regisss/math_qa huggingface dataset:
Problem: last year , for every 100 million vehicles that traveled on a certain highway , 100 vehicles were involved in accidents . if 2 billion vehicles traveled on the highway last year , how many of those vehicles were involved in accidents ? ( 1 billion = 1,000 , 000,000 )
Options: a ) 500 , b ) 1500 , c ) 2500 , d ) 2000 , e ) 1000
Rationale: "to solve we will set up a proportion . we know that “ 100 million vehicles is to 100 accidents as 2 billion vehicles is to x accidents ” . to express everything in terms of “ millions ” , we can use 2,000 million rather than 2 billion . creating a proportion we have : 100 / 100 = 2,000 / x cross multiplying gives us : 100 x = 2,000 * 100 x = 20 * 100 = 2000 answer : d"
Answer: d
Problem: two men started from the same place walk at the rate of 10 kmph and 12 kmph respectively . what time will they take to be 40 km apart , if they walk in the same direction ?
Options: a ) 5 hours , b ) 40 hours , c ) 8 hours , d ) 20 hours , e ) 30 hours
Rationale: "to be 2 km apart they take 1 hour to be 10 km apart they take = 1 / 2 * 40 = 20 hours answer is d"
Answer: d
Problem: the population of locusts in a certain swarm doubles every two hours . if 4 hours ago there were 1000 locusts in the swarm , in approximately how many hours will the swarm population exceed 128000 locusts ?
Options: a ) 12 , b ) 8 , c ) 4 , d ) 10 , e ) 16
Rationale: - 4 hours : 1,000 - 2 hours : 2,000 now : 4,000 + 2 hours : 8,000 + 4 hours : 16,000 + 6 hours : 32,000 + 8 hours : 64,000 + 10 hours : 128,000 answer : d
Answer: d
Problem: an error 2 % in excess ismade while measuring the side ofa square . the % of error in the calculated area of the square is ?
Options: a ) 4.00 %
b ) 4.04 %
c ) 4.16 %
d ) 4.30 %
e ) 5 %
Rationale: 100 cm is read as 102 cm . a 1 = ( 100 x 100 ) cm 2 and a 2 ( 102 x 102 ) cm 2 . ( a 2 - a 1 ) = [ ( 102 ) 2 - ( 100 ) 2 ] = ( 102 + 100 ) x ( 102 - 100 ) = 404 cm 2 . percentage error = 404 x 100 % = 4.04 % 100 x 100 b
Answer: b
Problem: if x is the product of the positive integers from 1 to 9 , inclusive , and if i , k , m , and p are positive integers such that x = 2 i 3 k 5 m 7 px = 2 i 3 k 5 m 7 p , then i + k + m + p =
Options: a ) 4 , b ) 7 , c ) 8 , d ) 11 , e ) 13
Rationale: "x = 9 ! = 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = ( 3 ^ 2 ) * ( 2 ^ 3 ) * 7 * ( 2 * 3 ) * 5 * 2 ^ 2 * 3 * 2 * 1 = 2 ^ 7 * 3 ^ 4 * 5 * 7 = 2 ^ i * 3 ^ k * 5 ^ m * 7 ^ p i + k + m + p = 7 + 4 + 1 + 1 = 13 answer e"
Answer: e
Problem: of the diplomats attending a summit conference , 22 speak french , 32 do not speak russian , and 20 % of the diplomats speak neither french nor russian . if 10 % of the diplomats speak both languages , then how many diplomats attended the conference ?
Options: a ) 72 , b ) 96 , c ) 100 , d ) 120 , e ) 150
Rationale: "{ total } = { french } + { russian } - { both } + { neither } { total } = 22 + ( { total } - 32 ) - ( 0.1 * { total } ) + 0.2 * { total } solving gives { total } = 100 . answer : c ."
Answer: c
Problem: a football team lost 5 yards and then gained 10 . what is the team ' s progress ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: "for lost , use negative . for gain , use positive . progress = - 5 + 10 = 5 yards c"
Answer: c
Problem: find the sum of first 20 natural numbers
Options: a ) 470 , b ) 210 , c ) 465 , d ) 463 , e ) 485
Rationale: "explanation : sum of n natural numbers = n ( n + 1 ) / 2 = 20 ( 20 + 1 ) / 2 = 20 ( 21 ) / 2 = 210 answer : option b"
Answer: b
Problem: weights of two friends ram and shyam are in the ratio 2 : 5 . if ram ' s weight is increased by 10 % and total weight of ram and shyam become 82.8 kg , with an increases of 15 % . by what percent did the weight of shyam has to be increased ?
Options: a ) 17 % , b ) 10 % , c ) 21 % , d ) 16 % , e ) none
Rationale: "solution : given ratio of ram and shayam ' s weight = 2 : 5 hence , ( x - 15 ) / ( 15 - 10 ) = 2 / 5 or , x = 17 % . answer : option a"
Answer: a
Problem: what is the tens digit of 36 ^ 12 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "36 ^ 10 = 6 ^ 24 ( 6 ^ 2 ) = 6 * 6 = 36 ( 6 ^ 3 ) = 36 * 6 = . 16 ( 6 ^ 4 ) = . 16 * 6 = . . 96 ( 6 ^ 5 ) = . . 96 * 6 = . . 76 ( 6 ^ 6 ) = . . 76 * 6 = . . . 56 ( 6 ^ 7 ) = . . . . 56 * 6 = . . . . 36 if you see there is a pattern here in tens digits 3 , 1,9 , 7,5 , 3,1 and so on . . . continue the pattern up to 6 ^ 24 ( dont actually calculate full values ) and answer is e : 9"
Answer: e
Problem: the smallest number which when diminished by 8 , is divisible 8 , 16 , 24 , 32 and 40 is :
Options: a ) 1008 , b ) 1015 , c ) 488 , d ) 490 , e ) 590
Rationale: "required number = ( l . c . m . of 8 , 16 , 24 , 32 , 40 ) + 8 = 480 + 8 = 488 answer : option c"
Answer: c
Problem: how many numbers from 2 to 15 are exactly divisible by 2 ?
Options: a ) a ) 2 , b ) b ) 3 , c ) c ) 5 , d ) d ) 7 , e ) e ) 8
Rationale: "2 / 2 = 1 and 15 / 2 = 7 7 - 1 = 6 6 + 1 = 7 numbers . answer : d"
Answer: d
Problem: the area of a triangle is with base 3 m and height 4 m ?
Options: a ) 4 m 2 , b ) 6 m 2 , c ) 18 m 2 , d ) 19 m 2 , e ) 12 m 2
Rationale: "1 / 2 * 3 * 4 = 6 m 2 answer : b"
Answer: b
Problem: calculate 469160 x 9999 = ?
Options: a ) 4691130840 , b ) 4686970743 , c ) 4691100843 , d ) 4586870843 , e ) none
Rationale: "answer 469160 x 9999 = 469160 x ( 10000 - 1 ) = 4691600000 - 469160 = 4691130840 . option : a"
Answer: a
Problem: the average age of students of a class is 15.8 years . the average age of boys in the class is 16.4 years and that of the girls is 15.4 years , the ratio of the number of boys to the number of girls in the class is :
Options: a ) 2 : 9 , b ) 2 : 3 , c ) 2 : 1 , d ) 2 : 2 , e ) 2 : 6
Rationale: "explanation : let the ratio be k : 1 . then , k * 16.4 + 1 * 15.4 = ( k + 1 ) * 15.8 < = > ( 16.4 - 15.8 ) k = ( 15.8 - 15.4 ) < = > k = 0.4 / 0.6 = 2 / 3 . required ratio = 2 / 3 : 1 = 2 : 3 . answer : b"
Answer: b
Problem: at what rate percent on simple interest will rs . 850 amount to rs . 950 in 5 years ?
