Cheukting/mathqa huggingface dataset:
Question (physics): if a child walks at the rate of 5 m / min from his home , he is 6 minutes late for school , if he walks at the rate of 7 m / min he reaches half an hour earlier . how far is his school from his home ?
Options: a ) 450 min , b ) 540 min , c ) 630 min , d ) 360 min , e ) none of these
Rationale: let the distance between home and school is x . let actual time to reach be t . thus , x / 5 = t + 6 - - - - ( 1 ) and x / 7 = t - 30 - - - - - ( 2 ) solving equation 1 and 2 x = 630 min answer : c
Answer: c
Question (general): evaluate : | 9 - 8 ( 3 - 12 ) | - | 5 - 11 | = ?
Options: a ) 75 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: according to order of operations , inner brackets first . hence | 9 - 8 ( 3 - 12 ) | - | 5 - 11 | = | 9 - 8 * ( - 9 ) | - | 5 - 11 | according to order of operations , multiplication within absolute value signs ( which may be considered as brackets when it comes to order of operations ) next . hence = | 9 + 72 | - | 5 - 11 | = | 81 | - | - 6 | = 81 - 6 = 75 correct answer a ) 75
Answer: a
Question (gain): in town x , 64 percent of the population are employed , and 50 percent of the population are employed males . what percent of the employed people in town x are females ?
Options: a ) 16 % , b ) 22 % , c ) 32 % , d ) 40 % , e ) 52 %
Rationale: "we are asked to find the percentage of females in employed people . total employed people 64 % , out of which 50 are employed males , hence 14 % are employed females . ( employed females ) / ( total employed people ) = 14 / 64 = 22 % answer : b ."
Answer: b
Question (physics): a train passes a station platform in 35 sec and a man standing on the platform in 20 sec . if the speed of the train is 54 km / hr . what is the length of the platform ?
Options: a ) 228 , b ) 240 , c ) 225 , d ) 166 , e ) 1811
Rationale: "speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 20 = 300 m . let the length of the platform be x m . then , ( x + 300 ) / 35 = 15 = > x = 225 m . answer : c"
Answer: c
Question (gain): the cash difference between the selling prices of an book at a profit of 5 % and 10 % is $ 3 . the ratio of the two selling prices is :
Options: a ) 21 : 22 , b ) 52 : 33 , c ) 52 : 53 , d ) 45 : 53 , e ) 51 : 34
Rationale: "let c . p . of the book be $ x . then , required ratio = 105 % of x / 110 % of x = 105 / 110 = 21 / 22 = 21 : 22 a"
Answer: a
Question (general): what is the greatest prime factor of 3 ^ 6 - 1 ?
Options: a ) 2 , b ) 3 , c ) 7 , d ) 13 , e ) 17
Rationale: "3 ^ 6 - 1 = ( 3 ^ 3 ) ^ 2 - 1 = ( 27 ^ 2 ) - 1 dividing ( 27 ^ 2 ) - 1 by 13 will give us a reminder of 0 ( hint : ( 2 * 13 + 1 ) ^ 2 - 1 / 13 = ( reminder 1 ) - 1 = 0 hence the greatest prime factor must be 13 . answer : d"
Answer: d
Question (general): village p ’ s population is 1200 greater than village q ' s population . if village q ’ s population were reduced by 800 people , then village p ’ s population would be 6 times as large as village q ' s population . what is village q ' s current population ?
Options: a ) 1050 , b ) 1100 , c ) 1150 , d ) 1200 , e ) 1250
Rationale: "p = q + 1200 . p = 6 ( q - 800 ) . 6 ( q - 800 ) = q + 1200 . 5 q = 6000 . q = 1200 . the answer is d ."
Answer: d
Question (gain): a person buys an article at rs . 800 . at what price should he sell the article so as to make a profit of 35 % ?
