Cheukting/mathqa huggingface dataset:
Question (geometry): the radius of the two circular fields is in the ratio 3 : 5 the area of the first field is what percent less than the area of the second ?
Options: a ) 23 % , b ) 62 % , c ) 92 % , d ) 64 % , e ) 22 %
Rationale: "r = 3 π r 2 = 9 r = 5 π r 2 = 25 25 π – 16 π 100 - - - - ? = > 64 % answer : d"
Answer: d
Question (general): find the lowest common multiple of 25 , 35 and 50 .
Options: a ) 350 , b ) 420 , c ) 510 , d ) 320 , e ) 280
Rationale: lcm = 2 * 5 * 5 * 7 = 350 . answer is a
Answer: a
Question (gain): a side of beef lost 35 percent of its weight in processing . if the side of beef weighed 580 pounds after processing , how many pounds did it weigh before processing ?
Options: a ) 191 , b ) 355 , c ) 737 , d ) 892 , e ) 1,560
Rationale: "let weight of side of beef before processing = x ( 65 / 100 ) * x = 580 = > x = ( 580 * 100 ) / 65 = 892 answer d"
Answer: d
Question (general): country x imported approximately $ 1.20 billion of goods in 1996 . if country x imported $ 288 million of goods in the first two months of 1997 and continued to import goods at the same rate for the rest of the year , by how much would country xs 1997 imports exceed those of 1996 ?
Options: a ) $ 24 million , b ) $ 120 million , c ) $ 144 million , d ) $ 240 million , e ) $ 528 million
Rationale: "convert units to millions as answer is in millions 1996 imports = $ 1.20 bill = $ 1200 mill i . e . 1200 / 12 = $ 100 mill / month 1997 imports = $ 288 mill / 2 month i . e . $ 144 mill / month difference / month = 144 - 100 = 44 difference / year = $ 44 mill * 12 = $ 528 mill answer : e"
Answer: e
Question (physics): a man goes from a to b at a speed of 21 kmph and comes back to a at a speed of 21 kmph . find his average speed for the entire journey ?
Options: a ) 23.3 kmph , b ) 25.3 kmph , c ) 22.5 kmph , d ) 22.3 kmph , e ) 22.9 kmph
Rationale: "distance from a and b be ' d ' average speed = total distance / total time average speed = ( 2 d ) / [ ( d / 21 ) + ( d / 24 ] = ( 2 d ) / [ 15 d / 168 ) = > 22.3 kmph . answer : d"
Answer: d
Question (physics): a man rows his boat 72 km downstream and 30 km upstream , taking 3 hours each time . find the speed of the stream ?
Options: a ) 6 kmph , b ) 5 kmph , c ) 2 kmph , d ) 8 kmph , e ) 7 kmph
Rationale: "speed downstream = d / t = 72 / ( 3 ) = 24 kmph speed upstream = d / t = 30 / ( 3 ) = 10 kmph the speed of the stream = ( 24 - 10 ) / 2 = 7 kmph answer : e"
Answer: e
Question (other): a certain fruit stand sold apples for $ 0.70 each and bananas for $ 0.60 each . if a customer purchased both apples and bananas from the stand for a total of $ 5.60 , what total number of apples and bananas did the customer purchase ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "let ' s start with 1 apple for $ 0.70 . let ' s subtract $ 0.70 from $ 5.60 until we get a multiple of $ 0.60 . $ 5.60 , $ 4.90 , $ 4.20 = 7 * $ 0.60 the customer purchased 7 bananas and 2 apples . the answer is b ."
Answer: b
Question (general): 25 liters of a mixture is created by mixing liquid p and liquid q in the ratio 3 : 2 . how many liters of liquid q must be added to make the ratio 5 : 4 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "let x be the amount of liquid q to be added . ( 2 / 5 ) * 25 + x = ( 4 / 9 ) * ( 25 + x ) 450 + 45 x = 500 + 20 x 25 x = 50 x = 2 the answer is b ."