Options: a ) 2.35 % , b ) 5.95 % , c ) 4.35 % , d ) 5.33 % , e ) 6.33 %
Rationale: "100 = ( 850 * 5 * r ) / 100 r = 2.35 % answer : a"
Answer: a
Problem: if 4 people are selected from a group of 9 married couples , what is the probability that none of them would be married to each other ?
Options: a ) 1 / 33 , b ) 2 / 85 , c ) 1 / 3 , d ) 56 / 85 , e ) 11 / 85
Rationale: if we are to select 4 people from 9 couples without any restriction , how many ways can we make the selection ? 18 ! / 4 ! 14 ! = 3060 if we are to select 4 people from 9 couples with restriction that no married couple can both make it to the group , only a representative ? 9 ! / 4 ! 5 ! = 126 but we know that to select a person from each couple , take 2 possibilities 126 * 2 * 2 * 2 * 2 = 2016 probability = desired / all possibilities = 2016 / 3060 = 56 / 85 answer : d
Answer: d
Problem: joe went on a diet 4 months ago when he weighed 222 pounds . if he now weighs 198 pounds and continues to lose at the same average monthly rate , in approximately how many months will he weigh 180 pounds ?
Options: a ) 3 , b ) 3.5 , c ) 3 , d ) 4.5 , e ) 5
Rationale: 222 - 198 = 24 pounds lost in 4 months 24 / 4 = 6 , so joe is losing weight at a rate of 6 pounds per month . . . . in approximately how many months will he weigh 180 pounds ? a simple approach is to just list the weights . now : 198 lbs in 1 month : 192 lbs in 2 months : 186 lbs in 3 months : 180 lbs answer : c
Answer: c
Problem: how many integers are divisible by 3 between 10 ! and 10 ! + 40 inclusive ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 13 , e ) 10
Rationale: "d - 7 10 ! is divisible by 3 there are 12 numbers between 10 ! and 10 ! + 40 that are divisible by 3 . hence 13"
Answer: d
Problem: if the perimeter of a rectangular stadium is 800 m , its length when its breadth is 300 m is ?
Options: a ) 500 , b ) 400 , c ) 300 , d ) 200 , e ) 100
Rationale: 2 ( l + 300 ) = 800 = > l = 100 m answer : e
Answer: e
Problem: the ratio between the current age of a and b is 6 : 7 . if b is 4 years old than a . what will be the ratio of the ages of a and b after 4 years ?
Options: a ) 7 : 8 , b ) 8 : 9 , c ) 4 : 6 , d ) 4 : 8 , e ) 5 : 8
Rationale: a 7 : 8 if a ’ s age and b ’ s age will be 6 a years and 7 a years correspondingly then , 7 a – 6 a = 4 a = 4 needed ratio = ( 6 a + 4 ) : ( 7 a + 4 ) = 28 : 32 = 7 : 8
Answer: a
Problem: the milk level in a rectangular box measuring 56 feet by 25 feet is to be lowered by 6 inches . how many gallons of milk must be removed ? ( 1 cu ft = 7.5 gallons )
Options: a ) 100 , b ) 250 , c ) 750 , d ) 5250 , e ) 5635
Rationale: "6 inches = 1 / 2 feet ( there are 12 inches in a foot . ) , so 56 * 25 * 1 / 2 = 700 feet ^ 3 of milk must be removed , which equals to 700 * 7.5 = 5250 gallons . answer : d ."
Answer: d
Problem: what is the sum of all even numbers from 1 to 501 ?
Options: a ) 122821 , b ) 281228 , c ) 281199 , d ) 62750 , e ) 128111
Rationale: "explanation : 500 / 2 = 250 250 * 251 = 62750 answer : d"
Answer: d
Problem: during 2005 , a company produced an average of 2,500 products per month . how many products will the company need to produce from 2006 through 2008 in order to increase its monthly average for the period from 2005 through 2008 by 300 % over its 2005 average ?
Options: a ) 450,000 , b ) 475,000 , c ) 500,000 , d ) 525,000 , e ) 550,000
Rationale: "company produced 12 * 2500 = 30,000 products in 2005 . if company produces x products from 2006 to 2008 , then total amount of product produced in 4 years ( 2005 through 2008 ) is x + 30,000 . the gives the average of ( x + 30,000 ) / 4 . this average needs to be 200 % higher than that in 2005 . in math terms , 30,000 + 300 % ( 30,000 ) = 120,000 . so : ( x + 30,000 ) / 4 = 120,000 x + 30,000 = 480,000 x = 450,000 the answer is a ."
Answer: a
Problem: how many quarters are equal to 3 dollars ?
Options: a ) 1 , b ) 8 , c ) 12 , d ) 9 , e ) 7
Rationale: "3 * 4 = 12 quarters answer : c"
Answer: c
Problem: if k ^ 3 is divisible by 60 , what is the least possible value of integer k ?
Options: a ) 12 , b ) 30 , c ) 60 , d ) 90 , e ) 120
Rationale: "60 = 2 ^ 2 * 3 * 5 therefore k must include at least 2 * 3 * 5 = 30 . the answer is b ."
Answer: b
Problem: the purchase price of an article is $ 48 . in order to include 20 % of cost for overhead and to provide $ 12 of net profit , the markup should be
Options: a ) 15 % , b ) 25 % , c ) 35 % , d ) 40 % , e ) 45 %
Rationale: "cost price of article = 48 $ % of overhead cost = 20 net profit = 12 $ we need to calculate % markup net profit as % of cost price = ( 12 / 48 ) * 100 = 25 % total markup should be = 25 + 20 = 45 % answer e"
Answer: e
Problem: pipe a can fill a tank in 10 hrs and pipe b can fill it in 8 hrs . if both the pipes are opened in the empty tank . there is an outlet pipe in 3 / 4 th of the tank . in how many hours will it be fill 3 / 4 th of that tank ?
Options: a ) 3 hr , b ) 3.10 hr , c ) 3.15 hr , d ) 3.20 hr , e ) 3.30 hr
Rationale: part filled a in 1 hr = ( 1 / 10 ) part filled b in 1 hr = ( 1 / 8 ) part filled by ( a + b ) together in 1 hr = ( 1 / 10 ) + ( 1 / 8 ) = 18 / 80 so , the tank will be full in 80 / 18 hrs . time taken to fill exact 3 / 4 th of the tank = ( 80 / 18 ) * ( 3 / 4 ) = 3.20 hrs answer : d
Answer: d
Problem: a no . when divided by the sum of 555 and 445 gives 2 times their difference as quotient & 30 as remainder . find the no . is ?
Options: a ) 122443 , b ) 154546 , c ) 165454 , d ) 186545 , e ) 220030
Rationale: "( 555 + 445 ) * 2 * 110 + 30 = 220000 + 30 = 220030 e"
Answer: e
Problem: there are some rabbits and peacocks in a zoo . the total number of their heads is 60 and total number of their legs is 192 . find the number of total rabbits ?
