Cheukting/mathqa huggingface dataset:
Question (general): what is the least possible value of x ^ 2 - 15 where x is a positive number .
Options: a ) - 15 , b ) - 14 , c ) - 13 , d ) - 12 , e ) - 11
Rationale: if x is a positive integer , the lowest value would be x = 1 , because 0 is not included in the natural numbers . that ' s a technicality the gmat would not expect students to know . if x = 1 , then the expression equals - 14 . answer = ( b ) .
Answer: b
Question (general): little john had $ 16.10 . he spent $ 3.25 on sweets and gave to his two friends $ 2.20 each . how much money was left ?
Options: a ) $ 6.45 , b ) $ 8.35 , c ) $ 8.75 , d ) $ 8.85 , e ) $ 8.45
Rationale: john spent and gave to his two friends a total of 3.25 + 2.20 + 2.20 = $ 7.65 money left 16.10 - 7.65 = $ 8.45 answer : e
Answer: e
Question (physics): 3 pumps , working 8 hours a day , can empty a tank in 2 days . how many hours a day must 10 pumps work to empty the tank in 1 day ?
Options: a ) 4.8 , b ) 3.6 , c ) 1.1 , d ) 1.2 , e ) 1.3
Rationale: "3 pumps take 16 hrs total ( 8 hrs a day ) if 1 pump will be working then , it will need 16 * 3 = 48 hrs 1 pump need 48 hrs if i contribute 10 pumps then 48 / 10 = 4.8 hrs . answer : a"
Answer: a
Question (geometry): the surface area of a sphere is 4 π r 2 , where r is the radius of the sphere . if the area of the base of a hemisphere is 3 , what is the surface area e of that hemisphere ?
Options: a ) 6 / π
b ) 9 / π
c ) 6
d ) 9
e ) 12
Rationale: given area of the base of a hemisphere is 3 = pi * r ^ 2 thus r = sqrt ( 3 / pi ) . surface area of whole sphere = 4 * pi * r ^ 2 . = 4 * pi * 3 / pi = 12 . since the hemisphere is half of a sphere the surface area of the hemisphere = 12 / 2 = 6 ( curved part , not including the flat rounded base ) . but the total surface area = 6 + area of the base of a hemisphere . = 6 + 3 = 9 . answer is d ! !
Answer: d
Question (general): 5354 x 51 = ?
Options: a ) 273054 , b ) 273243 , c ) 273247 , d ) 273250 , e ) 273258
Rationale: "5354 x 51 = 5354 x ( 50 + 1 ) = 5354 x 50 + 5354 x 1 = 267700 + 5354 = 273054 a"
Answer: a
Question (general): if n is a positive integer such that n ! / ( n - 2 ) ! = 342 , find n .
Options: a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 21
Rationale: we write n ! = n * ( n - 1 ) ( n - 2 ! ) therefore n ! / ( n - 2 ) ! = n ( n - 1 ) * ( n - 2 ) ! / ( n - 2 ) ! = n ( n - 1 ) . - - > n ( n - 1 ) = 342 - - > n ^ 2 - n - 342 = 0 - - > n ^ 2 - 19 n + 18 n - 342 = 0 - - > n ( n - 19 ) + 18 ( n - 19 ) = 0 - - > ( n - 19 ) ( n + 18 ) = 0 therefore n - 19 = 0 ; n + 18 = 0 ; ( i . e ) n = 19 ; n = - 18 we want positive integer . so , n = 19 . answer : c
Answer: c
Question (general): a person has 100 $ in 10 $ and 5 $ bill . if the 5 $ bill quantity is twice that of 10 $ bill . what is quantity of 10 $ .
Options: a ) 2 , b ) 6 , c ) 7 , d ) 8 , e ) 5
Rationale: let amount of 10 $ be x . then amount of 5 $ be 2 x . now 5 * 2 x + 10 * x = 100 . thus x = 5 . answer : e
Answer: e
Question (general): for a group of n people , k of whom are of the same sex , the ( n - k ) / n expression yields an index for a certain phenomenon in group dynamics for members of that sex . for a group that consists of 20 people , 5 of whom are females , by how much does the index for the females exceed the index for the males in the group ?
