regisss/math_qa huggingface dataset:
Problem: how many 3 - digit numbers are divisible by 6 in all ?
Options: a ) 149 , b ) 150 , c ) 151 , d ) 166 , e ) none
Rationale: solution required numbers are 102 , 018114 , . . . . 996 . this is an a . p with a = 102 , d = 6 . let the number of its terms be n . then a + ( n - 1 ) d ‹ = › 102 + ( n - 1 ) × 6 = 996 ‹ = › n = 150 . answer b
Answer: b
Problem: two pipes can fill a tank in 10 minutes and 25 minutes . an outlet pipe can empty the tank in 45 minutes . if all the pipes are opened when the tank is empty , then how many minutes will it take to fill the tank ?
Options: a ) 30 minutes , b ) 17 minutes , c ) 7 minutes , d ) 10 minutes , e ) 12 minutes
Rationale: "part of the filled by all the three pipes in one minute = 1 / 10 + 1 / 25 - 1 / 45 = ( 45 + 18 - 10 ) / 450 = 53 / 450 so , the tank becomes full in 7 minutes . answer : c"
Answer: c
Problem: if 7 ^ k = 2 , then 7 ^ ( 4 k + 2 ) =
Options: a ) 729 , b ) 754 , c ) 784 , d ) 783 , e ) 108
Rationale: "7 ^ k = 2 7 ^ 4 k = 2 ^ 4 7 ^ 4 k = 16 7 ^ ( 4 k + 2 ) = 7 ^ 4 k * 7 ^ 2 = 16 * 49 = 784 answer : c"
Answer: c
Problem: one day a car rental agency rented 3 / 4 of its cars , including 3 / 5 of its cars with cd players . if 3 / 5 of its cars have cd players , what percent of the cars that were not rented had cd players ?
Options: a ) 29 / 30 , b ) 24 / 25 , c ) 19 / 20 , d ) 14 / 15 , e ) 9 / 10
Rationale: "the cars with cd players which were not rented is ( 2 / 5 ) ( 3 / 5 ) = 6 / 25 of all the cars . the cars which were not rented is 1 / 4 of all the cars . the percent of non - rented cars which had cd players is ( 6 / 25 ) / ( 1 / 4 ) = 24 / 25 the answer is b ."
Answer: b
Problem: little john had $ 5.10 . he spent $ 1.05 on sweets and gave to his two friends $ 1.00 each . how much money was left ?
Options: a ) $ 2.15 , b ) $ 2.05 , c ) $ 2.45 , d ) $ 2.25 , e ) $ 2.85
Rationale: "john spent and gave to his two friends a total of 1.05 + 1.00 + 1.00 = $ 3.05 money left 5.10 - 3.05 = $ 2.05 answer : b"
Answer: b
Problem: a fair coin is tossed 3 times . what is the probability of getting at least 2 heads ?
Options: a ) 3 / 4 , b ) 3 / 2 , c ) 1 / 4 , d ) 1 / 2 , e ) 1 / 5
Rationale: "let ' s find the probability of 2 heads , 3 heads p ( hhh ) = ( ( 1 / 2 ) ^ 3 = 1 / 8 . p ( hht ) = ( 3 ! / 2 ! ) * ( 1 / 2 ) ^ 3 = 3 / 8 total probablity = 1 / 8 + 3 / 8 = 1 / 2 answer ( d )"
Answer: d
Problem: a , b and c enter into partnership . a invests some money at the beginning , b invests double the amount after 6 months , and c invests thrice the amount after 8 months . if the annual gain be rs . 18900 . a ' s share is ?
Options: a ) 6300 , b ) 2765 , c ) 6000 , d ) 1298 , e ) 1261
Rationale: "x * 12 : 2 x * 6 : 3 x * 4 1 : 1 : 1 1 / 3 * 18900 = 6300 answer : a"
Answer: a
Problem: bottle r contains 250 capsules and costs $ 8.25 . bottle t contains 130 capsules and costs $ 2.99 . what is the difference between the cost per capsule for bottle r and the cost per capsule for bottle t ?
Options: a ) $ 0.25 , b ) $ 0.01 , c ) $ 0.05 , d ) $ 0.03 , e ) $ 0.002
Rationale: "cost per capsule in r is 8.25 / 250 = 0.825 / 25 = 0.033 cost per capsule in t is 2.99 / 130 = 0.023 the difference is 0.01 the answer is b"
Answer: b
Problem: if albert ’ s monthly earnings rise by 30 % , he would earn $ 598 . if , instead , his earnings rise by only 35 % , how much ( in $ ) would he earn this month ?
Options: a ) 621 , b ) 652 , c ) 660 , d ) 690 , e ) 693
Rationale: "= 598 / 1.3 ∗ 1.35 = 621 = 621 answer is a"
Answer: a
Problem: the unit digit in the product 3421 * 6721 * 4584 * 6784 is ?
Options: a ) 0 , b ) 1 , c ) 6 , d ) 3 , e ) 4
Rationale: "unit digit in the given product = unit digit in 1 * 1 * 4 * 4 = 6 answer is c"
Answer: c
Problem: the sum of the present ages of two persons a and b is 60 . if the age of a is twice that of b , find the sum of their ages 4 years hence ?
Options: a ) 22 , b ) 77 , c ) 70 , d ) 68 , e ) 71
Rationale: "a + b = 60 , a = 2 b 2 b + b = 60 = > b = 20 then a = 40 . 4 years , their ages will be 44 and 24 . sum of their ages = 44 + 24 = 68 . answer : d"
Answer: d
Problem: robert is travelling on his cycle andhas calculated to reach point a at 2 pm . if he travels at 10 kmph , he will reach there at 12 pm if he travels at 15 kmph . at what speed must he travel to reach a at 1 pm ?
Options: a ) 8 kmph , b ) 9 kmph , c ) 12 kmph , d ) 14 kmph , e ) 16 kmph
Rationale: let the distance travelled by x km . then , x - x = 2 10 15 3 x - 2 x = 60 x = 60 km . time taken to travel 60 km at 10 km / hr = 60 hrs = 6 hrs . 10 so , robert started 6 hours before 2 p . m . i . e . , at 8 a . m . required speed = 60 kmph . = 12 kmph . 5 c
Answer: c
Problem: let f ( x , y ) be defined as the remainder when ( x – y ) ! is divided by x . if x = 36 , what is the maximum value of y for which f ( x , y ) = 0 ?
Options: a ) 9 , b ) 12 , c ) 18 , d ) 20 , e ) 30
Rationale: "the question is finding y such that ( 36 - y ) ! is a multiple of 36 . that means we need to have 2 ^ 2 * 3 ^ 2 in ( 36 - y ) ! 6 ! is the smallest factorial number with 2 ^ 2 * 3 ^ 2 as a factor . 36 - y = 6 y = 30 the answer is e ."
Answer: e
Problem: a computer factory produces 4032 computers per month at a constant rate , how many computers are built every 30 minutes assuming that there are 28 days in one month ?
Options: a ) 2.25 . , b ) 3.00 . , c ) 4.5 . , d ) 5.225 . , e ) 6.25 .
