Cheukting/mathqa huggingface dataset:
Question (general): let a , b , c be distinct digits . consider a two - digit number ‘ ab ’ and a 3 - digit number ‘ ccb ’ , both defined under the usual decimal number system , if ( ab ) 2 = ccb > 300 , then the value of b is
Options: a ) 1 , b ) 0 , c ) 5 , d ) 6 , e ) 7
Rationale: explanation : given , ( ab ) 2 = ccb . [ only 1 , 5 and 6 on squaring will result with same digits in units place . ] taking a = 2 , b = 1 , = > ( 21 ) ^ 2 = 441 > 300 . hence , the required value of b = 1 answer : a
Answer: a
Question (physics): a train running at the speed of 60 km / hr crosses a pole in 21 seconds . find the length of the train .
Options: a ) 350 m , b ) 145 m , c ) 240 m , d ) 135 m , e ) 255 m
Rationale: "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 15 = 350 meter answer : a"
Answer: a
Question (general): instead of multiplying a number by 7 , the number is divided by 7 . what is the percentage of error obtained ?
Options: a ) 97.959 % , b ) 98.959 % , c ) 99.959 % , d ) 96.959 % , e ) 95.959 %
Rationale: "let the number be x the right number is 7 x the wrong number is x / 7 error is ( 7 x - x / 7 ) = 48 x / 7 percentage of error is ( ( 48 x / 7 ) / 7 x ) * 100 = 97.959 % answer : a"
Answer: a
Question (general): find how many 4 digits no . is less then 1239 such that all 4 digits are distinct .
Options: a ) 68 , b ) 69 , c ) 70 , d ) 71 , e ) 72
Rationale: case 1 - 1000 - 1099 - there are 56 distinct digits case 2 - 1200 - 1209 - there are 7 distinct digits case 3 - 1230 - 1239 ( excluding 1239 ) - there are 6 distinct digits hence , 56 + 7 + 6 = 69 answer : b
Answer: b
Question (probability): if a coin is flipped , the probability that the coin will land tails is 1 / 2 . if the coin is flipped 3 times , what is the probability that it will land tails up on the first flip and not on the last 2 flips ?
Options: a ) 1 / 8 , b ) 1 / 4 , c ) 1 / 3 , d ) 1 / 2 , e ) 3 / 4
Rationale: ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) = 1 / 8 answer : a
Answer: a
Question (general): a whale goes on a feeding frenzy that lasts for 9 hours . for the first hour he catches and eats x kilos of plankton . in every hour after the first , it consumes 3 kilos of plankton more than it consumed in the previous hour . if by the end of the frenzy the whale will have consumed a whopping accumulated total 360 kilos of plankton , how many kilos did he consume on the sixth hour ?
Options: a ) 38 , b ) 43 , c ) 50 , d ) 53 , e ) 62
Rationale: "if you list the amount eaten each hour , you ' ll get an equally spaced list , increasing by 3 each hour . in any equally spaced list , the median equals the mean . here , the mean is 360 / 9 = 40 , so the median is also 40 , and that is the amount eaten in the 5 th hour . we need to add 3 to find the total eaten in the next hour , so the answer is 43 . option b"
Answer: b
Question (physics): a factory produces 4340 toys per week . if the workers at this factory work 2 days a week and if these workers make the same number of toys everyday , how many toys are produced each day ?
