Cheukting/mathqa huggingface dataset:
Question (physics): working alone at its constant rate , machine a produces x boxes in 10 minutes and working alone at its constant rate , machine b produces 2 x boxes in 5 minutes . how many minutes does it take machines a and b , working simultaneously at their respective constant rates , to produce 7 x boxes ?
Options: a ) 3 minutes , b ) 4 minutes , c ) 5 minutes , d ) 14 minutes , e ) 12 minutes
Rationale: "rate = work / time given rate of machine a = x / 10 min machine b produces 2 x boxes in 5 min hence , machine b produces 4 x boxes in 10 min . rate of machine b = 4 x / 10 we need tofind the combined time that machines a and b , working simultaneouslytakeat their respective constant rates let ' s first find the combined rate of machine a and b rate of machine a = x / 10 min + rate of machine b = 4 x / 10 = 5 x / 10 now combine time = combine work needs to be done / combine rate = 7 x / 5 x * 10 = 14 min ans : d"
Answer: d
Question (gain): in a shop , the profit is 320 % of the cost . if the cost increases by 25 % but the selling price remains constant , approximately what percentage of the selling price is the profit ?
Options: a ) 70 % , b ) 50 % , c ) 100 % , d ) 60 % , e ) 55 %
Rationale: "cp . = rs . 100 . = > profit = rs . 320 , s . p . = rs . 420 . new c . p . = 125 % of rs . 100 = rs . 125 new s . p . = rs . 420 . profit = rs . ( 420 - 125 ) = rs . 295 . req = ( 295 / 420 * 100 ) = = > 70 % answer a"
Answer: a
Question (physics): 2 trains in same direction at 50 km / hr , 32 km / hr . a man in slower train observes 15 sec elapse before the faster train completely passed by him what is length of faster train ?
Options: a ) 65 meters , b ) 75 meters , c ) 85 meters , d ) 95 meters , e ) 55 meters
Rationale: relative speed = 18 k / hr = 5 m / sec distance covered = length of faster train = 5 * 15 = 75 meters answer : b
Answer: b
Question (physics): lionel left his house and walked towards walt ' s house , 48 miles away . four hours later , walt left his house and ran towards lionel ' s house . if lionel ' s speed was 2 miles per hour and walt ' s 6 miles per hour , how many miles had lionel walked when he met walt ?
Options: a ) 12 , b ) 18 , c ) 20 , d ) 24 , e ) 28
Rationale: "in the first 4 hours lionel at the rate of 2 miles per hour covered distance = rate * time = 4 * 2 = 8 miles . so , the distance between him and walt was 48 - 8 = 40 miles when walt left his house . now , their combined rate to cover this distance was 2 + 6 = 8 miles per hour , hence they will meet ( they will cover that distance ) in time = distance / rate = 40 / 8 = 5 hours . total time that lionel was walking is 4 + 5 = 9 hours , which means that he covered in that time interval distance = rate * time = 2 * 9 = 18 miles . answer : b ."
Answer: b
Question (gain): x and y started a business by investing rs . 36000 and rs . 42000 respectively after 4 months z joined in the business with an investment of rs . 48000 , then find share of z in the profit of rs . 13860 ?
Options: a ) 4032 , b ) 4000 , c ) 3250 , d ) 3825 , e ) 3985
Rationale: "ratio of investment , as investments is for different time . investment x number of units of time . ratio of investments x : y : z = 36000 : 42000 : 48000 = > 6 : 7 : 8 . x = 6 x 12 months = 72 , y = 7 x 12 = 84 , z = 8 x 8 = 64 = > 18 : 21 : 16 . ratio of investments = > x : y : z = 18 : 21 : 16 . investment ratio = profit sharing ratio . z = 13860 ã — 16 / 55 = rs . 4032 . share of z in the profit is rs . 4032 . option a"
Answer: a
Question (physics): a cyclist traveled for two days . on the second day the cyclist traveled 3 hours longer and at an average speed 10 mile per hour slower than she traveled on the first day . if during the two days she traveled a total of 280 miles and spent a total of 12 hours traveling , what was her average speed on the second day ?