Options: a ) 0.05 , b ) 0.0625 , c ) 0.5 , d ) 0.25 , e ) 0.6
Rationale: "index for females = ( 20 - 5 ) / 20 = 3 / 4 = 0.75 index for males = ( 20 - 15 / 20 = 1 / 4 = 0.25 index for females exceeds males by 0.75 - 0.25 = 0.5 answer : c"
Answer: c
Question (physics): tanks a and b are each in the shape of a right circular cylinder . the interior of tank a has a height of 10 meters and a circumference of 12 meters , and the interior of tank b has a height of 12 meters and a circumference of 10 meters . the capacity of tank a is what percent of the capacity of tank b ?
Options: a ) 80 % , b ) 90 % , c ) 100 % , d ) 110 % , e ) 120 %
Rationale: "the radius of tank a is 12 / ( 2 * pi ) . the capacity of tank a is 10 * pi * 144 / ( 4 * pi ^ 2 ) = 360 / ( pi ) the radius of tank b is 10 / ( 2 * pi ) . the capacity of tank b is 12 * pi * 100 / ( 4 * pi ^ 2 ) = 300 / ( pi ) tank a / tank b = 360 / 300 = 12 / 10 = 120 % the answer is e ."
Answer: e
Question (geometry): eric throws 2 dice , and his score is the sum of the values shown . sandra throws one dice and her score is the square of the value shown . what is the probabilty that sandras score will be strictly higher than erics score ? ?
Options: a ) 137 / 216
b ) 137 / 218
c ) 137 / 217
d ) 136 / 216
e ) 138 / 216
Rationale: sandra score can be like 1,4 , 9,16 , 25,36 eric score less then 1 - - > 0 eric score less then 4 = ( 1,1 ) , ( 1,2 ) ( 2,1 ) - - > 3 eric score less then 9 are ( 1,1 ) ( 1,2 ) ( 1,3 ) ( 1,4 ) ( 1,5 ) ( 1,6 ) ( 2,1 ) ( 2,2 ) ( 2,3 ) ( 2,4 ) ( 2,5 ) ( 2,6 ) ( 3,1 ) ( 3,2 ) ( 3,3 ) ( 3,4 ) ( 3,5 ) ( 4,1 ) ( 4,2 ) ( 4,3 ) ( 4,4 ) ( 5,1 ) ( 5,2 ) ( 5,3 ) ( 6,1 ) ( 6,2 ) - - > 26 eric score will always be less then 16 - - - > 36 eric score will always be less then 25 - - - > 36 eric score will always be less then 36 - - - > 36 total favorable outcomes = 3 + 26 + 36 + 36 + 36 = 137 total possible outcomes = 216 ( 36 * 6 ) probability = 137 / 216 answer : a
Answer: a
Question (other): if $ 910 are divided between worker a and worker b in the ratio 5 : 9 , what is the share that worker b will get ?
Options: a ) 62.27 % , b ) 63.28 % , c ) 64.29 % , d ) 65.31 % , e ) 66.32 %
Rationale: worker b will get 9 / 14 = 64.29 % the answer is c .
Answer: c
Question (physics): someone on a skateboard is traveling 8 miles per hour . how many feet does she travel in 5 seconds ? ( 1 mile = 5280 feet )
Options: a ) 60 ft , b ) 52 ft , c ) 53 ft , d ) 55 ft , e ) 58.65 ft
Rationale: "per second = > 8 * 5280 ft / 60 * 60 = 11.73 ft 5 seconds = > 11.73 * 5 = 58.65 ft answer : e"
Answer: e
Question (physics): a car traveling at a certain constant speed takes 30 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 30 kilometers per hour . at what speed , in kilometers per hour , is the car traveling ?
