Cheukting/mathqa huggingface dataset:
Question (geometry): a semicircle has a radius of 11 . what is the approximate perimeter of the semicircle ?
Options: a ) 45
b ) 51
c ) 57
d ) 63
e ) 69
Rationale: the perimeter of a circle is 2 * pi * r . the perimeter of a semicircle is 2 * pi * r / 2 + 2 r = pi * r + 2 r the perimeter is pi * 11 + 2 * 11 which is about 57 . the answer is c .
Answer: c
Question (gain): a milk man has 15 liters of milk . if he mixes 5 liters of water , which is freely available , in 20 liters of pure milk . if the cost of pure milk is rs . 18 per liter , then the profit of the milkman , when he sells all the mixture at cost price is :
Options: a ) 20 % , b ) 25 % , c ) 33.33 % , d ) 18 % , e ) none of these
Rationale: "explanation : when the water is freely available and all the water is sold at the price of the milk , then the water gives the profit on the cost of 20 liters of milk . therefore , profit percentage = 20 % . answer : a"
Answer: a
Question (physics): in a lake , there is a patch of lily pads . every day , the patch doubles in size . it takes 37 days for the patch to cover the entire lake , how many days would it take the patch to cover half of the lake ?
Options: a ) 36 , b ) 2 ^ 4 * 3 , c ) 24 , d ) 38 , e ) 47
Rationale: "working backward from the day it ' s covered : day 37 : fully covered day 36 : half covered so 36 days answer : a"
Answer: a
Question (physics): two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 64 hours and 25 hours respectively . the ratio of their speeds is ?
Options: a ) 4 : 9 , b ) 4 : 3 , c ) 4 : 5 , d ) 5 : 8 , e ) 4 : 2
Rationale: "let us name the trains a and b . then , ( a ' s speed ) : ( b ' s speed ) = √ b : √ a = √ 25 : √ 64 = 5 : 8 answer : d"
Answer: d
Question (general): the total circumference of two circles is 80 . if the first circle has a circumference that is exactly twice the circumference of the second circle , then what is the approximate sum of their two radii ?
Options: a ) 5.7 , b ) 6.0 , c ) 10.6 , d ) 9.7 , e ) 18.0
Rationale: "let r = radius of smaller circle . let r = radius of larger circle therefore : 2 π r + 2 π r = 80 where 2 r = r thus : 2 π r + 4 π r = 80 6 π r = 80 r = approx 4.2 π r + 2 r π = 80 3 π r = 80 r = approx 8.4 r + r = approx 10.6 answer is c"
Answer: c
Question (general): 20 is added to a certain number , the sum is multiplied by 2 , the product is divided by 2 and 2 is subtracted from the quotient . the remainder left is half of 88 . what is the number ?
Options: a ) 21 , b ) 20 , c ) 26 , d ) 30 , e ) 45
Rationale: "let number is x . when 20 added to it , = ( x + 20 ) 2 multiplied to sum , = 2 * ( x + 20 ) now , = [ { 2 * ( x + 20 ) } / 2 ] and , = [ { 2 * ( x + 20 ) } / 2 ] - 2 according to question , [ { 2 * ( x + 20 ) } / 2 ] - 2 = half of 88 [ ( 2 x + 40 ) / 2 ) = 44 + 2 2 x + 40 = 46 * 2 x + 20 = 46 x = 46 - 20 x = 26 so , required number is : 26 . answer : c"
Answer: c
Question (general): 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 e 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 e = 2 / 14 = 1 / 7 . answer : e
Answer: e
Question (gain): a shopkeeper sold an article at $ 100 with 40 % profit . then find its cost price ?
Options: a ) $ 120 , b ) $ 100 , c ) $ 91 , d ) $ 71 , e ) $ 69
Rationale: cost price = selling price * 100 / ( 100 + profit ) c . p . = 100 * 100 / 140 = $ 71 ( approximately ) answer is d
Answer: d
Question (physics): a plant manager must assign 12 new workers to one of five shifts . she needs a first , second , and third shift , and two alternate shifts . each of the shifts will receive 2 new workers . how many different ways can she assign the new workers ?