Rationale: number of hours in 28 days = 28 * 24 number of 30 mins in 28 days = 28 * 24 * 2 number of computers built every 30 mins = 4032 / ( 28 * 24 * 2 ) = 3 answer b
Answer: b
Problem: the ratio of the radius of two circles is 1 : 4 , and then the ratio of their areas is ?
Options: a ) 1 : 16 , b ) 1 : 6 , c ) 1 : 9 , d ) 1 : 3 , e ) 1 : 2
Rationale: "r 1 : r 2 = 1 : 4 π r 12 : π r 22 r 12 : r 22 = 1 : 16 answer : a"
Answer: a
Problem: the average age of a class of 39 students is 15 years . if the age of the teacher be included , then the average increased by 3 months . find the age of the teacher ?
Options: a ) 25 , b ) 28 , c ) 30 , d ) 35 , e ) 39
Rationale: "total age of 39 persons = 39 * 15 = 585 years average age of 40 persons = 15 yrs 3 months = 61 / 4 years total age of 40 persons = 61 / 4 * 40 = 610 years age of the teacher = 610 - 585 = 25 years answer is a"
Answer: a
Problem: country x imported approximately $ 1.44 billion of goods in 1996 . if country x imported $ 488 million of goods in the first two months of 1997 and continued to import goods at the same rate for the rest of the year , by how much would country xs 1997 imports exceed those of 1996 ?
Options: a ) $ 1124 million , b ) $ 1120 million , c ) $ 1144 million , d ) $ 1240 million , e ) $ 1488 million
Rationale: convert units to millions as answer is in millions 1996 imports = $ 1.44 bill = $ 1440 mill i . e . 1440 / 12 = $ 120 mill / month 1997 imports = $ 488 mill / 2 month i . e . $ 244 mill / month difference / month = 244 - 120 = 124 difference / year = $ 124 mill * 12 = $ 1488 mill answer : e
Answer: e
Problem: the ratio of 2 numbers is 2 : 7 and their h . c . f . is 18 . their l . c . m . is ?
Options: a ) 252 , b ) 243 , c ) 521 , d ) 361 , e ) 600
Rationale: "let the numbers be 2 x and 7 x their h . c . f . = 18 so the numbers are 2 * 18 , 7 * 18 = 36,126 l . c . m . = 252 answer is a"
Answer: a
Problem: 110 people are attending a newspaper conference . 45 of them are writers and more than 38 are editors . of the people at the conference , x are both writers and editors and 2 x are neither . what is the largest possible number of people who are both writers and editors ?
Options: a ) 34 , b ) 32 , c ) 30 , d ) 26 , e ) 28
Rationale: "{ total } = { writers } + { editors } - { both } + { neither } . { total } = 110 ; { writers } = 45 ; { editors } > 38 ; { both } = x ; { neither } = 2 x ; 110 = 45 + { editors } - x + 2 x - - > x = 65 - { editors } . we want to maximize x , thus we should minimize { editors } , minimum possible value of { editors } is 39 , thus x = { both } = 65 - 39 = 26 . answer : d ."
Answer: d
Problem: in may mrs lee ' s earnings were 70 percent of the lee family ' s total income . in june mrs lee earned 20 percent more than in may . if the rest of the family ' s income was the same both months , then , in june , mrs lee ' s earnings were approximately what percent of the lee family ' s total income ?
Options: a ) 64 % , b ) 68 % , c ) 72 % , d ) 74 % , e ) 83 %
Rationale: "let in may lee family ' s total income = 100 in may mrs lee ' s income = 70 in may rest of the family ' s income = 30 in june mrs lees income = 70 * 120 / 100 = 84 in june total income = 84 + 30 = 114 % of mrs lee ' s income = 84 / 114 = 73.68 ( d )"
Answer: d
Problem: one year ago , the ratio of roonie ’ s and ronaldo ’ s age was 6 : 7 respectively . 4 years hence , this ratio would become 7 : 8 . how old is ronaldo ?
Options: a ) 32 , b ) 33 , c ) 34 , d ) 35 , e ) 36
Rationale: 7 ( x - 1 ) = 6 ( y - 1 ) = > 7 x - 6 y - 1 = 0 - - - - eq 1 8 ( x + 4 ) = 7 ( y + 4 ) = > 8 x - 7 y + 4 = 0 - - - - eq 2 on solving eq 1 n eq 2 y = 36 answer : e
Answer: e
Problem: a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets rs . 900 more than d , what is b ' s share ?
Options: a ) rs . 500 , b ) rs . 1800 , c ) rs . 2000 , d ) rs . 2500 , e ) none of the above
Rationale: "let the shares of a , b , c and d be rs . 5 x , rs . 2 x , rs . 4 x and rs . 3 x respectively . then , 4 x - 3 x = 900 x = 900 . b ' s share = rs . 2 x = rs . ( 2 x 900 ) = rs . 1800 . answer = b"
Answer: b
Problem: the speed at which a man can row a boat in still water is 14 kmph . if he rows downstream , where the speed of current is 2 kmph , what time will he take to cover 40 metres ?
Options: a ) 16 seconds , b ) 34 seconds , c ) 9 seconds , d ) 12 seconds , e ) 15 seconds
Rationale: "speed of the boat downstream = 14 + 2 = 16 kmph = 16 * 5 / 18 = 40 / 9 m / s hence time taken to cover 40 m = 40 * 9 / 40 = 9 seconds . answer : c"
Answer: c
Problem: a , b and c started a business with a total investment of rs . 90000 . a invests rs . 6000 more than b and b invests rs . 3000 less than c . if the total profit at the end of a year is rs . 8640 , find c ' s share .
Options: a ) rs . 3240 , b ) rs . 2520 , c ) rs . 2880 , d ) rs . 3360 , e ) none of these
Rationale: "explanation : let c ' s investment = rs . x b ' s investment = rs . ( x - 3000 ) a ' s investment = rs . ( x - 3000 + 6000 ) = rs . ( x + 3000 ) now , ( a + b + c ) ' s investment = rs . 90000 = > x + ( x - 3000 ) + ( x + 3000 ) = 90000 = > 3 x = 90000 = > x = 30000 hence , a ' s investment = rs . 33000 b ' s investment = rs . 27000 c ' s investment = rs . 30000 ratio of the capitals of a , b and c = 33000 : 27000 : 30000 = 11 : 9 : 10 a ' s share = rs . [ ( 10 / 30 ) ã — 8640 ] = rs . 2880 answer : option c"
Answer: c
Problem: the ratio of the present age of sandy to that of molly is 9 : 2 . sixteen years from now , the ratio of the ages of sandy to molly will be 5 : 2 . what was sandy ' s age 6 years ago ?
Options: a ) 30 , b ) 36 , c ) 42 , d ) 48 , e ) 54
Rationale: "let the present age of sandy be 9 x years and that of molly be 2 x years . ( 9 x + 16 ) / ( 2 x + 16 ) = 5 / 2 8 x = 48 x = 6 six years ago , sandy ' s age was 9 ( 6 ) - 6 = 48 the answer is d ."
Answer: d
Problem: how many 3 - digits number are palindromic numbers ? a palindromic number reads the same forward and backward , example 121 .
