Cheukting/mathqa huggingface dataset:
Question (gain): a retailer buys a radio for rs 225 . his overhead expenses are rs 28 . he sellis the radio for rs 300 . the profit percent of the retailer is
Options: a ) 10 % , b ) 50 % , c ) 25 % , d ) 52 % , e ) 18.5 %
Rationale: "explanation : cost price = ( 225 + 28 ) = 253 sell price = 300 gain = ( 47 / 253 ) * 100 = 18.5 % . answer : e"
Answer: e
Question (gain): mr . hernandez , who was a resident of state x for only 10 months last year , had a taxable income of $ 22,500 for the year . if the state tax rate were 4 percent of the year ’ s taxable income prorated for the proportion of the year during which the taxpayer was a resident , what would be the amount of mr . hernandez ’ s state x tax for last year ?
Options: a ) $ 900 , b ) $ 750 , c ) $ 600 , d ) $ 300 , e ) $ 60
Rationale: "total tax for the year = 22,500 x 4 % = 900 as stated annual tax is prorated as per the duration of stay . prorated tax = 900 ( 10 / 12 ) = 750 answer b"
Answer: b
Question (gain): the cost price of 12 articles is equal to the selling price of 8 articles . what is the profit percent ?
Options: a ) 40 % , b ) 45 % , c ) 50 % , d ) 55 % , e ) 60 %
Rationale: "8 * sp = 12 * cp sp = 1.5 * cp the profit percent is 50 % . the answer is c ."
Answer: c
Question (physics): two parallel sides of a trapezium are 4 cm and 5 cm respectively . the perpendicular distance between the parallel sides is 6 cm . find the area of the trapezium .
Options: a ) 24 cm 2
b ) 25 cm 2
c ) 26 cm 2
d ) 27 cm 2
e ) 28 cm 2
Rationale: area of trapezium when height and two parallel sides are given = 1 / 2 × h × ( a + b ) = 1 / 2 x 6 x ( 4 + 5 ) = 27 cm 2 answer d
Answer: d
Question (general): in a certain lottery , the probability that a number between 12 and 20 , inclusive , is drawn is 1 / 5 . if the probability that a number 12 or larger is drawn is 2 / 3 , what is the probability that a number less than or equal to 20 is drawn ?
Options: a ) 8 / 15 , b ) 1 / 6 , c ) 1 / 3 , d ) 1 / 2 , e ) 5 / 6
Rationale: "you can simply use sets concept in this question . the formula total = n ( a ) + n ( b ) - n ( a and b ) is applicable here too . set 1 : number 12 or larger set 2 : number 20 or smaller 1 = p ( set 1 ) + p ( set 2 ) - p ( set 1 and set 2 ) ( combined probability is 1 because every number will be either 12 or moreor 20 or lessor both ) 2 / 3 + p ( set 2 ) - 1 / 5 = 1 p ( set 2 ) = 8 / 15 answer ( a )"
Answer: a
Question (geometry): a ring x of diameter 16 inches is placed inside another ring y of diameter of 18 inches . how much fraction of the ring x surface is not covered by the ring y ?
Options: a ) 13 / 15
b ) 12 / 4
c ) 16 / 17
d ) 22 / 16
e ) 17 / 81
Rationale: the questions asks us to find the surface which is not covered by the ring x i . e . , area of the surface not covered . where as circumference is the length along the edge of the circle , 2 * pi * r implies the length of the curve pi * r ^ 2 implies area enclosed by that curve . . hence area of the circle is considered for this problem area of the ring x = pi * r ^ 2 , where r = 8 = > pi * 64 area of the ring y = pi * 81 surface not covered by the ring x = pi * 81 - pi * 64 = pi * 17 fraction of ring y ' s surface is not covered by a ring x = pi * 17 / total area of the ring y = > pi * 17 / pi * 81 17 / 81 answer e
Answer: e
Question (general): 7 / 9 of 3 / 5 of a number is greater than 2 / 9 of 5 / 6 of the same number by 152 . what is half of that number ?