Answer: b
Question (general): an amount of rs . 1560 was divided among a , b and c in the ratio 1 / 2 : 1 / 3 : 1 / 4 . find the share of c ?
Options: a ) rs . 278 , b ) rs . 361 , c ) rs . 369 , d ) rs . 360 , e ) rs . 363
Rationale: "let the shares of a , b and c be a , b and c respectively . a : b : c = 1 / 2 : 1 / 3 : 1 / 4 a : b : c = 6 / 12 : 4 / 12 : 3 : 12 = 6 : 4 : 3 share of c = 3 / 13 * 1560 = rs . 360 . answer : d"
Answer: d
Question (general): elena purchased brand x pens for $ 4.00 apiece and brand y for $ 2.20 apiece . if elena purchased a total of 12 of these pens for $ 42.00 , how many brand x pens did she purchase ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: 4 x + 2.8 y = 42 - - > multiply by 2.5 ( to get the integers ) - - > 10 x + 7 y = 105 - - > only one positive integers solutions x = 6 and y = 5 ( how to solve : 7 y must have the last digit of 5 in order the last digit of the sum to be 5 ) . answer : c .
Answer: c
Question (physics): walking at 5 / 6 th of its usual speed a cab is 6 mnts late . find its usual time to cover the journey ?
Options: a ) 25 m , b ) 30 m , c ) 32 m , d ) 50 m , e ) 62 m
Rationale: "new speed = 5 / 6 th of usual speed new time = 6 / 5 th of usual time 6 / 5 ut - ut = 6 m ut / 5 = 6 m ut = 30 m answer is b"
Answer: b
Question (general): on the number line , if x is halfway between - 6 and 4 , and if y is halfway between - 2 and 6 , what number is halfway between x and y ?
Options: a ) - 2.5 , b ) - 1.5 , c ) - 0.5 , d ) 0.5 , e ) 1.5
Rationale: "x = - 1 and y = 2 . the answer is d ."
Answer: d
Question (general): what is the sum of the digits of integer k , if k = ( 10 ^ 50 - 50 )
Options: a ) 337 , b ) 437 , c ) 457 , d ) 537 , e ) 412
Rationale: "there are 51 digits in 10 ^ 50 when we subtract 50 from it , there will be 50 digits left . 10 ^ 50 can be written as 9999999 . . . . ( 50 times ) + 1 so , 10 ^ 50 - 50 = 9999999 . . . . ( 50 times ) + 1 - 50 = 9999999 . . . . ( 50 times ) - 49 consider the last 2 digits , 99 - 49 = 50 the last 2 digits will be 50 . and our number would be 99999 . . . . . . 99950 with 2 less 9 s after subtraction . number of 9 s left are 48 and the last two digits are 50 the sum of the digits will be ( 48 * 9 ) + 5 + 0 = 437 answer : - b"
Answer: b
Question (general): what is the least number which when divided by 6 , 9 , 12 and 18 leaves remainder 4 in each care ?
Options: a ) 30 , b ) 40 , c ) 36 , d ) 56 , e ) 66
Rationale: "explanation : lcm of 6 , 9 , 12 and 18 is 36 required number = 36 + 4 = 40 answer : option b"
Answer: b
Question (general): the population of a town increased from 1 , 75,000 to 2 , 80,000 in a decade . the average percent increase of population per year is
Options: a ) 4.37 % , b ) 5 % , c ) 6 % , d ) 8.75 % , e ) none
Rationale: "solution increase in 10 years = ( 280000 - 175000 ) = 105000 . increase % = ( 105000 / 175000 ã — 100 ) % = 60 % . required average = ( 60 / 10 ) % = 6 % . answer c"
Answer: c
Question (physics): a bullet train 200 m long is running with a speed of 69 kmph . in what time will it pass a man who is running at 3 kmph in the direction opposite to that in which the bullet train is going ?