Options: a ) 90 , b ) 610 , c ) 729 , d ) 900 , e ) 1000
Rationale: "take the task of building palindromes and break it intostages . stage 1 : select the hundreds digit we can choose 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , or 9 so , we can complete stage 1 in 9 ways stage 2 : select the tens digit we can choose 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , or 9 so , we can complete stage 2 in 10 ways important : at this point , the remaining digits are alreadylocked in . stage 3 : select the units digit this digit must be the same as the thousands digit ( which we already chose in stage 2 ) so , we can complete this stage in 1 way . by thefundamental counting principle ( fcp ) , we can complete all 5 stages ( and thus build a 3 - digit palindrome ) in ( 9 ) ( 10 ) ( 1 ) ways ( = 900 ways ) answer : a"
Answer: a
Problem: the average of the 5 numbers is 6.8 . if one of the numbers is multiplied by 3 , the average of the numbers increases to 9.2 . which of the 5 numbers is multiplied by 3 ?
Options: a ) 1.5 , b ) 3.0 , c ) 3.9 , d ) 4.0 , e ) 6.0
Rationale: initial avg is 6.8 so the summation of the nos is 6.8 * 5 = 34 now the new avg is 9.2 so summation will be 9.2 * 5 = 46 . so change in summation is 12 . this comes when a number is multiplied by 3 . in the original sum we already have that number added once . to bring additional 12 increment by multiplying by 3 , we get a total increase of 18 . thus , 6 is multiplied by 3 . answer : e
Answer: e
Problem: ( 3192 + 6160 ) / 28
Options: a ) 380 , b ) 350 , c ) 334 , d ) 310 , e ) none of these
Rationale: "explanation : as per bodmas rule , first we will solve the equation in bracket then we will go for division = ( 9352 ) / 28 = 334 option c"
Answer: c
Problem: a ferry can transport 100 tons of vehicles . automobiles range in weight from 1,800 to 3,200 pounds . what is the greatest number of automobiles that can be loaded onto the ferry ?
Options: a ) 115 , b ) 120 , c ) 110 , d ) 100 , e ) 90
Rationale: "to get maximum vehicles we must take into consideration the minimum weight i . e 1800 pounds here since , 1 ton = 2000 pounds 78 tons will be 200,000 pounds from the answer choices : let max number of vehicles be 110 total weight will be = 110 * 1800 = 198000 pounds , which is lesser than the maximum weight allowed . ans : c"
Answer: c
Problem: when positive integer n is divided by positive integer j , the remainder is 25 . if n / j = 204.05 , what is value of j ?
Options: a ) 600 , b ) 500 , c ) 800 , d ) 200 , e ) 900
Rationale: "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 204.05 here 204 is the quotient . given that remainder = 25 so , 204.05 = 204 + 25 / j so , j = 500 answer : b"
Answer: b
Problem: a , b , c subscribe rs . 50000 for a business . a subscribes rs . 4000 more than b and b rs . 5000 more than c . out of a total profit of rs . 30000 , b receives :
Options: a ) s . 10,000 , b ) s . 10,200 , c ) s . 10,400 , d ) s . 10,700 , e ) s . 10,800
Rationale: let c = x . then , b = x + 5000 and a = x + 5000 + 4000 = x + 9000 . so , x + x + 5000 + x + 9000 = 50000 3 x = 36000 x = 12000 a : b : c = 21000 : 17000 : 12000 = 21 : 17 : 12 . b ' s share = rs . ( 30000 x 17 / 50 ) = rs . 10,200 . b
Answer: b
Problem: a man swims downstream 48 km and upstream 18 km taking 3 hours each time , what is the speed of the man in still water ?
Options: a ) 2 , b ) 8 , c ) 9 , d ) 11 , e ) 14
Rationale: "48 - - - 3 ds = 16 ? - - - - 1 18 - - - - 3 us = 6 ? - - - - 1 m = ? m = ( 16 + 6 ) / 2 = 11 answer : d"
Answer: d
Problem: if the population of a certain country increases at the rate of one person every 30 seconds , by how many persons does the population increase in 10 minutes ?
Options: a ) 20 , b ) 30 , c ) 15 , d ) 10 , e ) 80
Rationale: "answer = 2 * 10 = 20 answer = a"
Answer: a
Problem: a can complete a project in 20 days and b can complete the same project in 30 days . if a and b start working on the project together and b quits 15 days before the project is completed , in how many days total will the project be completed ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "a ' s rate is 1 / 20 of the project per day . b ' s rate is 1 / 30 of the project per day . the combined rate is 1 / 12 of the project per day . in the last 15 days , a can do 3 / 4 of the project . thus a and b must complete 1 / 4 of the project , which takes 3 days . the total number of days is 3 + 15 = 18 . the answer is d ."
Answer: d
Problem: a meeting has to be conducted with 4 managers . find the number of ways in which the managers be selected from among 7 managers , if 2 managers will not attend the meeting together ?
Options: a ) 25 , b ) 20 , c ) 35 , d ) 36 , e ) 38
Rationale: "we can either choose all 4 people from 5 manager who have no problems or choose 3 from the 5 and 1 from the 2 managers who have a problem sitting together so 5 c 4 + ( 5 c 3 * 2 c 1 ) this is 5 + 20 = 25 answer : a"
Answer: a
Problem: two trains each 150 m in length each , are running on two parallel lines in opposite directions . if one goes at the speed of 95 km / h while the other travels at 85 km / h . how long will it take for them to pass each other completely .
Options: a ) 25 sec , b ) 23 sec , c ) 34 sec , d ) 22 sec , e ) 6 sec
Rationale: "explanation : d = 150 m + 150 m = 300 m rs = 95 + 85 = 180 * 5 / 18 = 50 t = 300 * 1 / 50 = 6 sec answer : option e"
Answer: e
Problem: p is 10 % more efficient than q . p can complete a work in 21 days . if p and q work together , how many days will it take to complete the same work ?
Options: a ) 7 , b ) 9 , c ) 11 , d ) 13 , e ) 15
Rationale: "the work done by p in 1 day = 1 / 21 let work done by q in 1 day = q q × ( 110 / 100 ) = 1 / 21 q = 100 / ( 21 × 110 ) = 10 / ( 21 × 11 ) the work done by p and q in 1 day = 1 / 21 + 10 / ( 21 × 11 ) = 21 / ( 21 × 11 ) = 1 / 11 p and q together can do the work in 11 days . the answer is c ."
Answer: c
Problem: the average weight of a , b and c is 44 kg . if the average weight of a and b be 40 kg and that of b and c be 43 kg , then the weight of b is :
Options: a ) 17 kg , b ) 28 kg , c ) 26 kg , d ) 31 kg , e ) 35 kg
Rationale: "let d sum of a , b , c is 3 * 44 = 132 and sum of a and b s 2 * 40 = 80 sum of b and c is 2 * 43 = 86 hence 80 + 86 - 132 = 28 ans = 28 answer : b"
Answer: b
Problem: a , b , k start from the same place and travel in the same direction at speeds of 30 km / hr , 40 km / hr , 100 km / hr respectively . b starts two hours after a . if b and k overtake a at the same instant , how many hours after a did k start ?