Options: a ) 165 , b ) 195 , c ) 240 , d ) 270 , e ) 315
Rationale: "let no . be x 7 / 9 * 3 / 5 * x - 2 / 9 * 5 / 6 * x = 152 by further solving 21 x / 45 - 10 x / 54 = 152 114 x / 405 = 152 x = 540 we have to find x / 2 = 540 / 2 = 270 answer : d"
Answer: d
Question (general): the smallest number which when diminished by 3 is divisible by 21 , 2836 and 45 is . . .
Options: a ) 829 , b ) 869 , c ) 859 , d ) 4320 , e ) 427
Rationale: 427 answer : e
Answer: e
Question (gain): if 45 % of z is 96 % of y and y is 75 % of x , what percent of x is z ?
Options: a ) 200 , b ) 160 , c ) 100 , d ) 65 , e ) 50
Rationale: "( 45 / 100 ) z = ( 96 / 100 ) y and y = ( 75 / 100 ) x i . e . y = ( 3 / 4 ) x i . e . ( 45 / 100 ) z = ( 96 / 100 ) * ( 3 / 4 ) x i . e . z = ( 96 * 3 ) x / ( 45 * 4 ) i . e . z = ( 1.6 ) x = ( 160 / 100 ) x i . e . z is 160 % of x answer : option b"
Answer: b
Question (geometry): the area of a triangle is with base 4.5 m and height 6 m ?
Options: a ) 11 m 2 , b ) 10 m 2 , c ) 13.5 m 2 , d ) 19 m 2 , e ) 12.5 m 2
Rationale: "1 / 2 * 4.5 * 6 = 13.5 m 2 answer : c"
Answer: c
Question (general): if ( 5 ^ 15 ) ( 9 ^ 8 ) = 3 ( 15 ^ x ) , what is the value of x ?
Options: a ) 7 , b ) 9 , c ) 11 , d ) 13 , e ) 15
Rationale: "( 5 ^ 15 ) ( 9 ^ 8 ) = 3 ( 15 ^ x ) = > 5 ^ 15 * 3 ^ 16 = 3 * 3 ^ x * 5 ^ x = > 5 ^ 15 * 3 ^ 16 = 3 ^ ( x + 1 ) * 5 ^ x value of x = 15 answer e"
Answer: e
Question (gain): a sum of money at simple interest amounts to rs . 825 in 3 years and to rs . 830 in 4 years . the sum is ?
Options: a ) s . 738 , b ) s . 638 , c ) s . 650 , d ) s . 810 , e ) s . 735
Rationale: "s . i . for 1 year = ( 830 - 825 ) = rs . 5 s . i . for 3 years = 5 * 3 = rs . 15 principal = ( 825 - 15 ) = rs . 810 . answer : d"
Answer: d
Question (gain): at a particular graduation party with 300 guests , 70 % of the guests brought gifts , and 40 % of the female guests brought gifts . if 45 males did not bring gifts to the party , how many females did bring gifts ?
Options: a ) 18 , b ) 30 , c ) 42 , d ) 68 , e ) 70
Rationale: "the correct method total = 300 . . 70 % of 300 = 210 got gifts . . 90 did not get gift , out of which 48 are males , so remaining 90 - 45 = 50 are females . . but 40 % females brought gift , so 60 % did not get it . . so 60 % = 45 , 100 % = 45 * 100 / 60 = 75 . . ans 40 % of 75 = 30 b"
Answer: b
Question (general): after playing 40 games , the lesley basketball team had won 50 % of the games . the additional games played gave the team a 20 % total winning average . how many additional games must the team have won to obtain this average ?