Options: a ) 23760 , b ) 47520 , c ) 33000 , d ) 48600 , e ) 54000
Rationale: "whatever : my take selecting team of 2 out of 12 to assign to the shifts = 12 c 2 = 66 ways . now 2 out of 12 means total of 6 group possible . so putting them in shifts = counting methode : first , second , third , alt , alt = 6 * 5 * 4 * 3 * 2 * 1 = 720 here alt and alt are the same : so 720 / 2 = 360 ways . total ways of selecting = ( selecting 2 out of 12 ) * arranging those teams in shifts = 66 * 360 = 23760 ans : a"
Answer: a
Question (general): instead of multiplying a number by 5 , the number is divided by 10 . what is the percentage of error obtained ?
Options: a ) 96 % , b ) 98 % , c ) 95 % , d ) 97 % , e ) 96 %
Rationale: "let the number be x the right number is 5 x the wrong number is x / 10 error is ( 5 x - x / 10 ) = 49 x / 10 percentage of error is ( ( 49 x / 10 ) / 5 x ) * 100 = 98 % answer : b"
Answer: b
Question (physics): a car going at 30 miles per hour set out on an 80 - mile trip at 9 : 00 a . m . exactly 10 minutes later , a second car left from the same place and followed the same route . how fast , in miles per hour , was the second car going if it caught up with the first car at 10 : 30 a . m . ?
Options: a ) 45 , b ) 50 , c ) 53 , d ) 55 , e ) 60
Rationale: let car a = car that starts at 9 am car b = car that starts at 9 : 10 am time for which car a travels at speed of 30 m per hour = 1.5 hours distance travelled by car a = 30 * 1.5 = 45 miles since car b catches up car a at 10 : 30 , time = 80 mins = 4 / 3 hour speed of car b = 45 / ( 4 / 3 ) = 60 miles per hour answer e
Answer: e
Question (physics): a train moves at average speed of 60 kmph reaches its destination on time . what its average speed becomes 50 kmph , then it reaches its destination 15 late . find the length of the journey ?
Options: a ) 4.86 km , b ) 2.5 km , c ) 6.86 km , d ) 5.867 km , e ) 3.25 km
Rationale: "difference between timings = 15 min = 1 / 4 hr let the length of the journey be x km . then x / 50 - x / 60 = 1 / 4 x / 10 = 1 / 4 x = 2.5 km answer ( b )"
Answer: b
Question (general): if 325 / 999 = 0.125 , what is the 81 st digit to the right of the decimal point in the decimal equivalent of the fraction ?
Options: a ) 3 , b ) 3.5 , c ) 4 , d ) 4.5 , e ) 5
Rationale: "0 . [ u ] 325 [ / u = 0.325325325 . . . . . every 3 rd digit is 5 and every multiple of 3 will be the digit 5 . since 81 is multiple of 3 , the 81 st digit is 5 . answer e"
Answer: e
Question (general): how many liters of pure alcohol must be added to a 100 - liter solution that is 20 percent alcohol in order to produce a solution that is 35 percent alcohol ?
Options: a ) 7 / 2 , b ) 300 / 13 , c ) 20 / 3 , d ) 8 , e ) 39 / 4
Rationale: "20 % alcohol solution means ; in the 100 liter solution , 20 liters of solution is alcohol and 80 liters other solvents . if we addxliters of alcohol to the solution , the solution becomes 100 + xliters and alcohol , which was 20 liters , becomes 20 + x liters . according to the statement ; 20 + x = 35 % of ( 100 + x ) or 20 + x = ( 100 + x ) 7 / 20 400 + 20 x = 700 + 7 x 13 x = 300 x = 300 / 13 ans : b"
Answer: b
Question (physics): pipe p can fill a tank in 2 hours , pipe q in 4 hours and pipe r in 12 hours . if all the pipes are open , in how many hours will the tank be filled ?
Options: a ) 2 hours , b ) 1.2 hours , c ) 3 hours , d ) 1.5 hours , e ) 2.5 hours
Rationale: "explanation : part filled by ( p + q + r ) in 1 hour = ( 1 / 2 + 1 / 4 + 1 / 12 ) = 5 / 6 all the three pipes together will fill the tank = 6 / 5 = 1.2 hours answer b"
Answer: b
Question (physics): 300 metres long yard , 26 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between 2 consecutive trees
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: 26 trees have 25 gaps between them , required distance ( 300 / 25 ) = 12 b
Answer: b
Question (physics): one pipe can fill a tank three times as fast as another pipe . if together the two pipes can fill tank in 40 min , then the slower pipe alone will be able to fill the tank in ?