Options: a ) 10 sec , b ) 15 sec , c ) 12 sec , d ) 11 sec , e ) 16 sec
Rationale: "a 10 sec speed of the bullet train relative to man = ( 69 + 3 ) kmph = 72 * 5 / 18 m / sec = 60 / 3 m / sec . time taken by the bullet train to cross the man = time taken by it to cover 200 m at ( 60 / 3 ) m / sec = ( 200 * 3 / 60 ) sec = 10 sec"
Answer: a
Question (physics): in what time will a railway train 90 m long moving at the rate of 36 kmph pass a telegraph post on its way ?
Options: a ) 8 sec , b ) 1 sec , c ) 9 sec , d ) 6 sec , e ) 2 sec
Rationale: "t = 90 / 36 * 18 / 5 = 9 sec answer : c"
Answer: c
Question (gain): after successive discounts of 20 % , 10 % and 5 % a certain good is sold for rs . 6800 . find the actual price of the good .
Options: a ) s . 6000 , b ) s . 9000 , c ) s . 10800 , d ) s . 9942 , e ) s . 9980
Rationale: "let actual price was 100 . after three successive discount this will become , 100 = = 20 % discount = > 80 = = 10 % discount = > 72 = = 5 % discount = 68.4 now compare , 68.4 = 6800 1 = 6800 / 68.4 100 = ( 6800 * 100 ) / 68.4 = rs . 9942 . answer : option d"
Answer: d
Question (physics): a can run 160 metre in 28 seconds and b in 32 seconds . by what distance a beat b ?
Options: a ) 38 metre , b ) 28 metre , c ) 20 metre , d ) 15 metre , e ) 28 metre
Rationale: "clearly , a beats b by 4 seconds now find out how much b will run in these 4 seconds speed of b = distance / time taken by b = 160 / 32 = 5 m / s distance covered by b in 4 seconds = speed ã — time = 5 ã — 4 = 20 metre i . e . , a beat b by 20 metre answer is c"
Answer: c
Question (general): a club wants to mix 20 pounds of candy worth $ 8.00 per pound with candy worth $ 5.00 per pound to reduce the cost of the mixture to $ 6.00 per pound . how many pounds of the $ 5.00 per pound candy should be used ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60
Rationale: let number of pounds of 5 $ candy to be used be w 6 = ( 20 * 8 + 5 * w ) / ( 20 + w ) = > 120 + 6 w = 160 + 5 w = > w = 40 answer c
Answer: c
Question (gain): by selling an article at rs . 600 , a profit of 30 % is made . find its cost price ?
Options: a ) 400 , b ) 267 , c ) 287 , d ) 480 , e ) 811
Rationale: "sp = 600 cp = ( sp ) * [ 100 / ( 100 + p ) ] = 600 * [ 100 / ( 100 + 50 ) ] = 600 * [ 100 / 150 ] = rs . 400 answer : a"
Answer: a
Question (gain): a student gets 60 % in one subject , 70 % in the other . to get an overall of 70 % how much should get in third subject .
Options: a ) 75 % , b ) 80 % , c ) 45 % , d ) 55 % , e ) 65 %
Rationale: "let the 3 rd subject % = x 60 + 70 + x = 3 * 70 130 + x = 210 x = 210 - 130 = 80 answer : b"
Answer: b
Question (general): if a ' s height is 30 % less than that of b , how much percent b ' s height is more than that of a ?
Options: a ) 42.85 % , b ) 66.68 % , c ) 66.766 % , d ) 86.66 % , e ) 66.65 %
Rationale: excess of b ' s height over a ' s = [ ( 30 / ( 100 - 30 ) ] x 100 % = 42.85 % answer : a )
Answer: a
Question (general): if 13 = 13 w / ( 1 - w ) , then ( 2 w ) 2 =
Options: a ) 1 / 4 , b ) 1 / 2 , c ) 1 , d ) 2 , e ) 3
Rationale: "13 - 13 w = 13 w 26 w = 13 w = 1 / 2 2 w = 1 2 w * 2 = 1 * 2 = 2 answer : d"
Answer: d
Question (geometry): what is the perimeter of a square field whose diagonal is 4 √ 2 ?