Options: a ) 2 , b ) 15 , c ) 7 , d ) 10 , e ) 9
Rationale: explanation : identify the parts , set up equation , and solve . number of games initially won by the team : 50 % * 40 = 20 additional games won by the team leaving a 20 % average . ( let x represent the unknown number of additional games won . ) therefore , the total number of games played is 40 + x , and the total number of games won is 20 + x . this gives the equation as : 20 % * ( 40 + x ) = 20 + x solve : let ' s get rid of the percent sign 20 / 100 * ( 40 + x ) = 20 + x 1 / 5 * ( 40 + x ) = 20 + x get rid of the fraction : 5 [ 1 / 5 * ( 40 + x ) ] = 5 ( 20 + x ) 1 * ( 40 + x ) = 100 + 5 x 40 + x = 100 + 5 x ( 40 - 100 ) + x = ( 100 - 100 ) + 5 x - 60 + x = 5 x - 60 + ( x - x ) + 5 x - x - 60 = 4 x 15 = x answer : b
Answer: b
Question (other): what is the square root of 5,625 ?
Options: a ) a ) 18 , b ) b ) 75 , c ) c ) 45 , d ) d ) 62 , e ) e ) 81
Rationale: "a square root of a number is a number times itself equals the original number . ex ) the square root of 81 is 9 because 9 times itself ( 9 ) equals the original number ( 81 ) . 75 * 75 = 5,625 5625 divided by x = 75 x = 75 ( b ) 75"
Answer: b
Question (general): ( x ) + 9088 + 1090 - 9156 = 19845 . calculate the value of x
Options: a ) 11123 , b ) 18153 , c ) 11282 , d ) 18825 , e ) 18823
Rationale: "( x ) + 9088 + 1090 - 9156 = 19845 = x + 9088 + 1090 = 19845 + 9156 = x + 10178 = 29001 = x = 29001 - 10178 = 18823 answer is e"
Answer: e
Question (gain): a and b invests rs . 8000 and rs . 15000 in a business . after 4 months , a withdraws half of his capital and 2 months later , b withdraws one - third of his capital . in what ratio should they share the profits at the end of the year ?
Options: a ) 32 : 75 , b ) 82 : 31 , c ) 32 : 45 , d ) 34 : 89 , e ) 35 : 21
Rationale: "a : b ( 8000 * 4 ) + ( 4000 * 8 ) : ( 15000 * 6 ) + ( 10000 * 6 ) 64000 : 150000 32 : 75 answer : a"
Answer: a
Question (gain): the market value of a certain machine decreased by 15 percent of its purchase price each year . if the machine was purchased in 1982 for its market value of $ 8,000 , what was its market value two years later ?
Options: a ) $ 8,000 , b ) $ 5,600 , c ) $ 3,200 , d ) $ 4,400 , e ) $ 800
Rationale: "b . market value in 1982 = $ 8000 market value in 1983 = $ 8000 - ( $ 8000 x 15 / 100 ) = 8000 - 1200 = $ 6800 market value in 1984 = market value in 1983 - ( 15 % of $ 8000 ) = 6800 - 1200 = $ 5600"
Answer: b
Question (physics): a water tank is four - fifths full . pipe a can fill a tank in 10 minutes and pipe b can empty it in 6 minutes . if both the pipes are open , how many minutes will it take to empty or fill the tank completely ?
Options: a ) 6 , b ) 9 , c ) 10 , d ) 12 , e ) 15
Rationale: the combined rate of filling / emptying the tank = 1 / 10 - 1 / 6 = - 1 / 15 since the rate is negative , the tank will be emptied . a full tank would take 15 minutes to empty . since the tank is only four - fifths full , the time is ( 4 / 5 ) * 15 = 12 minutes the answer is d .
Answer: d
Question (general): a doctor prescribed 12 cubic centimeters of a certain drug to a patient whose body weight was 120 pounds . if the typical dosage is 2 cubic centimeters per 15 pounds of the body weight , by what percent was the prescribed dosage lesser than the typical dosage ?