Options: a ) 600 , b ) 277 , c ) 269 , d ) 261 , e ) 1080
Rationale: "cost price = rs . 800 profit = 35 % of 800 = rs . 280 selling price = cost price + profit = 800 + 280 = 1080 answer : e"
Answer: e
Question (gain): how many liters of water must be added to 18 liters of milk and water containing 10 % water to make it 40 % water ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "by rule of alligation : 40 % - 10 % = 30 % 100 % - 40 % = 60 % quantity of pure water : quantity of the mixture = 1 : 2 there are 18 liters of mixture , so we need to add 9 liters of pure water . the answer is d ."
Answer: d
Question (general): dacid obtained 96 , 95 , 82 , 97 and 95 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 79 , b ) 93 , c ) 88 , d ) 88 , e ) 75
Rationale: "average = ( 96 + 95 + 82 + 97 + 95 ) / 5 = 465 / 5 = 93 . answer : b"
Answer: b
Question (general): the number 0.5 is how much greater than 1 / 6 ?
Options: a ) 1 / 3 , b ) 2 / 10 , c ) 1 / 50 , d ) 1 / 500 , e ) 2 / 500
Rationale: "let x be the difference then . 5 - 1 / 3 = x 5 / 10 - 1 / 3 = x x = 1 / 3 ans a"
Answer: a
Question (probability): there are 22 students in a class . in how many different ways can a committee of 3 students be formed ?
Options: a ) 1180 , b ) 1320 , c ) 1540 , d ) 1760 , e ) 1920
Rationale: "22 c 3 = 22 * 21 * 20 / 6 = 1540 the answer is c ."
Answer: c
Question (physics): a 70 cm long wire is to be cut into two pieces so that one piece will be 2 / 5 th of the other , how many centimeters will the shorter piece be ?
Options: a ) 12 , b ) 20 , c ) 88 , d ) 77 , e ) 14
Rationale: "1 : 2 / 5 = 5 : 2 2 / 7 * 70 = 20 answer : b"
Answer: b
Question (geometry): the slant height of a cone is 20 cm and radius of the base is 10 cm , find the curved surface of the cone .
Options: a ) 330 , b ) 159 , c ) 150 , d ) 200 , e ) 628
Rationale: "π * 10 * 20 = 628 answer : e"
Answer: e
Question (general): evaluate : 6602.5 + 660.25 + 66.025 + 6.6025 + 0.66025
Options: a ) 6819.59775 , b ) 7336.03775 , c ) 6918.59775 , d ) 6198.59775 , e ) 6891.59775
Rationale: "6602.5 660.25 66.025 6.6025 + 0.66025 - - - - - - - - - - - - - - - 7336.03775 answer is b ."
Answer: b
Question (general): the least number which when divided by 3 , 4 , 5 and 6 leaves a remainder 6 , but when divided by 9 leaves no remainder , is
Options: a ) 117 , b ) 126 , c ) 252 , d ) 336 , e ) none of these
Rationale: "explanation : l . c . m of 3 , 4 , 5 , 6 = 60 therefore required number is of the form 60 k + 6 . least value of k for which ( 60 k + 6 ) is divisible by 9 is k = 2 therefore required number = ( 60 x 2 + 6 ) = 126 . answer : b"
Answer: b
Question (general): the temperature of a certain cup of coffee 10 minutes after it was poured was 120 degrees fahrenheit . if the temperature f of the coffee t minutes after it was poured can be determined by the formula f = 120 ( 2 ^ - at ) + 60 , where f is in degrees fahrenheit and a is a constant . then the temperature of the coffee 20 minutes after it was poured was how many degrees fahrenheit ?
Options: a ) 65 , b ) 75 , c ) 80 , d ) 85 , e ) 90
Rationale: "answer : b the temperature of coffee 10 minutes after it was poured ( 120 f ) will help in solving the constant “ a ” . 120 = 120 ( 2 ^ 10 a ) + 60 2 ^ - 1 = 2 ^ 10 a a = - 1 / 10 the temperature of coffee 20 minutes after it was poured is : f = 120 ( 2 ^ - 20 / 10 ) + 60 f = 120 * 1 / 4 + 60 f = 30 + 60 f = 90 e"
Answer: e
Question (general): the ratio 10 : 20 expressed as percent equals to
Options: a ) 50 % , b ) 80 % , c ) 40 % , d ) 90 % , e ) 100 %
Rationale: "explanation : actually it means 10 is what percent of 20 , which can be calculated as , ( 10 / 20 ) * 100 = 10 * 5 = 50 answer : option a"
Answer: a
Question (physics): the speed of a train is 120 kmph . what is the distance covered by it in 40 minutes ?