Options: a ) 5 mph , b ) 10 mph , c ) 20 mph , d ) 30 mph , e ) 40 mph
Rationale: "solution : d = 280 mi t = 12 hrs day 1 time = t 1 day 2 time = t 2 t 2 - t 1 = 4 hrs - - - - - ( i ) t 1 + t 2 = 12 hrs - - - - - ( ii ) adding i and ii , t 2 = 8 hrs and t 1 = 4 hrs day 1 rate = r 1 day 2 rate = r 2 r 1 - r 2 = 10 mph i . e . r 1 = 10 + r 2 280 = 8 r 2 + 4 r 1 i . e . 280 = 8 r 2 + 4 ( 10 + r 2 ) i . e . r 2 = 20 mph answer : b"
Answer: b
Question (general): from the digits 2 , 3 , 4 , 5 , 6 and 7 , how many 5 - digit numbers can be formed that have distinct digits and are multiples of 12 ?
Options: a ) 36 , b ) 60 , c ) 84 , d ) 72 , e ) 86
Rationale: detailed solution any multiple of 12 should be a multiple of 4 and 3 . first , let us look at the constraint for a number being a multiple of 3 . sum of the digits should be a multiple of 3 . sum of all numbers from 2 to 7 is 27 . so , if we have to drop a digit and still retain a multiple of 3 , we should drop either 3 or 6 . so , the possible 5 digits are 2 , 4 , 5 , 6 , 7 or 2 , 3 , 4 , 5 , 7 . when the digits are 2 , 4 , 5 , 6 , 7 . the last two digits possible for the number to be a multiple of 4 are 24 , 64 , 52 , 72 , 56 , 76 . for each of these combinations , there are 6 different numbers possible . so , with this set of 5 digits we can have 36 different numbers . when the digits are 2 , 3 , 4 , 5 , 7 . the last two digits possible for the number to be a multiple of 4 are 32 , 52 , 72 , 24 . for each of these combinations , there are 6 different numbers possible . so , with this set of 5 digits we can have 24 different numbers . overall , there are 60 different 5 - digit numbers possible . correct answer : b
Answer: b
Question (general): what is the least common multiple of 8,12 , 32,14
Options: a ) 672 , b ) 682 , c ) 328 , d ) 964 , e ) 285
Rationale: "the given numbers are 8,12 , 32,14 thus the l . c . m is 2 * 2 * 2 * 1 * 3 * 4 * 7 = 672 the answer is a"
Answer: a
Question (general): the difference between the local value and the face value of 8 in the numeral 96348621 is
Options: a ) 6992 , b ) 6982 , c ) 7982 , d ) 7972 , e ) 7992
Rationale: "explanation : ( local value of 8 ) - ( face value of 8 ) = ( 8000 - 8 ) = 7992 e )"
Answer: e
Question (other): find the ratio in which rice at rs . 7.20 a kg be mixed with rice at rs . 5.80 a kg to produce a mixture worth rs . 6.30 a kg ?
Options: a ) 5 : 9 , b ) 2 : 3 , c ) 3 : 4 , d ) 4 : 5 , e ) none of these
Rationale: "solution required ratio = 50 : 90 = 5 : 9 answer a"
Answer: a
Question (physics): three pipes , a , b , & c are attached to a tank . a & b can fill it in 20 & 30 minutes respectively while c can empty it in 15 minutes . if a , b & c are kept open successively for 4 minute each , how soon will the tank be filled ?
Options: a ) 2 hours , b ) 12 hours , c ) 3 hours , d ) 5 hours , e ) 6 hours
Rationale: in three minute 1 / 20 + 1 / 30 - 1 / 15 = 1 / 60 part is filled 12 min - - - - - - - - 1 / 60 parts x min - - - - - - - - - 1 part ( full ) x = 720 min = 12 hours answer : b
Answer: b
Question (general): when positive integer x is divided by 8 , the quotient is y and the remainder is 2 . when 2 x is divided by 7 , the quotient is 2 y and the remainder is 4 . what is the value of 6 y – x ?
Options: a ) - 1 , b ) 1 , c ) - 2 , d ) 2 , e ) - 3
Rationale: "( 1 ) x = 8 y + 2 ( 2 ) 2 x = 14 y + 4 ( 2 ) - ( 1 ) : x = 6 y + 2 6 y - x = - 2 the answer is c ."