Options: a ) 8 % , b ) - 25 % , c ) 11 % , d ) 12.5 % , e ) 14.8 %
Rationale: "typical dosage per 15 pound of the body weight = 2 c . c typical dosage per 120 pound of the body weight = 2 * ( 120 / 15 ) = 2 * 8 = 16 c . c dosage prescribed by doctor for 120 pound patient = 12 c . c % prescribed dosage greater than the typical dosage = ( 12 - 16 / 16 ) * 100 % = ( - 4 / 16 ) * 100 % = - 25 % answer b"
Answer: b
Question (general): mr . smith calculated the average of 10 3 digit numbers . but due to a mistake he reversed the digits of a number and thus his average increased by 19.8 the difference between the unit digit and hundreds digit of that number is :
Options: a ) 2 , b ) 6 , c ) 5 , d ) 3 , e ) 4
Rationale: since the average increased by 29.7 and there were a total of 10 numbers , it means the incorrect number was 198 greater than the correct number . say , the correct number was abc ( where a , b and c are the digits of the 3 digit number ) then the incorrect number was cba . 100 c + 10 b + a - ( 100 a + 10 b + c ) = 198 99 c - 99 a = 99 ( c - a ) = 198 198 = 99 * 2 = 99 ( c - a ) so c - a = 2 answer ( a )
Answer: a
Question (general): a certain family has 3 sons : richard is 6 years older than david , and david is 8 years older than scott . if in 8 years , richard will be twice as old as scott , then how old was david 4 years ago ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "let ' s say age of richard is ` ` r ' ' age of david is ` ` d ' ' age of scott is ` ` s ' ' now richard is 6 years older than david , i . e . r = d + 6 david is 8 years older than scott i . e . d = s + 8 if in 8 years , richard will be twice as old as scott i . e . r + 8 = 2 x ( s + 8 ) i . e . r + 8 = 2 s + 16 i . e . r = 2 s + 8 but r = d + 6 = ( s + 8 ) + 6 = s + 14 therefore , 2 s + 8 = s + 14 i . e . s = 6 i . e . r = 20 i . e . d = 14 now , how old was david 4 years ago ? i . e . d - 4 = 14 - 4 = 10 years answer : b"
Answer: b
Question (geometry): cubes with each side one inch long are glued together to form a larger cube . the larger cube ' s face is painted with red color and the entire assembly is taken apart . 24 small cubes are found with no paints on them . how many of unit cubes have at least one face that is painted red ?
Options: a ) 64 , b ) 72 , c ) 86 , d ) 98 , e ) 101
Rationale: "use the options . the options which after getting added to 24 shows a cube of a number could be right . here 64 + 24 = 88 72 + 24 = 96 86 + 24 = 110 98 + 24 = 122 101 + 24 = 125 - - - ( 5 * 5 * 5 ) so we have 101 as the answer ! e"
Answer: e
Question (gain): in a certain pond , 30 fish were caught , tagged , and returned to the pond . a few days later , 50 fish were caught again , of which 2 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what is the approximate number of fish in the pond ?
Options: a ) 750 , b ) 625 , c ) 1,250 , d ) 2,500 , e ) 10,000
Rationale: "this is a rather straight forward ratio problem . 1 . 30 fish tagged 2 . 2 out of the 50 fish caught were tagged thus 2 / 50 2 / 50 = 30 / x thus , x = 750 think of the analogy : 2 fish is to 50 fish as 50 fish is to . . . ? you ' ve tagged 50 fish and you need to find what that comprises as a percentage of the total fish population - we have that information with the ratio of the second catch . a"
Answer: a
Question (general): in an examination , there are 100 questions divided into 3 groups a , b and c such that each group contains at least one question . each question in group a carries 1 mark , each question in group b carries 2 marks and each question in group c carries 3 marks . it is known that the questions in group a together carry at least 60 % of the total marks . if group b contains 23 questions , then how many questions are there in group c ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: explanation : since group b contains 23 questions , the marks associated with this group are 46 . now , check for option ( 1 ) , if group ( c ) has one question , the marks associated with this group will be 3 . thus total marks will be 49 . total number of questions = 100 , group ( a ) will have 76 questions , the corresponding weightage being 76 marks . answer : a
Answer: a
Question (general): 897.7 – 573.07 – 95.007 = ?