Options: a ) 160 , b ) 787 , c ) 144 , d ) 128 , e ) 121
Rationale: "let the slower pipe alone fill the tank in x min . then , faster pipe will fill it in x / 3 min . 1 / x + 3 / x = 1 / 40 4 / x = 1 / 40 = > x = 160 min . answer : a"
Answer: a
Question (other): find the ratio in which rice at rs . 10.0 a kg be mixed with rice at rs . 5.70 a kg to produce a mixture worth rs . 6.30 a kg ?
Options: a ) 1 : 3 , b ) 2 : 3 , c ) 3 : 5 , d ) 4 : 5 , e ) none of these
Rationale: "solution required ratio = 60 : 100 = 3 : 5 answer c"
Answer: c
Question (physics): in a 100 m race , sam beats john by 6 seconds . on the contrary , if sam allowed john to start 36 m ahead of sam , then sam and john reach the finishing point at the same time . how long does sam take to run the 100 m race ?
Options: a ) 10.66 seconds , b ) 25 seconds , c ) 29 seconds , d ) 21 seconds , e ) 6.25 seconds
Rationale: "their difference is 6 second but this difference is 0 if john allows sam to start the race from 36 m ahead . that means jhon was 36 m away from finishing line when they started together . so he will cover 36 m in 6 seconds . so his speed = 36 / 6 = 6 metre / second . so time taken = 100 / 6 = 16.66 seconds . so sam took = 10.66 seconds . correct answer = a"
Answer: a
Question (probability): a bag contains 3 red , 5 yellow and 4 green balls . 3 balls are drawn randomly . what is the probability that balls drawn contain exactly two green balls ?
Options: a ) 9 / 16 , b ) 7 / 18 , c ) 12 / 55 , d ) 14 / 67 , e ) 19 / 87
Rationale: total number of balls = 3 + 5 + 4 = 12 n ( s ) = 12 c 3 = 12 * 11 * 10 / 3 * 2 = 220 n ( e ) = 4 c 2 * 8 c 1 = 6 * 8 = 48 probability = 48 / 220 = 12 / 55 answer is c
Answer: c
Question (physics): debanshu normally drives to work in 45 minutes at an average speed of 40 miles per hour . this week , however , she plans to bike to work along a route that decreases the total distance she usually travels when driving by 20 % . if debanshu averages between 12 and 16 miles per hour when biking , how many minutes earlier will she need to leave in the morning in order to ensure she arrives at work at the same time as when she drives ?
Options: a ) 135 , b ) 105 , c ) 95 , d ) 75 , e ) 45
Rationale: debanshu normally drives to work in 45 minutes at an average speed of 40 miles per hour . use formula d = rt car : t 1 : 45 min r 1 : 40 mph d 1 : [ ( 40 * 45 ) / 60 ] = 30 miles bike : t 1 : ? r 2 : 12 - 16 mph d 2 : 08 * d 1 = 24 miles t 1 : [ ( 24 * 60 ) / 12 ] = 120 min ( only 12 mph speed yields an answer given in the choices ) therefore , deb has to leave 120 min - 45 min = 75 min early answer : d
Answer: d
Question (general): if d is the standard deviation a , b , and c , what is the standard deviation of a + 2 , b + 2 , c + 2 ?
Options: a ) 2 d , b ) d , c ) 2 d + 2 , d ) 8 d , e ) 2 d + 4
Rationale: concept : standard deviation is defined as average deviation of terms in the set from the mean value of the set . i . e . 1 ) it depends on the separation between the successive terms of the set 2 ) if a constant value is added / subtracted in every terms of set then the separation between successive terms does not change hence s . d . remains constant e . g . { 1 , 2 , 3 , 4 , 5 } will have same standard deviation as { 1 + 10 , 2 + 10 , 3 + 10 , 4 + 10 , 5 + 10 } 3 ) if a constant value is multiplied in every terms then the separation between succesive terms gets multiplied by the constant hence s . d . remains gets multiplied by same number e . g . { 0.7 , 1.4 , 2.1 , 2.8 , 3.5 } will have standard deviation = 0.7 * standard deviation of set { 1 , 2 , 3 , 4 , 5 } when 2 is added in each term of set { a , b , c } then the new set { a + 2 , b + 2 , c + 2 } will remain same as the previous standard deviation i . e . d answer : b
Answer: b
Question (general): at the end of year x , automobile installment credit accounted for 36 % of all outstanding consumer installment credit . at that time automobile finance companies extended $ 75 billion of credit , or 1 / 2 of the automobile installment credit . how many billion dollars of consumer installment credit was outstanding at that time ?