Options: a ) 16 m , b ) 32 m , c ) 27 m , d ) 26 m , e ) 76 m
Rationale: "4 a = 16 m answer : a"
Answer: a
Question (geometry): if the sides of a triangle are 4 cm , 9 cm and 13 cm , what is its area ?
Options: a ) 18 , b ) 20 , c ) 22 , d ) 26 , e ) 28
Rationale: "the triangle with sides 4 cm , 9 cm and 13 cm is right angled , where the hypotenuse is 13 cm . area of the triangle = 1 / 2 * 4 * 9 = 18 cm 2 answer : option a"
Answer: a
Question (other): of the 65 cars on a car lot , 45 have air - bag , 30 have power windows , and 12 have both air - bag and power windows . how many of the cars on the lot have neither air - bag nor power windows ?
Options: a ) 8 , b ) 2 , c ) 10 , d ) 15 , e ) 18
Rationale: total - neither = all air bag + all power windows - both or 65 - neither = 45 + 30 - 12 = 63 . = > neither = 2 , hence b . answer : b
Answer: b
Question (general): a large field of 700 hectares is divided into two parts . the difference of the areas of the two parts is one - fifth of the average of the two areas . what is the area of the smaller part in hectares ?
Options: a ) 315 , b ) 339 , c ) 288 , d ) 299 , e ) 111
Rationale: explanation : let the areas of the two parts be x and ( 700 - x ) hectares therefore , so , the two parts are 385 and 315 . hence , area of the smaller = 315 hectares answer : a ) 315
Answer: a
Question (general): if 2994 ã · 14.5 = 177 , then 29.94 ã · 1.45 = ?
Options: a ) 17.1 , b ) 17.3 , c ) 17.5 , d ) 17.7 , e ) 17.2
Rationale: "29.94 / 1.45 = 299.4 / 14.5 = ( 2994 / 14.5 ) x 1 / 10 ) [ here , substitute 177 in the place of 2994 / 14.5 ] = 177 / 10 = 17.7 answer is d ."
Answer: d
Question (general): a part - time employee whose hourly wage was decreased by 20 percent decided to increase the number of hours worked per week so that the employee ' s total income did not change . by what percent t should the number of hours worked be increased ?
Options: a ) 12.5 % , b ) 20 % , c ) 25 % , d ) 50 % , e ) 100 %
Rationale: correct answer : c solution : c . we can set up equations for income before and after the wage reduction . initially , the employee earns w wage and works h hours per week . after the reduction , the employee earns . 8 w wage and works x hours . by setting these equations equal to each other , we can determine the increase in hours worked : wh = . 8 wx ( divide both sides by . 8 w ) 1.25 h = x we know that the new number of hours worked t will be 25 % greater than the original number . the answer is c .
Answer: c
Question (general): tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random . what is the probability that the ticket drawn has a number which is a multiple of 4 or 15 ?
Options: a ) 9 / 10 , b ) 6 / 10 , c ) 2 / 10 , d ) 3 / 10 , e ) 5 / 10
Rationale: "explanation : here , s = { 1 , 2 , 3 , 4 , . . . . , 19 , 20 } = > n ( s ) = 20 let e = event of getting a multiple of 4 or 15 = multiples od 4 are { 4 , 8 , 12 , 16 , 20 } and multiples of 15 means multiples of 3 and 5 = { 3 , 6 , 9 , 12 , 15 , 18 , 5 , 10 , 15 , 20 } . = the common multiple is only ( 15 ) . = > e = n ( e ) = 6 required probability = p ( e ) = n ( e ) / n ( s ) = 6 / 20 = 3 / 10 . answer is d"
Answer: d
Question (physics): cole drove from home to work at an average speed of 75 kmh . he then returned home at an average speed of 105 kmh . if the round trip took a total of 4 hours , how many minutes did it take cole to drive to work ?