Options: a ) 4.2 , b ) 4.8 , c ) 5.6 , d ) 6.4 , e ) 7.2
Rationale: "in 2 hours , a travels 60 km . b can catch a at a rate of 10 km / hr , so b catches a 6 hours after b starts . so a and b both travel a distance of 240 km . c needs 2.4 hours to travel 240 km , so c leaves 5.6 hours after a . the answer is c ."
Answer: c
Problem: a shopkeeper bought 600 oranges and 400 bananas . he found 15 % of oranges and 4 % of bananas were rotten . find the percentage of fruits in good condition ?
Options: a ) 92.5 % , b ) 89.4 % , c ) 85.2 % , d ) 96.8 % , e ) 78.9 %
Rationale: "total number of fruits shopkeeper bought = 600 + 400 = 1000 number of rotten oranges = 15 % of 600 = 15 / 100 × 600 = 9000 / 100 = 90 number of rotten bananas = 4 % of 400 = 16 therefore , total number of rotten fruits = 90 + 16 = 106 therefore number of fruits in good condition = 1000 - 106 = 894 therefore percentage of fruits in good condition = ( 894 / 1000 × 100 ) % = ( 89400 / 1000 ) % = 89.4 % answer : b"
Answer: b
Problem: james took a 3 - hour bike ride . in the second hour he travlled 18 miles , which was 20 percent farther than he traveled the first hour . if he traveled 25 percent farther in the third hour than he did in the second hour , how many miles did jose travel during the entire ride ?
Options: a ) 54.0 , b ) 54.9 , c ) 55.5 , d ) 57.0 , e ) 63.0
Rationale: let the distance travelled in the first hour be x . thus , 1.2 x = 18 , x = 15 . now , the distance travelled in the 3 rd hour = 18 + 1 / 4 ∗ 18 = the only option ending with a 0.5 in the decimal place is c . answer : c
Answer: c
Problem: by weight , liquid x makes up 2 percent of solution p and 7.5 percent of solution q . if 400 grams of solution p are mixed with 600 grams of solution q , then liquid x accounts for what percent of the weight of the resulting solution ?
Options: a ) 4.5 % , b ) 4.7 % , c ) 4.9 % , d ) 5.1 % , e ) 5.3 %
Rationale: "the number of grams of liquid x is 2 ( 400 ) / 100 + 7.5 ( 600 ) / 100 = 8 + 45 = 53 grams . 53 / 1000 = 5.3 % the answer is e ."
Answer: e
Problem: a train traveling at 216 kmph crosses a platform in 30 seconds and a man standing on the platform in 12 seconds . what is the length of the platform in meters ?
Options: a ) 240 meters , b ) 360 meters , c ) 420 meters , d ) 720 meters , e ) can not be determined
Rationale: "answer distance covered by the train when crossing a man and when crossing a platform when a train crosses a man standing on a platform , the distance covered by the train is equal to the length of the train . however , when the same train crosses a platform , the distance covered by the train is equal to the length of the train plus the length of the platform . the extra time that the train takes when crossing the platform is on account of the extra distance that it has to cover . i . e . , length of the platform . compute length of platform length of the platform = speed of train * extra time taken to cross the platform . length of platform = 216 kmph * 12 seconds convert 216 kmph into m / sec 1 kmph = 5 / 18 m / s ( this can be easily derived . but if you can remember this conversion , it saves a good 30 seconds ) . ∴ 216 kmph = 5 / 18 ∗ 216 = 60 m / sec therefore , length of the platform = 60 m / s * 12 sec = 720 meters . choice d"
Answer: d
Problem: for my anniversary , i decided to surprise my wife . since she is a voracious reader , i decided to collect a lot of books for her . on the first day of the month , i bought one book , on the second , i bought two and on the third , i bought three . this process went on till the anniversary and on the day , i had 190 books with me to gift her . can you calculate , on which day is our anniversary ?
Options: a ) 31 , b ) 28 , c ) 19 , d ) 33 , e ) 25
Rationale: c 19 rd day 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 = 190 thus our anniversary falls on the 19 rd day of the month . you can apply other formulas to shorten the process but that is the simplest way to do it .
Answer: c
Problem: at a tanning salon , customers are charged $ 10 for their first visit in a calendar month and $ 3 for each visit after that in the same calendar month . in the last calendar month , 100 customers visited the salon , of which 30 made a second visit , and 10 made a third visit . all other customers made only one visit . if those visits were the only source of revenue for the salon , what was the revenue for the last calendar month at the salon ?
Options: a ) $ 1220 , b ) $ 1120 , c ) $ 1300 , d ) $ 1340 , e ) $ 1880
Rationale: "i get b . this question seems too straightforward for 600 + . am i missing something ? 100 first - time visits - - > 100 ( 10 ) = $ 1000 30 + 10 = 40 subsequent visits - - > 40 ( 3 ) = $ 120 total revenue : 1000 + 120 = $ 1120 the answer is b ."
Answer: b
Problem: there are 7 players in a bowling team with an average weight of 94 kg . if two new players join the team , one weighs 110 kg and the second weighs 60 kg , what will be the new average weight ?
Options: a ) 75 kg . , b ) 80 kg . , c ) 86 kg . , d ) 90 kg . , e ) 92 kg .
Rationale: "the new average will be = ( 94 * 7 + 110 + 60 ) / 9 = 92 kgs e is the answer"
Answer: e
Problem: the average weight of 12 person ' s increases by 4 kg when a new person comes in place of one of them weighing 58 kg . what is the weight of the new person ?
Options: a ) 85 , b ) 80 , c ) 95 , d ) 90 , e ) 106
Rationale: "total increase in weight = 12 × 4 = 48 if x is the weight of the new person , total increase in weight = x − 58 = > 48 = x - 58 = > x = 48 + 58 = 106 answer : e"
Answer: e
Problem: a cube 125 mt is colored pink on two opposite surfaces and then cut in to 125 smaller cubes then find how many number of cubes have pink color ?
Options: a ) 3
b ) 4
c ) 5
d ) 6
e ) 7
Rationale: answer : b
Answer: b
Problem: 6 ) a marketing firm determined that , of 180 households surveyed , 80 used neither brand a nor brand b soap . 60 used only brand a soap and for every household that used both brands of soap , 3 used only brand b soap . how many of the 200 household surveyed used both brands of soap ?
Options: a ) a ) 15 , b ) b ) 20 , c ) c ) 30 , d ) d ) 10 , e ) e ) 45
Rationale: 100 = at least one of soap a or b both brands = x brand b = 3 x = > 60 + x + 3 x = 100 = > 4 x = 40 = > x = 10 answer - d
Answer: d
Problem: one machine takes 3 minutes to check fault in 100 km fiber optic cable . another machine does the same job in 3 seconds . what time will it take to do the same job when both machines are put to work ?