Answer: c
Question (general): if n = 2 ^ 0.15 and n ^ b = 32 , b must equal
Options: a ) 3 / 80 , b ) 3 / 5 , c ) 4 , d ) 100 / 3 , e ) 80 / 3
Rationale: "15 / 100 = 3 / 20 n = 2 ^ 3 / 20 n ^ b = 2 ^ 5 ( 2 ^ 3 / 20 ) ^ b = 2 ^ 5 b = 100 / 3 answer : d"
Answer: d
Question (general): a man is 25 years older than his son . in two years , his age will be twice the age of his son . the present age of his son is
Options: a ) 21 , b ) 22 , c ) 20 , d ) 18 , e ) 23
Rationale: "explanation : let the son ' s present age be x years . then , man ' s present age = ( x + 25 ) years = > ( x + 25 ) + 2 = 2 ( x + 2 ) = > x + 27 = 2 x + 4 so , x = 23 . answer : e"
Answer: e
Question (gain): during a special promotion , a certain filling station is offering a 10 percent discount on gas purchased after the first 5 gallons . if kim purchased 20 gallons of gas , and isabella purchased 25 gallons of gas , then isabella ‟ s total per - gallon discount is what percent of kim ‟ s total per - gallon discount ?
Options: a ) 80 % , b ) 107 % , c ) 116.7 % , d ) 120 % , e ) 140 %
Rationale: "kim purchased 20 gallons of gas . she paid for 5 + 0.9 * 15 = 18.5 gallons , so the overall discount she got was 1.5 / 20 = 7.5 % . isabella purchased 25 gallons of gas . she paid for 5 + 0.9 * 20 = 23 gallons , so the overall discount she got was . 5 / 25 = 8 % . 8 is 8 / 7.5 * 100 = 107 % of 7.5 . answer : b ."
Answer: b
Question (gain): jerome anticipated that the webweb . com stock price would fall and sold all his webweb . com stocks for $ 5 per stock . he paid $ 10,000 tax on the revenue . a week later , jerome became convinced that the webweb . com stock price would rise , and he used the money that he had gotten from selling the webweb . com stocks to purchase them again , this time at $ 6 per stock . if jerome ended up having 2000 webweb . com stocks fewer than the number he had before selling them , how many webweb . com stocks did he have originally ?
Options: a ) 10,000 , b ) 11,600 , c ) 12,000 , d ) 14,000 , e ) 16,400
Rationale: let the number of shares be x . 5 * x - 10000 ( money paid in taxes ) = 6 ( x - 2000 ) solving for x , we get the shares as 12000 . ans : ( option c )
Answer: c
Question (general): if m is a positive integer and m ^ 2 is divisible by 54 , then the largest positive integer that must divide m is ?
Options: a ) 3 , b ) 6 , c ) 18 , d ) 12 , e ) 16
Rationale: m ^ 2 is divisible by 48 so m ^ 2 must be multiple of 48 . if the value of m is multiples of 18 then it will satisfy the condition . if we if m is 12 or 24 or 36 then it ans is c but if m = 54 then answer should be 16 . is the question right ? or am i missing some thing ? c
Answer: c
Question (physics): if 24 lines are drawn in a plane such that no two of them are parallel and no three are concurrent , then in how many points do they intersect ?
Options: a ) 276 , b ) 350 , c ) 425 , d ) 512 , e ) 648
Rationale: "if two lines are not parallel , then they will intersect in exactly one point . lines can be extended infinitely on both ends so somewhere they will intersect with each other if they are not parallel . we are also given that no three lines are concurrent . this means that no three lines intersect at the same point . so every pair of two lines we select will have a unique point of intersection which they will not share with any third line . the number of ways to select 2 lines from 24 lines is 24 c 2 = 276 the answer is a ."
Answer: a
Question (general): a marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each . there can be no less than 8 musicians per row and no more than 30 musicians per row . how many different rectangular formations p are possible ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) p = 8
Rationale: "the combinations could be p { ( 1,240 ) , ( 2,120 ) , ( 3,80 ) , ( 4,60 ) , ( 5,48 ) , ( 6,40 ) , ( 8,30 ) , ( 10,24 ) , ( 12,20 ) , ) 15,16 ) , ( 16,15 ) , ( 20,12 ) , ( 24,10 ) , ( 30,8 ) , ( 40,6 ) , ( 48,5 ) , ( 60,4 ) , ( 80,3 ) , ( 120,2 ) , ( 240,1 ) } of these we are told 8 < = t < = 30 so we can remove these pairs , and we are left only with . { ( 8,30 , ( 10,24 ) , ( 12,20 ) , ( 15,16 ) , ( 16,15 ) , ( 20,12 ) , ( 24,10 ) , ( 30,8 ) } hence 8 . e"
Answer: e
Question (general): in the x - y plane , there are 4 points ( 0,0 ) , ( 0,4 ) , ( 9,4 ) , and ( 9,0 ) . if these 4 points makes a rectangle , what is the probability that x + y < 4 ?
