regisss/math_qa huggingface dataset:
Problem: sari and ken climb up a mountain . at night , they camp together . on the day they are supposed to reach the summit , sari wakes up at 05 : 00 and starts climbing at a constant pace . ken starts climbing only at 07 : 00 , when sari is already 700 meters ahead of him . nevertheless , ken climbs at a constant pace of 500 meters per hour , and reaches the summit before sari . if sari is 50 meters behind ken when he reaches the summit , at what time did ken reach the summit ?
Options: a ) 13 : 00 , b ) 13 : 30 , c ) 14 : 00 , d ) 15 : 00 , e ) 12 : 00
Rationale: "both sari and ken climb in the same direction . speed of sari = 700 / 2 = 350 meters / hr ( since she covers 700 meters in 2 hrs ) speed of ken = 500 meters / hr at 8 : 00 , distance between ken and sari is 700 meters . ken needs to cover this and another 50 meters . time he will take = total distance to be covered / relative speed = ( 700 + 50 ) / ( 500 - 350 ) = 5 hrs starting from 7 : 00 , in 5 hrs , the time will be 12 : 00 answer ( e )"
Answer: e
Problem: the mean of 50 observations was 36 . it was found later that an observation 48 was wrongly taken as 23 . the corrected new mean is ?
Options: a ) 36.6 , b ) 36.1 , c ) 36.5 , d ) 36.2 , e ) 36.9
Rationale: "correct sum = ( 36 * 50 + 48 - 23 ) = 1825 . correct mean = 1825 / 50 = 36.5 answer : c"
Answer: c
Problem: it takes 3 workers a total of 12 hours to build a giant machine with each worker working at the same rate . if 4 workers start to build the machine at 11 : 00 am , and one extra worker per hour is added beginning at 3 : 00 pm , at what time will the machine be complete ?
Options: a ) 5 : 30 , b ) 5 : 45 , c ) 6 : 00 , d ) 6 : 15 , e ) 6 : 30
Rationale: "3 workers build 1 / 12 of a machine in one hour . 1 worker builds 1 / 36 of a machine in one hour . in the first 4 hours , 4 workers build 4 * ( 1 / 36 ) * 4 = 16 / 36 of a machine from 3 : 00 to 4 : 00 , 5 workers build another 5 / 36 . the total is 21 / 36 . from 4 : 00 to 5 : 00 , 6 workers build another 6 / 36 . the total is 27 / 36 . from 5 : 00 to 6 : 00 , 7 workers build another 7 / 36 . the total is 34 / 36 . to build another 2 / 36 , 8 workers need ( 2 / 8 ) * 60 minutes which is 15 minutes . the machine is complete at 6 : 15 . the answer is d ."
Answer: d
Problem: buffalo gives 4 liter milk , cow gives ( 1 / 2 ) liter milk and goat gives 1 / 4 liter milk . you have to get 20 liter milk by 20 animals . what is the number of cows ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: "assume number of respective animals are x , y , z . x + y + z = 20 - - - ( 1 ) as the total number of animal has to be 20 amt of milk will be 4 x + ( 1 / 2 ) y + ( 1 / 4 ) z = 20 - - - ( 2 ) solving equation 1 and 2 we get 15 x + y = 60 - - - - ( 3 ) since buffalo gives 4 litre and total milk is 20 , x < 5 but from eq 3 , x can not be more than 4 ; further if x = 1 or 2 ; y > 20 . . . not possible , since total animal is 20 thus , x = 3 , y = 15 , z = 2 15 cows answer : d"
Answer: d
Problem: claire has a total of 80 pets consisting of gerbils and hamsters only . one - quarter of the gerbils are male , and one - third of the hamsters are male . if there are 25 males altogether , how many gerbils does claire have ?
Options: a ) 39 , b ) 50 , c ) 54 , d ) 57 , e ) 36
Rationale: "g + h = 80 . . . 1 ; g / 4 + h / 3 = 25 . . . . 2 or 3 g + 4 h = 25 * 12 = 300 g = 80 - h or 3 ( 80 - h ) + 4 h = 300 h = 300 - 240 = 60 then g = 96 - 60 = 36 e"
Answer: e
Problem: a , band c can do a piece of work in 11 days , 45 days and 55 days respectively , working alone . how soon can the work be done if a is assisted by band c on alternate days ?
Options: a ) 7 days , b ) 8 days , c ) 9 days , d ) 10 days , e ) 11 days
Rationale: "( a + b ) ' s 1 day ' s work = 1 / 11 + 1 / 45 = 56 / 495 ( a + c ) ' s 1 day ' s work = 1 / 11 + 1 / 55 = 6 / 55 work done in 2 day ' s = 56 / 495 + 6 / 55 = 2 / 9 2 / 9 th work done in 2 days work done = 9 / 2 * 2 = 9 days answer : c"
Answer: c
Problem: 15 people can write 90 book in 20 days working 7 hour a day . then in how many day 240 can be written by 72 people ?
Options: a ) 240 / 9 , b ) 309 / 28 , c ) 100 / 9 , d ) 200 / 9 , e ) 339 / 26
Rationale: "work per day epr hour per person = 90 / ( 20 * 7 * 15 ) / / eq - 1 people = 72 ; let suppose day = p ; per day work for 8 hours acc . to condition work per day epr hour per person = 240 / ( p * 7 * 72 ) / / eq - 2 eq - 1 = = eq - 2 ; p = 100 / 9 answer : c"
Answer: c
Problem: a number , x is chosen at random from the set of positive integers less than 10 . what is the probability that ( 7 / x ) > x ?
Options: a ) 1 / 5 , b ) 7 / 9 , c ) 1 / 3 , d ) 2 / 3 , e ) 2 / 9
Rationale: "number x has to be chosen from numbers 1 - 9 ( 7 / x ) > x = > 7 > x ^ 2 = > x ^ 2 - 7 < 0 x can have 2 values only 1 , 2 therefore , probability = 2 / 9 answer e"
Answer: e
Problem: a factory producing tennis balls stores them in either big boxes , 25 balls per box , or small boxes , with 17 balls per box . if 94 freshly manufactured balls are to be stored , what is the least number of balls that can be left unboxed ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "there is no way to store 94 balls without leftovers : 94 − 0 ∗ 25 = 94 - 94 − 2 ∗ 25 = 44 , 94 − 3 ∗ 25 = 19 are not divisible by 17 . 93 balls can be stored successfully : 93 − 1 ∗ 25 = 68 is divisible by 17 . thus , 93 = 1 ∗ 25 + 4 ∗ 17 and we need 1 big box and 4 small boxes . answer : b"
Answer: b
Problem: what is x if x + 3 y = 33 and y = 10 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "substitute y by 10 in x + 3 y = 33 x + 3 ( 10 ) = 33 x + 30 = 33 if we substitute x by 3 in x + 30 = 33 , we have 3 + 30 = 33 . hence x = 3 correct answer c"
Answer: c
Problem: a shopkeeper sold 50 articles at the cost price of 60 articles . then find the profit % or lost %
Options: a ) 20 % , b ) 22 % , c ) 25 % , d ) 30 % , e ) 35 %
Rationale: "here 50 articles selling price = 60 articles cost price so the difference = 60 - 50 = 10 % of profit = 10 * 100 / 50 = 20 % correct option is a"
Answer: a
Problem: the owner of a furniture shop charges his customer 20 % more than the cost price . if a customer paid rs . 3000 for a computer table , then what was the cost price of the computer table ?