Options: a ) 2.00 seconds , b ) 2.20 seconds , c ) 2.50 seconds , d ) 2.95 seconds , e ) 3.00 seconds
Rationale: by guess it is clear that the time taken will be less than 3 seconds and very near to it . therefore , answer 2.95 seconds will be correct . answer - d
Answer: d
Problem: a certain telescope increases the visual range at a particular location from 60 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 ) 150 %
Rationale: "original visual range = 60 km new visual range = 150 km percent increase in the visual range by using the telescope = ( 150 - 60 ) / 60 * 100 % = 3 / 2 * 100 % = 150 % answer e"
Answer: e
Problem: a small company reduced its faculty by approximately 13 percent to 181 employees . what was the original number of employees ?
Options: a ) a ) 182 , b ) b ) 208 , c ) c ) 220 , d ) d ) 224 , e ) e ) 302
Rationale: "if x is the original number of employees , then after 13 % reduction in employees number is . 87 x but we are given . 87 x = 181 x = 208 so the original number of employees is 208 correct answer - b"
Answer: b
Problem: 66 small identical cubes are used to form a large cube . how many more cubes are needed to add one top layer of small cube all over the surface of the large cube ?
Options: a ) 64 , b ) 150 , c ) 152 , d ) 216 , e ) 256
Rationale: "66 small cube will make a large cube with 4 cubes in each line i . e . adding one layer will require one cube at each end and hence new cube will have 6 cubes in each line . total number of small cubes in new cube = 6 ^ 3 = 216 extra cube required = 216 - 66 = 150 hence , b is the answer ."
Answer: b
Problem: 0.9 * 0.007 = ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ _________
Options: a ) 0.063 , b ) 0.0063 , c ) 0.63 , d ) 0.00063 , e ) 63
Rationale: 9 * 7 = 63 sum of decimal places = 4 so , 0.9 * 0.007 = 0.0063 answer : b
Answer: b
Problem: a train passes a station platform in 31 sec and a man standing on the platform in 20 sec . if the speed of the train is 54 km / hr . what is the length of the platform ?
Options: a ) 228 , b ) 240 , c ) 165 , d ) 166 , e ) 1811
Rationale: "speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 20 = 300 m . let the length of the platform be x m . then , ( x + 300 ) / 31 = 15 = > x = 165 m . answer : c"
Answer: c
Problem: the length of a rectangular garden is three times its width . if the area of the rectangular garden is 768 square meters , then what is the width of the rectangular garden ?
Options: a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 20
Rationale: "let x be the width of the garden . 3 x ^ 2 = 768 x ^ 2 = 256 x = 16 the answer is a ."
Answer: a
Problem: mr . hernandez , who was a resident of state x for only 9 months last year , had a taxable income of $ 42,500 for the year . if the state tax rate were 4 percent of the year ’ s taxable income prorated for the proportion of the year during which the taxpayer was a resident , what would be the amount of mr . hernandez ’ s state x tax for last year ?
Options: a ) $ 900 , b ) $ 1275 , c ) $ 1200 , d ) $ 1300 , e ) $ 1060
Rationale: total tax for the year = 42,500 x 4 % = 1700 as stated annual tax is prorated as per the duration of stay . prorated tax = 1700 ( 9 / 12 ) = 1275 answer b
Answer: b
Problem: if a man lost 10 % by selling oranges at the rate of 10 a rupee at how many a rupee must he sell them to gain 50 % ?
Options: a ) 6 , b ) 8 , c ) 7 , d ) 4 , e ) 2
Rationale: "90 % - - - - 10 150 % - - - - ? 90 / 150 * 10 = 6 answer : a"
Answer: a
Problem: a candidate appearing for an examination has to secure 42 % marks to pass paper i . but he secured only 42 marks and failed by 22 marks . what is the maximum mark for paper i ?
Options: a ) 110 , b ) 120 , c ) 130 , d ) 152 , e ) 150
Rationale: "he secured 42 marks nd fail by 22 marks so total marks for pass the examinatn = 64 let toal marks x x * 42 / 100 = 64 x = 152 answer : d"
Answer: d
Problem: if ( - 3 ) ^ ( 2 x ) = 3 ^ ( 12 - x ) and x is an integer , what is the value of x ?
Options: a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1
Rationale: since x is an integer , ( - 3 ) ^ ( 2 x ) is always positive . so , 3 ^ 2 x = 3 ^ ( 12 - x ) 2 x = 12 - x 3 x = 12 x = 4 answer : b
Answer: b
Problem: in a division sum , the divisor is 10 times the quotient and 5 times the remainder . if the remainder is 46 , what is the dividend ?
Options: a ) 5336 , b ) 5242 , c ) 6524 , d ) 3526 , e ) 4526
Rationale: "divisor = ( 5 * 46 ) = 230 10 * quotient = 230 quotient = 230 / 10 = 23 . dividend = ( divisor * quotient ) + remainder = ( 230 * 23 ) + 46 = ( 5290 + 46 ) = 5336 . answer is a"
Answer: a
Problem: find the perimeter and area of a square of side 11 cm .
Options: a ) 11 cm ² , b ) 21 cm ² , c ) 22 cm ² , d ) 113 cm ² , e ) 121 cm ²
Rationale: "we know that the perimeter of square = 4 × side side = 11 cm therefore , perimeter = 4 × 11 cm = 44 cm now , area of the square = ( side × side ) sq . units = 11 × 11 cm ² = 121 cm ² answer : option e"
Answer: e
Problem: a company plans to gradually replace its fleet of 20 cars with newer models . at the end of every year starting with 2000 it retires 5 of its old cars and buys 6 new models . how many years did it take before the number of older cars left in the company ' s fleet was less than 50 percent of the fleet ?
Options: a ) 6 , b ) 3 , c ) 2 , d ) 4 , e ) 5
Rationale: total fleet - - 20 end of year 2000 - - ( retires 5 and buys 6 ) total fleet - - 21 ( 15 old 6 new ) . end of year 2001 - - ( retires 5 and buys 6 ) total fleet - - 22 ( 10 old 12 new ) . answer is c - - after 2 years the company has a total of 22 cars ( 10 old 12 new ) , the old cars are already less than 50 % of its fleet .
Answer: c
Problem: the ratio of radius of a circle and the side of a square is 2 : 3 . find the ratio of their areas :
Options: a ) 2 : 1 , b ) 4 : 9 , c ) 8 : 77 , d ) 4 : 121 , e ) none
Rationale: "radius / side = 2 / 3 â ‡ ’ area of circle / area of square = 4 / 9 answer : b"
Answer: b
Problem: find the compound interest on $ 500 in 5 years at 5 % per annum , the interest being compounded yearly ?
Options: a ) $ 138.14 , b ) $ 150.12 , c ) $ 142.65 , d ) $ 152 , e ) $ 164.12
Rationale: "principle = $ 500 rate = 5 % yearly amount = 500 * ( 1 + 5 / 100 ) ^ 5 = 500 * 21 / 20 * 21 / 20 * 21 / 20 * 21 / 20 * 21 / 20 = $ 638.14 c . i . = 638.14 - 500 = $ 138.14 answer is a"
Answer: a
Problem: during 2003 , a company produced an average of 1,000 products per month . how many products will the company need to produce from 2004 through 2007 in order to increase its monthly average for the period from 2003 through 2007 by 200 % over its 2003 average ?
