer is e"
Answer: e
Problem: what is the probability that when a hand o f 6 cards is drawn from a well shuffled deck of 52 cards , it contains 2 queen ?
Options: a ) 1 / 23445 , b ) 113 / 22434 , c ) 29187 by 1017926 , d ) 1017926 / 29187 , e ) none of these
Rationale: ncr = n ! / ( n - r ) ! r ! total number of possible hands = 52 c 6 52 c 6 = ( 52 ! ) / ( ( 52 - 6 ) ! × 6 ! ) 52 c 6 = 61075560 . number of hands with 2 queen and 4 non - queen cards = 4 c 2 × 48 c 4 4 c 2 = ( 4 ! ) / ( 2 ! × 2 ! ) = 6 . 48 c 4 = ( 48 ! ) / ( 44 ! × 4 ! ) = 3 × 47 × 46 × 45 = 291870 ( other 2 cards must be chosen from the rest 48 cards ) p ( 2 queen ) = ( 4 c 2 × 48 c 4 ) / 52 c 6 = 29187 / 1017926 c
Answer: c
Problem: carina has 130 ounces of coffee divided into 5 - and 10 - ounce packages . if she has 2 more 5 - ounce packages than 10 - ounce packages , how many 10 - ounce packages does she have ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "lets say 5 and 10 ounce packages be x and y respectively . given that , 5 x + 10 y = 130 and x = y + 2 . what is the value of y . substituting the x in first equation , 5 y + 10 + 10 y = 130 - > y = 120 / 15 . = 8 d"
Answer: d
Problem: if x = 1 / q and y = ( 2 / q ) - 6 , then for what value of q , x is equal to y ?
Options: a ) 1 / 3 , b ) 1 / 6 , c ) 6 , d ) 3 , e ) 2
Rationale: explanation : x = y < = > 1 / q = ( 2 / q ) - 6 < = > 1 / q = 6 < = > q = 1 / 6 . answer : b
Answer: b
Problem: a watch was sold at a loss of 10 % . if it was sold for rs . 140 more , there would have been a gain of 4 % . what is the cost price ?
Options: a ) rs . 1000 , b ) rs . 1100 , c ) rs . 1200 , d ) rs . 1250 , e ) rs . 1500
Rationale: "explanation : 90 % 104 % - - - - - - - - 14 % - - - - 140 100 % - - - - ? = > rs . 1000 a )"
Answer: a
Problem: arun and tarun can do a work in 10 days . after 4 days tarun went to his village . how many days are required to complete the remaining work by arun alone . arun can do the work alone in 50 days .
Options: a ) 16 days . , b ) 17 days . , c ) 18 days . , d ) 30 days . , e ) 20 days .
Rationale: they together completed 4 / 10 work in 4 days . balance 6 / 10 work will be completed by arun alone in 50 * 6 / 10 = 30 days . answer : d
Answer: d
Problem: a certain telescope increases the visual range at a particular location from 70 kilometers to 150 kilometers . by what percent is the visual range increased by using the telescope ?
Options: a ) 30 % , b ) 33 1 / 2 % , c ) 40 % , d ) 60 % , e ) 114.28 %
Rationale: "original visual range = 70 km new visual range = 150 km percent increase in the visual range by using the telescope = ( 150 - 70 ) / 70 * 100 % = 8 / 7 * 100 % = 114.28 % answer e"
Answer: e
Problem: circular gears l and r start to rotate at the same time at the same rate . gear l makes 10 complete revolutions per minute and gear r makes 40 revolutions per minute . how many seconds after the gears start to rotate will gear r have made exactly 9 more revolutions than gear l ?
Options: a ) a ) 6 , b ) b ) 8 , c ) c ) 10 , d ) d ) 18 , e ) e ) 15
Rationale: "gear l - - 10 rotations per 60 seconds - - 1 rotation per 6 seconds . gear r - - 40 rotations per 60 seconds - - 4 rotations per 6 seconds . first 6 seconds - - gear l makes 1 rotation . - - gear r makes 4 rotations - - net difference - - 3 rotations hence every 6 seconds the difference between the number of rotations of r and l gear is 3 units . required net difference should be 9 rotations = > 3 ( 6 seconds later ) = = > 18 seconds . answer : d ) ."