Options: a ) 2 / 5 , b ) 3 / 5 , c ) 3 / 7 , d ) 4 / 7 , e ) 2 / 9
Rationale: "the line y = - x + 4 intersects the rectangle and these three points of intersection ( 0,0 ) , ( 0,4 ) and ( 4,0 ) form a triangle . the points below the line y = - x + 4 satisfy x + y < 4 . the area of this triangle is ( 1 / 2 ) ( 4 ) ( 4 ) = 8 the area of the rectangle is 36 . p ( x + y < 4 ) = 8 / 36 = 2 / 9 the answer is e ."
Answer: e
Question (general): for every x , the action [ x ] is defined : [ x ] is the greatest integer less than or equal to x . what is the value of [ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.4 ] - 6.2 ?
Options: a ) 12.6 . , b ) 14.4 . , c ) 15.8 . , d ) 16.2 . , e ) 16.4 .
Rationale: "[ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.4 ] - 6.2 = 6 * 0 + 2 * 7.2 + 8 - 6.2 = 0 + 14.4 + 1.8 16.2 answer d"
Answer: d
Question (physics): machine a takes 100 hours to complete a certain job and starts that job at 6 am . after ten hour of working alone , machine a is joined by machine b and together they complete the job at 6 pm . how long would it have taken machine b to complete the job if it had worked alone for the entire job ?
Options: a ) 24.65 , b ) 22.27 , c ) 2.273 , d ) 11.62 , e ) 21.13
Rationale: "let us assume total job = 100 units a finishes 100 units in 100 hrs ( given ) hence a ( working rate ) = 1 units / hr now given that a works for 10 hr ( so 10 units done ) then a and b finish total work in 12 hours . hence a and b finish 90 units in 2 hours . of these 1 x 2 = 2 units were done by a . hence b did 88 units in 2 hours . hence b ( working rate ) = 44 units / hr hence b takes 100 / 44 = 2.273 hours to complete the job . answer c ."
Answer: c
Question (physics): efrida and frazer who live 12 miles apart , meet at a restaurant that is directly north of efrida ' s home and directly east of frazer ' s home . if the restaurant is two miles closer to efrida ' s home , than to frazer ' s home , how many miles is the restaurant from frazer ' s home ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 10 , e ) 11
Rationale: "it ' s a simple geometry problem . look at the diagram below : answer : d ."
Answer: d
Question (geometry): a full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet . oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck ' s tank is completely filled . if the truck ' s tank has a radius of 7 feet and a height of 10 feet , how far ( in feet ) did the oil level drop in the stationary tank ?
Options: a ) 0.07 , b ) 0.049 , c ) 0.7 , d ) 0.49 , e ) 4.9
Rationale: "the volume of oil pumped to the tank = the volume of oil taken away from stationary cylinder . pi * 49 * 10 = pi * h * 100 * 100 ( h is distance that the oil level dropped ) h = 490 / 10,000 = 49 / 1000 = 0.049 ft the answer is b ."
Answer: b
Question (gain): at the end of the first quarter , the share price of a certain mutual fund was 25 percent higher than it was at the beginning of the year . at the end of the second quarter , the share price was 80 percent higher than it was at the beginning of the year . what was the percent increase in the share price from the end of the first quarter to the end of the second quarter ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 33 % , e ) 44 %
Rationale: "another method is to use the formula for 2 successive percentage changes : total = a + b + ab / 100 80 = 25 + b + 25 b / 100 b = 44 answer ( e )"
Answer: e
Question (gain): an article is bought for rs . 1200 and sold for rs . 1300 , find the loss percent ?
Options: a ) 8.33 % , b ) 9.33 % , c ) 10.00 % , d ) 11.11 % , e ) 7.56 %
Rationale: "1200 - - - - 100 100 - - - - ? = > 16 2 / 3 % answer : a"
Answer: a
Question (gain): by selling an article for $ 100 a man gains $ 20 then his gain % ?