Options: a ) 2500 , b ) 2772 , c ) 1991 , d ) 6725 , e ) 2099
Rationale: "cp = sp * ( 100 / ( 100 + profit % ) ) = 3000 ( 100 / 120 ) = rs . 2500 . answer : a"
Answer: a
Problem: suresh can complete a job in 15 hours . ashutosh alone can complete the same job in 20 hours . suresh works for 9 hours and then the remaining job is completed by ashutosh . how many hours will it take ashutosh to complete the remaining job alone ?
Options: a ) 4 , b ) 5 , c ) 8 , d ) 12 , e ) none of these
Rationale: the part of job that suresh completes in 9 hours = 9 â  „ 15 = 3 â  „ 5 remaining job = 1 - 3 â  „ 5 = 2 â  „ 5 remaining job can be done by ashutosh in 2 â  „ 5 ã — 20 = 8 hours answer c
Answer: c
Problem: sonika deposited rs . 9000 which amounted to rs . 10200 after 3 years at simple interest . had the interest been 2 % more . she would get how much ?
Options: a ) 9680 , b ) 2277 , c ) 2999 , d ) 10700 , e ) 10740
Rationale: "( 9000 * 3 * 2 ) / 100 = 540 10200 - - - - - - - - 10740 answer : e"
Answer: e
Problem: jerry ’ s average ( arithmetic mean ) score on the first 3 of 4 tests is 85 . if jerry wants to raise his average by 3 points , what score must he earn on the fourth test ?
Options: a ) 97 , b ) 89 , c ) 90 , d ) 93 , e ) 95
Rationale: "total score on 3 tests = 85 * 3 = 255 jerry wants the average to be = 88 hence total score on 4 tests should be = 88 * 4 = 352 score required on the fourth test = 352 - 255 = 97 option a"
Answer: a
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 4 points if you must draw exactly 2 “ low ” cards ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
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 3 times . as a result , the formula is : 3 ! / 2 ! which represents ( 3 * 2 * 1 ) / ( 2 * 1 ) which simplifies to just 4 , giving you answer c ."
Answer: c
Problem: calculate how much time could be saved if the train would run at its usual speed , given that it ran at 4 / 9 of its own speed and got to its destination in 13 hours ?
Options: a ) 1.22 hrs , b ) 2.22 hrs , c ) 5.22 hrs , d ) 6.22 hrs , e ) 7.22 hrs
Rationale: "new speed = 4 / 9 of usual speed new time = 4 / 9 of usual time 4 / 9 of usual time = 13 hrs usual time = 13 * 4 / 9 = 5.78 hrs time saved = 13 - 5.78 = 7.22 hrs answer is e"
Answer: e
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 15.3 years . the ration of the number of boys to the number of girls in the class is ?
Options: a ) 5 : 6 , b ) 2 : 3 , c ) 2 : 5 , d ) 2 : 1 , e ) 2 : 4
Rationale: "let the ratio be k : 1 . then , k * 16.4 + 1 * 15.3 = ( k + 1 ) * 15.8 = ( 16.4 - 15.8 ) k = ( 15.8 - 15.3 ) = k = 0.5 / 0.6 = 5 / 6 required ratio = 5 / 6 : 1 = 5 : 6 . answer : a"
Answer: a
Problem: a boy is travelling from his home to school at 6 km / hr and reached 7 min late . next day he travelled at 12 km / hr and reached 8 min early . distance between home and school ?
Options: a ) 2 km , b ) 3 km , c ) 4 km , d ) 5 km , e ) 6 km
Rationale: "let the distance be x t 1 = x / 6 hr t 2 = x / 12 hr difference in time = 7 + 8 = 15 = 1 / 4 hr x / 6 - x / 12 = 1 / 4 x / 12 = 1 / 4 x = 3 km answer is b"
Answer: b
Problem: 44 cubic centimetres of silver is drawn into a wire 1 mm in diameter . the length of the wire in metres will be :
Options: a ) 56 m , b ) 88 m , c ) 120 m , d ) 137 m , e ) none
Rationale: "sol . let the length of the wire b h . radius = 1 / 2 mm = 1 / 20 cm . then , 22 / 7 * 1 / 20 * 1 / 20 * h = 44 ⇔ = [ 44 * 20 * 20 * 7 / 22 ] = 5600 cm = 56 m . answer a"
Answer: a
Problem: a boat can travel with a speed of 24 km / hr in still water . if the speed of the stream is 4 km / hr , find the time taken by the boat to go 84 km downstream
Options: a ) 3 hours , b ) 4 hours , c ) 5 hours , d ) 6 hours , e ) 7 hours
Rationale: "explanation : speed of the boat in still water = 24 km / hr speed of the stream = 4 km / hr speed downstream = ( 22 + 5 ) = 28 km / hr distance travelled downstream = 84 km time taken = distance / speed = 84 / 28 = 3 hours answer : option a"
Answer: a
Problem: if 75 % of a boys answered the first question on a certain test correctly , 55 % answered the second question on the test correctly , and 20 % answered neither of the questions correctly , what % answered both correctly ?
Options: a ) 10 % , b ) ( 8 ) 20 % , c ) 50 % , d ) 60 % , e ) 65 %
Rationale: { total } = { first } + { second } - { both } + { neither } 100 % = 75 % + 55 % - { both } + 20 % - - > { both } = 50 % . answer : c
Answer: c
Problem: the sum of ages of 5 children born at the intervals of 3 years each is 50 years . find out the age of the youngest child ?
Options: a ) 9 , b ) 8 , c ) 7 , d ) 6 , e ) 4
Rationale: let the age of the youngest child = x then , the ages of 5 children can be written as x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 50 ⇒ 5 x + 30 = 50 ⇒ 5 x = 20 ⇒ x = 205 = 4 answer is e .
Answer: e
Problem: if the volume of two cubes are in the ratio 27 : 8 , the ratio of their edges is :
Options: a ) 3 : 1 , b ) 3 : 2 , c ) 3 : 5 , d ) 3 : 7 , e ) none of these
Rationale: "explanation : let the edges be a and b of two cubes , then a 3 / b 3 = 27 / 8 = > ( a / b ) 3 = ( 3 / 2 ) 3 a / b = 3 / 2 = > a : b = 3 : 2 option b"
Answer: b
Problem: a trained covered x km at 40 kmph and another 2 x km at 20 kmph . find the average speed of the train in covering the entire 6 x km .