Options: a ) 412.16 , b ) 150 , c ) 400 , d ) 416.67 , e ) 420.34
Rationale: "system of equations a = ( 36 / 100 ) c ( 1 / 2 ) a = 75 - - > a = 150 substitution 150 = ( 36 / 100 ) c c = ( 100 / 36 ) 150 calculate 150 / 36 * 100 the correct answer is d - the correct answer will be slightly smaller than 513 . therefore , the correct answer is 475 ."
Answer: d
Question (geometry): three table runners have a combined area of 204 square inches . by overlapping the runners to cover 80 % of a table of area 175 square inches , the area that is covered by exactly two layers of runner is 24 square inches . what is the area of the table that is covered with three layers of runner ?
Options: a ) 18 square inches , b ) 20 square inches , c ) 24 square inches , d ) 28 square inches , e ) 30 square inches
Rationale: "total = a + b + c - ( sum of exactly 2 - group overlaps ) - 2 * ( all three ) + neither 80 % * 175 = 204 - 24 - 2 * ( all three ) + 0 2 * ( all three ) = 204 - 24 - 140 all three = 20 answer : b"
Answer: b
Question (general): nr books bought nr of people 6 3 7 1 8 5 9 2 what is the median of books bought per person ?
Options: a ) a ) 2 , b ) b ) 4 , c ) c ) 6 , d ) d ) 8 , e ) e ) 18
Rationale: 6 , 6,6 , 7,8 , 8,8 , 8,8 , 9,9 so you will observer that the median of the list is 8 . ans d
Answer: d
Question (physics): a flagpole 18 meters high casts a shadow of length 45 meters . if a building under similar conditions casts a shadow of length 55 meters , what is the height of the building ( in meters ) ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 28
Rationale: "the height : length ratio will be equal in both cases . 18 / 45 = x / 55 x = 22 the answer is b ."
Answer: b
Question (general): for every even positive integer m , f ( m ) represents the product of all even integers from 2 to m , inclusive . for example , f ( 12 ) = 2 x 4 x 6 x 8 x 10 x 12 . what is the greatest prime factor of f ( 34 ) ?
Options: a ) 2 , b ) 7 , c ) 13 , d ) 17 , e ) 19
Rationale: "f ( 34 ) = 2 * 4 * 6 * 8 * 10 * 12 * 14 * 16 * 18 * 20 * 22 * 24 * 26 * 28 * 30 * 32 * 34 the greatest prime factor in this list is 17 . the answer is d ."
Answer: d
Question (geometry): nitin ' s age was equal to square of some number last year and the following year it would be cube of a number . if again nitin ' s age has to be equal to the cube of some number , then for how long he will have to wait ?
Options: a ) 10 years
b ) 38 years
c ) 39 years
d ) 64 years
e ) 44 years
Rationale: current age = 26 years because nitin ' s age was equal to square of some number ( 25 = 5 ^ 2 ) last year and the following year it would be cube of a number ( 27 = 3 ^ 3 ) . next cube age will be 64 = 4 ^ 3 which will come after 64 - 26 = 38 years . answer : b
Answer: b
Question (general): a family pays $ 900 per year for an insurance plan that pays 60 percent of the first $ 1,000 in expenses and 100 percent of all medical expenses thereafter . in any given year , the total amount paid by the family will equal the amount paid by the plan when the family ' s medical expenses total how much ?
Options: a ) $ 1,000 , b ) $ 1,200 , c ) $ 1,400 , d ) $ 1,500 , e ) $ 1,700
Rationale: "assuming the medical expenses are $ 1000 or more , the family pays $ 900 + $ 400 = $ 1300 . the total amount paid by insurance plan for the first $ 1000 of expenses is $ 600 . the insurance will pay another $ 700 when the medical expenses are $ 1700 . the answer is e ."