Answer: d
Problem: find the simple interest on rs . 68,000 at 16 2 / 3 % per annum for 9 months .
Options: a ) rs . 8500 , b ) rs . 8000 , c ) rs . 7500 , d ) rs . 7000 , e ) rs . 6500
Rationale: "p = rs . 68000 , r = 50 / 3 % p . a and t = 9 / 12 years = 3 / 4 years . s . i . = ( p * r * t ) / 100 = rs . ( 68,000 * ( 50 / 3 ) * ( 3 / 4 ) * ( 1 / 100 ) ) = rs . 8500 answer is a ."
Answer: a
Problem: three cubes of iron whose edges are 6 cm , 8 cm and 10 cm respectively are melted and formed into a single cube . the edge of the new cube formed is
Options: a ) 10 cm
b ) 12 cm
c ) 16 cm
d ) 18 cm
e ) none
Rationale: sol . volume of the new cube = ( 63 + 83 + 103 ) cm 3 = 1728 cm 3 . let the edge of the new cube be a cm . ∴ a 3 = 1728 ⇒ a = 12 . answer b
Answer: b
Problem: two trains are moving in the same direction at 126 kmph and 54 kmph . the faster train crosses a man in the slower train in 14 seconds . find the length of the faster train ?
Options: a ) 280 , b ) 290 , c ) 300 , d ) 310 , e ) 320
Rationale: "relative speed = ( 126 - 54 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in 27 sec = 14 * 20 = 280 m . the length of the faster train = 280 m . answer : a"
Answer: a
Problem: if n is a prime number greater than 17 , what is the remainder when n ^ 2 is divided by 12 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5
Rationale: "there are several algebraic ways to solve this question , but the easiest way is as follows : since we can not have two correct answers just pick a prime greater than 17 , square it and see what would be the remainder upon division of it by 12 . n = 19 - - > n ^ 2 = 361 - - > remainder upon division 361 by 12 is 1 . answer : b ."
Answer: b
Problem: what is the remainder when 17 ^ 200 is divided by 18 ?
Options: a ) 3 , b ) 1 , c ) 2 , d ) 4 , e ) 7
Rationale: "( 17 ^ 200 - 1 ^ 200 ) is completely divisible by ( 17 + 1 ) as 200 is even . = > ( 17 ^ 200 - 1 ) is completely divisible by 18 . hence , when 17 ^ 200 is divided by 18 , we will get 1 as remainder . answer is b"
Answer: b
Problem: a block of wood has dimensions 10 cm x 10 cm x 90 cm . the block is painted red and then cut evenly at the 45 cm mark , parallel to the sides , to form two rectangular solids of equal volume . what percentage of the surface area of each of the new solids is not painted red ?
Options: a ) 5 % , b ) 10 % , c ) 15 % , d ) 20 % , e ) 25 %
Rationale: "the area of each half is 100 + 4 ( 450 ) + 100 = 2000 the area that is not painted is 100 . the fraction that is not painted is 100 / 2000 = 1 / 20 = 5 % the answer is a ."
Answer: a
Problem: after 6 games , team b had an average of 75 points per game . if it got only 47 points in game 7 , how many more points does it need to score to get its total above 500 ?
Options: a ) 5 , b ) 4 , c ) 7 , d ) 3 , e ) 8
Rationale: "( 6 * 75 ) + 47 + x > 500 450 + 47 + x > 500 497 + x > 500 = > x > 3 option d"
Answer: d
Problem: if both 5 ^ 2 and 3 ^ 3 are factors of n x ( 2 ^ 5 ) x ( 6 ) x ( 7 ^ 3 ) , what is the smallest possible positive value of n ?
Options: a ) 75 , b ) 125 , c ) 145 , d ) 175 , e ) 225
Rationale: ( 2 ^ 5 ) x ( 6 ) x ( 7 ^ 3 ) has one appearance of 3 ( in the 6 ) and no appearances of 5 . thus n must include at least 3 ^ 2 * 5 ^ 2 = 9 * 25 = 225 the answer is e .