Options: a ) 1375 toys , b ) 2170 toys , c ) 2375 toys , d ) 2175 toys , e ) 5375 toys
Rationale: "to find the number of toys produced every day , we divide the total number of toys produced in one week ( of 2 days ) by 2 . 4340 / 2 = 2170 toys correct answer b"
Answer: b
Question (gain): at what price must an article costing rs . 47.50 be marked in order that after deducting 9 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 65.25 , b ) 62.6 , c ) 62.1 , d ) 62.7 , e ) 62.2
Rationale: "cp = 47.50 sp = 47.50 * ( 125 / 100 ) = 59.375 mp * ( 91 / 100 ) = 59.375 mp = 65.25 answer : a"
Answer: a
Question (general): the mean of 50 observations was 36 . it was found later that an observation 34 was wrongly taken as 23 . the corrected new mean is :
Options: a ) 36.0 , b ) 36.5 , c ) 36.24 , d ) 36.12 , e ) 36.22
Rationale: "explanation : correct sum = ( 36 * 50 + 434 - 23 ) = 1825 . correct mean = = 1811 / 50 = 36.5 answer : e ) 36.22"
Answer: e
Question (general): in the coordinate plane , line a has a slope of - 1 and an x - intercept of 1 . line b has a slope of 3 and a y - intercept of - 3 . if the two lines intersect at the point ( a , b ) , what is the sum a + b ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "the equation of line a is y = - x + 1 the equation of line b is y = 3 x - 3 3 x - 3 = - x + 1 x = 1 y = 0 the point of intersection is ( 1,0 ) and then a + b = 1 . the answer is b ."
Answer: b
Question (general): if - 11 and - 8 are negative integers , then - 11 * - 8 + 5 is
Options: a ) - 14 , b ) 14 , c ) 33 , d ) 83 , e ) 93
Rationale: answer : e
Answer: e
Question (general): if there are 20 apples and the apples have to be shared equally among 3 babies . what number of apples are to be added ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: given there are 20 apples . if 1 extra apple is added , then it becomes 21 which can be divided equally that is 7 apples to each baby . option a is correct .
Answer: a
Question (general): 8 people are planning to share equally the cost of a rental car . if one person withdraws from the arrangement and the others share equally the entire rest of the car , then the share of each of the remaining persons increased by ?
Options: a ) 1 / 9 , b ) 1 / 8 , c ) 1 / 7 , d ) 7 / 8 , e ) 8 / 7
Rationale: when there are eight people , the share of each person is 1 / 8 th the total cost answer : b
Answer: b
Question (probability): a box contains 3 red balls and 4 black balls . one by one , every ball is selected at random without replacement . what is the probability that the fourth ball selected is black ?
Options: a ) 7 / 4 , b ) 1 / 2 , c ) 1 / 2 , d ) 5 / 8 , e ) 2 / 3
Rationale: my complicated version of your simple approach let the 5 black balls be bbbbb and 3 red balls be rrr they can be arranged in 8 slots _ _ _ _ _ _ _ _ in ( 7 ! ) / ( 4 ! x 3 ! ) if the fourth slot is black ball then the arrangement will be to fill _ _ _ b _ _ _ _ we have 7 slots and 3 black ( bbb ) and 3 red ( rrr ) they can be arranged in ( 6 ! ) / ( 3 ! x 3 ! ) hence required probability = [ ( 7 ! ) / ( 4 ! x 3 ! ) ] / [ ( 6 ! ) / ( 3 ! x 3 ! ) ] ans = 7 / 4 a
Answer: a
Question (general): in kaya ' s teacher ' s desk there are 4 pink highlighters , 2 yellow highlighters , and 5 blue highlighters . how many highlighters are there in all ?
Options: a ) 11 , b ) 22 , c ) 77 , d ) 33 , e ) 88
Rationale: "add the numbers of highlighters . 4 + 2 + 5 = 11 . answer is a ."
Answer: a
Question (general): the average weight of 10 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg . what is the weight of the new person ?
Options: a ) 75 kg , b ) 50 kg , c ) 85 kg , d ) 90 kg , e ) 60 kg
Rationale: "explanation : total increase in weight = 10 ã — 2.5 = 25 if x is the weight of the new person , total increase in weight = x â ˆ ’ 65 = > 25 = x - 65 = > x = 25 + 65 = 90 answer : option d"
Answer: d
Question (physics): on a map , 1 inch represents 28 miles . how many z inches would be necessary to represent a distance of 383.6 miles ?