Answer: e
Question (general): a certain basketball team that has played 2 / 3 of its games has a record of 13 wins and 7 losses . what is the greatest number of the remaining games that the team can lose and still win at least 3 / 4 of all of its games ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 4 , e ) 3
Rationale: 13 wins , 7 losses - total 20 games played . the team has played 2 / 3 rd of all games so total number of games = 30 3 / 4 th of 30 is 22.5 so the team must win 23 games and can afford to lose at most 7 total games . it has already lost 7 games so it can lose another 0 at most . answer ( a )
Answer: a
Question (physics): two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 4 hours and 49 hours respectively . the ratio of their speeds is :
Options: a ) 2 : 3 , b ) 4 : 3 , c ) 6 : 7 , d ) 7 : 2 , e ) none of these
Rationale: "let us name the trains as a and b . then , ( a ' s speed ) : ( b ' s speed ) = â ˆ š b : â ˆ š a = â ˆ š 49 : â ˆ š 4 = 7 : 2 . answer d"
Answer: d
Question (general): find 62976 ÷ ? = 123
Options: a ) 412 , b ) 502 , c ) 512 , d ) 522 , e ) none
Rationale: "answer let 62976 / n = 123 then n = 62976 / 123 = 512 . option : c"
Answer: c
Question (physics): x alone can do a piece of work in 15 days and y alone can do it in 10 days . x and y undertook to do it for rs . 720 . with the help of z they finished it in 5 days . how much is paid to z ?
Options: a ) rs . 360 , b ) rs . 120 , c ) rs . 240 , d ) rs . 300 , e ) none
Rationale: solution : in one day x can finish 1 / 15 th of the work . in one day y can finish 1 / 10 th of the work . let us say that in one day z can finish 1 / zth of the work . when all the three work together in one day they can finish 1 / 15 + 1 / 10 + 1 / z = 1 / 5 th of the work . therefore , 1 / z = 1 / 30 . ratio of their efficiencies = 1 / 15 : 1 / 10 : 1 / 30 = 2 : 3 : 1 . therefore z receives 1 / 6 th of the total money . according to their efficiencies money is divided as 240 : 360 : 120 . hence , the share of z = rs . 120 . answer b
Answer: b
Question (general): 4 , 25,49 ,
Options: a ) 149 , b ) 169 , c ) 189 , d ) 209 , e ) 121
Rationale: "11 ^ 2 = 121 because follow sequence of square of the prime numbers answer : e"
Answer: e
Question (other): the weights of one liter vegetable ghee packet of two brands ‘ a ’ and ‘ b ’ are 950 gm and 850 gm respectively . if they are mixed in the ratio of 3 : 2 by volumes to form a mixture of 4 liters , what is the weight ( in kg ) of the mixture ?
Options: a ) 3.64 , b ) 1.75 , c ) 3.52 , d ) 2.72 , e ) none of these
Rationale: "here ' s how i did it . my notes from reading the problem were : 1 l a = 950 gm 1 l b = 850 gm we are mixing five parts ( 3 parts a plus 2 parts b , 5 parts total ) to get 4 l , so 5 x = 4 - - - > x = 4 / 5 . each part is 4 / 5 of a liter . so if we have 3 parts a , we have 950 * 3 * ( 4 / 5 ) = 2280 if we have 2 parts b , we have 850 * 2 * ( 4 / 5 ) = 1360 2280 + 1360 = 3640 solving for units gives us 3.64 so the answer is a"
Answer: a
Question (physics): a , b , c can complete a piece of work in 24 , 6,12 days . working together , they complete the same work in how many days ?
Options: a ) 2 , b ) 4 / 5 , c ) 7 / 9 , d ) 10 , e ) 24 / 7
Rationale: "a + b + c 1 day work = 1 / 24 + 1 / 6 + 1 / 12 = 7 / 24 a , b , c together will complete the job in 24 / 7 days answer is e"
Answer: e
Question (general): company c sells a line of 25 products with an average retail price of $ 1,000 . if none of these products sells for less than $ 400 , and exactly 10 of the products sell for less than $ 1,000 , what is the greatest possible selling price of the most expensive product ?
Options: a ) 9000 , b ) 8000 , c ) 7000 , d ) 6000 , e ) 5000
Rationale: "the average price of 25 products is $ 1,000 means that the total price of 25 products is 25 * 1,000 = $ 25,000 . next , since exactly 10 of the products sell for less than $ 1,000 , then let ' s make these 10 items to be at $ 400 each ( min possible ) . now , the remaining 14 items can not be priced less than $ 1,000 , thus the minimum possible price of each of these 14 items is $ 1,000 . thus the minimum possible value of 24 products is 10 * 400 + 14 * 1,000 = $ 18,000 . therefore , the greatest possible selling price of the most expensive product is $ 25,000 - $ 18,200 = $ 7,000 . answer : c ."
Answer: c
Question (general): a caterer ordered 200 ice - cream bars and 200 sundaes . if the total price was $ 200.00 and the price of each ice - cream bar was $ 0.40 , what was the price of each sundae ?