Options: a ) 40 kmph , b ) 45 kmph , c ) 48 kmph , d ) 50 kmph , e ) 55 kmph
Rationale: "total time taken = x / 40 + 2 x / 20 hours = 5 x / 40 = x / 8 hours average speed = 6 x / ( x / 8 ) = 48 kmph answer : c"
Answer: c
Problem: mary works in a restaurant a maximum of 45 hours . for the first 20 hours , she is paid $ 8 per hour . for each overtime hour , she is paid at a rate which is 25 % higher than her regular rate . how much mary can earn in a week ?
Options: a ) 300 , b ) 420 , c ) 410 , d ) 320 , e ) 400
Rationale: "mary receives $ 8 ( 20 ) = $ 160 for the first 20 hours . for the 25 overtime hours , she receives $ 8 ( 0.25 ) + $ 8 = $ 10 per hour , that is $ 10 ( 25 ) = $ 250 . the total amount is $ 160 + $ 250 = $ 410 answer c 410 ."
Answer: c
Problem: a 20 % stock yielding 8 % is quoted at ?
Options: a ) 165 , b ) 170 , c ) 250 , d ) 180 , e ) 185
Rationale: "assume that face value = rs . 100 as it is not given to earn rs . 8 , money invested = rs . 100 to earn rs . 20 , money invested = 100 × 20 / 8 = rs . 250 ie , market value of the stock = rs . 250 answer is c ."
Answer: c
Problem: two stations a and b are 110 km apart on a straight line . one train starts from a at 9 a . m . and travels towards b at 20 kmph . another train starts from b at 8 a . m . and travels towards a at a speed of 25 kmph . at what time will they meet ?
Options: a ) 11 , b ) 10 , c ) 8 , d ) 12 , e ) 15
Rationale: "suppose they meet x hours after 9 a . m . distance covered by a in x hours = 20 x km . distance covered by b in ( x - 1 ) hours = 25 ( x - 1 ) km . therefore 20 x + 25 ( x - 1 ) = 110 45 x = 135 x = 3 . so , they meet at 12 a . m . answer : d"
Answer: d
Problem: annie and sam set out together on bicycles traveling at 15 and 12 km per hour respectively . after 40 minutes , annie stops to fix a flat tire . if it takes annie 25 minutes to fix the flat tire and sam continues to ride during this time , how many minutes will it take annie to catch up with sam assuming that annie resumes riding at 15 km per hour ?
Options: a ) 20 , b ) 40 , c ) 60 , d ) 80 , e ) 100
Rationale: "annie gains 3 km per hour ( or 1 km every 20 minutes ) on sam . after 40 minutes annie is 2 km ahead . sam rides 1 km every 5 minutes . in the next 25 minutes , sam rides 5 km so sam will be 3 km ahead . it will take annie 60 minutes to catch sam . the answer is c ."
Answer: c
Problem: if 5 a = 3125 , then the value of 5 ( a - 3 ) is
Options: a ) 25 , b ) 50 , c ) 250 , d ) 300 , e ) none
Rationale: "sol . 5 a = 3125 = 5 a = 55 a = 5 . 5 ( 1 - 3 ) = 5 ( 5 - 3 ) = 5 ( 2 ) = 25 . answer a"
Answer: a
Problem: if the area of a circle is 100 pi square feet , find its circumference .
Options: a ) 65 pi feet , b ) 20 pi feet , c ) 42 pi feet , d ) 18 pi feet , e ) 64 pi feet
Rationale: "the area is given by pi * r * r . hence pi * r * r = 100 pi r * r = 100 ; hence r = 10 feet the circumference is given by 2 * pi * r = 2 * pi * 10 = 20 pi feet correct answer b"
Answer: b
Problem: a train of length 250 m runs at a speed of 70 km / hr . what will be the time taken to cross any stationary object standing at the railway station ?
Options: a ) 20 sec , b ) 17.23 sec , c ) 12.86 sec , d ) 9.5 sec , e ) 8.5 sec
Rationale: explanation : length of train = 250 m , speed of train = 70 km / hr length of train is always considered as distance , and hence here distance = 250 m 1 ) first convert speed of km / hr into m / s speed of train = 70 x 5 = 19.44 m / s 18 2 ) we know that , speed = distance / time time taken to cross stationary object = 250 / 19.44 time taken to cross stationary object = 12.86 sec answer is c
Answer: c
Problem: two pipes a and b can fill a tank in 4 and 5 hours respectively . if they are turned up alternately for one hour each , the time taken to fill the tank is ?
Options: a ) 4 hrs 29 min , b ) 4 hrs 24 min , c ) 8 hrs 24 min , d ) 4 hrs 44 min , e ) 5 hrs 24 min
Rationale: 1 / 4 + 1 / 5 = 9 / 20 20 / 9 = 2 2 / 9 9 / 20 * 2 = 9 / 10 - - - - 4 hours wr = 1 - 9 / 10 = 1 / 10 1 h - - - - 1 / 4 ? - - - - - 1 / 10 2 / 5 * 60 = 24 = 4 hrs 24 min answer : b
Answer: b
Problem: if a ( a - 6 ) = 27 and b ( b - 6 ) = 27 , where a ≠ b , then a + b =
Options: a ) − 48 , b ) − 2 , c ) 6 , d ) 46 , e ) 48
Rationale: "i . e . if a = - 3 then b = 9 or if a = 9 then b = - 3 but in each case a + b = - 3 + 9 = 6 answer : option c"
Answer: c
Problem: when n is divided by 5 the remainder is 3 . what is the remainder when ( n - 1 ) ^ 2 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: n = 5 x + 3 , for some integer x ( n - 1 ) ^ 2 = ( 5 x + 2 ) ^ 2 = 5 y + 4 , for some integer y when we divide this by 5 , the remainder is 4 . the answer is e .
Answer: e
Problem: how many 1 / 12 s are there in 37 1 / 2 ?
Options: a ) 350 , b ) 450 , c ) 500 , d ) 650 , e ) 700
Rationale: "required number = ( 75 / 2 ) / ( 1 / 12 ) = ( 75 / 2 x 12 / 1 ) = 450 . answer : b"
Answer: b
Problem: . the price of commodity p increases by 40 paise every year , while the price of commodity q increases by 15 paise every year . if in 2001 , the price of commodity p was rs . 4.20 and that of q was rs . 6.30 , in which year commodity p will cost 40 paise more than the commodity q ?