Answer: e
Problem: a can finish a work in 36 days , b in 9 days and c in 2 days , b and c start the work but are forced to leave after 3 days . the remaining work was done by a in ?
Options: a ) 15 days , b ) 12 days , c ) 6 days , d ) 7 days , e ) 8 days
Rationale: "b + c 1 day work = 1 / 9 + 1 / 12 = 7 / 36 work done by b and c in 3 days = 7 / 36 * 3 = 7 / 12 remaining work = 1 - 7 / 12 = 5 / 12 1 / 36 work is done by a in 1 day 5 / 12 work is done by a in 36 * 5 / 12 = 15 days answer is a"
Answer: a
Problem: there are 20 poles with a constant distance between each pole . a car takes 26 second to reach the 12 th pole . how much will it take to reach the last pole .
Options: a ) 44.4543 , b ) 44.9091 , c ) 44.95128 , d ) 44.91288 , e ) 44.91222
Rationale: "assuming the car starts at the first pole . to reach the 12 th pole , the car need to travel 11 poles ( the first pole does n ' t count , as the car is already there ) . 11 poles 26 seconds 1 pole ( 26 / 11 ) seconds to reach the last ( 20 th ) pole , the car needs to travel 19 poles . 19 pole 19 x ( 26 / 11 ) seconds = 44.9091 seconds answer : b"
Answer: b
Problem: p has $ 21 more than what q and r together would have had if both b and c had 1 / 5 of what p has . how much does p have ?
Options: a ) $ 35 , b ) $ 36 , c ) $ 37 , d ) $ 38 , e ) $ 39
Rationale: "p = ( 2 / 5 ) * p + 21 ( 3 / 5 ) * p = 21 p = 35 the answer is a ."
Answer: a
Problem: a large box contains 18 small boxes and each small box contains 25 chocolate bars . how many chocolate bars are in the large box ?
Options: a ) 350 , b ) 250 , c ) 450 , d ) 550 , e ) 650
Rationale: "the number of chocolate bars is equal to 18 ? 25 = 450 correct answer c"
Answer: c
Problem: because he ’ s taxed by his home planet , mork pays a tax rate of 40 % on his income , while mindy pays a rate of only 30 % on hers . if mindy earned 5 times as much as mork did , what was their combined tax rate ?
Options: a ) 32.5 % , b ) 34 % , c ) 35 % , d ) 31.67 % , e ) 37.5 %
Rationale: "say morks income is - 100 so tax paid will be 40 say mindys income is 5 * 100 = 500 so tax paid is 30 % * 500 = 150 total tax paid = 40 + 150 = 190 . combined tax % will be 190 / 100 + 500 = 31.67 %"
Answer: d
Problem: if p ( a ) = 0.4 , p ( b ) = 0.6 and p ( a ∪ b ) = 0.8 . what is the value of p ( a ∩ b ' ) = ?
Options: a ) 0.1 , b ) 0.2 , c ) 0.3 , d ) 0.4 , e ) none
Rationale: "solution : p ( a ∪ b ) = p ( a ) + p ( b ) - p ( a ∩ b ' ) = > 0.8 = 0.4 - p ( a ∩ b ) = > p ( a ∩ b ) = 0.2 p ( a ∩ b ' ) = p ( a ) - p ( a ∩ b ) = 0.4 - 0.2 = 0.2 answer b"
Answer: b
Problem: a started a business with an investment of rs . 70000 and after 6 months b joined him investing rs . 120000 . if the profit at the end of a year is rs . 26000 , then the share of b is ?
Options: a ) s . 12028 , b ) s . 12000 , c ) s . 12003 , d ) s . 12029 , e ) s . 24029
Rationale: "ratio of investments of a and b is ( 70000 * 12 ) : ( 120000 * 6 ) = 7 : 6 total profit = rs . 26000 share of b = 6 / 13 ( 26000 ) = rs . 12000 answer : b"
Answer: b
Problem: find the number which is nearest to 3105 and is exactly divisible by 21 .