Options: a ) 66 , b ) 70 , c ) 95 , d ) 112 , e ) 140
Rationale: first round distance travelled ( say ) = d speed = 75 k / h time taken , t 2 = d / 75 hr second round distance traveled = d ( same distance ) speed = 105 k / h time taken , t 2 = d / 105 hr total time taken = 4 hrs therefore , 4 = d / 75 + d / 105 lcm of 75 and 105 = 525 4 = d / 75 + d / 105 = > 4 = 7 d / 525 + 5 d / 525 = > d = 525 / 3 km therefore , t 1 = d / 75 = > t 1 = 525 / ( 3 x 75 ) = > t 1 = ( 7 x 60 ) / 3 - - in minutes = > t 1 = 140 minutes . e
Answer: e
Question (general): what could be the range of a set consisting of odd multiples of ( 6 + 1 ) ?
Options: a ) 70 , b ) 24 , c ) 35 , d ) 62 , e ) 21
Rationale: "range = the difference between the greatest and the smallest numbers in the sequence . our sequence is odd and is a multiple of 7 . every number in that sequence can be represented like this : 7 * ( 2 n + 1 ) where n is any positive integer . range = 7 * ( 2 m + 1 ) - 7 * ( 2 n + 1 ) = 7 * 2 * ( m - n ) = 14 * ( m - n ) . m , n - any positive integers the answer must be divisible by 14 , which is only 70 . the correct answer is a ."
Answer: a
Question (general): the apartment on king - williams street is an asset that its value is tramping about . from the year 1973 to 1983 it ' s value decreased by 16 % and from 1983 to 1993 it ' s value increased by 16 % . what is the value of the asset in 1993 if in 1973 it was worth $ 55000 ?
Options: a ) $ 38,796 . , b ) $ 40,000 . , c ) $ 38,976 . , d ) $ 39,679 . , e ) $ 53,592 .
Rationale: 55,000 * 1.16 * . 84 = 53,592 answer e
Answer: e
Question (general): in the xy - coordinate system , if ( m , n ) and ( m + 2 , n + k ) are two points on the line with the equation x = 2 y + 5 , then k =
Options: a ) 1 / 2 , b ) 1 , c ) 2 , d ) 5 / 2 , e ) 4
Rationale: "the equation of the line can be re written as y = ( 1 / 2 ) x - 5 / 2 . slope = 1 / 2 , which means for every 1 unit increase in the y co - ordinate , x will increase by 2 units . hence k = 1 . answer : b"
Answer: b
Question (gain): the difference between c . i . and s . i . on an amount of $ 15,000 for 2 years is $ 54 . what is the rate of interest per annum ?
Options: a ) 5 % , b ) 6 % , c ) 7 % , d ) 8 % , e ) 9 %
Rationale: "$ 54 is the interest on the first year of interest . let x be the interest rate . the interest after the first year is 15000 * x . the interest on the first year ' s interest is 15000 * x * x 15000 * x ^ 2 = 54 x = 0.06 the answer is b ."
Answer: b
Question (general): $ 600 is divided amongst a , b and c so that a may get 2 / 3 as much as b and c together , b may get 6 / 9 as much as a and c together , then the share of a is
Options: a ) $ 100 , b ) $ 150 , c ) $ 125 , d ) $ 200 , e ) $ 240
Rationale: "a : ( b + c ) = 2 : 3 a ' s share = 600 * 2 / 5 = $ 240 answer is e"
Answer: e
Question (general): what is the smallest no . which must be added to 532869 so as to obtain a sum which is divisible by 9 ?
Options: a ) 9 , b ) 2 , c ) 1 , d ) 3 , e ) 6
Rationale: "for 532869 , 5 + 3 + 2 + 8 + 6 + 9 = 33 3 must be added to 532869 to make it divisible by 9 . now , 5 + 3 + 2 + 8 + 7 + 2 = 27 = > 27 is a multiple of 9 and hence 532869 is also divisible by 9 d"
Answer: d
Question (physics): the speed of a boat in still water is 20 km / hr and the rate of current is 5 km / hr . the distance travelled downstream in 12 minutes is :
Options: a ) 9 , b ) 5 , c ) 7 , d ) 6 , e ) 51
Rationale: "explanation : speed downstream = ( 20 + 5 ) kmph = 25 kmph distance travelled = ( 25 * ( 12 / 60 ) ) km = 5 km . answer : b"
Answer: b
Question (gain): a sum was put at simple interest at a certain rate for 6 years had it been put at 4 % higher rate , it would have fetched 144 more . find the sum .