Options: a ) 2008 , b ) 2009 , c ) 2010 , d ) 2011 , e ) none of these
Rationale: explanation : let the commodity p costs 40 paise more than the commodity q after n years price of the commodity p in 2001 = rs . 4.20 since the price of the commodity p increases by rs 0.40 every year , price of the commodity p after n years from 2001 = rs . 4.20 + ( n × . 40 ) price of the commodity q in 2001 = rs . 6.30 since the price of the commodity q increases by rs 0.15 every year , price of the commodity q after n years from 2001 = rs . 6.30 + ( n × . 15 ) since the commodity p costs rs . 0.40 more that the commodity q after n years from 2001 , 4.20 + ( n × . 40 ) = 6.30 + ( n × . 15 ) + 0.40 = > ( 40 n - . 15 n ) = 6.30 - 4.20 + 0.40 = 2.5 = > . 25 n = 2.5 ⇒ n = 2.5 / . 25 = 250 / 25 = 101.15 ¯ = > commodity p costs rs . 0.40 more that the commodity q after 10 years from 2001 . i . e . , in 2011 . answer : option d
Answer: d
Problem: a wholesaler wishes to sell 100 pounds of mixed nuts at $ 2.50 a pound . she mixes peanuts worth $ 1.50 a pound with cashews worth $ 7.00 a pound . how many pounds of cashews must she use ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 60
Rationale: "from the question stem we know that we need a mixture of 100 pounds of peanuts and cashews . if we represent peanuts as x and cashews as y , we get x + y = 100 . since the wholesaler wants to sell the mixture of 100 pounds @ $ 2.50 , we can write this as : $ 2.5 * ( x + y ) = $ 1.5 x + $ 4 y from the equation x + y = 100 , we can rewrite y as y = 100 - x and substitute this into our equation to get : $ 2.5 * ( x + 100 - x ) = $ 1.5 x + $ 4 ( 100 - x ) if you solve for x , you will get x = 60 , and therefore y = 40 . so the wholesaler must use 40 pounds of cashews . you can substitute into the original equation to see that : $ 250 = $ 1.5 ( 60 ) + $ 4 ( 40 ) answer is d ."
Answer: d
Problem: when positive integer n is divided by 5 , the remainder is 1 . when n is divided by 7 , the remainder is 3 . what is the smallest positive integer k such that k + n is a multiple of 39 ?
Options: a ) 3 , b ) 8 , c ) 12 , d ) 32 , e ) 35
Rationale: "n = 5 p + 1 = 6,11 , 16,21 , 26,31 n = 7 q + 3 = 3 , 10,17 , 24,31 = > n = 39 m + 31 to get this , we need to take lcm of co - efficients of p and q and first common number in series . so we need to add 8 more to make it 39 m + 39 answer - b"
Answer: b
Problem: a rectangular region has a fence along three sides and a wall along the fourth side . the fenced side opposite the wall is twice the length of each of the other two fenced sides . if the area of the rectangular region is 800 square feet , what is the total length of the fence , in feet ?
Options: a ) 40 , b ) 80 , c ) 100 , d ) 120 , e ) 200
Rationale: "two sides each = x the third = 2 x and the wall length is thus 2 x too x * 2 x = 2 x ^ 2 = 800 ie x ^ 2 = 400 ie x = 20 l = 40 w = 20 total length of fence = 2 * 20 + 40 = 80 my answer is b"
Answer: b
Problem: if a certain coin is flipped , the probability that the coin will land heads is 1 / 2 . if the coin is flipped 6 times , what is the probability that it will land heads up on the first 3 flips but not on the last 3 flips ?
Options: a ) 1 / 8 , b ) 1 / 16 , c ) 1 / 32 , d ) 1 / 64 , e ) 1 / 128
Rationale: "p ( hhhttt ) = 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 64 the answer is d ."
Answer: d
Problem: a merchant marks his goods up by 50 % and then offers a discount of 20 % on the marked price . what % profit does the merchant make after the discount ?
Options: a ) 20 % , b ) 25 % , c ) 69 % , d ) 31 % , e ) 19 %
Rationale: "let the price be 100 . the price becomes 150 after a 50 % markup . now a discount of 20 % on 150 . profit = 120 - 100 20 % answer a"
Answer: a
Problem: a number when divided by a divisor leaves a remainder of 27 . when twice the original number is divided by the same divisor , the remainder is 11 . what is the value of the divisor ?
Options: a ) 12 , b ) 13 , c ) 35 , d ) 40 , e ) 59
Rationale: "let the number is n , the divisor = d , i will make the two equations - n = xd + 27 2 n = yd + 11 where x and y are integers solving them : d ( y - 2 x ) = 40 as d is also integer and 40 is a prime number , the d should be 40 to satisfy the above equation . hence answer is ' d '"
Answer: d
Problem: the triplicate ratio of 1 : 6 is ?
Options: a ) 1 : 7 , b ) 1 : 8 , c ) 1 : 3 , d ) 1 : 1 , e ) 1 : 216
Rationale: "1 ^ 3 : 6 ^ 3 = 1 : 216 answer : e"
Answer: e
Problem: for a race a distance of 224 meters can be covered by p in 14 seconds and q in 32 seconds . by what distance does p defeat q eventually ?
Options: a ) 232 m , b ) 288 m , c ) 324 m , d ) 231 m , e ) 236 m
Rationale: explanation : this is a simple speed time problem . given conditions : = > speed of p = 224 / 14 = 16 m / s = > speed of q = 224 / 32 = 7 m / s = > difference in time taken = 18 seconds therefore , distance covered by p in that time = 16 m / s x 18 seconds = 288 metres answer : b
Answer: b
Problem: in an office , totally there are 2200 employees and 40 % of the total employees are males . 30 % of the males in the office are at - least 50 years old . find the number of males aged below 50 years ?
Options: a ) 661 , b ) 600 , c ) 620 , d ) 616 , e ) none of these
Rationale: "number of male employees = 2200 * 40 / 100 = 880 required number of male employees who are less than 50 years old = 880 * ( 100 - 30 ) % = 880 * 75 / 100 = 616 . answer : d"
Answer: d
Problem: the sum of ages of 5 children born at theintervals of 3 years each is 50 years . what is the age of the youngest child ?
Options: a ) 4 , b ) 5 , c ) 9 , d ) 8 , e ) 10
Rationale: "the age of children x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 50 5 x = 20 , x = 4 . correct answer ( a )"
Answer: a
Problem: if jake loses 35 pounds , he will weigh thrice as much as his sister . together they now weigh 275 pounds . what is jake ' s present weight , in pounds ?
Options: a ) 131 , b ) 135 , c ) 139 , d ) 147 , e ) 188
Rationale: j = jake ’ s current weight , in pounds s = sister ’ s current weight , in pounds we are told that “ if jake loses 8 pounds , he will weigh twice as much as his sister . we put this into an equation : j – 35 = 3 s j = 3 s + 35 ( equation 1 ) next , we are told that “ together they now weigh 275 pounds . ” we can also put this into an equation . j + s = 275 ( equation 2 ) to solve this equation , we can substitute 2 s + 8 from equation 1 for the variable j in equation 2 : 3 s + 35 = 275 - s 4 s = 240 s = 60 j + 60 = 275 j = 215 answer : e
Answer: e
Problem: pipe a fills a tank of capacity 900 liters at the rate of 40 liters a minute . another pipe b fills the same tank at the rate of 30 liters a minute . a pipe at the bottom of the tank drains the tank at the rate of 20 liters a minute . if pipe a is kept open for a minute and then closed and pipe b is open for a minute and then closed and then pipe c is open for a minute and then closed and the cycle is repeated , when will the tank be full ?