Options: a ) 16 , b ) 18 , c ) 20 , d ) 22 , e ) 24
Rationale: "30 * t = 1 km = > t = 1 / 30 km / h v * ( t + 30 / 3600 ) = 1 v ( 1 / 30 + 30 / 3600 ) = 1 v ( 150 / 3600 ) = 1 v = 24 km / h the answer is e ."
Answer: e
Question (general): of the families in city x in 1998 , 30 percent owned a personal computer . the number of families in city x owning a computer in 2002 was 20 percent greater than it was in 1998 , and the total number of families in city x was 8 percent greater in 2002 than it was in 1998 . what percent of the families in city x owned a personal computer in 2002 ?
Options: a ) 50.12 % , b ) 52.66 % , c ) 56.33 % , d ) 33.33 % , e ) 74.12 %
Rationale: say a 100 families existed in 1998 then the number of families owning a computer in 1998 - 30 number of families owning computer in 2002 = 30 * 120 / 100 = 36 number of families in 2002 = 108 the percentage = 36 / 108 * 100 = 33.33 % . option : d
Answer: d
Question (physics): recently , i decided to walk down an escalator of a tube station . i did some quick calculation in my mind . i found that if i walk down 20 ` ` 6 steps , i require thirty seconds to reach the bottom . however , if i am able to step down thirty ` ` 4 stairs , i would only require eighteen seconds to get to the bottom . if the time is measured from the moment the top step begins to descend to the time i step off the last step at the bottom ?
Options: a ) 43 , b ) 44 , c ) 45 , d ) 40 , e ) 46
Rationale: 26 steps 30 seconds and for 34 steps only 18 seconds left to reach botto . means he covered 8 steps ( i . e . 34 - 26 ) in 12 ( i . e 30 - 18 ) seconds the spped of the boy is 8 steps in 12 seconds after further simplyfy . . 2 steps in 3 seconds after 34 steps only 18 seconds , means 12 more steps are left total steps are 34 + 12 = 46 answer : e
Answer: e
Question (general): if y > 0 , ( 2 y ) / 20 + ( 3 y ) / 10 is what percent of y ?
Options: a ) 40 % , b ) 50 % , c ) 60 % , d ) 70 % , e ) 80 %
Rationale: "soln : - can be reduced to y / 10 + 3 y / 10 = 2 y / 5 = 40 % answer : a"
Answer: a
Question (physics): at a loading dock , each worker on the night crew loaded 2 / 3 as many boxes as each worker on the day crew . if the night crew has 5 / 6 as many workers as the day crew , what fraction of all the boxes loaded by the two crews did the day crew load ?
Options: a ) 6 / 11 , b ) 7 / 12 , c ) 8 / 13 , d ) 9 / 14 , e ) 11 / 15
Rationale: let x be the number of workers on the day crew . let y be the number of boxes loaded by each member of the day crew . then the number of boxes loaded by the day crew is xy . the number of boxes loaded by the night crew is ( 5 x / 6 ) ( 2 y / 3 ) = 5 xy / 9 the total number of boxes is xy + 5 xy / 9 = 14 xy / 9 the fraction loaded by the day crew is xy / ( 14 xy / 9 ) = 9 / 14 the answer is d .
Answer: d
Question (physics): if a train , travelling at a speed of 90 kmph , crosses a pole in 6 sec , then the length of train is ?
Options: a ) 281 m , b ) 112 m , c ) 117 m , d ) 125 m , e ) 150 m
Rationale: "e e = 90 * 5 / 18 * 6 = 150 m"
Answer: e
Question (other): find the number of different prime factors of 25650
Options: a ) 4 , b ) 2 , c ) 3 , d ) 5 , e ) 6
Rationale: explanation : l . c . m of 25650 = 2 x 3 x 3 x 3 x 5 x 5 x 19 3 , 2 , 5,19 number of different prime factors is 4 . answer : option a
Answer: a
Question (general): the mean of 50 observations was 36 . it was found later that an observation 58 was wrongly taken as 43 . the corrected new mean is ?