Options: a ) 5.2 , b ) 7.4 , c ) 13.7 , d ) 21.2 , e ) 28.7
Rationale: "z inches necessary to represent a distance of 383.6 miles = 383.6 / 28 = 13.7 answer c"
Answer: c
Question (physics): a train 150 m long is running with a speed of 60 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 9 , e ) 8
Rationale: "speed of train relative to man = 60 + 6 = 66 km / hr . = 66 * 5 / 18 = 55 / 3 m / sec . time taken to pass the men = 150 * 3 / 55 = 8 sec . answer : e"
Answer: e
Question (other): the h . c . f . of two numbers is 40 and the other two factors of their l . c . m . are 11 and 15 . the larger of the two numbers is :
Options: a ) 276 , b ) 600 , c ) 699 , d ) 722 , e ) 745
Rationale: "the numbers are ( 40 x 11 ) and ( 40 x 15 ) . larger number = ( 40 x 15 ) = 600 . answer : b"
Answer: b
Question (physics): excluding stoppages , the speed of a train is 54 kmph and including stoppages it is 40 kmph . of how many minutes does the train stop per hour ?
Options: a ) a ) 13.55 , b ) b ) 14.55 , c ) c ) 15.55 , d ) d ) 16.55 , e ) e ) 17.55
Rationale: "explanation : t = 14 / 54 * 60 = 15.55 answer : option c"
Answer: c
Question (physics): a train 385 meters long is running with a speed of 60 kmph . in what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ?
Options: a ) 5 , b ) 21 , c ) 7 , d ) 8 , e ) 9
Rationale: "speed of train relative to man = ( 60 + 6 ) km / hr = 66 km / hr [ 66 * 5 / 18 ] m / sec = [ 55 / 3 ] m / sec . time taken to pass the man = [ 385 * 3 / 55 ] sec = 21 sec answer : option b"
Answer: b
Question (gain): a fashion designer sold a pair of jeans to a retail store for 40 percent more than it cost to manufacture the pair of jeans . a customer bought the pair of jeans for 15 percent more than the retailer paid for them . the price the customer paid was what percent greater than the cost of manufacturing the jeans ?
Options: a ) 61 % , b ) 70 % , c ) 75 % , d ) 85 % , e ) 95 %
Rationale: "find the product of the two increases : ( 1.4 ) * ( . 15 ) , which is 1.61 and a 61 % increase . a"
Answer: a
Question (general): a mixture contains alcohol and water in the ratio 4 : 3 . if 9 litres of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture
Options: a ) 15 litres , b ) 10 litres , c ) 30 litres , d ) 22 litres , e ) 18 litres
Rationale: "let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 4 x / ( 3 x + 9 ) = 4 / 5 20 x = 4 ( 3 x + 9 ) 8 x = 36 x = 4.5 quantity of alcohol = ( 4 x 4.5 ) litres = 18 litres . answer is e"
Answer: e
Question (physics): if 12 men or 20 women can do a piece of work in 54 days , then in how many days can 9 men and 39 women together do the work ?
Options: a ) 10 days , b ) 30 days , c ) 20 days , d ) 80 days , e ) 40 days
Rationale: c 20 days given that 12 m = 20 w = > 3 m = 5 w 9 men + 39 women = 15 women + 39 women = 54 women 20 women can do the work in 54 days . so , 54 women can do it in ( 20 * 54 ) / 54 = 20 days .
Answer: c
Question (gain): in an election , candidate a got 79 % of the total valid votes . if 15 % of the total votes were declared invalid and the total numbers of votes is 560000 , find the number of valid vote polled in favour of candidate .