Options: a ) 1208 , b ) 3108 , c ) 241 , d ) 217 , e ) 3147
Rationale: "sol . on dividing 3105 by 21 , we get 18 as remainder . number to be added to 3105 = ( 21 - 18 ) - 3 . hence , required number = 3105 + 3 = 3108 . option b"
Answer: b
Problem: evaluate : 980 x 436 + 980 x 764
Options: a ) 1176000 , b ) 968000 , c ) 978000 , d ) 117000 , e ) none of them
Rationale: "980 x 436 + 980 x 764 = 986 x ( 436 + 664 ) = 986 x 1200 = 117600 . answer is a ."
Answer: a
Problem: how many terminating zeroes r does 200 ! have ?
Options: a ) 40 , b ) 48 , c ) 49 , d ) 55 , e ) 64
Rationale: you have 40 multiples of 5 , 8 of 25 and 1 of 125 . this will give 49 zeros . c
Answer: c
Problem: a girl walking at the rate of 9 km per hour crosses a square field diagonally in 12 seconds . the area of the field is :
Options: a ) 430 sq . m
b ) 425 sq . m
c ) 450 sq . m
d ) 475 sq . m
e ) 350 sq . m
Rationale: distance covered in ( 9 × 1000 ) / ( 3600 ) × 12 = 30 m diagonal of squarre field = 30 m . area of square field = 30 ( power ) 2 / 2 = 900 / 2 = 450 sq . m answer is c .
Answer: c
Problem: x , y , and z are all unique numbers . if x is chosen randomly from the set { 6 , 7 , 8 , 9 , 10 , 11 } and y and z are chosen randomly from the set { 20 , 21 , 22 , 23 } , what is the probability that x and y are prime and z is not ?
Options: a ) 1 / 5 , b ) 3 / 20 , c ) 2 / 15 , d ) 1 / 12 , e ) 1 / 10
Rationale: "p ( x is prime ) = 1 / 3 p ( y is prime ) = 1 / 4 if y is prime , then z is not prime since y and z are unique . then the probability is 1 / 3 * 1 / 4 = 1 / 12 the answer is d ."
Answer: d
Problem: what is the total number of integers between 20 and 100 that are divisible by 9 ?
Options: a ) 5 , b ) 15 , c ) 12 , d ) 7 , e ) 9
Rationale: "27 , 36 , 45 , . . . , 90,99 this is an equally spaced list ; you can use the formula : n = ( largest - smallest ) / ( ' space ' ) + 1 = ( 99 - 27 ) / ( 9 ) + 1 = 8 + 1 = 9 answer is e"
Answer: e
Problem: the perimeter of a triangle is 40 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle
Options: a ) a ) 72 , b ) b ) 828 , c ) c ) 50 , d ) d ) 34 , e ) e ) 35
Rationale: "explanation : area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 40 / 2 = 50 cm 2 answer : option c"
Answer: c
Problem: the price of an article is cut by 10 % . to restore it to the former value . the new price must be increased by ?
Options: a ) 10 % , b ) 9 1 / 11 , c ) 11 1 / 9 , d ) 11 % , e ) none of these
Rationale: answer let original price = rs . 100 . then , new price = rs . 90 . ∴ increased on rs . 90 = rs . 10 required increase % = ( 10 x 100 ) / 90 % = 111 / 9 % correct option : c
Answer: c
Problem: the probability that event b occurs is 0.6 , and the probability that events a and b both occur is 0.25 . if the probability that either event a or event b occurs is 0.4 , what is the probability that event a will occur ?
Options: a ) 0.05 , b ) 0.15 , c ) 0.45 , d ) 0.5 , e ) 0.55
Rationale: p ( a or b ) = p ( a ) + p ( b ) - p ( a n b ) 0.4 = 0.6 + p ( a ) - 0.25 p ( a ) = 0.05 ans : a
Answer: a
Problem: if x and y are both odd prime numbers and x < y , how many distinct positive integer e factors does 2 xy have ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 12
Rationale: since 2 xy prime e factors are x ^ 1 * y ^ 1 * 2 ^ 1 , its total number or factors must be ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 2 ^ 3 = 8 . thus , i think d would be the correct answer .