Options: a ) 25 % , b ) 30 % , c ) 50 % , d ) 20 % , e ) 10 %
Rationale: "s . p . = $ 100 gain = $ 20 c . p . = 100 - 20 = 80 gain % = 20 / 80 * 100 = 25 % answer is a"
Answer: a
Question (physics): john traveled 80 % of the way from yellow - town to green - fields by train at an average speed of 80 miles per hour . the rest of the way john traveled by car at an average speed of v miles per hour . if the average speed for the entire trip was 50 miles per hour , what is v in miles per hour ?
Options: a ) 20 , b ) 40 , c ) 50 , d ) 55 , e ) 70
Rationale: hibunuel the question seems incorrect . it should not be 80 % at the speed of 80 . however if it ' s 20 % at the speed of 80 , answer comes out 55 . the question is correct . here ' s the explanation : let distance be d . we can find the total timeequate it , which comes as : 0.8 d / 80 + 0.2 d / v = d / 50 = > v = 20 ( option a ) .
Answer: a
Question (gain): john purchased a grinder and a mobile for rs . 15000 & rs . 8000 respectively . he sold the grinder at a loss of 5 % and the mobile phone at a profit of 10 % . overall how much he make a profit .
Options: a ) s . 90 , b ) s . 120 , c ) s . 200 , d ) s . 50 , e ) s . 290
Rationale: let the sp of the refrigerator and the mobile phone be rs . r and rs . m respectively . r = 15000 ( 1 - 5 / 100 ) = 15000 - 750 m = 8000 ( 1 + 10 / 100 ) = 8000 + 800 total sp - total cp = r + m - ( 15000 + 8000 ) = - 750 + 800 = rs . 50 as this is positive , an overall profit of rs . 50 was made . d
Answer: d
Question (gain): the manufacturing cost of a shoe is rs . 230 and the transportation lost is rs . 500 for 100 shoes . what will be the selling price if it is sold at 20 % gains
Options: a ) s 282 , b ) s 216 , c ) s 220 , d ) s 210 , e ) s 217
Rationale: "explanation : total cost of a watch = 230 + ( 500 / 100 ) = 235 . gain = 20 % = > sp = 1.2 cp = 1.2 x 235 = 282 answer : a"
Answer: a
Question (general): we have boxes colored either red or blue . in each blue box there is a fixed number of blueberries . in each red box there is a fixed number of strawberries . if we dispose of one blue box for one additional red box , the total number of berries would increase by 15 , and the difference between the total number of strawberries and the total number of blueberries would increase by 87 . each blue box contains how many blueberries ?
Options: a ) 28 , b ) 30 , c ) 32 , d ) 34 , e ) 36
Rationale: "let x be the number of blueberries in each blue box . then there are x + 15 strawberries in each red box . x + ( x + 15 ) = 87 x = 36 the answer is e ."
Answer: e
Question (physics): suppose you work for a manufacturing plant that pays you $ 12.50 an hour plus $ 0.16 for each widget you make . how many widgets must you produce in a 40 hour week to earn $ 700 ( before payroll deductions ) ?
Options: a ) 1220 , b ) 1250 , c ) 1280 , d ) 1310 , e ) 1340
Rationale: "total pay = 40 * $ 12.50 + $ 0.16 * x = 700 x = 200 / 0.16 = 1250 the answer is b ."
Answer: b
Question (probability): how many positive integers less than 500 can be formed using the numbers 1 , 2 , 3 and 5 for the digits ?
Options: a ) 48 , b ) 52 , c ) 66 , d ) 68 , e ) 84
Rationale: "notice that we can find the number of 2 and 3 digit numbers by just assuming the first digit can also be zero : 0 1 1 1 2 2 2 3 3 3 5 5 number of possibilities = 4 * 4 * 4 = 64 . then , just add up the number of 1 digits numbers = 4 , so total is 64 + 4 = 68 . answer : d"
Answer: d
Question (general): a rope of which a calf is tied is increased from 12 m to 25 m , how much additional grassy ground shall it graze ?
Options: a ) 1400 , b ) 141.71 , c ) 1210 , d ) 1511.71 , e ) 1500
Rationale: "π ( 252 – 122 ) = 1511.71 answer : d"
Answer: d
Question (physics): two pipes a and b can fill a tank in 30 and 60 minutes respectively . if both the pipes are used together , then how long will it take to fill the tank ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 24 , e ) 25
Rationale: "part filled by a in 1 min . = 1 / 30 part filled by b in 1 min . = 1 / 60 part filled by ( a + b ) in 1 min . = 1 / 30 + 1 / 60 = 1 / 20 . both the pipes can fill the tank in 20 minutes . answer : b"
Answer: b
Question (gain): by selling 22 pencils for a rupee a man loses 40 % . how many for a rupee should he sell in order to gain 40 % ?