Options: a ) 50 kmph , b ) 60 kmph , c ) 70 kmph , d ) 80 kmph , e ) 85 kmph
Rationale: "120 * 40 / 60 = 80 kmph answer : d"
Answer: d
Question (geometry): a right triangle aec has to be constructed in the xy - plane so that the right angle is at a and ae is parallel to x axis . the coordinates of a , e and c are integers and satisfy the inequalities - 1 ≤ x ≤ 7 and 1 ≤ y ≤ 7 . how many different triangles can be constructed with these properties ?
Options: a ) 63 , b ) 336 , c ) 567 , d ) 3024 , e ) 5040
Rationale: all the cordinates are integer hence , possible ae values are { - 10 } , { - 11 } . . . . { - 17 } : 8 ways . . . . { 7 , - 1 } , { 70 } . . . . . . { 76 } : 8 ways 9 * 8 ways = 72 for ac values can be { 12 } , { 13 } . . . . { 17 } : 6 ways . . . . . . { 71 } , { 72 } . . . . . { 76 } : 6 ways 7 * 6 = 42 total = 72 * 42 = 3024 hence d
Answer: d
Question (general): if a ^ 2 + b ^ 2 = 25 and ab = 10 , what is the value of the expression ( a - b ) ^ 2 + ( a + b ) ^ 2 ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 50 , e ) 70
Rationale: "( a - b ) ^ 2 = a ^ 2 + b ^ 2 - 2 ab = 25 - 20 = 5 ( a + b ) ^ 2 = a ^ 2 + b ^ 2 + 2 ab = 25 + 20 = 45 so ( a + b ) ^ 2 + ( a - b ) ^ 2 = 45 + 5 = 50 d"
Answer: d
Question (physics): if 25 typists can type 60 letters in 20 minutes , then how many letters will 75 typists working at the same rate complete in 1 hour ?
Options: a ) 270 , b ) 540 , c ) 610 , d ) 510 , e ) 500
Rationale: no . of letters typing by 25 typists in 20 minutes = 60 no . of letters typing by 25 typists in 60 minutes = 60 * 3 = 180 no . of letters typing by 75 typists in 60 minutes = 180 / 25 * 75 = 540 answer : b
Answer: b
Question (gain): a shopkeeper labeled the price of his articles so as to earn a profit of 20 % on the cost price . he then sold the articles by offering a discount of 10 % on the labeled price . what is the actual percent profit earned in the deal ?
Options: a ) 18 % , b ) 20 % , c ) 17 % , d ) 19 % , e ) none of these
Rationale: "explanation : let the cp of the article = rs . 100 . then labeled price = rs . 120 . sp = rs . 120 - 10 % of 120 = rs . 120 - 13 = rs . 118 . gain = rs . 118 â € “ rs . 100 = rs . 18 therefore , gain / profit percent = 18 % . answer : option d"
Answer: d
Question (physics): a person can row at 9 kmph and still water . he takes 6 1 / 2 hours to row from a to b and back . what is the distance between a and b if the speed of the stream is 1 kmph ?
Options: a ) 32 , b ) 28 , c ) 29 , d ) 54 , e ) 20
Rationale: "let the distance between a and b be x km . total time = x / ( 9 + 1 ) + x / ( 9 - 1 ) = 6.5 = > x / 10 + x / 8 = 13 / 2 = > ( 4 x + 5 x ) / 40 = 13 / 2 = > x = 29 km . answer : c"
Answer: c
Question (general): in the junior basketball league there are 18 teams , 2 / 3 of them are bad and ½ are rich . what ca n ' t be the number of teams that are rich and bad
Options: a ) 4 . , b ) 6 . , c ) 7 . , d ) 10 . , e ) 8 .