Options: a ) 36.7 , b ) 36.1 , c ) 36.5 , d ) 36.9 , e ) 36.3
Rationale: "correct sum = ( 36 * 50 + 58 - 43 ) = 1815 . correct mean = 1815 / 50 = 36.3 answer : e"
Answer: e
Question (gain): in a school of 450 boys , 44 % of muslims , 28 % hindus , 10 % sikhs and the remaining of other communities . how many belonged to the other communities ?
Options: a ) 72 , b ) 75 , c ) 80 , d ) 81 , e ) 90
Rationale: "44 + 28 + 10 = 82 % 100 – 82 = 18 % 450 * 18 / 100 = 81 answer : d"
Answer: d
Question (general): what is the remainder when 1250 * 1040 * 1057 * 1145 is divided by 32 ?
Options: a ) 3 , b ) 5 , c ) 0 , d ) 2 , e ) 9
Rationale: "oa is ' c ' . oe : take the remainder from each of 1250 / 32 , 1040 / 32 and so on . . 1250 / 32 gives remainder = 2 1040 / 32 gives remainder = 16 1057 / 32 gives remainder = 1 1145 / 32 gives remainder = 25 the net remainder is the product of above individual remainders . i . e = 2 * 16 * 1 * 25 break them into pairs 2 * 16 / 32 gives remainder 0 and 1 * 25 / 32 gives remainder 25 so 0 * 25 / 32 gives remainder 0 . answer : c"
Answer: c
Question (gain): if the selling price of 80 articles is equal to the cost price of 40 articles , then the loss or gain percent is :
Options: a ) 30 % , b ) 35 % , c ) 50 % , d ) 55 % , e ) 40 %
Rationale: "let c . p . of each article be re . 1 . then , c . p . of 80 articles = rs . 80 ; s . p . of 80 articles = rs . 40 . loss % = 40 / 80 * 100 = 50 % answer : c"
Answer: c
Question (geometry): find the volume and surface area of a cuboid 16 m long , 14 m broad and 7 m high .
Options: a ) 878 cm ^ 2
b ) 858 cm ^ 2
c ) 838 cm ^ 2
d ) 868 cm ^ 2
e ) none of them
Rationale: volume = ( 16 x 14 x 7 ) m ^ 3 = 1568 m ^ 3 . surface area = [ 2 ( 16 x 14 + 14 x 7 + 16 x 7 ) ] cm ^ 2 = ( 2 x 434 ) cm ^ 2 = 868 cm ^ 2 . answer is d
Answer: d
Question (general): 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 . 24000 , my total savings for the two - year is
Options: a ) s . 8000 , b ) s . 7000 , 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 ) - ( 24000 + 35000 ) = 66000 - 59000 = rs . 7000 b"
Answer: b
Question (general): 3 - twentieths of the members of a social club are retirees who are also bridge players , 5 - twentieths of the members are retirees , and one - half of the members are bridge players . if 120 of the members are neither retirees nor bridge players , what is the total number of members in the social club ?
Options: a ) 240 , b ) 300 , c ) 200 , d ) 400 , e ) 480
Rationale: { total } = { retirees } + { bridge players } - { both } + { neither } x = 5 / 20 * x + x / 2 - 3 / 20 * x + 120 20 x = 5 x + 10 x - 3 x + 120 * 20 ( multiply by 20 ) 12 x = 120 * 20 x = 200 . answer : c
Answer: c
Question (general): the sum of digits of a two digit number is 8 , the difference between the digits is 6 . find the number
Options: a ) 85 , b ) 94 , c ) 83 , d ) 71 , e ) none
Rationale: "description : = > x + y = 8 , x - y = 6 adding these 2 x = 14 = > x = 7 , y = 1 . thus the number is 71 answer d"
Answer: d
Question (general): the total marks obtained by a student in mathematics and physics is 80 and his score in chemistry is 20 marks more than that in physics . find the average marks scored in mathamatics and chemistry together .
Options: a ) 40 , b ) 30 , c ) 25 , d ) 50 , e ) none of these .