Options: a ) 132,000 , b ) 235,000 , c ) 175,000 , d ) 200,000 , e ) 250,000
Rationale: "company produced 12 * 1000 = 12,000 products in 2003 . if company produces x products from 2004 to 2007 , then total amount of product produced in 4 years ( 2003 through 2007 ) is x + 12,000 . the gives the average of ( x + 12,000 ) / 4 . this average needs to be 200 % higher than that in 2003 . in math terms , 12,000 + 200 % ( 12,000 ) = 36,000 . so : ( x + 12,000 ) / 4 = 36,000 x + 12,000 = 144,000 x = 132,000 the answer is a ."
Answer: a
Problem: the sum of two numbers is 45 . their difference is 5 . the bigger number is
Options: a ) 20 , b ) 25 , c ) 30 , d ) 35 , e ) 45
Rationale: x + y = 45 x - y = 5 adding 2 x = 50 = = > x = 25 and y = 45 - 25 = 20 bigger number is x = 25 answer b .
Answer: b
Problem: the present worth of rs . 338 due in 2 years at 4 % per annum compound interest is
Options: a ) rs . 312.5 , b ) rs . 154.75 , c ) rs . 156.25 , d ) rs . 158 , e ) none
Rationale: "solution present worth = rs . [ 338 / ( 1 + 4 / 100 ) ² ] = rs . ( 338 x 25 / 26 x 25 / 26 ) = rs . 312.5 answer a"
Answer: a
Problem: the average of 6 observations is 11 . a new observation is included and the new average is decreased by 1 . the seventh observation is ?
Options: a ) 4 , b ) 3 , c ) 5 , d ) 6 , e ) 7
Rationale: "let seventh observation = x . then , according to the question we have = > ( 66 + x ) / 7 = 10 = > x = 4 . hence , the seventh observation is 4 . answer : a"
Answer: a
Problem: a company wants to spend equal amounts of money for the purchase of two types of computer printers costing $ 350 and $ 200 per unit , respectively . what is the fewest number of computer printers that the company can purchase ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "the smallest amount that the company can spend is the lcm of 350 and 200 , which is 1400 for each , which is total 2800 . the number of 1 st type of computers which costing $ 350 = 1400 / 350 = 4 . the number of 2 nd type of computers which costing $ 200 = 1400 / 200 = 7 . total = 4 + 7 = 11 answer is c ."
Answer: c
Problem: if the height of a cone is increased by 120 % then its volume is increased by ?
Options: a ) 100 , b ) 777 , c ) 998 , d ) 729 , e ) 120
Rationale: "120 % answer : e"
Answer: e
Problem: after decreasing 40 % in the price of an article costs rs . 1050 . find the actual cost of an article ?
Options: a ) 1200 , b ) 1750 , c ) 1050 , d ) 1570 , e ) 1005
Rationale: "cp * ( 60 / 100 ) = 1050 cp = 17.5 * 100 = > cp = 1750 answer : b"
Answer: b
Problem: a fair sided dice labeled 1 to 6 is tossed 2 times . what is the probability the sum of the 2 throws is 5 ?
Options: a ) 1 / 6 , b ) 7 / 216 , c ) 4 / 36 , d ) 9 / 216 , e ) 11 / 216
Rationale: the total possible number of combination if the dice is thrown 2 times is 36 . there are 4 possible outcomes that the sum of the number is 5 which is ( 2 + 3 ) ( 3 + 2 ) ( 1 + 4 ) and ( 4 + 1 ) answer : c
Answer: c
Problem: a merchant marks his goods up by 50 % and then offers a discount of 10 % on the marked price . what % profit does the merchant make after the discount ?
Options: a ) 21 % , b ) 25 % , c ) 69 % , d ) 35 % , e ) 19 %
Rationale: "let the price be 100 . the price becomes 150 after a 50 % markup . now a discount of 10 % on 150 . profit = 135 - 100 35 % answer d"
Answer: d
Problem: i bought two books ; for rs . 460 . i sold one at a loss of 15 % and other at a gain of 19 % and then i found each book was sold at the same price . find the cost of the book sold at a loss ?
Options: a ) 337.33 , b ) 280.33 , c ) 299.33 , d ) 268.33 , e ) 289.33
Rationale: "x * ( 85 / 100 ) = ( 460 - x ) 119 / 100 x = 280 answer : d"
Answer: d
Problem: what is the least number of squares tiles required to pave the floor of a room 6 m 75 cm long and 4 m 5 cm broad ?
Options: a ) 15 , b ) 20 , c ) 40 , d ) 44 , e ) 54
Rationale: "length of largest tile = h . c . f . of 675 cm and 405 cm = 135 cm . area of each tile = ( 135 x 135 ) cm 2 . required number of tiles = 675 x 405 / ( 135 ^ 2 ) = 15 answer : a"
Answer: a
Problem: in how many years will a sum of money doubles itself at 5 % per annum simple interest
Options: a ) 25 years , b ) 28 years , c ) 10 years , d ) 20 years , e ) 21 years
Rationale: "let the initial sum be x then , amount = 2 x ( because sum will be double ) amount = principal + s . i 2 x = x + s . i s . i = x s . i = ( p * r * t ) / 100 x = ( x * 5 * t ) / 100 therefore , t = 20 years answer : d"
Answer: d
Problem: for any positive integer n , the sum of the first n positive integers equals n ( n + 1 ) / 2 . what is the sum of odd all the integers between 1 and 50 ?
Options: a ) 500 , b ) 625 , c ) 750 , d ) 550 , e ) 600
Rationale: "numbers are 1 , 3,5 - - - - - - - , 47,49 average of the set : ( largest + smallest ) / 2 = ( 49 + 1 ) / 2 = 25 ; # of terms : ( largest - smallest ) / 2 + 1 = ( 49 - 1 ) / 2 + 1 = 25 the sum = 25 * 25 = 625 answer : b"
Answer: b
Problem: on dividing a number by 357 , we get 41 as remainder . on dividing the same number by 17 , what will be the remainder ?
Options: a ) 4 , b ) 5 , c ) 8 , d ) 7 , e ) 2
Rationale: "let x be the number and y be the quotient . then , x = 357 * y + 41 = ( 17 * 21 * y ) + ( 17 * 2 ) + 7 = 17 * ( 21 y + 2 ) + 7 . required number = 7 . answer is d"
Answer: d
Problem: machines x and y produce bottles at their respective constant rates . machine x produces k bottles in 6 hours and machine y produces k bottles in 12 hours . how many hours does it take machines x and y , working simultaneously , to produce 12 k bottles ?
Options: a ) 8 , b ) 12 , c ) 15 , d ) 48 , e ) 24
Rationale: "x rate = k / 6 y rate = k / 12 k / 6 + k / 12 = 12 k / t solving t = 48 answer d"
Answer: d
Problem: a certain music store stocks 800 cellos and 600 violas . of these instruments , there are 80 cello - viola pairs , such that a cello and a viola were both made with wood from the same tree ( each tree can make at most one viola and one cello , so there are no pairs other than these 90 ) . if one viola and one cello are chosen at random , what is the probability that the two instruments are made with wood from the same tree ?