Answer: d
Problem: in a certain group of 10 developers , 4 developers code only in python and the rest program in either ruby on rails or php - but not both . if a developer organization is to choose a 3 - member team , which must have at least 1 developer who codes in python , how many different programming teams can be chosen ?
Options: a ) 100 , b ) 40 , c ) 66 , d ) 80 , e ) 75
Rationale: two ways . . . 1 ) total ways = 10 c 3 = 10 ! / 7 ! 3 ! = 120 . . ways without python developer = 6 c 3 = 6 ! / 3 ! 3 ! = 20 . . ways of at least one python developer = 120 - 20 = 100 . . 2 ) ways of selecting only one = 4 * 6 c 2 = 4 * 15 = 60 . . ways of selecting only two = 4 c 2 * 6 c 1 = 6 * 6 = 36 . . ways of selecting all three = 4 c 3 = 4 = 4 . . total = 60 + 36 + 4 = 100 . . . answer : a
Answer: a
Problem: a dishonest shopkeeper professes to sell pulses at the cost price , but he uses a false weight of 920 gm . for a kg . his gain is … % .
Options: a ) 5.26 % , b ) 5.36 % , c ) 4.26 % , d ) 6.26 % , e ) 8.69 %
Rationale: "his percentage gain is 100 * 80 / 920 as he is gaining 80 units for his purchase of 920 units . so 8.69 % . answer : e"
Answer: e
Problem: 5.40 can be expressed in terms of percentage as
Options: a ) 5.04 % , b ) 50.4 % , c ) 209 % , d ) 540 % , e ) none of these
Rationale: "explanation : while calculation in terms of percentage we need to multiply by 100 , so 5.40 * 100 = 540 answer : option d"
Answer: d
Problem: a pet store regularly sells pet food at a discount of 10 percent to 30 percent from the manufacturer ’ s suggested retail price . if during a sale , the store discounts an additional 20 percent from the discount price , what would be the lowest possible price of a container of pet food that had a manufacturer ’ s suggested retail price o f $ 25.00 ?
Options: a ) $ 14.00 , b ) $ 11.20 , c ) $ 14.40 , d ) $ 16.00 , e ) $ 18.00
Rationale: "for retail price = $ 25 first maximum discounted price = 25 - 30 % of 25 = 25 - 7.5 = 17.5 price after additional discount of 20 % = 17.5 - 20 % of 17.5 = 17.5 - 3.5 = 14 answer : option a"
Answer: a
Problem: a number is mistakenly divided by 5 instead of being multiplied by 5 . find the percentage change in the result due t this mistake .
Options: a ) 96 % , b ) 95 % , c ) 2400 % , d ) 200 % , e ) 400 %
Rationale: lets take a number 20 20 / 5 = 4 20 * 5 = 100 diff = 100 - 4 = 96 % answer : a
Answer: a
Problem: the first , second and third terms of the proportion are 56 , 16 , 49 . find the fourth term .
Options: a ) 10 , b ) 14 , c ) 40 , d ) 50 , e ) 60
Rationale: explanation : let the fourth term be x . thus 56 , 16 , 49 , x are in proportion . product of extreme terms = 56 x product of mean terms = 16 x 49 since , the numbers make up a proportion therefore , 56 x = 16 49 or , x = ( 16 49 ) / 56 or , x = 14 therefore , the fourth term of the proportion is 14 . answer : b
Answer: b
Problem: during a sale , the price of a pair of shoes is marked down 10 % from the regular price . after the sale ends , the price goes back to the original price . what is the percent of increase to the nearest percent from the sale price back to the regular price for the shoes ?