Rationale: "total teams = 18 bad teams = ( 2 / 3 ) * 18 = 12 rich teams = 9 so maximum value that the both rich and bad can take will be 9 . so e = 10 can not be that value . ans d ."
Answer: d
Question (general): the sum of the present age of henry and jill is 43 . what is their present ages if 5 years ago henry was twice the age of jill ?
Options: a ) and 27 , b ) and 24 , c ) and 22 , d ) and 29 , e ) of these
Rationale: "let the age of jill 5 years ago be x , age of henry be 2 x x + 5 + 2 x + 5 = 43 x = 11 present ages will be 16 and 27 answer : a"
Answer: a
Question (general): a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 84 percent of the distribution lies within one standard deviation d of the mean , what percent of the distribution is less than m + d ?
Options: a ) 16 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 %
Rationale: "this is easiest to solve with a bell - curve histogram . m here is equal to µ in the gaussian normal distribution and thus m = 50 % of the total population . so , if 84 % is one st . dev , then on either side of m we have 84 / 2 = 42 % . so , 84 % are to the right and left of m ( = 50 % ) . in other words , our value m + d = 50 + 42 = 92 % goingfrom the mean m , to the right of the distributionin the bell shaped histogram . . this means that 92 % of the values are below m + d . like i said , doing it on a bell - curve histogram is much easier to fullygethow this works , or you could apply gmat percentile jargon / theory to it e"
Answer: e
Question (other): the compound ratio of 5 : 8 , 3 : 2 and 4 : 5 ?
Options: a ) 1 : 1 , b ) 1 : 87 , c ) 3 : 4 , d ) 1 : 9 , e ) 1 : 2
Rationale: "5 / 8 * 3 / 2 * 4 / 5 = 3 / 4 1 : 1 answer : c"
Answer: c
Question (gain): by selling 14 pencils for a rupee a man loses 22 % . how many for a rupee should he sell in order to gain 22 % ?
Options: a ) 10 , b ) 9 , c ) 7 , d ) 6 , e ) 4
Rationale: "88 % - - - 14 122 % - - - ? 88 / 122 * 14 = 10 answer : a"
Answer: a
Question (physics): i travel the first part of my journey at 40 kmph and the second part at 60 kmph and cover the total distance of 240 km to my destination in 5 hours . how long did the first part of my journey last
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: the total time of journey = 5 hours . let ' x ' hours be the time that i travelled at 40 kmph therefore , 5 – x hours would be time that i travelled at 60 kmph . hence , i would have covered x × 40 + ( 5 − x ) 60 kms in the 5 hours = 240 kms . solving , for x in the equation 40 x + ( 5 – x ) × 60 = 240 , we get 40 x + 300 – 60 x = 240 ⇒ 20 x = 60 or x = 3 hours answer : c
Answer: c
Question (physics): if 4 cats can kill 4 rats in 4 minutes , how long will it take 100 cats to kill 100 rats ?
Options: a ) 1 minutes , b ) 2 minutes , c ) 3 minutes , d ) 4 minutes , e ) 5 minutes
Rationale: "it will take 4 minutes for 100 cats to kill 100 rats . 1 cat can kill 1 rat in 4 minutes , so 100 cats can kill 100 rats in 4 minutes answer d"
Answer: d
Question (physics): how many seconds will a 500 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 75 km / hr ?
Options: a ) 25 , b ) 30 , c ) 99 , d ) 88 , e ) 61
Rationale: "speed of train relative to man = 75 - 3 = 72 km / hr . = 72 * 5 / 18 = 20 m / sec . time taken to pass the man = 500 * 1 / 20 = 25 sec . answer : a"
Answer: a
Question (geometry): if the volume of the cube is 729 , then the surface area of the cube will be
Options: a ) 486
b ) 255
c ) 2866
d ) 265
e ) 872
Rationale: explanation : \ inline \ fn _ jvn a ^ 3 = 729 ; a = 9 surface area = ( 6 x 9 x 9 ) = 486 \ inline \ fn _ jvn cm ^ 2 answer : a ) 486 sq . cm
Answer: a
Question (geometry): when the circumference and area of a circle are numerically equal , then the diameter is numerically equal to
Options: a ) area
b ) circumference
c ) 4
d ) 2 π
e ) none of these
Rationale: according to question , circumference of circle = area of circle or π d = π ( d ⁄ 2 ) 2 [ where d = diameter ] ∴ d = 4 answer c
Answer: c
Question (general): if x and y are integers such that ( x + 1 ) ^ 2 is less than or equal to 49 and ( y - 1 ) ^ 2 is less than 64 , what is the sum of the maximum possible value of xy and the minimum possible value of xy ?