Options: a ) 36 , b ) 77 , c ) 88 , d ) 99 , e ) 22
Rationale: let the number of rabbits and peacocks be ' r ' and ' p ' respectively . as each animal has only one head , so r + p = 60 - - - ( 1 ) each rabbit has 4 legs and each peacock has 2 legs . total number of legs of rabbits and peacocks , 4 r + 2 p = 192 - - - ( 2 ) multiplying equation ( 1 ) by 2 and subtracting it from equation ( 2 ) , we get = > 2 r = 72 = > r = 36 . answer : a
Answer: a
Problem: two unbiased coins are tossed . what is probability of getting at most one tail ?
Options: a ) 12 , b ) 13 , c ) 32 , d ) 34 , e ) none of these
Rationale: "explanation : total 4 cases = [ hh , tt , th , ht ] favourable cases = [ hh , th , ht ] please note we need atmost one tail , not atleast one tail . so probability = 3 / 4 answer : d"
Answer: d
Problem: when positive integer n is divided by 5 , the remainder is 2 . when n is divided by 11 , the remainder is 8 . what is the smallest positive integer k such that k + n is a multiple of 55 ?
Options: a ) 2 , b ) 3 , c ) 6 , d ) 7 , e ) 10
Rationale: "n = 5 p + 2 = 11 q + 8 n + 3 = 5 p + 5 = 11 q + 11 n + 3 is a multiple of 5 and 11 , so it is a multiple of 55 . the answer is b ."
Answer: b
Problem: a person can row at 10 kmph in still water . if the velocity of the current is 2 kmph and it takes him 10 hour to row to a place and come back , how far is the place ?
Options: a ) 24 km , b ) 30 km , c ) 48 km , d ) 12 km , e ) 48 km
Rationale: "speed of down stream = 10 + 2 = 12 kmph speed of upstream = 10 - 2 = 8 kmph let the required distance be xkm x / 12 + x / 8 = 10 2 x + 3 x = 240 x = 48 km answer is e"
Answer: e
Problem: what is the least number of square tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad ?
Options: a ) 724 , b ) 804 , c ) 814 , d ) 844 , e ) none
Rationale: "solution length of largest tile = h . c . f . of 1517 cm & 902 cm = 41 cm . area of each tile = ( 41 x 41 ) cm 2 ∴ required number of tiles = [ 1517 x 902 / 41 x 41 ] = 814 . answer c"
Answer: c
Problem: the average of first 8 prime numbers is ?
Options: a ) 10.11 , b ) 9.625 , c ) 12.11 , d ) 13.11 , e ) 14.11
Rationale: "sum of first 8 prime nos . = 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 = 77 average = 77 / 8 = 9.625 answer : b"
Answer: b
Problem: from a group of 3 boys and 3 girls , 2 children are to be randomly selected . what is the probability that 1 boy and 1 girl will be selected ?
Options: a ) 1 / 10 , b ) 4 / 9 , c ) 1 / 2 , d ) 9 / 15 , e ) 2 / 3
Rationale: "the total number of ways to choose 2 children from 6 is 6 c 2 = 15 the number of ways to choose 1 boy and 1 girl is 3 * 3 = 9 p ( 1 boy and 1 girl ) = 9 / 15 the answer is d ."
Answer: d
Problem: the average of first five multiples of 7 is ?
Options: a ) 6 , b ) 8 , c ) 9 , d ) 5 , e ) 21
Rationale: "average = 7 ( 1 + 2 + 3 + 4 + 5 ) / 5 = 105 / 5 = 21 . answer : e"
Answer: e
Problem: in one hour , a boat goes 21 km / hr along the stream and 11 km / hr against the stream . the speed of the boat in still water ( in km / hr ) is :
Options: a ) 12 kmph , b ) 13 kmph , c ) 14 kmph , d ) 15 kmph , e ) 16 kmph
Rationale: "explanation : let the speed downstream be a km / hr and the speed upstream be b km / hr , then speed in still water = 1 / 2 ( a + b ) km / hr rate of stream = 1 / 2 ( a − b ) km / hr speed in still water = 1 / 2 ( 21 + 11 ) kmph = 16 kmph . answer : option e"
Answer: e
Problem: two pipes p and q can fill a cistern in 12 and 10 minutes respectively . both are opened together , but at the end of 3 minutes the first is turned off . how much longer will the cistern take to fill ?
Options: a ) 1 / 8 , b ) 1 / 2 , c ) 2 / 4 , d ) 1 / 4 , e ) 1 / 4
Rationale: "3 / 12 + x / 10 = 1 x = 8 1 / 2 answer : b"
Answer: b
Problem: ( 169 ) ^ 2 - ( 168 ) ^ 2 =
Options: a ) 1 , b ) 100 , c ) 229 , d ) 329 , e ) 337
Rationale: using the formula : ( a + 1 ) ^ 2 - a ^ 2 = 2 a + 1 so , answer = 168 * 2 + 1 = 336 + 1 = 337 = answer = e
Answer: e
Problem: a meal cost $ 33.50 and there was no tax . if the tip was more than 10 pc but less than 15 pc of the price , then the total amount paid should be :
Options: a ) 40 - 42 , b ) 39 - 41 , c ) 38 - 40 , d ) 37 - 39 , e ) 36 - 37
Rationale: "10 % ( 33.5 ) = 3.35 15 % ( 33.5 ) = 5.025 total amount could have been 33.5 + 3.35 and 33.5 + 5.025 = > could have been between 36.85 and 38.525 = > approximately between 37 and 39 answer is d ."
Answer: d
Problem: what least number should be added to 1054 , so that the sum is completely divisible by 23
Options: a ) a ) 4 , b ) b ) 1 , c ) c ) 2 , d ) d ) 3 , e ) e ) 5
Rationale: "explanation : ( 1054 / 23 ) gives remainder 19 19 + 4 = 23 , so we need to add 4 answer : option a"
Answer: a
Problem: in a recent head - to - head run - off election , 15,000 absentee ballets were cast . 1 / 5 of the absentee ballets were thrown out and 1 / 4 of the remaining absentee ballets were cast for candidate a . how many absentee votes did candidate b receive ?
Options: a ) 2,000 , b ) 3,000 , c ) 6,000 , d ) 8,000 , e ) 9,000
Rationale: "4 / 5 * 3 / 4 ( total absentee votes ) = 3 / 5 ( total votes ) = 3 / 5 * 15000 = 9000 answer is e"
Answer: e
Problem: the operation is defined for all integers a and b by the equation ab = ( a - 1 ) ( b - 1 ) . if y 10 = 90 , what is the value of y ?
Options: a ) 10 , b ) 12 , c ) 15 , d ) 11 , e ) 20
Rationale: "ab = ( a - 1 ) ( b - 1 ) y 10 = ( y - 1 ) ( 10 - 1 ) = 90 - - > y - 1 = 10 - - > y = 11 answer : d"
Answer: d
Problem: how many 4 x 4 x 4 cubes could fit in a 9 x 13 x 16 box ?
Options: a ) 22 , b ) 28 , c ) 29 , d ) 31 , e ) 32
Rationale: the answer is c ) 29 . 9 x 13 x 16 gives the box an area of 1,872 . if you divide 1,872 by 64 ( the total of 4 x 4 x 4 ) , you get 29.25 . this means 29 full boxes will fit in the larger box .