Options: a ) 3 / 16,000 , b ) 1 / 8,100 , c ) 1 / 600 , d ) 1 / 90 , e ) 2 / 45
Rationale: "solution provided by stanford 2012 is correct : 80 / 800 choosing one of the cellos which has a pair viola , 1 / 600 choosing the viola which is the pair of chosen cello - - > p = 80 / 800 * 1 / 600 = 1 / 6,000 . answer : c ."
Answer: c
Problem: in a race where 8 cars are running , the chance that car x will win is 1 / 2 , that y will win is 1 / 4 and that z will win is 1 / 3 . assuming that a dead heat is impossible , find the chance that one of them will win .
Options: a ) 1 / 140 , b ) 11 / 12 , c ) 14 / 8 , d ) 13 / 12 , e ) 57 / 120
Rationale: required probability = p ( x ) + p ( y ) + p ( z ) ( all the events are mutually exclusive ) . = 1 / 2 + 1 / 4 + 1 / 3 = 13 / 12 answer : d
Answer: d
Problem: at a tanning salon , customers are charged $ 10 for their first visit in a calendar month and $ 4 for each visit after that in the same calendar month . in the last calendar month , 100 customers visited the salon , of which 30 made a second visit , and 10 made a third visit . all other customers made only one visit . if those visits were the only source of revenue for the salon , what was the revenue for the last calendar month at the salon ?
Options: a ) $ 1220 , b ) $ 1160 , c ) $ 1300 , d ) $ 1340 , e ) $ 1880
Rationale: "i get b . this question seems too straightforward for 600 + . am i missing something ? 100 first - time visits - - > 100 ( 10 ) = $ 1000 30 + 10 = 40 subsequent visits - - > 40 ( 4 ) = $ 160 total revenue : 1000 + 160 = $ 1160 the answer is b ."
Answer: b
Problem: 3 pumps , working 8 hours a day , can empty a tank in 2 days . how many hours a day should 4 pumps work in order to empty the tank in 1 day ?
Options: a ) 10 , b ) 12 , c ) 8 , d ) 15 , e ) 18
Rationale: "explanation : let the required hours needed be x more pumps , less hours ( indirect proportion ) more days , less hours ( indirect proportion ) hence we can write as ( pumps ) 3 : 4 ( days ) 2 : 1 } : : x : 8 ⇒ 3 × 2 × 8 = 4 × 1 × x ⇒ 3 × 2 × 2 = x ⇒ x = 12 answer : option b"
Answer: b
Problem: in what ratio must rice of rs . 54 per kg be mixed with rice of rs . 35 per kg so that cost of mixture is rs . 42 per kg ?
Options: a ) 9 : 7 , b ) 7 : 12 , c ) 12 : 7 , d ) 5 : 6 , e ) 7 : 9
Rationale: ( 42 - 35 ) / ( 54 - 42 ) = 7 / 12 = 7 : 12 answer : b
Answer: b
Problem: the sum of the numbers is 264 . if the first number be twice the second and third number be one - third of the first , then the second number is :
Options: a ) 48 , b ) 54 , c ) 72 , d ) 84 , e ) 27
Rationale: let the second number be x . then , first number = 2 x and third number = 2 x / 3 . 2 x + x + 2 x / 3 = 264 11 x / 3 = 264 x = 72 answer : c
Answer: c
Problem: if rs . 64 amount to rs . 83.20 in 2 years , what will rs . 86 amount to in 4 years at the same rate percent per annum ?
Options: a ) rs . 114.80 , b ) rs . 86.70 , c ) rs . 55.40 , d ) rs . 51.60 , e ) none
Rationale: "solution p = rs . 64 , s . i . = rs . ( 83.20 - 64 ) = rs . 19.20 , t = 2 years . so , rate = ( 100 x 19.20 / 64 x 2 ) = 15 % . now , p = rs . 86 , r = 15 % , t = 4 years . ∴ s . i . = rs . ( 86 x 15 x 4 / 100 ) rs . 51.60 . answer d"
Answer: d
Problem: nd the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 12 cm ?
Options: a ) 243 cm 2 , b ) 239 cm 2 , c ) 267 cm 2 , d ) 230 cm 2 , e ) 228 cm 2
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 12 ) = 228 cm 2 answer : e"
Answer: e
Problem: if x = 6 ^ 36 and x ^ x = 6 ^ k , what is k ?
Options: a ) 6 ^ 36 , b ) 6 ^ 38 , c ) 6 ^ 72 , d ) 6 ^ 216 , e ) 6 ^ 432
Rationale: "solution : we know that x = 6 ^ 36 which implies x ^ x = ( 6 ^ 36 ) ^ ( 6 ^ 36 ) = 6 ^ ( 36 * 6 ^ 36 ) [ because ( x ^ y ) ^ z = x ^ ( y * z ) ) ] so 6 ^ ( 6 ^ 2 * 6 ^ 36 ) = 6 ^ ( 6 ^ ( 2 + 36 ) ) [ because x ^ a * x ^ b = x ^ ( a + b ) ] therefore x ^ x = 6 ^ ( 6 ^ 38 ) given that x ^ x = 6 ^ k so 6 ^ ( 6 ^ 38 ) = 6 ^ k since the base is same the exponent will also be same therefore k = 6 ^ 38 answer : b"
Answer: b
Problem: a cylindrical can has a radius of 6 centimeters and a height of 12 centimeters . what is the area , in square centimeters , of a rectangular label that completely covers the curved surface of the can without over - lapping ?
Options: a ) 16 pi , b ) 64 pi , c ) 96 pi , d ) 144 pi , e ) 576 pi
Rationale: "they are asking the lateral surface area of the cylinder . the lateral surface area = 2 * pi * r * h = 2 * pi * 6 * 12 = 144 pi answer is d ."
Answer: d
Problem: a digital wristwatch was set accurately at 8.30 a . m and then lost 2 seconds every 5 minutes . what time was indicated on the watch at 6.30 p . m of the same day if the watch operated continuously that time ?
Options: a ) 5.56 , b ) 5.58 , c ) 6.0 , d ) 6.23 , e ) 6.26
Rationale: for every 5 min watch looses 2 secs , so for 60 ms it looses 24 sec , i . e . , for 1 hr it looses 24 secs 8.30 amto 6.30 pm = 10 hr it looses 240 secs i . e . , 4 mins , hence d watch will show 6.26 answer : e
Answer: e
Problem: what is the remainder of w = 3 ^ 19 when divided by 10 ?
Options: a ) 0 , b ) 1 , c ) 5 , d ) 7 , e ) 9
Rationale: "i looked for patterns : ^ 2 - units digit 9 ^ 3 - units digit 7 ^ 4 - units digit 1 ^ 5 - units digit 3 hence , we can see that when raised to a power which is multiple of 4 , the units digit is 1 , and when to an even power not multiple of 4 , the units digit is 9 and we can then see : ^ 16 - units digit 1 , or ^ 18 - units digit 9 and ^ 19 - units digit 7 therefore , w = when divided by 10 , the remainder must be 7 . d"
Answer: d
Problem: if each edge of cube increased by 10 % , the percentage increase in surface area is :
Options: a ) 33.1
b ) 33.5
c ) 33.7
d ) 33.2
e ) 33.9
Rationale: 100 × ( 110 ) / 100 × ( 110 ) / 100 × ( 110 ) / 100 = > 1331 / 100 = 33.1 % answer is a .