Options: a ) 42 minutes , b ) 14 minutes , c ) 54 minutes , d ) 40 minutes 20 seconds , e ) none of these
Rationale: "in one cycle they fill 40 + 30 - 20 = 50 liters 900 = 50 * n = > n = 18 here n = number of cycles . total time = 18 * 3 = 54 as in one cycle there are 3 minutes . thus 54 minutes answer : c"
Answer: c
Problem: how many even number in the range between 6 to 100 inclusive are not divisible by 3
Options: a ) 15 , b ) 30 , c ) 32 , d ) 33 , e ) 46
Rationale: "we have to find the number of terms that are divisible by 2 but not by 6 ( as the question asks for the even numbers only which are not divisible by 3 ) for 2 , 6 , 8,10 , 12,14 . . . 100 using ap formula , we can say 100 = 10 + ( n - 1 ) * 2 or n = 48 . for 6 , 6 , 12,18 , . . . 96 using ap formula , we can say 96 = 12 + ( n - 1 ) * 6 or n = 16 . hence , only divisible by 2 but not 3 = 48 - 16 = 32 . hence , answer c"
Answer: c
Problem: 6 workers should finish a job in 8 days . after 3 days came 4 workers join them . how many days z do they need to finish the same job ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "let rate of one worker be r = > ( 6 * r ) * 8 = 1 ( rate * time = work ) = > r = 1 / 48 = > work remaining after 3 days 1 - ( 3 * 6 ) / 48 = 30 / 48 after 4 ppl joined in ( ( 6 + 4 ) * time ) / 48 = 30 / 48 time z = 3 days to finish the task imo a"
Answer: a
Problem: of the diplomats who attended a summit conference : 20 spoke latin , 32 did not speak russian and 20 % of the diplomats spoke neither latin nor russian . if 10 % of the diplomats spoke both latin and russian , then how many diplomats attended the conference ?
Options: a ) 70 , b ) 96 , c ) 108 , d ) 120 , e ) 150
Rationale: 2 x 2 matrix will be the easiest way to calculate this . text in black : given statements text in red : calculated values thus d = 120 is the correct answer
Answer: d
Problem: if there is an equal probability of a child being born a boy or a girl , what is the probability that a couple who have 3 children have two children of the same sex and one of the opposite sex ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 1 / 4 , d ) 3 / 4 , e ) 3 / 5
Rationale: "let boy be represented by b and girl by g . the possible outcomes of two children of same sex and one of opposite sex can be : bbg or gbb or bgb or ggb or bgg or gbg ( 1 / 2 * 1 / 2 * 1 / 2 ) + ( 1 / 2 * 1 / 2 * 1 / 2 ) + ( 1 / 2 * 1 / 2 * 1 / 2 ) + ( 1 / 2 * 1 / 2 * 1 / 2 ) + ( 1 / 2 * 1 / 2 * 1 / 2 ) + ( 1 / 2 * 1 / 2 * 1 / 2 ) 1 / 8 + 1 / 8 + 1 / 8 + 1 / 8 + 1 / 8 + 1 / 8 = 6 / 8 = 3 / 4 answer : ( d )"
Answer: d
Problem: a man buys 12 lts of liquid which contains 20 % of the liquid and the rest is water . he then mixes it with 10 lts of another mixture with 30 % of liquid . what is the % of water in the new mixture ?
Options: a ) 75.45 , b ) 76.45 , c ) 77.45 , d ) 74.45 , e ) 73.45
Rationale: "20 % in 12 lts is 2.4 . so water = 12 - 2.4 = 9.6 lts . 30 % of 10 lts = 3 . so water in 2 nd mixture = 10 - 3 = 7 lts . now total quantity = 12 + 10 = 22 lts . total water in it will be 9.6 + 7 = 16.6 lts . % of water = ( 100 * 16.6 ) / 22 = 75.45 answer : a"
Answer: a
Problem: a and b can do a work in 20 days , b and c can do it in 30 days ; a , b and c together can finish it in 40 days . a and c together will do it in ?
Options: a ) 25 days , b ) 30 days , c ) 20 days , d ) 15 days , e ) 10 days
Rationale: a + b + c 1 day work = 1 / 40 a + b 1 day work = 1 / 20 b + c 1 day work = 1 / 30 a + c 1 day work = 2 * 1 / 40 - 1 / 20 + 1 / 30 = 1 / 30 a and c together will do the work in 30 days . answer is b
Answer: b
Problem: the least perfect square , which is divisible by each of 21 , 36 and 66 is :
Options: a ) 213444 , b ) 214344 , c ) 214434 , d ) 231444 , e ) 233444
Rationale: "explanation : l . c . m . of 21 , 36 , 66 = 2772 . now , 2772 = 2 x 2 x 3 x 3 x 7 x 11 to make it a perfect square , it must be multiplied by 7 x 11 . so , required number = 22 x 32 x 72 x 112 = 213444 answer is a"
Answer: a
Problem: find the greatest number that will divide 54 , 87 and 172 so as to leave the same remainder in each case
Options: a ) 13 , b ) 3 , c ) 15 , d ) 1 , e ) 2
Rationale: explanation : required number = ( 87 - 54 ) , ( 172 - 87 ) , ( 172 - 54 ) = h . c . f of 33,85 and 118 is 1 answer : option d
Answer: d
Problem: sally has a gold credit card with a certain spending limit , and a platinum card with twice the spending limit of the gold card . currently , she has a balance on her gold card that is 1 / 3 of the spending limit on that card , and she has a balance on her platinum card that is 1 / 9 of the spending limit on that card . if sally transfers the entire balance on her gold card to her platinum card , what portion of her limit on the platinum card will remain unspent ?
Options: a ) 11 / 30 , b ) 29 / 60 , c ) 17 / 30 , d ) 13 / 18 , e ) 11 / 15
Rationale: "let s assume the platinum card spending limit = x gold card spending limit will be = x / 2 balance on gold card is = x / 2 * 1 / 3 = x / 6 platinum card unspent limit is = x - 1 / 9 x = 8 / 9 x so if gold card balance is transferred then the rest unspent will be 8 / 9 x - x / 6 = 13 / 18 x so the ans is d"
Answer: d
Problem: the number which exceeds 12 % of it by 52.8 is :
Options: a ) 60 , b ) 77 , c ) 269 , d ) 26 , e ) 91
Rationale: "explanation : let the number be x . then , x – 12 % of x = 52.8 x – ( 12 / 100 ) x = 52.8 x ( 1 – 12 / 100 ) = 52.8 ( 88 / 100 ) x = 52.8 x = ( 100 x 52.8 ) / 88 = 60 answer : a"
Answer: a
Problem: according to the directions on the can of frozen orange juice concentrate , 1 can of concentrate is to be mixed with 3 cans of water to make orange juice . how many 12 ounces cans of the concentrate are required to prepare 360 6 ounces servings of orange juice ?