Answer: c
Problem: the distance between two cities a and b is 330 km . a train starts from a at 8 a . m . and travel towards b at 60 km / hr . another train starts from b at 9 a . m . and travels towards a at 75 km / hr . at what time will they meet ?
Options: a ) 10.30 a . m , b ) 11 a . m , c ) 10 a . m , d ) 12 noon , e ) none of these
Rationale: "explanation : assume that they meet x hours after 8 a . m . then , train 1 , starting from a , travelling towards b , travels x hours till the trains meet ⇒ distance travelled by train 1 in x hours = speed × time = 60 x then , train 2 , starting from b , travelling towards a , travels ( x - 1 ) hours till the trains meet ⇒ distance travelled by train 2 in ( x - 1 ) hours = speed × time = 75 ( x - 1 ) total distance travelled = distance travelled by train 1 + distance travelled by train 2 = > 330 = 60 x + 75 ( x - 1 ) = > 12 x + 15 ( x - 1 ) = 66 = > 12 x + 15 x - 15 = 66 = > 27 x = 66 + 15 = 81 = > 3 x = 9 = > x = 3 hence the trains meet 3 hours after 8 a . m . , i . e . at 11 a . m . answer : option b"
Answer: b
Problem: a card game called “ high - low ” divides a deck of 52 playing cards into 2 types , “ high ” cards and “ low ” cards . there are an equal number of “ high ” cards and “ low ” cards in the deck and “ high ” cards are worth 2 points , while “ low ” cards are worth 1 point . if you draw cards one at a time , how many ways can you draw “ high ” and “ low ” cards to earn 5 points if you must draw exactly 2 “ low ” cards ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 12
Rationale: "great question ravih . this is a permutations problem ( order matters ) with repeating elements . given thatlowcards are worth 1 pt andhigh cards 2 pts , and you must draw 3 low cards , we know that you must also draw 1 high card . the formula for permutations problems with repeating elements isn ! / a ! b ! . . . where n represents the number of elements in the group and a , b , etc . represent the number of times that repeating elements are repeated . here there are 4 elements and thelowcard is repeated 2 times . as a result , the formula is : 4 ! / 2 ! which represents ( 4 * 3 * 2 * 1 ) / ( 2 * 1 ) which simplifies to just 4 , giving you answer e ."
Answer: e
Problem: one pump drains one - half of a pond in 2.5 hours , and then a second pump starts draining the pond . the two pumps working together finish emptying the pond in one - half hour . how long would it take the second pump to drain the pond if it had to do the job alone ?
Options: a ) 1 hour , b ) 1.2 hour , c ) 3 hours , d ) 1.25 hours , e ) 6 hours
Rationale: "the tricky part here , i believed is one half hour = 1 / 2 . then everything would be easy . we have the 1 st pump working rate / hour = 1 / 2 : 5 / 2 = 1 / 5 working rate of 2 pumps : 1 / 2 : 1 / 2 = 1 . working rate of 2 nd pump : 1 - 1 / 5 = 4 / 5 - - > time taken for the 2 nd pump to finish : 1 : 4 / 5 = 5 / 4 = 1.25 hours . d"
Answer: d
Problem: a high school has 400 students 1 / 2 attend the arithmetic club , 5 / 8 attend the biology club and 3 / 4 attend the chemistry club . 3 / 8 attend all 3 clubs . if every student attends at least one club how many students attend exactly 2 clubs .
Options: a ) 35 , b ) 45 , c ) 55 , d ) 60 , e ) 50
Rationale: a - club has 200 members ( 1 / 2 of 400 ) b - club has 250 members ( 5 / 8 of 400 ) c - club has 300 members ( 3 / 4 of 400 ) we can create an equation to solve this : 200 + 250 + 150 = n + x + 2 y where n is the number of students , x is the number of students in two clubs , and y is the number of students in three clubs . the question provides y for us ( 150 ) . 750 = 400 + x + 300 x = 50 e
Answer: e
Problem: in a group of cows and hens , the number of legs are 30 more than twice the number of heads . the number of cows is
Options: a ) 15 , b ) 7 , c ) 10 , d ) 12 , e ) 14
Rationale: "explanation : let the number of cows be x and the number of hens be y . then , 4 x + 2 y = 2 ( x + y ) + 30 4 x + 2 y = 2 x + 2 y + 30 2 x = 30 x = 15 answer : a"
Answer: a
Problem: a train , 800 meter long is running with a speed of 78 km / hr . it crosses a tunnel in 1 minute . what is the length of the tunnel ?
Options: a ) 650 meter , b ) 555 meter , c ) 500 meter , d ) 458 meter , e ) none of these
Rationale: explanation : let length of tunnel is x meter distance = 800 + x meter time = 1 minute = 60 seconds speed = 78 km / hr = 78 * 5 / 18 m / s = 65 / 3 m / s distance = speed * time = > 800 + x = 65 / 3 ∗ 60 = > 800 + x = 20 ∗ 65 = 1300 = > x = 1300 − 800 = 500 so the length of the tunnel is 500 meters . option c
Answer: c
Problem: how many digits are in ( 8 × 10 ^ 14 ) ( 10 × 10 ^ 10 ) ?
Options: a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28
Rationale: "he question simplifies to ( 8 × 10 ^ 14 ) ( 10 ^ 11 ) = > 8 * 10 ^ 25 = > will contain 25 zeros + 1 digit 8 = > 26 ans c"
Answer: c
Problem: richard walks along sunrise boulevard daily . he starts walking at 07 : 00 from block 10 and walks to block 90 where he turns around and walks back to block 70 , where he stops at 07 : 30 . the blocks along the boulevard are numbered sequentially ( 1 , 2,3 ) , and each block measures 40 meters . what is richard ' s speed in meters per minute ?
Options: a ) 75 , b ) 180 , c ) 198 , d ) 216 , e ) 252
Rationale: total distance from 10 to 90 = 80 + from 90 to 70 = 20 so the dist is 100 × 30 ( per block dist ) speed = 3000 mts / 40 min = 75 m / min a is the answer
Answer: a
Problem: when n is divided by 32 , the remainder is 5 . what is the remainder when 4 n is divided by 8 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "let n = 5 ( leaves a remainder of 5 when divided by 32 ) 4 n = 4 ( 5 ) = 20 , which leaves a remainder of 4 when divided by 8 . answer b"
Answer: b
Problem: a person ' s present age is two - fifth of the age of his mother . after 10 years , he will be one - half of the age of his mother . how old is the mother at present ?