Options: a ) $ 0.60 , b ) $ 0.80 , c ) $ 1.00 , d ) $ 1.20 , e ) $ 1.60
Rationale: "let price of a sundae = s price of ice cream bar = . 4 $ 200 * . 4 + 200 * s = 200 = > 200 * s = 200 = > s = 0.6 answer a"
Answer: a
Question (general): what is the least value of k . so that 123 k 578 is divisible by 11 .
Options: a ) 8 , b ) 7 , c ) 5 , d ) 6 , e ) 4
Rationale: explanation : the difference of the sum of the digits at odd place and the sum of the digits at even place of the number , is either 0 or a number divisible by 11 . ( 1 + 3 + 5 + 8 ) - ( 2 + k + 7 ) = 17 - 9 - k = 8 - k therefore if k = 8 , then the value become zero . k = 8 is the least value so that 123 k 578 is divisible by 11 . answer : option a
Answer: a
Question (other): local kennel has cats and dogs in the ratio of 3 : 4 . if there are 8 fewer cats than dogs , how many dogs are in the kennel ?
Options: a ) 28 , b ) 26 , c ) 24 , d ) 32 , e ) 30
Rationale: "lets work with the data given to us . we know that there ratio of cats to dogs is 3 : 4 or cats 3 dogs 4 we can write number of cats as 3 x and number of dogs as 4 x and we know that 4 x - 3 x = 8 ( therefore x = 8 ) then # of dogs = 4 x 8 = 32 answer is d"
Answer: d
Question (general): the ratio of ducks and frogs in a pond is 37 : 39 respectively . the average number of ducks and frogs in the pond is 142 . what is the number of frogs in the pond ?
Options: a ) 148 , b ) 152 , c ) 156 , d ) 145 , e ) none
Rationale: "solution : ratio of ducks and frogs in pond , = 37 : 39 . average of ducks and frogs in pond , = 142 . so , total number of ducks and frogs in the pond , = 2 * 142 = 284 . therefore , number of frogs , = ( 284 * 39 ) / 76 = 145 . answer : option d"
Answer: d
Question (gain): john had a stock of 1400 books in his bookshop . he sold 75 on monday , 50 on tuesday , 64 on wednesday , 78 on thursday and 135 on friday . what percentage of the books were not sold ?
Options: a ) 50.4 % , b ) 71.3 % , c ) 66.5 % , d ) 34.9 % , e ) 43.5 %
Rationale: "let n be the total number of books sold . hence n = 75 + 50 + 64 + 78 + 135 = 402 let m be the books not sold m = 1400 - n = 1400 - 402 = 998 percentage books not sold / total number of books = 998 / 1400 = 0.713 = 71.3 % correct answer b"
Answer: b
Question (general): two numbers a and b are such that the sum of 8 % of a and 4 % of b is two - third of the sum of 6 % of a and 8 % of b . find the ratio of a : b .
Options: a ) 2 : 1 , b ) 1 : 2 , c ) 4 : 3 , d ) 1 : 3 , e ) 3 : 2
Rationale: "explanation : 8 % of a + 4 % of b = 2 / 3 ( 6 % of a + 8 % of b ) 8 a / 100 + 4 b / 100 = 2 / 3 ( 6 a / 100 + 8 b / 100 ) ⇒ 8 a + 4 b = 2 / 3 ( 6 a + 8 b ) ⇒ 24 a + 12 b = 12 a + 16 b ⇒ 12 a = 4 b ⇒ ab = 4 / 12 ⇒ a : b = 1 : 3 answer : option d"
Answer: d
Question (other): the compound ratio of 5 : 6 , 3 : 4 and 4 : 5 ?
Options: a ) 1 : 1 , b ) 1 : 87 , c ) 1 : 6 , d ) 1 : 9 , e ) 1 : 2
Rationale: "5 / 6 * 3 / 4 * 4 / 5 = 1 / 2 1 : 2 answer : e"
Answer: e
Question (general): 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 15.1 years , the ratio of the number of boys to the number of girls in the class is
Options: a ) 7 : 6 , b ) 2 : 3 , c ) 9 : 3 , d ) 6 : 3 , e ) 2 : 5
Rationale: explanation : let the ratio be k : 1 . then , k * 16.4 + 1 * 15.1 = ( k + 1 ) * 15.8 < = > ( 16.4 - 15.8 ) k = ( 15.8 - 15.1 ) < = > k = 0.7 / 0.6 = 7 / 6 . required ratio = 7 / 6 : 1 = 7 : 6 . answer : a
Answer: a