Options: a ) 8.56 , b ) 9.35 , c ) 9.43 , d ) 6.56 , e ) 5.5
Rationale: "60 % - - - 22 140 % - - - ? 60 / 140 * 22 = 9.43 answer : c"
Answer: c
Question (general): the difference between the place values of two threes in the numerical 40378273 is
Options: a ) 29997 , b ) 299997 , c ) 297 , d ) 0 , e ) none of them
Rationale: "required difference = ( 300000 - 3 ) = 299997 . answer is b"
Answer: b
Question (other): if m = 3 ^ n , what is the greatest value of n for which m is a factor of 22 !
Options: a ) 8 , b ) 10 , c ) 9 , d ) 14 , e ) 16
Rationale: "solution - consider multiples of 25 ! = > 3 , 6,9 , 12,15 , 18,21 count no . of 3 in each multiple . 3 = 3 x 1 - > 1 6 = 3 x 2 - > 1 9 = 3 x 3 - > 2 12 = 3 x 4 - > 1 15 = 3 x 5 - > 1 18 = 3 x 3 x 2 - > 2 21 = 3 x 7 - > 1 - - - - count 3 ' s = 9 so answer is 9 answer : c"
Answer: c
Question (gain): a shopkeeper sold an book offering a discount of 5 % and earned a profit of 14 % . what would have been the percentage of profit earned if no discount was offered ?
Options: a ) 140 , b ) 120 , c ) 130 , d ) 110 , e ) 150
Rationale: "let c . p . be $ 100 . then , s . p . = $ 114 let marked price be $ x . then , 95 / 100 x = 114 x = 114 / 95 = $ 120 now , s . p . = $ 120 , c . p . = $ 100 profit % = 20 % . b"
Answer: b
Question (geometry): three table runners have a combined area of 212 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 = 212 - 24 - 2 * ( all three ) + 0 2 * ( all three ) = 212 - 24 - 140 all three = 24 answer : c"
Answer: c
Question (physics): two goods trains each 500 m long are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 75 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 48 , b ) 30 , c ) 26 , d ) 23 , e ) 12
Rationale: "relative speed = 45 + 75 = 120 km / hr . 120 * 5 / 18 = 100 / 3 m / sec . distance covered = 500 + 500 = 1000 m . required time = 1000 * 3 / 100 = 30 sec . answer : b"
Answer: b
Question (general): patty ran a marathon at an average speed of 3 mph for some time and then at an average speed of 6 mph for the rest of the marathon . if she made no stops during the run and her average speed for the entire marathon was 5 mph , for what fraction of the total time did she run at 3 mph ?
Options: a ) 1 / 5 , b ) 2 / 3 , c ) 2 / 5 , d ) 3 / 5 , e ) 1 / 3
Rationale: we do n ' t need to get into calculations for solving this question . we can use the concept of weighted averages . we know that if the average speed for the entire marathon was 5 mph , she ran at 6 mph for a longer duration . 2 1 3 - - 5 - - - - 6 this shows that you can divide the entire journey in 3 equal parts . thus , 2 / 3 part she ran at 6 mph and 1 / 3 part she ran at 3 mph . answer : e
Answer: e
Question (general): kamal obtained 66 , 65 , 77 , 62 and 75 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 65 , b ) 69 , c ) 72 , d ) 75 , e ) none
Rationale: sol . average = 66 + 65 + 77 + 62 + 75 / 5 ) = ( 345 / 5 ) = 69 . answer b
Answer: b
Question (general): a furniture store owner decided to drop the price of her recliners by 20 % to spur business . by the end of the week she had sold 25 % more recliners . what is the percentage increase of the gross ?
Options: a ) 00 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 50 %
Rationale: "say a recliner is actually worth $ 100 if she sells 100 recliners then she earns $ 10000 after the discount of 20 % , she will earn $ 80 per recliner and she sells 25 % more ie . , 125 recliners hence her sales tields 125 * 80 = $ 10000 increase in sales = 10000 - 10000 = $ 0 so % increase = 0 * 100 / 10000 = 0 % a is the answer"
Answer: a