Answer: a
Problem: a train 110 m long is running with a speed of 56 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 5 , b ) 6.4 , c ) 7 , d ) 8 , e ) 9
Rationale: "speed of train relative to man = 56 + 6 = 62 km / hr . = 62 * 5 / 18 = 155 / 9 m / sec . time taken to pass the men = 110 * 9 / 155 = 6.4 sec . answer : option b"
Answer: b
Problem: if a and b are integers and ( a * b ) ^ 5 = 48 y , y could be :
Options: a ) 8 , b ) 16 , c ) 162 , d ) 144 , e ) 100
Rationale: "distribute the exponent . a ^ 5 * b ^ 5 = 48 y find the prime factorization of 48 . this is 2 ^ 4 * 3 ^ 1 . we need 2 ^ 1 * 3 ^ 4 ( or some other power of 3 that will give us a multiple of 3 ^ 5 as our second term ) . 3 ^ 4 * 2 = 81 * 2 = 162 the answer is c ."
Answer: c
Problem: 5 men are equal to as many women as are equal to 8 boys . all of them earn rs . 105 only . men â € ™ s wages are ?
Options: a ) 6 rs , b ) 7 rs , c ) 8 rs , d ) 4 rs , e ) 1 rs
Rationale: "5 m = xw = 8 b 5 m + xw + 8 b - - - - - 105 rs . 5 m + 5 m + 5 m - - - - - 105 rs . 15 m - - - - - - 105 rs . = > 1 m = 7 rs . answer : b"
Answer: b
Problem: the pilot of a small aircraft with a 40 - gallon fuel tank wants to fly to cleveland , which is 520 miles away . the pilot recognizes that the current engine , which can fly only 8 miles per gallon , will not get him there . by how many miles per gallon must the aircraft ’ s fuel efficiency be improved to make the flight to cleveland possible ?
Options: a ) 5 , b ) 4 , c ) 12 , d ) 40 , e ) 160
Rationale: "actual miles / gallon is = 520 / 40 = 13 miles / gallon . current engine miles / gallon is 8 miles / gallon . additional 5 miles / gallon is required to match the actual mileage . imo option a ."
Answer: a
Problem: jerry travels 8 miles at an average speed of 40 miles per hour , stops for 11 minutes , and then travels another 20 miles at an average speed of 60 miles per hour . what is jerry ’ s average speed , in miles per hour , for this trip ?
Options: a ) 37 , b ) 42.5 , c ) 44 , d ) 50 , e ) 52.5
Rationale: "total time taken by jerry = ( 8 / 40 ) * 60 minutes + 11 minutes + ( 20 / 60 ) * 60 minutes = 45 minutes average speed = total distance / total time = ( 8 + 20 ) miles / ( 45 / 60 ) hours = 28 * 60 / 45 = 37 miles per hour answer : option a"
Answer: a
Problem: car a runs at the speed of 65 km / hr & reaches its destination in 8 hr . car b runs at the speed of 75 km / h & reaches its destination in 4 h . what is the respective ratio of distances covered by car a & car b ?
Options: a ) 26 : 15 , b ) 12 : 7 , c ) 13 : 7 , d ) 15 : 6 , e ) 13 : 6
Rationale: "sol . distance travelled by car a = 65 ã — 8 = 520 km distance travelled by car b = 75 ã — 4 = 300 km ratio = 520 / 300 = 26 : 15 a"
Answer: a
Problem: 30 ^ 10 / 90 ^ 5 = ?
Options: a ) 6 ^ 5 , b ) 5 ^ 6 , c ) 3 ^ 6 , d ) 10 ^ 5 , e ) 15 ^ 3
Rationale: "30 ^ 10 / 90 ^ 5 = ? a . 6 ^ 5 b . 5 ^ 6 c . 3 ^ 6 d . 10 ^ 5 e . 15 ^ 3 - > 30 ^ 10 / 90 ^ 5 = ( 30 ^ 10 ) / ( 3 ^ 5 ) ( 30 ^ 5 ) = ( 30 ^ 5 ) / ( 3 ^ 5 ) = ( 3 ^ 5 ) ( 10 ^ 5 ) / ( 3 ^ 5 ) = 10 ^ 5 . thus , d is the answer ."
Answer: d
Problem: the ratio of the areas of a square and rhombus whose base is same is :
Options: a ) 1 : 2 , b ) 2 : 1 , c ) 1 : 1 , d ) 3 : 1 , e ) 2 : 3
Rationale: "solution : the square and the rhombus are equal in area if they have a common base . answer is c"
Answer: c
Problem: a boat can travel with a speed of 25 km / hr in still water . if the speed of the stream is 5 km / hr , find the time taken by the boat to go 120 km downstream .
Options: a ) 1 hr , b ) 2 hrs , c ) 3 hrs , d ) 4 hrs , e ) 5 hrs
Rationale: "speed downstream = ( 25 + 5 ) km / hr = 30 km / hr . time taken to travel 120 km downstream = 120 / 30 hrs = 4 hrs . answer : d"
Answer: d
Problem: the banker â € ™ s gain on a sum due 3 years hence at 17 % per annum is rs . 100 . the banker â € ™ s discount is
Options: a ) rs . 960 , b ) rs . 840 , c ) rs . 296 , d ) rs . 760 , e ) none
Rationale: "solution t . d = ( b . g x 100 / r x t ) = rs . ( 100 x 100 / 17 x 3 ) = rs . 196 . b . d = rs ( 196 + 100 ) = rs . 296 . answer c"
Answer: c
Problem: an error 4 % in excess is made while measuring the side of a square . the percentage of error in the calculated area of the square is :
Options: a ) 4.16 , b ) 5.16 , c ) 7.16 , d ) 8.16 , e ) 9.16
Rationale: "explanation : 100 cm is read as 104 cm . a 1 = ( 100 × 100 ) cm 2 = 10000 and a 2 = ( 104 × 104 ) cm 2 = 10816 ( a 2 - a 1 ) = 10816 - 10000 = 816 = > 816 / 10000 * 100 = 8.16 answer : d"
Answer: d
Problem: a 90 - liter solution of cool - drink is made from 5 % jasmine water . if 8 liters of jasmine and 2 liters of water were added to the solution , what percent of the solution is jasmine ?
Options: a ) 6.5 % , b ) 8.5 % , c ) 10.5 % , d ) 12.5 % , e ) 14.5 %
Rationale: the percent of jasmine in the resulting solution is : ( amount of jasmine ) / ( total volume ) ( 0.05 ( 90 ) + 8 ) / 100 = 12.5 / 100 = 12.5 % the answer is d .
Answer: d
Problem: if the ratio of two number is 4 : 6 and lcm of the number is 280 then what is the number .
Options: a ) 12 , b ) 20 , c ) 25 , d ) 30 , e ) 35
Rationale: product of two no = lcm * hcf 4 x * 6 x = 280 * x x = 12 answer : a
Answer: a