Options: a ) 500 , b ) 600 , c ) 700 , d ) 800 , e ) 900
Rationale: "difference in s . i . = p × t / 100 ( r 1 − r 2 ) ⇒ 144 = p × 6 x 4 / 100 ( ∵ r 1 - r 2 = 2 ) ⇒ p = 144 × 100 / 6 × 4 = 600 answer b"
Answer: b
Question (general): what least no . must be subtracted from 427398 so that remaining no . is divisible by 10 ?
Options: a ) 8 , b ) 9 , c ) 7 , d ) 6 , e ) 3
Rationale: "explanation : on dividing 427398 by 10 we get the remainder 8 , so 8 should be subtracted option a"
Answer: a
Question (general): the number of students enrolled at school xx this year is 7 percent more than it was last year . the number of students enrolled at school yy this year is 3 percent more than it was last year . if school xx grew by 40 more students than school yy did , and if there were 4000 total enrolled students last year at both schools , how many students were enrolled at school yy last year ?
Options: a ) 480 , b ) 1600 , c ) 1920 , d ) 2080 , e ) 2400
Rationale: given info : no . of students enrolled in school x is = 7 % more than previous year ' s strength = 7 x / 100 no . of students enrolled in school y is = 3 % more than previous year ' s strength = 3 y / 100 given that ` ` this year ' ' school x have 40 students more than school y . so the increase in strength can be written as 7 x / 100 = 40 + 3 y / 100 7 x = 4000 + 3 y . . . . . . . . . . . . . . . . . . . . ( 1 ) and total students on previous year are x + y = 4000 . . . . . . . . . . . . . . . . . . . . . . ( 2 ) equating & solving we get , y = 2400 ans is e
Answer: e
Question (general): a 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2 . 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more . at the end of the two removal and replacement , what is the ratio t of milk and water in the resultant mixture ?
Options: a ) 17 : 3 , b ) 9 : 1 , c ) 3 : 17 , d ) 5 : 3 , e ) 11 : 2
Rationale: "he 20 litre mixture contains milk and water in the ratio of 3 : 2 . therefore , there will be 12 litres of milk in the mixture and 8 litres of water in the mixture . step 1 . when 10 litres of the mixture is removed , 6 litres of milk is removed and 4 litres of water is removed . therefore , there will be 6 litres of milk and 4 litres of water left in the container . it is then replaced with pure milk of 10 litres . now the container will have 16 litres of milk and 4 litres of water . step 2 . when 10 litres of the new mixture is removed , 8 litres of milk and 2 litres of water is removed . the container will have 8 litres of milk and 2 litres of water in it . now 10 litres of pure milk is added . therefore , the container will have 18 litres of milk and 2 litres of water in it at the end of the second step . therefore , the ratio of milk and water is 18 : 2 or 9 : 1 . shortcut . we are essentially replacing water in the mixture with pure milk . let w _ o be the amount of water in the mixture originally = 8 litres . let w _ r be the amount of water in the mixture after the replacements have taken place . then , { w _ r } / { w _ o } = ( 1 - r / m ) ^ n where r is the amount of the mixture replaced by milk in each of the steps , m is the total volume of the mixture and n is the number of times the cycle is repeated . hence , { w _ r } / { w _ o }   = ( 1 / 2 ) ^ 2   = 1 / 4 therefore , tw _ r   = { w _ o } / 4 = 8 / 4   = 2 litres . b"
Answer: b
Question (general): a collection of books went on sale , and 2 / 3 of them were sold for $ 3.50 each . if none of the 36 remaining books were sold , what was the total amount received for the books that were sold ?