Rationale: let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 80 and c - p = 20 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 80 + 20 ) / 2 = 50 . answer : d
Answer: d
Question (geometry): the perimeter of a triangle is 44 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle ?
Options: a ) 38 cm 2 , b ) 55 cm 2 , c ) 65 cm 2 , d ) 45 cm 2 , e ) 35 cm 2
Rationale: "area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 44 / 2 = 55 cm 2 answer : b"
Answer: b
Question (gain): the principal that amounts to rs . 4903 in 3 years at 6 1 / 4 % per annum c . i . compounded annually , is ?
Options: a ) s . 3096 , b ) s . 4076 , c ) s . 4085 , d ) s . 4096 , e ) s . 5096
Rationale: "principal = [ 4913 / ( 1 + 25 / ( 4 * 100 ) ) 3 ] = 4903 * 16 / 17 * 16 / 17 * 16 / 17 = rs . 4076 . answer : b"
Answer: b
Question (other): in a group of 95 students , 36 are taking history , and 32 are taking statistics . if 59 students are taking history or statistics or both , then how many students are taking history but not statistics ?
Options: a ) 9 , b ) 19 , c ) 23 , d ) 45 , e ) 27
Rationale: "number of students taking history = h = 36 number of students taking statistics = s = 32 total number of students = t = 90 number of students taking history or statistics or both = b = 59 number of students taking neither history nor statistics = n = 95 - 59 = 36 letxbe the number of students taking both history and statistics . then t = h + s + n - x or 95 = 36 + 32 + 36 - x or x = 9 now , number of students taking only history will be h - x or 36 - 9 = 27 answer : - e"
Answer: e
Question (general): the price of commodity x increases by 30 cents every year , while the price of commodity y increases by 20 cents every year . if in 2001 , the price of commodity x was $ 4.20 and the price of commodity y was $ 4.40 , in which year will commodity x cost 80 cents more than the commodity y ?
Options: a ) 2010 . , b ) 2011 . , c ) 2012 . , d ) 2013 . , e ) 2014 .
Rationale: "the cost of commodity x increases by 10 cents per year relative to commodity y . the price of x must gain 20 + 80 = $ 1.00 cents on commodity y , which will take 10 years . the answer is b ."
Answer: b
Question (probability): there are 13 clubs in a full deck of 52 cards . in a certain game , you pick a card from a standard deck of 52 cards . if the card is a club , you win . if the card is not a club , the person replaces the card to the deck , reshuffles , and draws again . the person keeps repeating that process until he picks a club , and the point is to measure how many draws it took before the person picked a club and , thereby , won . what is the probability that one will pick the first club on the forth draw or later ?
Options: a ) 1 / 2 , b ) 3 / 4 , c ) 7 / 8 , d ) 27 / 32 , e ) 27 / 64
Rationale: favorable case = the club is picked in the third draw or later unfavorable cases = the club is picked in either first draw , second draw or third draws probability = favorable outcomes / total out comes also probability = 1 - ( unfavorable outcomes / total out comes ) unfavorable case 1 : probability of club picked in first draw = 13 / 52 = 1 / 4 unfavorable case 2 : probability of club picked in second draw ( i . e . first draw is not club ) = ( 39 / 52 ) * ( 13 / 52 ) = ( 3 / 4 ) * ( 1 / 4 ) = 3 / 16 unfavorable case 3 : probability of club picked in third draw ( i . e . first and 2 nd draws are not clubs ) = ( 39 / 52 ) * ( 39 / 52 ) * ( 13 / 52 ) = ( 3 / 4 ) * ( 3 / 4 ) * ( 1 / 4 ) = 9 / 64 total unfavorable probability = ( 1 / 4 ) + ( 3 / 16 ) + ( 9 / 64 ) = ( 16 / 64 ) + ( 12 / 64 ) + ( 9 / 64 ) = 37 / 64 i . e . , favorable probability = 1 - ( 37 / 64 ) = 27 / 64 answer : option e
Answer: e
Question (general): the average ( arithmetic mean ) of 20 , 40 , and 60 is 5 more than the average of 10 , 70 , and what number ?