Options: a ) a ) 25 , b ) b ) 40 , c ) c ) 32 , d ) d ) 50 , e ) e ) 28
Rationale: let the mother ' s present age be x years then the person ' s present age = 2 x / 5 ( 2 x / 5 ) + 10 = 1 / 2 ( x + 10 ) 2 ( 2 x + 50 ) = 5 ( x + 10 ) x = 50 answer is d
Answer: d
Problem: | x + 3 | – | 4 - x | = | 5 + x | how many solutions will this equation have ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "you have | x + 3 | - | 4 - x | = | 8 + x | first , look at the three values independently of their absolute value sign , in other words : | x + 3 | - | 4 - x | = | 8 + x | ( x + 3 ) - ( 4 - x ) = ( 8 + x ) now , you ' re looking at x < - 8 , so x is a number less than - 8 . let ' s pretend x = - 10 here to make things a bit easier to understand . when x = - 10 i . ) ( x + 3 ) ( - 10 + 3 ) ( - 7 ) ii . ) ( 4 - x ) ( 4 - [ - 10 ] ) ( double negative , so it becomes positive ) ( 4 + 10 ) ( 14 ) iii . ) ( 8 + x ) ( 8 + - 10 ) ( - 2 ) in other words , when x < - 8 , ( x + 3 ) and ( 8 + x ) are negative . to solve problems like this , we need to check for the sign change . here is how i do it step by step . i . ) | x + 3 | - | 4 - x | = | 8 + x | ii . ) ignore absolute value signs ( for now ) and find the values of x which make ( x + 3 ) , ( 4 - x ) and ( 8 + x ) = to zero as follows : ( x + 3 ) x = - 3 ( - 3 + 3 ) = 0 ( 4 - x ) x = 4 ( 4 - 4 ) = 0 ( 8 + x ) x = - 8 ( 8 + - 8 ) = 4 e"
Answer: e
Problem: if the population of a certain country increases at the rate of one person every 40 seconds , by how many persons does the population increase in 1 hour ?
Options: a ) 90 , b ) 120 , c ) 150 , d ) 180 , e ) 160
Rationale: "answer = 1.5 * 60 = 90 answer is a"
Answer: a
Problem: when positive integer t is divided by 13 , the remainder is 2 . when n is divided by 8 , the remainder is 5 . how many such values are less than 180 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: the equation that can be formed t is 13 x + 2 = 8 y + 5 . . 13 x - 3 = 8 y . . . as we can see x can take only odd values as the rhs will always be even . . also x can take values till 13 as 13 * 14 > 180 . . now we have to substitue x as 1 , 35 , 79 , 1113 . . . once we find 7 fitting in , any other value need not be checked as every 4 th value will give us answer so next value will be 15 . . ans 1 . . b
Answer: b
Problem: a room 11 m 47 cm long and 7 m 77 cm broad is to be paved with square tiles . find the least number of square tiles required to cover the floor .
Options: a ) 636 , b ) 640 , c ) 647 , d ) 651 , e ) 675
Rationale: explanation : area of the room = ( 1147 x 777 ) cm 2 . size of largest square tile = h . c . f . of 1147 cm and 777 cm = 37 cm . area of 1 tile = ( 37 x 37 ) cm 2 . number of tiles required = ( 1147 × 777 ) / ( 37 × 37 ) = 651 answer : option d
Answer: d
Problem: the distance from city a to city b is 180 miles . while driving from city a to city b , cara drives at a constant speed of 30 miles per hour . dan leaves city a 60 minutes after cara . what is the minimum constant speed in miles per hour that dan must exceed in order to arrive in city b before cara ?
Options: a ) 42 , b ) 44 , c ) 46 , d ) 36 , e ) 50
Rationale: "the time it takes cara to drive to city b is 180 / 30 = 6 hours . dan needs to take less than 5 hours for the trip . dan needs to exceed a constant speed of 180 / 5 = 36 miles per hour . the answer is d ."
Answer: d
Problem: difference of two parallel sides of atrapezium is 4 cm . perpendicular distance between them is 10 cm . if the area of the trapezium is 250 cm ^ 2 . find the lengths of the parallel side ?
Options: a ) 20 cm and 21 cm
b ) 25 cm and 23 cm
c ) 27 cm and 23 cm
d ) 30 cm and 34 cm
e ) 28 cm and 36 cm
Rationale: let the two parallel sides of the trapezium be a cm and b cm . then , a - b = 4 - - - - - - ( 1 ) and , ( 1 / 2 ) x ( a + b ) x 10 = 475 = > ( a + b ) = ( ( 250 x 2 ) / 10 ) = > a + b = 50 - - - - - - - ( 2 ) solving 1 and 2 , we get : a = 27 , b = 23 so , the two parallel sides are 27 cm and 23 cm . c
Answer: c
Problem: a cube has a volume of 64 cubic feet . if a similar cube is twice as long , twice as wide , and twice as high , then the volume , in cubic feet of such cube is ?
Options: a ) 24
b ) 48
c ) 64
d ) 80
e ) 512
Rationale: volume = 64 = side ^ 3 i . e . side of cube = 4 new cube has dimensions 8 , 8 , and 8 as all sides are twice of teh side of first cube volume = 8 * 8 * 8 = 512 square feet answer : option e
Answer: e
Problem: the length of the longest tape in cm which can be used to measure exactly , the length 100 cm ; 2 m 25 cm ; and 7 m 80 cm is :
Options: a ) 30 , b ) 5 , c ) 10 , d ) 36 , e ) 25
Rationale: the three lengths in cm are 100 , 225 & 780 . hcf of 100 , 225 & 780 is 5 . hence , the answer is 5 cm . answer : b
Answer: b
Problem: how many positive factors do 180 and 90 have in common ?
Options: a ) 6 , b ) 12 , c ) 16 , d ) 18 , e ) 24
Rationale: "the number of common factors will be same as number of factors of the highest common factor ( hcf ) hcf of 180 and 90 is 90 number of factors of 90 = 12 answer : b"
Answer: b
Problem: the population of a town is 10000 . it increases annually at the rate of 27 % p . a . what will be its population after 2 years ?
Options: a ) 14000 , b ) 14400 , c ) 16129 , d ) 14600 , e ) 14700
Rationale: "formula : 10000 × 127 / 100 × 127 / 100 = 16129 answer : c"
Answer: c
Problem: the price of an item is discounted 10 percent on day 1 of a sale . on day 2 , the item is discounted another 10 percent , and on day 3 , it is discounted an additional 5 percent . the price of the item on day 3 is what percentage of the sale price on day 1 ?
Options: a ) 28 % , b ) 40 % , c ) 85.5 % , d ) 70 % , e ) 72 %
Rationale: "original price = 100 day 1 discount = 10 % , price = 100 - 10 = 90 day 2 discount = 10 % , price = 90 - 9 = 81 day 3 discount = 5 % , price = 81 - 4.05 = 76.95 which is 76.95 / 90 * 100 of the sale price on day 1 = ~ 8 answer c"
Answer: c
Problem: the captain of a cricket team of 11 members is 30 years old and the wicket keeper is 5 years younger . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average of the team ?
Options: a ) 20 , b ) 23 , c ) 32 , d ) 19 , e ) 29
Rationale: "let the average of the whole team be x years . 11 x - ( 30 + 25 ) = 9 ( x - 1 ) = 11 x - 9 x = 46 = 2 x = 46 = > x = 23 so , average age of the team is 23 years . answer : b"
Answer: b
Problem: a sum was put at simple interest at a certain rate for 10 years . had it been put at 5 % higher rate , it would have fetched rs . 300 more . what was the sum ?
Options: a ) s . 1200 , b ) s . 1300 , c ) s . 600 , d ) s . 800 , e ) s . 1200
Rationale: "at 5 % more rate , the increase in s . i for 10 years = rs . 300 ( given ) so , at 5 % more rate , the increase in si for 1 year = 300 / 10 = rs . 30 / - i . e . rs . 30 is 5 % of the invested sum so , 1 % of the invested sum = 30 / 5 therefore , the invested sum = 30 × 100 / 5 = rs . 600 answer : c"
Answer: c
Problem: in an exam 49 % candidates failed in english and 36 % failed in hindi and 15 % failed in both subjects . if the total number of candidates who passed in english alone is 630 . what is the total number of candidates appeared in exam ?