Options: a ) - 16 , b ) - 14 , c ) 0 , d ) 14 , e ) 16
Rationale: ( x + 1 ) ^ 2 < = 49 x < = 6 x > = - 8 ( y - 1 ) ^ 2 < 64 y < 9 y > - 7 max possible value of xy is - 8 × - 6 = 48 minimum possible value of xy is - 8 × 8 = - 64 - 64 + 48 = - 16 answer : a
Answer: a
Question (gain): in an election between two candidates , one got 55 % of the total valid votes , 20 % of the votes were invalid . if the total number of votes was 7500 , the number of valid votes that the other candidate got , was
Options: a ) 2500 , b ) 2700 , c ) 3000 , d ) 3100 , e ) nobe
Rationale: solution number of valid votes = 80 % of 7500 = 6000 . valid votes polled by other candidates = 45 % of 6000 ( 45 / 100 × 6000 ) = 2700 . answer b
Answer: b
Question (geometry): find the circumference and area of radius 6 cm .
Options: a ) 113 cm ²
b ) 144 cm ²
c ) 154 cm ²
d ) 184 cm ²
e ) 194 cm ²
Rationale: area of circle = π r ² = 22 / 7 × 6 × 6 cm ² = 113 cm ² answer : a
Answer: a
Question (general): cost is expressed by the formula tb ^ 4 . if b is doubled , the new cost r is what percent of the original cost ?
Options: a ) r = 200 , b ) r = 600 , c ) r = 800 , d ) r = 1600 , e ) r = 50
Rationale: original cost c 1 = t 1 * b 1 ^ 4 new cost c 2 = t 2 * b 2 ^ 4 . . . . only b is doubled so t 2 = t 1 and b 2 = 2 b 1 c 2 = t 2 * ( 2 b 1 ) ^ 4 = 16 ( t 1 * b 1 ^ 4 ) = 16 c 1 16 times c 1 = > 1600 % of c 1 ans d = 1600
Answer: d
Question (other): the ratio of three numbers is 5 : 3 : 4 and their sum is 108 . the second number of the three numbers is ?
Options: a ) 23 , b ) 27 , c ) 30 , d ) 32 , e ) 34
Rationale: "5 : 3 : 4 total parts = 12 12 parts - - > 108 1 part - - - - > 9 the second number of the three numbers is = 3 3 parts - - - - > 27 b )"
Answer: b
Question (gain): there are two concentric circles with radii 5 and 4 . if the radius of the outer circle is increased by 20 % and the radius of the inner circle decreased by 50 % , by what percent does the area between the circles increase ?
Options: a ) 56 , b ) 156 , c ) 256 , d ) 356 , e ) 456
Rationale: the area of a circle is pir ^ 2 , where r is the radius . the area of the big circle is 25 pi . the area of the small circle is 16 pi . the area a 1 between the circles is 9 pi . when the big circle ' s radius increases , the new area is 36 pi . when the small circle ' s radius decreases , the new area is 4 pi . the area a 2 between the circles is 32 pi . the ratio of a 2 / a 1 is 32 / 9 = 3.56 which is an increase of 256 % . the answer is c .
Answer: c
Question (gain): a sum of money at simple interest amounts to rs . 815 in 2 years and to rs . 854 in 3 years . the sum is :
Options: a ) 500 , b ) 698 , c ) 780 , d ) 737 , e ) none
Rationale: "sol . s . i . for 1 year = rs . ( 854 - 815 ) = rs . 39 . s . i . for 2 years = rs . ( 39 * 2 ) = rs . 78 . â ˆ ´ principal = rs . ( 815 - 78 ) = rs . 737 . answer d"
Answer: d
Question (geometry): the ratio of the area of a square to that of the square drawn on its diagonal is ?