Options: a ) 15 , b ) 25 , c ) 35 , d ) 45 , e ) 55
Rationale: "a 1 = 120 / 3 = 40 a 2 = a 1 - 5 = 35 sum of second list = 35 * 3 = 105 therefore the number = 105 - 80 = 25 answer : b"
Answer: b
Question (general): alan buys 4 tvs , a 26 inch , a 28 inch , a 30 inch , and a 32 inch , for his new house . each tv costs $ 200 more than the size below it . alan spends a total of $ 3,200 . how much would he have spent if he had bought only the 28 inch and 30 inch tvs ?
Options: a ) 850 , b ) 1,600 , c ) 1,700 , d ) 2,550 , e ) 3,400
Rationale: "assume the cost of the least sized ( 26 inch ) tv = x cost of 28 inches tv = x + 200 cost of 30 inches tv = x + 400 cost of 32 inches tv = x + 600 total cost = 4 x + 1200 = 3200 therefore x = 2000 / 4 = 500 price of 28 inch + 30 inch = 700 + 900 = 1600 option b"
Answer: b
Question (gain): if 28 % of a number exceeds 18 % of it by 7.2 , then find the number ?
Options: a ) 50 , b ) 34 , c ) 55 , d ) 60 , e ) 90
Rationale: use the elimination method to find the correct option . of all the options only 90 fits 28 % of 90 = 25.2 18 % of 90 = 16.2 25.2 - 16.2 = 7.2 required number is 90 . answer : e
Answer: e
Question (other): how many factors of 60 are odd numbers greater than 1 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 3 , e ) 7
Rationale: prime factors of 60 are 2 ^ 2,3 ^ 1,5 ^ 1 total divisors = ( power if a prime factor + 1 ) total no . of odd factors ( 3,5 , ) = ( 1 + 1 ) ( 1 + 1 ) = 4 since we need odd divisors other than 1 = > 4 - 1 = 3 odd divisors d is the answer
Answer: d
Question (general): a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 68 percent of the distribution lies within one standard deviation d of the mean , what percent e of the distribution is less than m + d ?
Options: a ) 16 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 %
Rationale: d the prompt says that 68 % of the population lies between m - d and m + d . thus , 32 % of the population is less than m - d or greater than m + d . since the population is symmetric , half of this 32 % is less than m - d and half is greater than m + d . thus , e = ( 68 + 16 ) % or ( 100 - 16 ) % of the population is less than m + d . d
Answer: d
Question (general): village p ’ s population is 1150 greater than village q ' s population . if village q ’ s population were reduced by 200 people , then village p ’ s population would be 4 times as large as village q ' s population . what is village q ' s current population ?
Options: a ) 600 , b ) 625 , c ) 650 , d ) 675 , e ) 700
Rationale: p = q + 1150 . p = 4 ( q - 200 ) . 4 ( q - 200 ) = q + 1150 . 3 q = 1950 . q = 650 . the answer is c .
Answer: c
Question (physics): an electric pump can fill a tank in 3 hours . because of a leak in the tank , it took 3 hours 30 min to fill the tank . in what time the leak can drain out all the water of the tank and will make tank empty ?
Options: a ) 10 hours , b ) 13 hours , c ) 17 hours , d ) 21 hours , e ) 25 hours
Rationale: "explanation : we can get the answer by subtrating work done by leak in one hour by subtraction of filling for 1 hour without leak and with leak , as work done for 1 hour without leak = 1 / 3 work done with leak = 3 1 / 2 = 7 / 2 work done with leak in 1 hr = 2 / 7 work done by leak in 1 hr = 1 / 3 = 2 / 7 = 1 / 21 so tank will be empty by the leak in 21 hours . answer is d"
Answer: d
Question (general): a clock store sold a certain clock to a collector for 35 percent more than the store had originally paid for the clock . when the collector tried to resell the clock to the store , the store bought it back at 15 percent of what the collector had paid . the shop then sold the clock again at a profit of 65 percent on its buy - back price . if the difference between the clock ' s original cost to the shop and the clock ' s buy - back price was $ 105 , for how much did the shop sell the clock the second time ?