Options: a ) 9 % , b ) 10 % , c ) 11 % , d ) 15 % , e ) 90 %
Rationale: "assume the price = 100 price during sale = 90 price after sale = 100 percent increase = 10 / 90 * 100 = 11 % approx . correct option : c"
Answer: c
Problem: sheila works 8 hours per day on monday , wednesday and friday , and 6 hours per day on tuesday and thursday . she does not work on saturday and sunday . she earns $ 324 per week . how much does she earn in dollars per hour ?
Options: a ) 2 , b ) 8 , c ) 9 , d ) 1 , e ) 2
Rationale: "explanation : total hours worked = 8 x 3 + 6 x 2 = 36 total earned = 324 . hourly wage = 324 / 36 = 9 answer : c ) 9"
Answer: c
Problem: determine the value of 3 * 27 / 31 + 81 / 93
Options: a ) 0 , b ) 156 / 31 , c ) 123 / 31 , d ) 151 / 31 , e ) none
Rationale: solution : both fractions should be reduced before performing arithmetic operations . we get 3 * 27 / 31 + 3.27 / 3.31 = 3 * 27 / 31 + 27 / 31 = 4 * 27 / 31 = 151 / 31 answer d
Answer: d
Problem: in goshawk - eurasian nature reserve 30 percent of the birds are hawks , and 40 percent of the non - hawks are paddyfield - warblers . if there are 25 percent as many kingfishers as paddyfield - warblers in the reserve , then what percent of the birds e in the nature reserve are not hawks , paddyfield - warblers , or kingfishers ?
Options: a ) 25 % , b ) 35 % , c ) 45 % , d ) 70 % , e ) 80 %
Rationale: "1 . we are given the following percentages : 30 ( 70 ) , 40 ( 60 ) , 25 ( 75 ) . there are two threads from here . first starts at 30 % and finishes there . second one starts at 70 , then 40 , and then 25 . we need a value that is divisible by 7 , 2 , and 5 at least once . lets pick a number now , say 700 . so say if non hawks are 700 ( this is 70 % of the total , so total = 1000 ) , then paddy warbs are 2 / 5 x 700 = 1400 / 5 = 280 . kingfishers , therefore , are 280 / 4 = 70 . lets add them up . 300 hawks + 280 peddy warbs + 70 kingsifhers = 650 . so all others are 1000 - 650 = 350 or 35 % of total birds . the main job here to to identify the smart number to start the question with . this can be time consuming , but once identified , this question can be solved fairly quickly . 2 . another method : if x is total - - > non hawks = 0.7 x - - > warbs = 0.4 ( 0.7 x ) - - > kfs = 0.25 ( 0.4 ( 0.7 x ) ) . our job is to find out e : ( 0.3 x + 0.28 x + 0.07 x ) / x . or 0.65 x / x = 0.65 . we need to find 1 - 0.65 = 0.35 or 35 % . b"
Answer: b
Problem: what is the smallest integer t greater than 1 that leaves a remainder of 1 when divided by any of the integers 6 , 8 , and 10 ?
Options: a ) 21 , b ) 41 , c ) t = 121 , d ) 241 , e ) 481
Rationale: or u can just use the answer choices here . since the answers are already arranged in ascending order , the first number which gives remainder t as 1 for all three is the correct answer . in the given question , the first number which gives a remainder of 1 for 6,8 and 10 is 121 . c
Answer: c
Problem: a train 150 m long running at 72 kmph crosses a platform in 20 sec . what is the length of the platform ?
Options: a ) 443 m , b ) 354 m , c ) 450 m , d ) 350 m , e ) 250 m
Rationale: "e 250 e = 72 * 5 / 18 = 20 = 400 â € “ 150 = 250"
Answer: e
Problem: in bangalore there is a well known science institute . during a visit i asked two of the men to tell me their ages . one replied , ' one of our ages subtracted from the other ' s equal 30 . ' then the other man spoke . ' our ages multiplied together equal 1624 . ' what were their ages ?