Options: a ) 2000 , b ) 3000 , c ) 3500 , d ) 3800 , e ) 4000
Rationale: not fail in english = 51 % not fail in hindi = 64 % not fail in both = 30 % ( 49 + 36 - 15 ) pass in english only = 51 - 30 = 21 21 / 100 * x = 630 x = 3000 answer : b
Answer: b
Problem: each of the three people individually can complete a certain job in 4 , 5 , and 6 hours , respectively . what is the lowest fraction of the job that can be done in 1 hour by 2 of the people working together at their respective rates ?
Options: a ) 4 / 15 , b ) 7 / 30 , c ) 11 / 30 , d ) 5 / 18 , e ) 7 / 18
Rationale: "the two slowest people work at rates of 1 / 5 and 1 / 6 of the job per hour . the sum of these rates is 1 / 5 + 1 / 6 = 11 / 30 of the job per hour . the answer is c ."
Answer: c
Problem: find the smallest number which when divided by 11 and 13 leaves respective remainders of 4 and 6 .
Options: a ) 187 , b ) 197 , c ) 207 , d ) 136 , e ) 227
Rationale: "let ' n ' is the smallest number which divided by 11 and 13 leaves respective remainders of 4 and 6 . required number = ( lcm of 11 and 13 ) - ( common difference of divisors and remainders ) = ( 143 ) - ( 7 ) = 136 . answer : d"
Answer: d
Problem: in what time will a train 100 meters long cross an electric pole , if its speed is 180 km / hr
Options: a ) 5 seconds , b ) 4.5 seconds , c ) 3 seconds , d ) 2 seconds , e ) none of these
Rationale: "explanation : first convert speed into m / sec speed = 180 * ( 5 / 18 ) = 50 m / sec time = distance / speed = 100 / 50 = 2 seconds answer : d"
Answer: d
Problem: a train consists of 12 boggies , each boggy 15 metres long . the train crosses a telegraph post in 9 seconds . due to some problem , two boggies were detached . the train now crosses a telegraph post in
Options: a ) 18 sec , b ) 7.5 sec , c ) 15 sec , d ) 20 sec , e ) none of these
Rationale: "length of train = 12 ã — 15 = 180 m . then , speed of train = 180 â  „ 9 = 20 m / s now , length of train = 10 ã — 15 = 150 m â ˆ ´ required time = 150 â  „ 20 = 7.5 sec . answer b"
Answer: b
Problem: in a box of 8 pens , a total of 2 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ?
Options: a ) 6 / 11 , b ) 8 / 15 , c ) 9 / 20 , d ) 11 / 25 , e ) 15 / 28
Rationale: "p ( neither pen is defective ) = 6 / 8 * 5 / 7 = 15 / 28 the answer is e ."
Answer: e
Problem: if x is invested in a bank at a rate of simple interest of y % p . a . for two years , then the interest earned is 500 . if x is invested at y % p . a . , for two years when the interest is compounded annually , the interest is 512.50 . what is the value of x ?
Options: a ) 8000 , b ) 6000 , c ) 5000 , d ) 4000 , e ) 3000
Rationale: "simple way to solve this question is to use options . from si , we know that x * y = 25,000 . now , put the value of x = 5000 , we will have y = 5 % to calculate ci , now , we know 1 st year amount = 5000 + 5 % of 5000 = 5250 . 2 nd year , amount = 5250 + 5 % of 5250 = 5512.50 . we can see after 2 years interest = 5512.50 - 5000 = 512.50 hence , it satisfies the question . hence c is the correct answer"
Answer: c
Problem: if 2 x + y = 7 and x + 2 y = 5 , then 5 xy / 3 = ?
Options: a ) a ) 5 , b ) b ) 2 , c ) c ) 17 / 5 , d ) d ) 18 / 5 , e ) e ) 4
Rationale: "2 * ( x + 2 y = 5 ) equals 2 x + 4 y = 10 2 x + 4 y = 10 - 2 x + y = 7 = 3 y = 3 therefore y = 1 plug and solve . . . 2 x + 1 = 7 2 x = 6 x = 3 ( 5 * 3 * 1 ) / 3 = 15 / 3 = 5 a"
Answer: a
Problem: every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 2880 ?
Options: a ) 8100 , b ) 3388 , c ) 7767 , d ) 2009 , e ) 3645
Rationale: "2880 * 9 / 8 * 9 / 8 = 3645 answer : e"
Answer: e
Problem: a man is walking at the rate of 5 km / hr crosses a bridge in 15 minutes . the length of the bridge is
Options: a ) 1000 meters , b ) 1050 meters , c ) 1200 meters , d ) 1250 meters , e ) none of these
Rationale: "explanation : we need to get the answer in meters . so we will first of change distance from km / hour to meter / sec by multiplying it with 5 / 18 and also change 15 minutes to seconds by multiplying it with 60 . answer : d"
Answer: d
Problem: a dishonest dealer professes to sell goods at the cost price but uses a weight of 840 grams per kg , what is his percent ?
Options: a ) 19 , b ) 25 , c ) 77 , d ) 88 , e ) 11
Rationale: "840 - - - 160 100 - - - ? = > 19 % answer : a"
Answer: a
Problem: a train 500 m long passes a man , running at 9 km / hr in the same direction in which the train is going , in 20 seconds . the speed of the train is :
Options: a ) 105 , b ) 95 , c ) 90 , d ) 99 , e ) 100
Rationale: "speed of the train relative to man = 500 / 20 m / sec = 25 m / sec . = 25 x 18 / 5 km / hr = 90 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 9 ) km / hr . x - 9 = 90 = 99 km / hr . answer : d"
Answer: d
Problem: the cost price of a radio is rs . 4800 and it was sold for rs . 4400 , find the loss % ?
Options: a ) 8 , b ) 9 , c ) 7 , d ) 6 , e ) 4
Rationale: "4800 - - - - 400 100 - - - - ? = > 8 % answer : a"
Answer: a
Problem: line m lies in the xy - plane . the y - intercept of line m is - 5 , and line m passes through the midpoint of the line segment whose endpoints are ( 2 , 4 ) and ( 6 , - 8 ) . what is the slope of line m ?
Options: a ) - 3 , b ) - 1 , c ) - 1 / 3 , d ) 0 , e ) undefined
Rationale: "ans : a solution : line m goes through midpoint of ( 2 , 4 ) and ( 6 , - 8 ) . midpoint is ( 4 , - 2 ) as we can see that the y axis of intercept point is ( 0 , - 5 ) means line m is parallel to x axis slope m = - 3 ans : a"
Answer: a
Problem: a certain machine produces 1,100 units of product p per hour . working continuously at this constant rate , this machine will produce how many units of product p in 6 days ?
Options: a ) 7,000 , b ) 24,000 , c ) 40,000 , d ) 100,000 , e ) 158,400
Rationale: since 6 days consist of 24 * 6 hours the total is 144 hours . since every hour the machine produces 1100 units of product p the total product during 144 hours is 144 * 1100 = 158,400 . correct option : e
Answer: e
Problem: linda spent 3 / 4 of her savings on furniture and the rest on a tv . if the tv cost her $ 150 , what were her original savings ?