Options: a ) 2 : 5
b ) 3 : 4
c ) 3 : 5
d ) 1 : 2
e ) 2 : 3
Rationale: explanation : a 2 : ( a â ˆ š 2 ) 2 a 2 : 2 a 2 - > 1 : 2 answer is d
Answer: d
Question (geometry): a rectangular floor that measures 8 meters by 10 meters is to be covered with carpet squares that each measure 2 meters by 2 meters . if the carpet squares cost $ 10 apiece , what is the total cost for the number of carpet squares needed to cover the floor ?
Options: a ) $ 200 , b ) $ 240 , c ) $ 480 , d ) $ 960 , e ) $ 1,920
Rationale: "the width of the rectangular floor ( 8 m ) is a multiple of one side of the square ( 2 m ) , and the length of the floor ( 10 m ) is also a multiple of the side of the square . so the number of carpets to cover the floor is ( 8 / 2 ) * ( 10 / 2 ) = 20 . the total cost is 20 * 10 = $ 200 . the answer is , therefore , a ."
Answer: a
Question (general): there are 6 positive and 8 negative numbers . 4 numbers are choosen at random and multiplied . the probability that the product is positive is :
Options: a ) 500 / 1001 , b ) 503 / 1001 , c ) 303 / 1001 , d ) 301 / 1001 , e ) 505 / 1001
Rationale: 6 c 4 / 14 c 4 + ( 6 c 2 * 8 c 2 ) / 14 c 4 + 8 c 4 / 14 c 4 = 505 / 1001 case 1 : only 4 positive no . case 2 : 2 positive and 2 negative no . case 3 : 4 negative no . answer : e
Answer: e
Question (gain): population of a city in 20004 was 1000000 . if in 2005 there isan increment of 15 % , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 35 % , then find the population of city atthe end of the year 2007
Options: a ) 976374 , b ) 979923 , c ) 1009125 , d ) 2356677 , e ) 1083875
Rationale: required population = p ( 1 + r 1 / 100 ) ( 1 - r 2 / 100 ) ( 1 + r 3 / 100 ) = p ( 1 + 15 / 100 ) ( 1 - 35 / 100 ) ( 1 + 35 / 100 ) = 1009125 c
Answer: c
Question (general): f ( x ) is a function such that f ( x ) + 3 f ( 8 - x ) = x for all real numbers x . find the value of f ( 2 ) .
Options: a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1
Rationale: f ( x ) + 3 f ( 8 - x ) = x : given f ( 2 ) + 3 f ( 6 ) = 2 : x = 2 above f ( 6 ) + 3 f ( 2 ) = 6 : x = 6 above f ( 6 ) = 6 - 3 f ( 2 ) : solve equation c for f ( 6 ) f ( 2 ) + 3 ( 6 - 3 f ( 2 ) ) = 2 : substitute f ( 2 ) = 2 : solve above equation . correct answer is d ) 2
Answer: d
Question (general): a bag contains an equal number of one rupee , 50 paise and 25 paise coins respectively . if the total value is 105 , how many coins of each type are there ?
Options: a ) 20 coins , b ) 30 coins , c ) 40 coins , d ) 60 coins , e ) none of these
Rationale: "let number of each type of coin = x . then , 1 × x + . 50 × x + . 25 x = 105 ⇒ 1.75 x = 105 ⇒ x = 60 coins answer d"
Answer: d
Question (physics): john can complete a given task in 20 days . jane will take only 10 days to complete the same task . john and jane set out to complete the task by beginning to work together . however , jane was indisposed 5 days before the work got over . in how many days did the work get over from the time john and jane started to work on it together ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 16 , e ) 20
Rationale: in such questions , you need to start from the end . last 5 days john works alone and completes 5 * ( 1 / 20 ) = 1 / 4 of the work . so 3 / 4 of the work should have been completed by the two of them together before jane left . their combined rate of work is 1 / 20 + 1 / 10 = 3 / 20 time taken to complete 3 / 4 of the work = ( 3 / 4 ) / ( 3 / 20 ) = 5 days . so total number of days taken to complete the work = 5 + 5 = 10 days . b
Answer: b
Question (gain): a man sold 20 articles for $ 60 and gained 10 % . how many articles should he sell for $ 90 to incur a loss 20 % ?