Options: a ) 229.623 , b ) 224.777 , c ) 233.523 , d ) 414.637 , e ) none of these
Rationale: "solution given expression = 897.7 - ( 573.07 + 95.007 ) = 897.7 - 668.077 = 229.623 . answer a"
Answer: a
Question (general): 78 , 64 , 48 , 30 , 10 , ( . . . )
Options: a ) - 12 number , b ) - 14 , c ) 2 , d ) 8 , e ) 6
Rationale: "explanation : 78 - 14 = 64 64 - 16 = 48 48 - 18 = 30 30 - 20 = 10 10 - 22 = - 12 answer : option a"
Answer: a
Question (physics): a and b finish the job in 15 days . while a , b and c can finish it in 5 days . c alone will finish the job in
Options: a ) 4.50 days , b ) 3.50 days , c ) 6.0 days , d ) 7.5 days , e ) 5.50 days
Rationale: "explanation : 5 = ( 15 * x ) / ( 15 + x ) 75 + 5 x = 15 x 10 x = 75 x = 7.5 answer : option d"
Answer: d
Question (gain): working together at their respective constant rates , machine a and machine b can produce 1,500 units in 8 hours . working alone , machine b would complete that same output in 50 % more time . if machine a were to work on its own for an 8 - hour shift , what percent of the 1,500 unit total would it produce ?
Options: a ) 25 , b ) 36 , c ) 30 , d ) 67 , e ) 75
Rationale: "1 / a + 1 / b = 1 / t 1 / a + 1 / 14 = 1 / 8 ( 50 % more of 8 is 14 ) 1 / a = 1 / 24 machine a can produce 1500 units in 24 hrs , so it can produce 1500 * 8 / 24 = 500 units is 8 hrs . 500 is 30 % of 1500 . c is the answer"
Answer: c
Question (gain): at a local appliance manufacturing facility , the workers received a 30 % hourly pay raise due to extraordinary performance . if one worker decided to reduce the number of hours that he worked so that his overall pay would remain unchanged , by approximately what percent would he reduce the number of hours that he worked ?
Options: a ) 83 % , b ) 80 % , c ) 23 % , d ) 17 % , e ) 12 %
Rationale: "let ' s say he works usually 10 hours and earns 100 per hour . 10 * 100 = 1000 10 * 130 = 1300 ( this are the new earnings after the raise ) to figure out how much he needs to work with the new salary in order to earn the original 1000 : 1000 / 130 = 7.67 so he can reduce his work by 2.33 hours . which is > 23 % . answer c"
Answer: c
Question (physics): calculate how many days it will take for 7 boys to wash a 35 m long wall if 5 boys can wash a 25 m long wall in 4 days ,
Options: a ) 6 days , b ) 3 days , c ) 4 days , d ) 2 days , e ) 5 days
Rationale: "the length of wall painted by one boy in one day = 25 / 5 * 1 / 4 = 1.25 m no . of days required to paint 50 m cloth by 8 boys = 35 / 7 * 1 / 1.25 = 4 days . c"
Answer: c
Question (general): how many diagonals does a 61 - sided convex polygon have ?
Options: a ) 1182 , b ) 1769 , c ) 2456 , d ) 3538 , e ) 4209
Rationale: "a 61 - sided convex polygon has 61 vertices . if we examine a single vertex , we can see that we can connect it with 58 other vertices to create a diagonal . note that we ca n ' t connect the vertex to itself and we ca n ' t connect it to its adjacent vertices , since this would not create a diagonal . if each of the 61 vertices can be connected with 58 vertices to create a diagonal then the total number of diagonals would be ( 61 ) ( 58 ) = 3538 however , we must recognize that we have counted every diagonal twice . to account for counting each diagonal twice , we must divide 3538 by 2 to get 1769 . the answer is b ."
Answer: b
Question (general): balls of equal size are arranged in rows to form an equilateral triangle . the top most row consists of one ball , the 2 nd row of two balls and so on . if 253 balls are added , then all the balls can be arranged in the shape of square and each of the sides of the square contain 8 balls less than the each side of the triangle did . how many balls made up the triangle ?