Options: a ) $ 500 , b ) $ 600 , c ) $ 700 , d ) $ 800 , e ) $ 900
Rationale: "if linda spent 3 / 4 of her savings on furniture , the rest 4 / 4 - 3 / 4 = 1 / 4 on a tv but the tv cost her $ 150 . so 1 / 4 of her savings is $ 150 . so her original savings are 4 times $ 150 = $ 600 correct answer b"
Answer: b
Problem: if 8 people can eat a gallon of ice cream in 10 days , how long would it take 5 people to eat a gallon of ice cream ?
Options: a ) 12 days , b ) 14 days , c ) 16 days , d ) 18 days , e ) 20 days
Rationale: 8 * 10 = 5 * x x = 16 answer : c
Answer: c
Problem: 8 x 2.4 - 5 x 1.4 / 1.5 = ?
Options: a ) 9.46 , b ) 2.03 , c ) 50.4 , d ) 14.65 , e ) 12.85
Rationale: "given expression = ( 19.2 - 5 x 1.4 ) / 1.5 = 14.2 / 1.5 = 14.2 / 1.5 = 9.46 answer is a"
Answer: a
Problem: in what time will a train 20 m long cross an electric pole , it its speed be 144 km / hr ?
Options: a ) 2.5 sec , b ) 2.8 sec , c ) 0.5 sec , d ) 2.3 sec , e ) 1.5 sec
Rationale: "speed = 144 * 5 / 18 = 40 m / sec time taken = 20 / 40 = 0.5 sec . answer : c"
Answer: c
Problem: the sum of number of boys and girls in a school is 150 . if the number of boys is x , then the number of girls becomes x % of the total number of students . the number of boys is ?
Options: a ) 50 , b ) 40 , c ) 60 , d ) 100 , e ) 70
Rationale: "we have x + x % of 150 = 150 x + x / 100 * 150 = 150 5 / 2 * x = 150 x = 150 * 2 / 5 = 60 answer is c"
Answer: c
Problem: two trains a and b are 175 m and 150 m long and are moving at one another at 54 km / hr and 36 km / hr respectively . arun is sitting on coach b 1 of train a . calculate the time taken by arun to completely cross train b .
Options: a ) 10 s , b ) 6 s , c ) 4 s , d ) 8 s , e ) 13 s
Rationale: detailed solution speed of a = 54 ∗ 1000 / 60 ∗ 60 = 15 m / s speed of b = 36 ∗ 1000 / 60 ∗ 60 = 10 m / s relative speed = s 1 + s 2 = 15 + 10 m / s = 25 m / s the length that needs to be crossed = length of train b = 150 m . therefore time taken = 150 / 25 = 6 s . what is the time taken for trains to completely cross each other ? the length that needs to be crossed = 175 + 150 = 325 m . time taken = 325 / 25 = 13 s . correct answer e .
Answer: e
Problem: a train traveling with constant speed crosses a 90 m long platform in 12 seconds and a 120 m long platform in 15 seconds . find the length of the train and its speed .
Options: a ) 30 , b ) 40 , c ) 60 , d ) 50 , e ) none
Rationale: let the length of the train be x m and its speed be y m / sec . then , x / y = 12 = > y = x / 12 ( x + 90 ) / 12 = x + 120 / 15 = > x = 30 m . answer : a
Answer: a
Problem: if the average ( arithmetic mean ) of a and b is 100 , and c – a = 120 , what is the average of b and c ?
Options: a ) 150 , b ) 140 , c ) 160 , d ) 170 , e ) 180
Rationale: "a + b / 2 = 100 = > a + b = 200 a = c - 120 . . . sub this value c - 120 + b = 200 = > c + b = 320 = > c + b / 2 = 160 answer : c"
Answer: c
Problem: how many seconds will a train 130 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph ?
Options: a ) 28 sec , b ) 23 sec , c ) 24 sec , d ) 25 sec , e ) 26 sec
Rationale: "d = 130 + 150 = 280 s = 36 * 5 / 18 = 10 mps t = 280 / 10 = 28 sec a"
Answer: a
Problem: a farmer spent $ 35 on feed for chickens and goats . he spent 40 % money on chicken feed , which he bought at a 20 % discount off the full price , and spent the rest on goat feed , which he bought at full price . if the farmer had paid full price for both the chicken feed and the goat feed , what amount would he have spent on the chicken feed and goat feed combined ?
Options: a ) $ 37.80 , b ) $ 38.50 , c ) $ 39.20 , d ) $ 39.50 , e ) $ 40.60
Rationale: "a farmer spent 40 % money on chicken feed , so he spent 0.4 * $ 35 = $ 14 on chicken feed , thus he spent the remaining 35 - 14 = $ 21 on goat feed . now , since he bought chicken feed at a 20 % discount then the original price of it was x * 0.8 = $ 14 - - > x = $ 17.5 . therefore if the farmer had paid full price for both the chicken feed and the goat feed , then he would he have spent 17.5 + 21 = $ 38.5 . answer : b ."
Answer: b
Problem: find the 18 th term of an arithmetic progression whose first term is 4 and the common difference is 5 .
Options: a ) 45 , b ) 38 , c ) 72 , d ) 74 , e ) 78
Rationale: "n th term of a . p = a + ( n - 1 ) * d = 4 + ( 18 - 1 ) * 4 , = 4 + 68 = 72 . answer : c"
Answer: c
Problem: if m is an integer such that ( - 2 ) ^ 2 m = 2 ^ ( 18 - m ) then m = ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "2 m = 18 - m 3 m = 18 m = 6 the answer is c ."
Answer: c
Problem: in a school of 850 boys , 44 % of muslims , 32 % hindus , 10 % sikhs and the remaining of other communities . how many belonged to the other communities ?
Options: a ) a ) 125 , b ) b ) 119 , c ) c ) 153 , d ) d ) 721 , e ) e ) 159
Rationale: "44 + 32 + 10 = 86 % 100 – 84 = 14 % 850 * 14 / 100 = 119 answer : b"
Answer: b
Problem: in 10 years , a will be twice as old 5 as b was 10 years ago . if a is now 12 years older than b , the present age of b is
Options: a ) 35 , b ) 37 , c ) 39 , d ) 41 , e ) 42
Rationale: "explanation : let b ' s age = x years . then , as age = ( x + 12 ) years . ( x + 12 + 10 ) = 2 ( x — 10 ) hence x = 42 . present age of b = 42 years answer : option e"
Answer: e
Problem: drum x is 1 / 2 full of oil and drum y , which has twice the capacity of drum x , is 1 / 5 full of oil . if all of the oil in drum x is poured into drum y , then drum y will be filled to what capacity ?
Options: a ) 3 / 10 , b ) 7 / 10 , c ) 9 / 10 , d ) 9 / 20 , e ) 13 / 20
Rationale: "( 1 / 2 ) x = ( 1 / 4 ) y ( 1 / 4 ) y + ( 1 / 5 ) y = ( 9 / 20 ) y the answer is d ."
Answer: d
Problem: the average age of 3 boys is 120 years and their ages are in proportion 2 : 6 : 8 . what is the age in years of the youngest boy ?