Options: a ) 45 , b ) 36 , c ) 40 , d ) 50 , e ) 48
Rationale: "production cost per article : $ 60 * ( 100 % - 10 % ) / 20 = $ 2.70 required production costs for a loss of 20 % : $ 90 * ( 100 % + 20 % ) = $ 108 number of articles to be sold for $ 108 to incur a 20 % loss : $ 108 / $ 2.70 = 40 thus , solution c is correct ."
Answer: c
Question (general): list k consists of 10 consecutive integers . if - 4 is the least integer in list k , what is the range of the positive integers in list k ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 11 , e ) 4
Rationale: "answer = e = 4 if least = - 4 , then largest = 5 range = 5 - 1 = 4"
Answer: e
Question (gain): in a school of 400 boys , 44 % of muslims , 28 % hindus , 10 % sikhs and the remaining of other communities . how many belonged to the other communities ?
Options: a ) 41 , b ) 63 , c ) 72 , d ) 63 , e ) 50
Rationale: "44 + 28 + 10 = 82 % 100 – 82 = 18 % 400 * 18 / 100 = 72 answer : c"
Answer: c
Question (physics): a train 120 m in length crosses a telegraph post in 6 seconds . the speed of the train is ?
Options: a ) 72 kmph , b ) 88 kmph , c ) 54 kmph , d ) 18 kmph , e ) 19 kmph
Rationale: "s = 120 / 6 * 18 / 5 = 72 kmph answer : a"
Answer: a
Question (physics): two boats are heading towards each other at constant speeds of 3 miles / hr and 21 miles / hr respectively . they begin at a distance 20 miles from each other . how far are they ( in miles ) one minute before they collide ?
Options: a ) 1 / 12 , b ) 5 / 12 , c ) 1 / 6 , d ) 1 / 3 , e ) 3 / 15
Rationale: "the question asks : how far apart will they be 1 minute = 1 / 60 hours before they collide ? since the combined rate of the boats is 3 + 21 = 24 mph then 1 / 60 hours before they collide they ' ll be rate * time = distance - - > 24 * 1 / 60 = 3 / 15 miles apart . answer : e ."
Answer: e
Question (physics): two trains of equal lengths take 12 sec and 20 sec respectively to cross a telegraph post . if the length of each train be 120 m , in what time will they cross other travelling in opposite direction ?
Options: a ) 16 sec , b ) 12 sec , c ) 17 sec , d ) 15 sec , e ) 23 sec
Rationale: "speed of the first train = 120 / 12 = 10 m / sec . speed of the second train = 120 / 20 = 6 m / sec . relative speed = 10 + 6 = 16 m / sec . required time = ( 120 + 120 ) / 16 = 15 sec . answer : d"
Answer: d
Question (gain): a couple who own an appliance store discover that if they advertise a sales discount of 10 % on every item in the store , at the end of one month the number of total items sold increases 20 % . their gross income from sales for one month increases by what percent ?
Options: a ) 2 % , b ) 4 % , c ) 5 % , d ) 8 % , e ) 12 %
Rationale: "let list price of an item = 100 discount on each item = 10 % discounted price of an item = . 9 * 100 = 90 if they advertise a sales discount of 10 % on every item in the store , at the end of one month the number of total items sold increases 20 % originally if 10 items were sold in a month , with the new discount 12 items will be sold original revenue = no of items * price of an item = 10 * 100 = 1000 new revenue = 12 * 90 = 1080 increase in gross income = 1080 - 1000 = 80 % increase in gross revenue = 80 / 1000 * 100 % = 8 % answer d"
Answer: d