Options: a ) 903 , b ) 2209 , c ) 2878 , d ) 1210 , e ) 1560
Rationale: "as expected , this question boils down to 2 equation , consider total number of balls in triangle = t and number of balls in last row = x . 1 + 2 + 3 + . . . + x = t x ( x + 1 ) / 2 = t - - - - ( a ) as mentioned in the question , side of a square will be ( x - 8 ) and total number of balls in square will be ( t + 253 ) ( x - 8 ) ^ 2 = t + 253 - - - - - ( b ) now the hardest part of the question will be to solve these 2 equations and this looks like time consuming but the easy way will be plug and play . also , we ' ve to find a value of t ( from 5 optiosn given below ) which can make a square of a a number . one we know this , it will be a cake walk . we can see that option a fits this criteria in eq ( b ) . add - 903 + 253 = 1156 = 34 ^ 2 = ( x - 8 ) ^ 2 hence , x = 42 . cross check by putting in eq ( a ) = x ( x + 1 ) / 2 = t = > 42 * 43 / 2 = 903 hence , answer is a ."
Answer: a
Question (general): a new home buyer pays 4 % annual interest on her first mortgage and 9 % annual interest on her second mortgage . if she borrowed a total of $ 310,000 , 80 % of which was in the first mortgage , what is her approximate monthly interest payment ?
Options: a ) $ 1,292 , b ) $ 1,733 , c ) $ 3,466 , d ) $ 12,917 , e ) $ 20,796
Rationale: 0.04 x + 0.09 y = 310000 [ 1 ] 0.04 x = 0.80 * 310000 = 248000 [ 2 ] 248000 + 0.09 y = 310000 - - > 0.09 y = 62000 [ 3 ] 248000 / 12 = 258333.3333 [ 4 ] 62000 / 12 = 5166.67 [ 5 ] adding [ 4,5 ] we get : 25833 [ 6 ] dividing [ 6 ] / 2 to get an average we get 1.292 , ans a
Answer: a
Question (general): what is ( 16 ^ 7 + 16 ) / 16 ?
Options: a ) 15467118 , b ) 16777217 , c ) 17827343 , d ) 18047455 , e ) 19357579
Rationale: "( 16 ^ 7 + 16 ) / 16 = 16 * ( 16 ^ 6 + 1 ) / 16 = 16 ^ 6 + 1 clearly this is a number which ends with a 7 in the units place . the answer is b ."
Answer: b
Question (geometry): if the sum of a number and its square is 240 , what is the number ?
Options: a ) 15 , b ) 77 , c ) 25 , d ) 87 , e ) 171
Rationale: "explanation : let the integer be x . then , x + x 2 = 240 x 2 + x - 240 = 0 ( x + 16 ) ( x – 15 ) = 0 x = 15 answer : a"
Answer: a
Question (physics): youseff lives x blocks from his office . it takes him 1 minute per block to walk to work and 20 seconds per block to ride his bike to work . it is takes him exactly 6 minutes more to walk to work than to ride his bike to work , then x equals ?
Options: a ) 4 , b ) 7 , c ) 9 , d ) 15 , e ) 20
Rationale: "please follow posting guidelines , link is in my signatures . as for your question , x / 60 = blocks / time / block = block ^ 2 / time . this is not what you want . you are given x blocks and 60 seconds per block . thus you need to put it as 60 * x to give you units of seconds as you are equating this to 360 ( which is time in seconds . ) . thus the correct equation is : 60 * x - 20 * x = 360 - - - - > 40 x = 360 - - > x = 9 . option c"
Answer: c
Question (other): two family reunions are happening at the leela hotel , the oates reunion and the hall reunion . all 100 guests at the hotel attend at least one of the reunions . if 50 people attend the oates reunion and 62 people attend the hall reunion , how many people attend both reunions ?