Options: a ) 357003 , b ) 357090 , c ) 37667 , d ) 379888 , e ) 287761
Rationale: "total number of invalid votes = 15 % of 560000 = 15 / 100 × 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 – 84000 = 476000 percentage of votes polled in favour of candidate a = 75 % therefore , the number of valid votes polled in favour of candidate a = 75 % of 476000 = 75 / 100 × 476000 = 35700000 / 100 = 357090 answer : b"
Answer: b
Question (physics): if a car had traveled 35 kmh faster than it actually did , the trip would have lasted 30 minutes less . if the car went exactly 105 km , at what speed did it travel ?
Options: a ) 50 kmh , b ) 55 kmh , c ) 60 kmh , d ) 65 kmh , e ) 70 kmh
Rationale: "time = distance / speed difference in time = 1 / 2 hrs 105 / x - 105 / ( x + 35 ) = 1 / 2 substitute the value of x from the options . - - > x = 70 - - > 105 / 70 - 105 / 105 = 3 / 2 - 1 = 1 / 2 answer : e"
Answer: e
Question (geometry): the base of pyramid p is an isosceles right triangle whose leg is 3 . if the height of p is 4 , what is the volume of p ?
Options: a ) 36
b ) 18
c ) 12
d ) 8
e ) 6
Rationale: volume of a pyramid is given by v = 1 / 3 ah , where a is the area of the triangular base and h is the height of the pyramid . area of triangular base = 1 / 2 * 3 * 3 = 9 / 2 so , v = 1 / 3 * 9 / 2 * 4 = 6 option e
Answer: e
Question (general): 10 % people of a village in sri lanka died by bombardment , 15 % of the remainder left the village on account of fear . if now the population is reduced to 6514 , how much was it in the beginning ?
Options: a ) 8545 , b ) 8770 , c ) 8515 , d ) 7999 , e ) 7989
Rationale: "x * ( 90 / 100 ) * ( 85 / 100 ) = 6514 x = 8515 answer : c"
Answer: c
Question (gain): if each year the population of the country grows by 10 % , how many years will elapse before the population of the country doubles ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 7 , e ) 8
Rationale: till year 2000 , population is 100 . year 2001 : population becomes 110 . . . . . . . . . . . . . 1 year elapsed year 2002 : population becomes 121 . . . . . . . . . . . . . 2 year elapsed year 2003 : population becomes > 133 . . . . . . . . . . . . . 3 year elapsed year 2004 : population becomes > 146 . . . . . . . . . . . . . . . . . . 4 year elapsed year 2005 : population becomes > 160 . . . . . . . . . . . . . . . . . . 5 year elapsed year 2006 : population becomes > 176 . . . . . . . . . . . . . . . . . . 6 year elapsed year 2007 : population becomes > 193 . . . . . . . . . . . . . . . . . . 7 year elapsed year 2008 : population > 200 . . . . . . . . . . . . . . . . . . 8 year elapsed answer : e
Answer: e
Question (gain): 5 percent of a certain grass seed is timothy . if the amount of the mixture needed to plant one acre contains 2 pounds of timothy , how many acres can be planted with 600 pounds of the seed mixture ?
Options: a ) 12 , b ) 15 , c ) 20 , d ) 24 , e ) 120
Rationale: if the mixture contains 2 pounds of timothy , the mixture must be 40 pounds . thus we need 40 pounds of mixture per acre . 600 / 40 = 15 acres the answer is b .
Answer: b
Question (gain): we invested a total of $ 1,000 . we invested one part of the money at 5 % and the rest of the money at 6 % . the total investment with interest at the end of the year was $ 1 , 054.50 . how much money did we invest at 5 % ?
Options: a ) $ 400 , b ) $ 450 , c ) $ 500 , d ) $ 550 , e ) $ 600
Rationale: "let x be the money invested at 5 % . 1.05 x + 1.06 ( 1000 - x ) = 1054.50 . 0.01 x = 1060 - 1054.50 . 0.01 x = 5.50 . x = 550 . the answer is d ."