Options: a ) a ) 45 , b ) b ) 34 , c ) c ) 50 , d ) d ) 67 , e ) e ) 100
Rationale: "its a . total juice rquired = 360 * 6 = 2160 ounce 12 ounce concentate makes = 12 * 4 = 48 ounce juice total cans required = 2160 / 48 = 45 . answer a"
Answer: a
Problem: solution for 2.01 + . 3 + . 34
Options: a ) 2.91 , b ) 2.65 , c ) 2.938 , d ) 2.986 , e ) 2.999
Rationale: "2.01 + . 3 + . 34 = 0 0 = 0 - 2.01 - 0.3 - 0.34 0 = - 2.65 answer : b"
Answer: b
Problem: two pipes p and q can fill a cistern in 12 and 15 minutes respectively . both are opened together , but at the end of 6 minutes the first is turned off . how many more minutes will it take for the cistern to fill after the first pipe is turned off ?
Options: a ) 1 , b ) 1.5 , c ) 2 , d ) 2.5 , e ) 3
Rationale: "let x be the total time it takes for the cistern to fill . 6 / 12 + x / 15 = 1 x / 15 = 1 / 2 x = 7.5 after the first pipe is turned off , it takes 1.5 more minutes to fill the cistern . the answer is b ."
Answer: b
Problem: in the xy - coordinate system , what is the slope of the line that goes through the point ( 1 , 1 ) and is equidistant from the two points p = ( 3 , 7 ) and q = ( 9 , 11 ) ?
Options: a ) 0.5 , b ) 0.625 , c ) 0.75 , d ) 0.875 , e ) 1.0
Rationale: "first , get the middle coordinate between ( 3,7 ) and ( 9,11 ) . . . x = 3 + ( 9 - 3 ) / 2 = 6 y = 7 + ( 11 - 7 ) / 2 = 9 second , get the slope of ( 9,6 ) and ( 1,1 ) . m = 6 - 1 / 9 - 1 = 5 / 8 = 0.625 answer : b"
Answer: b
Problem: a certain car can travel 40 minutes on a gallon of gasoline at 60 miles per hour . if the car had started with a full tank and had 12 gallons of gasoline left in its tank at the end , then what percent of the tank was used to travel 80 miles at 60 mph ?
Options: a ) 15 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 14 %
Rationale: "total time for travelling 80 miles @ 60 mph = 80 / 60 = 4 / 3 hour = 80 minutes . given , the car uses 1 gallon for every 40 minutes of driving @ 60 mph . thus in 80 minutes it will use = 2 gallons . thus , full tank = 2 + 12 = 14 gallons - - - > 2 / 14 = 14 % of the fuel used . e is the correct answer ."
Answer: e
Problem: the ratio of flour to water to sugar in a recipe is 11 : 5 : 2 . the ratio in a new recipe calls for a doubling of the ratio of flour to water from the original recipe and a halving of the ratio of flour to sugar . if the new recipe calls for 7.5 cups of water , how much sugar is required ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: the ratio of flour to water is 22 : 5 . the ratio of flour to sugar is 5.5 : 2 = 22 : 8 . the new ratio of flour to water to sugar is 22 : 5 : 8 if we need 7.5 cups of water , then we need 12 cups of sugar . the answer is e .
Answer: e
Problem: with a uniform speed a car covers the distance in 8 hours . had the speed been increased by 5 km / hr , the same distance could have been covered in 7 1 / 2 hours . what is the distance covered ?
Options: a ) 187 km , b ) 480 km , c ) 278 km , d ) 297 km , e ) 600 km
Rationale: "let the distance be x km . then , x / ( 7 1 / 2 ) - x / 8 = 5 2 x / 15 - x / 8 = 5 = > x = 600 km . answer : e"
Answer: e
Problem: a merchant marks goods up by 60 % and then offers a discount on the marked price . the profit that the merchant makes after offering the discount is 20 % . what % discount did the merchant offer ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 40 %
Rationale: "let p be the original price of the goods and let x be the rate after the markup . ( 1.6 p ) * x = 1.2 p x = 1.2 / 1.6 = 0.75 which is a discount of 25 % . the answer is b ."
Answer: b
Problem: a student scored an average of 65 marks in 3 subjects : physics , chemistry and mathematics . if the average marks in physics and mathematics is 90 and that in physics and chemistry is 70 , what are the marks in physics ?
Options: a ) 86 , b ) 165 , c ) 76 , d ) 125 , e ) 26
Rationale: "given m + p + c = 65 * 3 = 195 - - - ( 1 ) m + p = 90 * 2 = 180 - - - ( 2 ) p + c = 70 * 2 = 140 - - - ( 3 ) where m , p and c are marks obtained by the student in mathematics , physics and chemistry . p = ( 2 ) + ( 3 ) - ( 1 ) = 180 + 140 - 195 = 125 answer : d"
Answer: d
Problem: find the number of trailing zeros in the product of ( 1 ^ 1 ) * ( 5 ^ 5 ) * ( 10 ^ 10 ) * ( 15 ^ 15 ) * ( 20 ^ 20 ) * ( 25 ^ 25 ) … … … . * ( 50 ^ 50 ) .
Options: a ) 150 , b ) 200 , c ) 250 , d ) 245 , e ) 225
Rationale: looking at the numbers it looks like ( 1 x 5 ) ^ 5 ( 2 x 5 ) ^ 10 . . . ( 10 x 5 ) ^ 50 1 . determine the limiting factor . is it 2 or is it 5 ? we know that all the numbers are multiple of 5 but not of 2 . thus , the limiting factor in this case is 2 . let ' s drop all the 5 . then , we count factors of 2 of even multiples . 2 ^ 10 = 10 4 ^ 20 = 20 + 20 6 ^ 30 = 30 8 ^ 40 = 40 + 40 + 40 10 ^ 50 = 50 250 answer : c
Answer: c
Problem: how many numbers from 2 to 8 are exactly divisible by 2 ?
Options: a ) a ) 2 , b ) b ) 4 , c ) c ) 5 , d ) d ) 7 , e ) e ) 8
Rationale: "2 / 2 = 1 and 8 / 2 = 4 4 - 1 = 3 3 + 1 = 4 numbers . answer : b"
Answer: b
Problem: the length of a bridge in meters , which a train 80 - meters long and traveling at 45 km / hr can cross in 30 seconds is ?
Options: a ) 215 , b ) 235 , c ) 255 , d ) 275 , e ) 295
Rationale: "45 km / h = 45000 m / 3600 s = 12.5 m / s in 30 seconds , the train can go 30 ( 12.5 ) = 375 meters let x be the length of the bridge . x + 80 = 375 meters x = 295 meters the answer is e ."
Answer: e
Problem: find the smallest number which should be divided with 3872 to make it a perfect square .
Options: a ) 8 , b ) 6 , c ) 2 , d ) 4 , e ) 1
Rationale: "3872 = 11 * 11 * 2 * 2 * 2 * 2 * 2 required smallest number = 2 2 is the smallest number which should be divided with 3872 to make it a perfect square . answer : c"
Answer: c
Problem: x and y are both integers . if x / y = 59.80 , then what is the sum of all the possible two digit remainders of x / y ?