Options: a ) 2 , b ) 5 , c ) 12 , d ) 16 , e ) 22
Rationale: no of people in oates reunion = 50 no of people in hall reunion = 62 attending both = x all guests attend at least one . therefore , 100 = 50 + 62 - ( both ) both = 12 answer c
Answer: c
Question (gain): ashok and pyarelal invested money together in a business and share a capital of ashok is 1 / 9 of that of pyarelal . if the incur a loss of rs 1600 then loss of pyarelal ?
Options: a ) 600 , b ) 700 , c ) 840 , d ) 940 , e ) 1440
Rationale: "let the capital of pyarelal be x , then capital of ashok = x / 9 so ratio of investment of pyarelal and ashok = x : x / 9 = 9 x : x hence out of the total loss of 1600 , loss of pyarelal = 1600 * 9 x / 10 x = 1440 answer : e"
Answer: e
Question (general): following an increase in prices , the price of a candy box was 10 pounds and the price of a can of soda was 9 pounds . if the price of a candy box was raised by 25 % , and the price of a can of soda was raised by 50 % . what was the price of a box of candy plus a can of soda before prices were raised ?
Options: a ) 11 . , b ) 12 . , c ) 13 . , d ) 14 . , e ) 14.5
Rationale: "price of candy before price increase = 10 / 1.25 = 8 price of soda before price increase = 9 / 1.5 = 6 total price = 8 + 6 = 14 d is the answer"
Answer: d
Question (general): in a factory , an average of 65 tv ' s are produced per day for the fist 25 days of the months . a few workers fell ill for the next 5 days reducing the daily avg for the month to 60 sets / day . the average production per day for day last 5 days is ?
Options: a ) 20 , b ) 35 , c ) 48 , d ) 50 , e ) 59
Rationale: "production during these 5 days = total production in a month - production in first 25 days . = 30 x 60 - 25 x 65 = 175 ∴ average for last 5 days = 175 / 5 = 35 aswer : b"
Answer: b
Question (general): how many integers k greater than 100 and less than 1000 are there such that if the hundreds and the unit digits of k are reversed , the resulting integer is k + 99 ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: kk is 3 - digit integer . any 3 digit integer can be expressed as 100 a + 10 b + c 100 a + 10 b + c . now , we are told that ( 100 a + 10 b + c ) + 99 = 100 c + 10 b + a ( 100 a + 10 b + c ) + 99 = 100 c + 10 b + a - - > 99 c − 99 a = 9999 c − 99 a = 99 - - > c − a = 1 c − a = 1 - - > there are 8 pairs of cc and aa possible such that their difference to be 1 : ( 9,8 ) , ( 8,7 ) , . . . , and ( 2,1 ) ( note that aa can not be 0 as kk is 3 - digit integer and its hundreds digit , aa , is more than or equal to 1 ) . also , bb , tens digit of kk , could tale 10 values ( 0 , 1 , . . . , 9 ) so there are total of 8 * 10 = 80 such numbers possible . example : 102 - 201 ; 112 - 211 ; 122 - 221 ; . . . 899 - 998 . answer : d .
Answer: d
Question (general): if 225 / 999 = 0.225 , what is the 81 st digit to the right of the decimal point in the decimal equivalent of the fraction ?
Options: a ) 9 , b ) 8 , c ) 7 , d ) 6 , e ) 5
Rationale: "0 . [ u ] 225 [ / u = 0.225225225 . . . . . 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): if the numerator of a fraction is increased by 20 % and its denominator is diminished by 25 % value of the fraction is 2 / 15 . find the original fraction .
Options: a ) 1 / 12 , b ) 1 / 8 , c ) 1 / 6 , d ) 1 / 4 , e ) 1 / 2
Rationale: x * ( 120 / 100 ) - - - - - - - - - - - - - - - - = 2 / 15 y * ( 75 / 100 ) x / y = 1 / 12 answer : a
Answer: a
Question (general): . 007 / ? = . 01
Options: a ) . 7 , b ) . 07 , c ) . 007 , d ) . 0007 , e ) none of them
Rationale: "let . 007 / x = . 01 ; then x = . 007 / . 01 = . 7 / 1 = . 7 answer is a"
Answer: a