Options: a ) $ 75.44 , b ) $ 88.23 , c ) $ 64.77 , d ) $ 54.32 , e ) $ 43.99
Rationale: "now , in the question above , lets say the original cost of the clock to store was c $ and then it sold the same to the collector at 35 % profit . this means the clocks ' selling price was c ( 1.35 ) and this becomes cost price for the collector . now , when the collector tries to sell the same clock to the store , the store buys it for 15 % the price at which the collector bought it . thus , you get = 1.35 * 0.15 * c = 0.2025 c furthermore , the store sells the clock for the second time for 65 % profit and thus the selling price of the clock becomes = cost price of the clock for the store at buy - back * 1.65 = 1.65 * 0.2025 c finally given that c - 0.2025 c = 105 - - - - > c = 131.66 $ thus , the cost of the clock the second time around = 1.65 * 0.2025 c = 1.65 * 0.2025 * 131.66 = 43.99 $ . hence e is the correct answer ."
Answer: e
Question (general): the average age of a family of 6 members is 26 years . if the age of the youngest member is 10 years , what was the average age of the family at the birth of the youngest member ?
Options: a ) 15 , b ) 18 , c ) 16 , d ) 12 , e ) 19
Rationale: "present age of total members = 6 x 26 = 156 10 yrs back their ages were = 6 x 10 = 60 ages at the birth of youngest member = 156 - 60 = 96 therefore , avg age at the birth of youngest member = 96 / 6 = 16 . answer : c"
Answer: c
Question (physics): together , 15 type a machines and 7 type b machines can complete a certain job in 4 hours . together 8 type b machines and 15 type c machines can complete the same job in 11 hours . how many hours e would it take one type a machine , one type b machine , and one type c machine working together to complete the job ( assuming constant rates for each machine ) ?
Options: a ) 22 hours , b ) 30 hours , c ) 44 hours , d ) 60 hours , e ) it can not be determined from the information above .
Rationale: say the rates of machines a , b and c are a , b , and c , respectively . together 15 type a machines and 7 type b machines can complete a certain job in 4 hours - - > 15 a + 7 b = 1 / 4 ; together 8 type b machines and 15 type c machines can complete the same job in 11 hours - - > 8 b + 15 c = 1 / 11 . sum the above : 15 a + 15 b + 15 c = 1 / 4 + 1 / 11 = 15 / 44 - - > reduce by 15 : a + b + c = 1 / 44 - - > so , the combined rate of the three machines is 1 / 44 job / hour - - > time is reciprocal of the rate , thus machines a , b and c can do the job e in 44 hours . answer : c .
Answer: c
Question (general): 1 = 5,2 = 4,3 = 253,4 = 2,6 = 15 , then 15 = ?
Options: a ) 1 , b ) 255 , c ) 345 , d ) 445 , e ) 6
Rationale: "1 = 5,2 = 4,3 = 253,4 = 2,6 = 15 , then 15 = ? 15 = 6 check the fifth eqn . answer : e"
Answer: e
Question (general): 2 , 6 , 12 , 20 , 30 , 42 , 56 , ( . . . )
Options: a ) 62 , b ) 74 , c ) 72 , d ) 81 , e ) 58
Rationale: "the pattern is 1 × 2 , 2 × 3 , 3 × 4 , 4 × 5 , 5 × 6 , 6 × 7 , 7 × 8 . hence , next number is 8 × 9 = 72 answer is c"
Answer: c
Question (geometry): what is the area of a square field whose sides have a length of 16 meters ?
Options: a ) 225 sq m , b ) 286 sq m , c ) 298 sq m , d ) 256 sq m , e ) 231 sq m
Rationale: "16 * 16 = 256 sq m the answer is d ."
Answer: d