Answer: d
Question (general): the average of 1 st 3 of 4 numbers is 16 and of the last 3 are 15 . if the sum of the first and the last number is 19 . what is the last numbers ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 7
Rationale: "a + b + c = 48 b + c + d = 45 a + d = 19 a – d = 3 a + d = 19 2 d = 16 d = 8 answer d"
Answer: d
Question (probability): if two integers x , y ( x > y ) are selected from - 10 to 5 ( inclusive ) , how many possible cases are there ?
Options: a ) 105 , b ) 120 , c ) 190 , d ) 210 , e ) 240
Rationale: "if two integers x , y ( x > y ) are selected from - 10 to 5 ( inclusive ) , how many possible cases are there ? a . 150 b . 180 c . 190 d . 210 e . 240 - - > 16 c 2 = 16 * 15 / 2 = 120 . therefore , the answer is b ."
Answer: b
Question (physics): a cistern 8 m long and 6 m wide contains water up to a depth of 1 m 25 cm . the total area of the wet surface is :
Options: a ) 80 m 2 , b ) 50 m 2 , c ) 83 m 2 , d ) 86 m 2 , e ) 55 m 2
Rationale: area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 6 x 1.25 + 8 x 1.25 ) + 8 x 6 ] m 2 = 83 m 2 . answer : c
Answer: c
Question (general): in a certain accounting class of 90 students , 70 % of the students took the final exam on the assigned day while the rest of the students took the exam on a make - up date . if the students on the assigned day had an average score of 60 % , and the students on the make - up date had an average score of 70 % , what was the average score for the entire class ?
Options: a ) 63 % , b ) 64 % , c ) 65 % , d ) 66 % , e ) 67 %
Rationale: "70 % of the class scored 60 % and 30 % of the class scored 70 % . the difference between 60 % and 70 % is 10 % . the average will be 60 % + 0.3 ( 10 % ) = 63 % . the answer is a ."
Answer: a
Question (gain): a sum fetched a total simple interest of 4016.25 at the rate of 9 % . p . a . in 5 years . what is the sum ?
Options: a ) 4462.5 , b ) 8032.5 , c ) 8925 , d ) none of these , e ) can not be determined
Rationale: "explanation : principal = ( 100 x 4016.25 ) / ( 9 x 5 ) = 401625 / 45 = 8925 answer : option c"
Answer: c
Question (probability): a bag consists of 20 marbles , of which 5 are blue , 9 are red , and the remainder are white . if lisa is to select a marble from the bag at random , what is the probability that the marble will be red or white ?
Options: a ) 3 / 4 , b ) 2 / 4 , c ) 1 / 4 , d ) 1 / 8 , e ) 1 / 16
Rationale: "bag consists of 20 marbles , of which 5 are blue , 9 are red remainder are white . so , white = 20 - 5 - 9 = 6 . probability that the marble will be red or white = probability that the marble will be red + probability that the marble will be white probability that the marble will be red or white = 9 / 20 + 6 / 20 = 15 / 20 = 3 / 4 hence , answer will be a ."
Answer: a
Question (general): how many different positive integers exist between 10 ^ 6 and 10 ^ 7 , the sum of whose digits is equal to 2 ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 18
Rationale: "total cases = > 1000000 = > 6 cases for 1 being present at any of the 6 zero and last case 2000000 hence & cases answer : c"
Answer: c
Question (other): john distributes his pencil among his 4 friends rose , mary , ranjan , and rohit in the ratio 1 / 1 : 1 / 3 : 1 / 4 : 1 / 5 . what is the minimum no . of pencils that the person should have ?