Options: a ) 60 and 23 , b ) 66 and 25 , c ) 29 and 56 , d ) 71 and 43 , e ) 58 and 28
Rationale: e their ages were respectively 58 and 28
Answer: e
Problem: the smallest number when increased by ` ` 1 ` ` is exactly divisible by 2 , 8 , 24 , 36 is :
Options: a ) 71 , b ) 70 , c ) 72 , d ) 73 , e ) 36
Rationale: lcm = 72 72 - 1 = 71 answer : a
Answer: a
Problem: a person bought 135 glass bowls at a rate of rs . 15 per bowl . he sold 115 of them at rs . 18 and the remaining broke . what is the percentage gain for a ?
Options: a ) 40 , b ) 30 / 11 , c ) 20 / 9 , d ) 27 / 11 , e ) 29 / 8
Rationale: "cp = 135 * 15 = 2025 and sp = 115 * 18 = 2070 gain % = 100 * ( 2070 - 2025 ) / 2025 = 20 / 9 answer : c"
Answer: c
Problem: the price of an item is discounted 3 percent on day 1 of a sale . on day 2 , the item is discounted another 3 percent , and on day 3 , it is discounted an additional 10 percent . the price of the item on day 3 is what percentage of the sale price on day 1 ?
Options: a ) 85.1 % , b ) 86.9 % , c ) 87.3 % , d ) 88.8 % , e ) 89.5 %
Rationale: "let initial price be 100 price in day 1 after 3 % discount = 97 price in day 2 after 3 % discount = 94.09 price in day 3 after 10 % discount = 84.68 so , price in day 3 as percentage of the sale price on day 1 will be = 84.68 / 97 * 100 = > 87.3 % answer will definitely be ( c )"
Answer: c
Problem: the maximum number of students among them 1200 pens and 820 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils ?
Options: a ) 40 , b ) 20 , c ) 60 , d ) 80 , e ) 65
Rationale: "number of pens = 1200 number of pencils = 820 required number of students = h . c . f . of 1200 and 820 = 20 answer is b"
Answer: b
Problem: in a certain pond , 80 fish were caught , tagged , and returned to the pond . a few days later , 50 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 ) 400 , b ) 625 , c ) 1,250 , d ) 2,000 , e ) 10,000
Rationale: this is a rather straight forward ratio problem . 1 . 80 fish tagged 2 . 2 out of the 50 fish caught were tagged thus 2 / 50 2 / 50 = 80 / x thus , x = 2000 think of the analogy : 2 fish is to 50 fish as 50 fish is to . . . ? you ' ve tagged 50 fish and you need to find what that comprises as a percentage of the total fish population - we have that information with the ratio of the second catch . d
Answer: d
Problem: r is the set of positive odd integers less than 100 , and s is the set of the squares of the integers in r . how many elements does the intersection of r and s contain ?
Options: a ) none , b ) two , c ) four , d ) five , e ) seven
Rationale: "r is the set of positive odd integers less than 100 , and s is the set of the squares of the integers in r . how many elements does the intersection of r and s contain ? r = 1,3 , 5,7 , 9,11 , 13,15 . . . s = 1 , 9,25 , 49,81 . . . numbers : 1 , 9 , 25 , 49 , and 81 are odd integers ( less than 100 ) that are in both sets . solution : five answer : d"
Answer: d
Problem: a soccer store typically sells replica jerseys at a discount of 30 percent to 50 percent off list price . during the annual summer sale , everything in the store is an additional 20 percent off the original list price . if a replica jersey ' s list price is $ 80 , approximately what w percent of the list price is the lowest possible sale price ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 40 , e ) 50
Rationale: "let the list price be 2 x for min sale price , the first discount given should be 50 % , 2 x becomes x here now , during summer sale additional 20 % off is given ie sale price becomes 0.8 x it is given lise price is $ 80 = > 2 x = 80 = > x = 40 and 0.8 x = 32 so lowest sale price is 32 , which w is 40 % of 80 hence , d is the answer"
Answer: d
Problem: a brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 28 m * 2 m * 0.75 m ?
Options: a ) 28000 , b ) 27908 , c ) 78902 , d ) 25000 , e ) 27991
Rationale: "28 * 2 * 0.75 = 20 / 100 * 10 / 100 * 7.5 / 100 * x 28 = 1 / 100 * x = > x = 28000 answer : a"
Answer: a