Options: a ) 560 , b ) 616 , c ) 672 , d ) 200 , e ) 1024
Rationale: "remainder = 0.80 = - - > 80 / 100 - - > can be written as ( 80 / 4 ) / ( 100 / 4 ) = 20 / 25 so remainders can be 20 , 40 , 60 , 80 we need the sum of only 2 digit remainders - - > 20 + 40 + 60 + 80 = 200 answer : d"
Answer: d
Problem: a , b , c , d and e are 5 consecutive points on a straight line . if bc = 2 cd , de = 4 , ab = 5 and ac = 11 , what is the length of ae ?
Options: a ) 21 , b ) 26 , c ) 30 , d ) 18 , e ) 16
Rationale: "a - - - - - b - - - - c - - - - - - - - d - - - - e given : de = 4 - ( i ) ab = 5 - ( ii ) ac = 11 - ( iii ) bc = 2 cd - ( iv ) from ( ii ) and ( iii ) , bc = 6 from ( iv ) , cd = 3 length of ae = ac + cd + de = 11 + 3 + 4 = 18 correct option : d"
Answer: d
Problem: on a partly cloudy day , derek decides to walk back from work . when it is sunny , he walks at a speed of s miles / hr ( s is an integer ) and when it gets cloudy , he increases his speed to ( s + 1 ) miles / hr . if his average speed for the entire distance is 2.8 miles / hr , what fraction t of the total distance did he cover while the sun was shining on him ?
Options: a ) 1 / 4 , b ) 4 / 5 , c ) 1 / 5 , d ) 1 / 6 , e ) 1 / 7
Rationale: if s is an integer and we know that the average speed is 2.8 , s must be = 2 . that meanss + 1 = 3 . this implies that the ratio of time for s = 2 is 1 / 4 of the total time . the formula for distance / rate is d = rt . . . so the distance travelled when s = 2 is 2 t . the distance travelled for s + 1 = 3 is 3 * 4 t or 12 t . therefore , total distance covered while the sun was shining over him is t = 2 / 14 = 1 / 7 . answer : e
Answer: e
Problem: a train leaves delhi at 9 a . m . at a speed of 35 kmph . another train leaves at 2 p . m . at a speed of 40 kmph on the same day and in the same direction . how far from delhi , will the two trains meet ?
Options: a ) 229 , b ) 288 , c ) 600 , d ) 888 , e ) 1400
Rationale: "d = 35 * 5 = 175 rs = 40 – 35 = 5 t = 175 / 5 = 35 d = 40 * 35 = 1400 km answer : e"
Answer: e
Problem: rohan spends 40 % of his salary on food , 20 % on house rent , 10 % on entertainment and 10 % on conveyance . if his savings at the end of a month are rs . 2000 . then his monthly salary is
Options: a ) rs . 10000 , b ) rs . 6000 , c ) rs . 8000 , d ) rs . 4000 , e ) rs . 2000
Rationale: sol . saving = [ 100 - ( 40 + 20 + 10 + 10 ] % = 20 % . let the monthly salary be rs . x . then , 20 % of x = 2000 â ‡ ” 20 / 100 x = 2000 â ‡ ” x = 2000 ã — 5 = 10000 . answer a
Answer: a
Problem: a survey of employers found that during 1993 employment costs rose 3.5 percent , where employment costs consist of salary costs and fringe - benefit costs . if salary costs rose 3 percent and fringe - benefit costs rose 7.5 percent during 1993 , then fringe - benefit costs represented what percent of employment costs at the beginning of 1993 ?
Options: a ) 16.5 % , b ) 10 % , c ) 35 % , d ) 55 % , e ) 65 %
Rationale: "the amount by which employment costs rose is equal to 0.035 ( salary costs + fringe benefit costs ) ; on the other hand the amount by which employment costs rose is equal to 0.03 * salary costs + 0.075 * fringe benefit costs ; so , 35 ( s + f ) = 30 s + 75 f - - > s = 9 f - - > f / s = 1 / 9 - - > f / ( s + f ) = 1 / ( 1 + 9 ) = 1 / 10 = 0.1 . answer : b ."
Answer: b
Problem: excluding stoppages , the speed of a train is 45 kmph and including stoppages it is 42 kmph . of how many minutes does the train stop per hour ?
Options: a ) 16 , b ) 4 , c ) 15 , d ) 18 , e ) 12
Rationale: "t = 3 / 45 * 60 = 4 answer : b"
Answer: b
Problem: . 008 / ? = . 01
Options: a ) . 8 , b ) . 09 , c ) . 009 , d ) . 0009 , e ) none of them
Rationale: "let . 008 / x = . 01 ; then x = . 008 / . 01 = . 8 / 1 = . 8 answer is a"
Answer: a
Problem: a man spend 1 / 5 of his salary on food , 1 / 10 of his salary on house rent and 3 / 5 salary on clothes . he still has $ 17000 left with him . find salary . .
Options: a ) $ 10700 , b ) $ 17000 , c ) $ 180000 , d ) $ 1700 , e ) $ 170000
Rationale: "[ 1 / ( x 1 / y 1 + x 2 / y 2 + x 3 / y 3 ) ] * total amount = balance amount [ 1 - ( 1 / 5 + 1 / 10 + 3 / 5 ) } * total salary = $ 17000 , = [ 1 - 9 / 10 ] * total salary = $ 17000 , total salary = $ 17000 * 10 = $ 180000 , correct answer ( e )"
Answer: e
Problem: what is the lowest positive integer that is divisible by 8 through 11 , inclusive ?
Options: a ) 999 , b ) 7811 , c ) 6555 , d ) 9200 , e ) 7920
Rationale: "the integer should be divisible by : 8 , 9 , 10 and 11 . the least common multiple of these integers is lcm = 8 * 9 * 10 * 11 = 7920 answer : e"
Answer: e
Problem: the sector of a circle has radius of 20 cm and central angle 135 o . find its perimeter ?
Options: a ) 91.5 , b ) 87.1 , c ) 91.7 , d ) 91.3 , e ) 91.1
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 135 / 360 * 2 * 22 / 7 * 20 ) + 2 ( 20 ) = 47.1 + 40 = 87.1 cm answer : b"
Answer: b
Problem: tara bought 19 cartons of ice cream and 4 cartons of yoghurt . each carton of ice cream cost $ 7 and each carton of yoghurt cost $ 1 . how much more did tara spend on ice cream than on yoghurt ?
Options: a ) $ 144 , b ) $ 130 , c ) $ 80 , d ) $ 110 , e ) $ 129
Rationale: step 1 : find the cost of the ice cream . 19 × $ 7 = $ 133 step 2 : find the cost of the yoghurt . 4 × $ 1 = $ 4 step 3 : find how much more the ice cream cost than the yoghurt . $ 133 – $ 4 = $ 129 tara spent $ 129 more on ice cream . answer is e .
Answer: e
Problem: if 9 boys meet at a reunion and each boy shakes hands exactly once with each of the others , then what is the total number of handshakes
Options: a ) 41 , b ) 42 , c ) 36 , d ) 44 , e ) 45
Rationale: "n ( n - 1 ) / 2 = 9 * 8 / 2 = 36 answer : c"
Answer: c
Problem: car a runs at the speed of 50 km / hr and reaches its destination in 8 hours . car b runs at the speed of 65 km / h and reaches its destination in 4 hours . what is the ratio of distances covered by car a and car b ?