Options: a ) 45 , b ) 65 , c ) 98 , d ) 107 , e ) 198
Rationale: "rakesh : rahul : ranjan : rohit = 1 / 1 : 1 / 3 : 1 / 4 : 1 / 5 step 1 : at first we need to do is lcm of 2 , 3,4 and 5 is 60 . step 2 : then pencil are distributed in ratio among friends , rakesh = ( 1 / 1 x 60 ) = 60 . rahul = ( 1 / 3 x 60 ) = 20 . ranjan = ( 1 / 4 x 60 ) = 15 . rohit = ( 1 / 5 x 60 ) = 12 . step 3 : total number of pencils are ( 60 x + 20 x + 15 x + 12 x ) = 107 x . for minimum number of pencils x = 1 . the person should have at least 107 pencils . d )"
Answer: d
Question (gain): a sum of rs . 1550 was lent partly at 5 % and partly at 8 % p . a . simple interest . the total interest received after 3 years was rs . 300 . the ratio of the money lent at 5 % to that lent at 8 % is :
Options: a ) 16 : 15 , b ) 15 : 16 , c ) 15 : 8 , d ) 8 : 15 , e ) 8 : 17
Rationale: explanation : let the partial amount at 5 % be x and the partial amount at 8 % be ( 1550 - x ) interest on x at 5 % for 3 years + interest on ( 1550 - x ) at 8 % for 3 years = 300 x × 5 × 3 / 100 + ( 1550 - x ) × 8 × 3 / 100 = 300 x × 5 / 100 + ( 1550 - x ) × 8 / 100 = 100 5 x + 8 ( 1550 − x ) = 10000 5 x + 12400 − 8 x = 10000 3 x = 2400 x = 800 required ratio = x : ( 1550 - x ) = 800 : ( 1550 - 800 ) = 800 : 750 = 16 : 15 answer : option a
Answer: a
Question (general): a certain library assesses fines for overdue books as follows . on the first day that a book is overdue , the total fine is $ 0.20 . for each additional day that the book is overdue , the total fine is either increased by $ 0.30 or doubled , whichever results in the lesser amount . what is the total for a book on the third day it is overdue ?
Options: a ) $ 0.60 , b ) $ 0.70 , c ) $ 0.80 , d ) $ 0.90 , e ) $ 1.00
Rationale: "1 st day fine - 0.2 2 nd day fine - 0.2 * 2 = 0.4 ( as doubling gives lower value ) 3 rd day fine - 0.4 + 3 = 0.7 ( as doubling gives higher value ) answer : b ."
Answer: b
Question (general): a part - time employee ’ s hourly wage was increased by 15 % . she decided to decrease the number of hours worked per week so that her total income did not change . by approximately what percent should the number of hours worked be decreased ?
Options: a ) 13 % , b ) 15 % , c ) 25 % , d ) 50 % , e ) 100 %
Rationale: "let ' s plug in somenicenumbers and see what ' s needed . let ' s say the employee used to make $ 1 / hour and worked 100 hours / week so , the total weekly income was $ 100 / week after the 15 % wage increase , the employee makes $ 1.15 / hour we want the employee ' s income to remain at $ 100 / week . so , we want ( $ 1.15 / hour ) ( new # of hours ) = $ 100 divide both sides by 1.15 to get : new # of hours = 100 / 1.15 ≈ 87 hours so , the number of hours decreases from 100 hours to ( approximately ) 87 hours . this represents a 13 % decrease ( approximately ) . answer : a"
Answer: a
Question (general): if y is 60 % greater than x , than x is what % less than y ?
Options: a ) 29.3 % , b ) 33.4 % , c ) 37.5 % , d ) 41.6 % , e ) 45.7 %
Rationale: "y = 1.6 x x = y / 1.6 = 10 y / 16 = 5 y / 8 x is 3 / 8 less which is 37.5 % less than y . the answer is c ."
Answer: c
Question (gain): a student gets 50 % in one subject , 70 % in the other . to get an overall of 70 % how much should get in third subject .
Options: a ) 90 % , b ) 25 % , c ) 45 % , d ) 55 % , e ) 65 %
Rationale: "let the 3 rd subject % = x 50 + 70 + x = 3 * 70 120 + x = 210 x = 210 - 120 = 90 answer : a"
Answer: a
Question (general): the product of two successive numbers is 2652 . which is the smaller of the two numbers ?