Options: a ) 10 , b ) 9 , c ) 15 , d ) 6 , e ) 12
Rationale: 2 x + 6 x + 8 x = 120 x = 7.5 2 x = 15 answer : c
Answer: c
Problem: for 2 consecutive yrs , my incomes are in the ratio of 4 : 7 and expenses in the ratio of 3 : 5 . if my income in the 2 nd yr is rs . 42000 & my expenses in the first yr in rs . 25000 , my total savings for the two - year is
Options: a ) s . 6000 , b ) s . 9000 , c ) s . 9900 , d ) s . 9990 , e ) s . 10000
Rationale: "sol . income in first year = * x 42000 = rs . 24000 expenses in second year = \ x 21000 = rs . 35000 total savings = total income - total expenses = ( 42000 + 24000 ) - ( 25000 + 35000 ) = 66000 - 60000 = rs . 6000 a"
Answer: a
Problem: rahul played weel in this season . his current batting averagge is 50 . if he score 78 runs in today match . his batting average will become 54 . how many matches had he played in this season .
Options: a ) 8 , b ) 10 , c ) 9 , d ) 6 , e ) 5
Rationale: "50 x + 78 = 54 ( x + 1 ) = > 4 x = 24 = > x = 6 answer : d"
Answer: d
Problem: in 2 bags , there are to be put together 5 red and 12 white balls , neither bag being empty . how must the balls be divided so as to give a person who draws 1 ball from either bag - the greatest chance of drawing a red ball ?
Options: a ) 1 / 8 , b ) 2 / 8 , c ) 3 / 8 , d ) 4 / 8 , e ) 5 / 8
Rationale: "greatest chance . 1 / 2 * 1 + 1 / 2 * 4 / 16 = 5 / 8 answer : e"
Answer: e
Problem: a circular well with a diameter of 6 metres , is dug to a depth of 24 metres . what is the volume of the earth dug out ?
Options: a ) 678.6 m 3 , b ) 36 m 3 , c ) 40 m 3 , d ) 44 m 3 , e ) none
Rationale: "solution volume = π r 2 h ‹ = › ( 22 / 7 × 3 × 3 × 24 ) m 3 ‹ = › 678.6 m 3 . answer a"
Answer: a
Problem: a man cycling along the road noticed that every 12 minutes a bus overtakes him and every 4 minutes he meets an oncoming bus . if all buses and the cyclist move at a constant speed , what is the time interval between consecutive buses ?
Options: a ) 5 minutes , b ) 6 minutes , c ) 8 minutes , d ) 9 minutes , e ) 10 minutes
Rationale: "let ' s say the distance between the buses is d . we want to determine interval = \ frac { d } { b } , where b is the speed of bus . let the speed of cyclist be c . every 12 minutes a bus overtakes cyclist : \ frac { d } { b - c } = 12 , d = 12 b - 12 c ; every 4 minutes cyclist meets an oncoming bus : \ frac { d } { b + c } = 4 , d = 4 b + 4 c ; d = 12 b - 12 c = 4 b + 4 c , - - > b = 2 c , - - > d = 12 b - 6 b = 6 b . interval = \ frac { d } { b } = \ frac { 6 b } { b } = 6 answer : b ( 6 minutes ) ."
Answer: b
Problem: the average salary of a person for the months of january , february , march and april is rs . 8000 and that for the months february , march , april and may is rs . 8900 . if his salary for the month of may is rs . 6500 , find his salary for the month of january ?
Options: a ) s . 2900 , b ) s . 3570 , c ) s . 4500 , d ) s . 4550 , e ) s . 2500
Rationale: "sum of the salaries of the person for the months of january , february , march and april = 4 * 8000 = 32000 - - - - ( 1 ) sum of the salaries of the person for the months of february , march , april and may = 4 * 8900 = 35600 - - - - ( 2 ) ( 2 ) - ( 1 ) i . e . may - jan = 3600 salary of may is rs . 6500 salary of january = rs . 2900 answer : a"
Answer: a
Problem: ( 3 x + 4 ) ( 2 x - 5 ) = ax ^ 2 + kx + n . what is the value of a - n + k ?
Options: a ) 5 , b ) 8 , c ) 9 , d ) 10 , e ) 15
Rationale: "expanding we have 6 x ^ 2 - 15 x + 8 x - 20 6 x ^ 2 - 7 x - 20 taking coefficients , a = 6 , k = - 7 , n = - 20 therefore a - n + k = 6 - ( - 20 ) - 11 = 26 - 11 = 15 the answer is e ."
Answer: e
Problem: a shopkeeper has 280 kg of apples . he sells 45 % of these at 20 % profit and remaining 60 % at 30 % profit . find his % profit on total .
Options: a ) 24 % , b ) 25 % , c ) 27 % , d ) 28 % , e ) 35 %
Rationale: "if the total quantity was 100 then 45 x 20 % + 60 x 30 % = 27 this profit will remain same for any total quantity unless the % of products remains the same . hence ' c ' is the answer"
Answer: c
Problem: the majority owner of a business received 25 % of the profit , with each of 4 partners receiving 25 % of the remaining profit . if the majority owner and two of the owners combined to receive $ 40,000 , how much profit did the business make ?
Options: a ) $ 44,000 , b ) $ 54,000 , c ) $ 64,000 , d ) $ 84,000 , e ) $ 104,000
Rationale: "let p be the total profit . p / 4 + 1 / 2 * ( 3 p / 4 ) = p / 4 + 3 p / 8 = 5 p / 8 = 40000 p = $ 64,000 the answer is c ."
Answer: c
Problem: 70 % of the employees of a company are men . 50 % of the men in the company speak french and 40 % of the employees of the company speak french . what is % of the women in the company who do not speak french ?
Options: a ) 4 % , b ) 10 % , c ) 83.33 % , d ) 90.33 % , e ) 20 %
Rationale: "no of employees = 100 ( say ) men = 70 women = 30 men speaking french = 0.5 * 70 = 35 employees speaking french = 0.4 * 100 = 40 therefore women speaking french = 40 - 35 = 5 and women not speaking french = 30 - 5 = 25 % of women not speaking french = 25 / 30 * 100 = 83.33 % answer c"
Answer: c
Problem: a and b are partners in a business . a contributes 1 / 4 of the capital for 15 months and b received 2 / 3 of the profit . for how long b ' s money was used ?
Options: a ) 10 , b ) 37 , c ) 27 , d ) 18 , e ) 19
Rationale: let the total profit be rs . z . then , b ' s share = rs . 2 z / 3 , a ' s share = rs . ( z - 2 z / 3 ) = rs . z / 3 . a : b = z / 3 : 2 z / 3 = 1 : 2 let the total capital be rs , x and suppose b ' s money was used for x months . then . ( 1 ( x ) / 4 * 15 ) / ( 3 x ) / 4 * y ) = 1 / 2 < = > y = ( 15 * 2 / 3 ) = 10 . thus , b ' s money was used for 10 months . answer : a ) 10 months
Answer: a
Problem: 3 * 15 + 3 * 16 + 3 * 19 + 11 = ?
Options: a ) 125 , b ) 126 , c ) 130 , d ) 148 , e ) 161
Rationale: "3 * 15 + 3 * 16 + 3 * 19 + 11 = 45 + 48 + 57 + 11 = 161 the answer is e ."
Answer: e