Options: a ) $ 252 , b ) $ 135 , c ) $ 90 , d ) $ 60 , e ) $ 54
Rationale: "since 2 / 3 of the books in the collection were sold , 1 / 3 were not sold . the 36 unsold books represent 1 / 3 of the total number of books in the collection , and 2 / 3 of the total number of books equals 2 ( 36 ) or 72 . the total proceeds of the sale was 72 ( $ 3.50 ) or $ 252 . the best answer is therefore a . answer : a ."
Answer: a
Question (general): the average runs scored by a batsman in 35 matches is 36 . in the next 14 matches the batsman scored an average of 15 runs . find his average in all the 30 matches ?
Options: a ) 31 , b ) 35 , c ) 29 , d ) 25 , e ) 30
Rationale: total score of the batsman in 35 matches = 1260 . total score of the batsman in the next 14 matches = 210 . total score of the batsman in the 30 matches = 1470 . average score of the batsman = 1470 / 49 = 30 . answer : e
Answer: e
Question (general): the average ( arithmetic mean ) of the 5 positive integers k , m , r , s , and t is 18 , and k < m < r < s < t . if t is 40 , what is the greatest possible value of the median of the 5 integers ?
Options: a ) 16 , b ) 23 , c ) 19 , d ) 20 , e ) 22
Rationale: "we need to find the median which is the third value when the numbers are in increasing order . since k < m < r < s < t , the median would be r . the average of the positive integers is 18 which means that in effect , all numbers are equal to 18 . if the largest number is 40 , it is 22 more than 18 . we need r to be maximum so k and m should be as small as possible to get the average of 16 . since all the numbers are positive integers , k and m can not be less than 1 and 2 respectively . 1 is 17 less than 18 and 2 is 16 less than 18 which means k and m combined are 33 less than the average . 40 is already 22 more than 18 and hence we only have 33 - 22 = 11 extra to distribute between r and s . since s must be greater than r , r can be 18 + 5 = 23 and s can be 18 + 6 = 24 . so r is 23 answer ( b )"
Answer: b
Question (general): how many positive integers less than 7,000 are there in which the sum of the digits equals 5 ?
Options: a ) 52 , b ) 54 , c ) 56 , d ) 58 , e ) 60
Rationale: "basically , the question asks how many 4 digit numbers ( including those in the form 0 xxx , 00 xx , and 000 x ) have digits which add up to 5 . think about the question this way : we know that there is a total of 5 to be spread among the 4 digits , we just have to determine the number of ways it can be spread . let x represent a sum of 1 , and | represent a seperator between two digits . as a result , we will have 5 x ' s ( digits add up to the 5 ) , and 3 | ' s ( 3 digit seperators ) . so , for example : xx | x | x | x = 2111 | | xxx | xx = 0032 etc . there are 8 c 3 ways to determine where to place the separators . hence , the answer is 8 c 3 = 56 . c"
Answer: c
Question (general): 4 / [ ( 1 / 0.03 ) + ( 1 / 0.37 ) ] = ?
Options: a ) 0.004 , b ) 0.11111 , c ) 2.775 , d ) 3.6036 , e ) 36.036
Rationale: "approximate . 1 / . 03 = 100 / 3 = 33 1 / . 37 = 100 / 37 = 3 denominator becomes 33 + 3 = 36 4 / 36 = . 1111 answer ( b )"
Answer: b
Question (gain): by selling 16 pencils for a rupee a man loses 28 % . how many for a rupee should he sell in order to gain 28 % ?
Options: a ) 8 , b ) 9 , c ) 7 , d ) 6 , e ) 4
Rationale: "72 % - - - 16 128 % - - - ? 72 / 128 * 16 = 9 answer : b"
Answer: b
Question (geometry): if the radius of a circle is diminished by 10 % , then the area is diminished by :
Options: a ) 200 % , b ) 210 % , c ) 300 % , d ) 310 % , e ) none of these
Rationale: "explanation : let the original radius be r cm . new radius = 2 r area = π r 2 new area = π 2 r 2 = 4 π r 2 increase in area = ( 4 π r 2 − π r 2 ) = 3 π r 2 increase percent = 3 π r 2 / π r 2 ∗ 100 = 300 % option c"
Answer: c