Options: a ) 51 , b ) 68 , c ) 57 , d ) 55 , e ) 37
Rationale: "a 51 from the given alternatives , 51 × 52 = 2652 ∴ smaller number = 51"
Answer: a
Question (gain): a sum of money deposited at c . i . amounts to rs . 2560 in 3 years and to rs . 2989 in 4 years . find the rate percent ?
Options: a ) 30 % , b ) 10 % , c ) 20 % , d ) 16 % , e ) 50 %
Rationale: "2560 - - - 429 100 - - - ? = > 16 % answer : d"
Answer: d
Question (general): if k is a non - negative integer and 30 ^ k is a divisor of 929,260 then 3 ^ k - k ^ 3 =
Options: a ) 0 , b ) 1 , c ) 45 , d ) 130 , e ) 520
Rationale: 9 + 2 + 9 + 2 + 6 + 0 = 28 , so this number is not divisible by 3 and thus not divisible by 30 . therefore , k = 0 3 ^ k - k ^ 3 = 1 - 0 = 1 the answer is b .
Answer: b
Question (gain): a particular store purchased a stock of turtleneck sweaters and marked up its cost by 20 % . during the new year season , it further marked up its prices by 25 % of the original retail price . in february , the store then offered a discount of 18 % . what was its profit on the items sold in february ?
Options: a ) 27.5 % , b ) 30 % , c ) 35 % , d ) 23 % , e ) 40 %
Rationale: "assume the total price = 100 x price after 20 % markup = 120 x price after 25 % further markup = 1.25 * 120 x = 150 x price after the discount = 0.82 * 150 x = 123 x hence total profit = 23 % option d"
Answer: d
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 5500 , the number of valid votes that the other candidate got , was :
Options: a ) 2800 , b ) 1980 , c ) 2900 , d ) 2200 , e ) 2300
Rationale: "b number of valid votes = 80 % of 5500 = 4400 . valid votes polled by other candidate = 45 % of 4400 = ( 45 / 100 x 4400 ) = 1980 ."
Answer: b
Question (general): there are 7 players in a bowling team with an average weight of 103 kg . if two new players join the team , one weighs 110 kg and the second weighs 60 kg , what will be the new average weight ?
Options: a ) 95 kg . , b ) 99 kg . , c ) 89 kg . , d ) 90 kg . , e ) 92 kg .
Rationale: "the new average will be = ( 103 * 7 + 110 + 60 ) / 9 = 99 kgs b is the answer"
Answer: b
Question (general): find the average of all numbers between 3 and 86 which are divisible by 5
Options: a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 45
Rationale: "explanation : average = ( 5 + 10 + 15 + 20 + 25 + 30 + 35 + 40 + 45 + 50 + 55 + 60 + 65 + 70 + 75 + 80 + 85 ) / 17 = 765 / 17 = 45 answer : option e"
Answer: e
Question (gain): if the annual increase in the population of a town is 10 % and the present number of people is 14000 , what will the population be in 2 years ?
Options: a ) 12100 , b ) 15240 , c ) 12456 , d ) 16940 , e ) 10002
Rationale: "the required population is = 14000 ( 1 + 10 / 100 ) ^ 2 = 14000 * 11 / 10 * 11 / 10 = 16940 answer is d"
Answer: d
Question (general): the average of 21 numbers is 44 . average of the first 11 of them is 48 and that of the last 11 is 41 . find the 11 th number ?
Options: a ) 48 , b ) 51 , c ) 47 , d ) 49 , e ) 55
Rationale: sum of all the 21 numbers = 21 * 44 = 924 sum of the first 11 of them = 11 * 48 = 528 sum of the last 11 of them = 11 * 41 = 451 so , the 11 th number = 528 + 451 - 924 = 55 . answer : e
Answer: e