Options: a ) 3 : 7 , b ) 4 : 9 , c ) 20 : 13 , d ) 5 : 7 , e ) 6 : 11
Rationale: "car a travels 50 × 8 = 400 km car b travels 65 × 4 = 260 km the ratio is 400 : 260 = 40 : 26 = 20 : 13 the answer is c ."
Answer: c
Problem: a grocer is storing soap boxes in cartons that measure 25 inches by 48 inches by 60 inches . if the measurement of each soap box is 8 inches by 6 inches by 5 inches , then what is the maximum number of soap boxes that can be placed in each carton ?
Options: a ) 210 , b ) 252 , c ) 280 , d ) 320 , e ) 300
Rationale: "however the process of dividing the volume of box by the volume of a soap seems flawed but it does work in this case due to the numbers dimensions of the box = 25 * 48 * 60 dimensions of the soap = 5 * 6 * 8 we get = 5 x 6 x 10 = 300 so the question is why this particular arrangement , in order to maximize number of soaps we need to minimize the space wasted and this is the only config where we dont waste any space so we can expect the maximum number the answer is ( e )"
Answer: e
Problem: what is the greatest 5 - digit number when divided by 6 , 7 , 8 , 9 , and 10 leaves a remainder of 4 , 5 , 6 , 7 , and 9 respectively ?
Options: a ) 56780 , b ) 78910 , c ) 97479 , d ) 97918 , e ) 97920
Rationale: when you divide a positive integer by 10 , the remainder will just be the units digit . we know the remainder is 9 when we divide by 10 , so c is the only possible answer .
Answer: c
Problem: a collection of books went on sale , and 2 / 3 of them were sold for $ 5 each . if none of the 50 remaining books were sold , what was the total amount received for the books that were sold ?
Options: a ) $ 550 , b ) $ 600 , c ) $ 500 , d ) $ 400 , e ) $ 450
Rationale: "if 50 books constitute 1 / 3 rd of the total , then 2 / 3 rd of the total = 100 books amount received for sold books = 100 * 5 = $ 500 answer : c"
Answer: c
Problem: a rower can row 6 km / h in still water . when the river is running at 2 km / h , it takes the rower 1 hour to row to big rock and back . how many kilometers is it to big rock ?
Options: a ) 2.21 , b ) 2.45 , c ) 2.67 , d ) 2.83 , e ) 2.95
Rationale: "let x be the distance to big rock . time = x / 4 + x / 8 = 1 x = 32 / 12 = 2.67 km 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 . 75 only . men â € ™ s wages are ?
Options: a ) 6 rs , b ) 7 rs , c ) 8 rs , d ) 5 rs , e ) 1 rs
Rationale: "5 m = xw = 8 b 5 m + xw + 8 b - - - - - 75 rs . 5 m + 5 m + 5 m - - - - - 75 rs . 15 m - - - - - - 75 rs . = > 1 m = 5 rs . answer : d"
Answer: d
Problem: the radius of a cylindrical vessel is 7 cm and height is 6 cm . find the whole surface of the cylinder ?
Options: a ) 281 , b ) 771 , c ) 440 , d ) 767 , e ) 572
Rationale: "r = 7 h = 6 2 π r ( h + r ) = 2 * 22 / 7 * 7 ( 13 ) = 572 answer : e"
Answer: e
Problem: the value of ( 34.31 * 0.473 * 1.5 ) / ( 0.0673 * 23.25 * 7.57 ) is close to
Options: a ) 2 , b ) 1.15 , c ) 2.01 , d ) 2.06 , e ) 2.35
Rationale: "( 34.31 * 0.473 * 1.5 ) / ( 0.0673 * 23.25 * 7.57 ) = 24.343 / 11.845 = 2.06 answer : d"
Answer: d
Problem: elvin ' s monthly telephone bill is the sum of the charge for the calls he made during the month and a fixed monthly charge for internet service . elvin ' s total telephone bill for january was $ 40 and elvin ' s total telephone bill for february was 76 $ . if elvin ' s charge for the calls he made in february was twice the charge for the calls he made in january , what is elvin ' s fixed monthly charge for internet service ?
Options: a ) $ 5 , b ) $ 10 , c ) $ 14 , d ) $ 4 , e ) $ 28
Rationale: bill = fixed charge + charge of calls made in jan , bill = fixed charge ( let , y ) + charge of calls made in jan ( let , x ) = $ 40 in feb , bill = fixed charge ( let , y ) + charge of calls made in feb ( then , 2 x ) = $ 76 i . e . x + y = 40 and 2 x + y = 76 take the difference if two equations i . e . ( 2 x + y ) - ( x + y ) = 76 - 40 i . e . x = 36 i . e . fixed monthly charge , y = 4 answer : option d
Answer: d
Problem: how many seconds does puja take to cover a distance of 500 m , if she runs at a speed of 30 km / hr ?
Options: a ) 60 sec , b ) 82 sec , c ) 95 sec , d ) 100 sec , e ) 120 sec
Rationale: hint : time = distance / speed we see that the distance is given in metres while the speed is given in km / hr and the answer is asked in seconds . so , convert km / hr into m / s by multiplying 5 / 18 m / s to the given value of speed . 30 km / hr = 30 x 5 / 18 = 75 / 9 m / sec i . e . place these values in the formula : time = 500 x 9 / 75 = 60 sec answer is a
Answer: a
Problem: the l . c . m . of 2 numbers is 40 . the numbers are in the ratio 4 : 5 . find their sum ?
Options: a ) 18 , b ) 40 , c ) 48 , d ) 32 , e ) 56
Rationale: "let the numbers be 4 x and 5 x l . c . m . = 20 x 20 x = 40 x = 2 the numbers are = 8 and 10 required sum = 8 + 10 = 18 answer is a"
Answer: a
Problem: the sum of the ages 4 members of a family 5 years ago was 94 . today , when the daughter has been married off and replaced by a daughter - in - law , the sum of their ages is 100 . assuming that there has been no other change in the family structure and all members are alive , what is the difference in the ages of daughter and daughter - in - law ?
Options: a ) 22 , b ) 11 , c ) 25 , d ) 14 , e ) 16
Rationale: solution : sum of ages of 4 members 5 years ago = 94 = > sum of present ages of 4 members = 94 + 4 * 5 = 114 difference in the sum of the ages = difference in the ages of daughter and daughter - in - law difference in the sum of the ages = 114 - 100 = 14 = > difference in the ages of daughter and daughter - in - law = 14 answer d
Answer: d
Problem: 35 binders can bind 1400 books in 21 days . how many binders will be required to bind 1600 books in 20 days ?
Options: a ) 87 , b ) 18 , c ) 42 , d ) 16 , e ) 10
Rationale: "binders books days 35 1400 21 x 1600 20 x / 35 = ( 1600 / 1400 ) * ( 21 / 20 ) = > x = 42 answer : c"
Answer: c