Cheukting/mathqa huggingface dataset:
Question (general): the “ connection ” between any two positive integers a and b is the ratio of the smallest common multiple of a and b to the product of a and b . for instance , the smallest common multiple of 8 and 12 is 24 , and the product of 8 and 12 is 96 , so the connection between 8 and 12 is 24 / 96 = 1 / 4 the positive integer y is less than 20 and the connection between y and 6 is equal to 1 / 1 . how many possible values of y are there ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: since “ connection ” between y and 6 is 1 / 1 then lcm ( 6 , y ) = 6 y , which means that 6 and y are co - prime ( they do not share any common factor but 1 ) , because if the had any common factor but 1 then lcm ( 6 , y ) would be less than 6 y . so , we should check how many integers less than 20 are co - prime with 6 , which can be rephrased as how many integers less than 20 are not divisible by 2 or 3 ( 6 = 2 * 3 ) . there are ( 18 - 2 ) / 2 + 1 = 9 multiples of 2 in the range from 0 to 20 , not inclusive ; there are ( 18 - 3 ) / 3 + 1 = 6 multiples of 3 in the range from 0 to 20 , not inclusive ; there are 3 multiples of 6 in the range from 0 to 20 , not inclusive ( 6 , 12 , 18 ) - overlap of the above two sets ; total multiples of 2 or 6 in the range from 0 to 20 , not inclusive is 9 + 6 - 3 = 12 ; total integers in the range from 0 to 20 , not inclusive is 19 ; hence , there are total of 19 - 12 = 7 numbers which have no common factor with 6 other than 1 : 1 , 5 , 7 , 11 , 13 , 17 and 19 . answer : a .
Answer: a
Question (other): the probability of two events a and b are 0.15 and 0.40 respectively . the probability that both a and b occur is 0.15 . the probability that neither a nor b occur is _________
Options: a ) 0.45 , b ) 0.4 , c ) 0.5 , d ) 0.05 , e ) 0.6
Rationale: "we are apply that formula . . . . . . . . . . . . . . p ( aorb ) = p ( a ) + p ( b ) - p ( a and b ) = . 15 + . 40 - . 15 = . 40 but the probability of neither a nor b = 1 - . 40 = 0.60 answer : e"
Answer: e
Question (general): ( 0.8 ) ( power 3 ) - ( 0.5 ) ( power 3 ) / ( 0.8 ) ( power 2 ) + 0.40 + ( 0.5 ) ( power 2 ) is :
Options: a ) 0.6 , b ) 0.5 , c ) 0.35 , d ) 0.3 , e ) none of them
Rationale: "given expression = ( 0.8 ) ( power 3 ) - ( 0.5 ) ( power 3 ) / ( 0.8 ) ( power 2 ) + ( 0.8 x 0.5 ) + ( 0.5 ) ( power 2 ) = a ( power 3 ) - b ( power 3 ) / a ( power 2 ) + ab + b ( power 2 ) = ( a - b ) = ( 0.8 - 0.5 ) = 0.30 answer is d ."
Answer: d
Question (geometry): if the length of the sides of two cubes are in the ratio 7 : 1 , what is the ratio of their total surface area ?
Options: a ) 7 : 1 , b ) 14 : 1 , c ) 21 : 1 , d ) 42 : 1 , e ) 49 : 1
Rationale: "let x be the length of the small cube ' s side . the total surface area of the small cube is 6 x ^ 2 . the total surface area of the large cube is 6 ( 7 x ) ^ 2 = 294 x ^ 2 . the ratio of surface areas is 49 : 1 . the answer is e ."
Answer: e
Question (general): when a merchant imported a certain item , she paid a 7 percent import tax on the portion of the total value of the item in excess of $ 1,000 . if the amount of the import tax that the merchant paid was $ 110.60 , what was the total value of the item ?
Options: a ) $ 2160 , b ) $ 2370 , c ) $ 2580 , d ) $ 2790 , e ) $ 2950
Rationale: "let x be the value of the item . 0.07 * ( x - 1000 ) = 110.60 x = 2580 the answer is c ."
Answer: c
Question (physics): on a trip covering 400 km , a bicyclist travels the first 100 km at 20 km per hour and the remainder of the distance at 15 km per hour . what is the average speed , in km per hour , for the entire trip ?
Options: a ) 15.5 , b ) 16.0 , c ) 16.5 , d ) 17.0 , e ) 17.5
Rationale: time 1 = 100 / 20 = 5 hours time 2 = 300 / 15 = 20 hours total time = 25 hours average speed = 400 / 25 = 16 km / hr the answer is b .
Answer: b
Question (general): eighteen years ago , a father was 3 times as old as his son . now the father is only twice as old his son . then the sum of the present ages of the son and the father is :
Options: a ) 53 , b ) 108 , c ) 77 , d ) 107 , e ) 109
Rationale: explanation : let the present ages of the father and son be 2 x and x years respectively . then , ( 2 x - 18 ) = 3 ( x - 18 ) = > x = 36 required sum = ( 2 x + x ) = 108 years . answer : option d
Answer: d
Question (geometry): how many pieces can a square pizza be cut into by making 5 linear cuts ?
Options: a ) 16 , b ) 17 , c ) 13 , d ) 14 , e ) 15
Rationale: "1 cut can make 2 pieces a second cut can make 4 pieces by cutting through 2 pieces a third cut can make 7 pieces by cutting through 3 of the pieces a fourth cut can make 11 pieces by cutting through 4 of the pieces a fifth cut can make 16 pieces by cutting through 5 of the pieces a"
Answer: a
Question (geometry): the area of a parallelogram is 128 sq m . then the area of a triangle formed by its diagonal is - - - - - - - - - - ?
Options: a ) 128 m
b ) 64 m
c ) 64 m ^ 2
d ) 128 m ^ 2
e ) none
Rationale: b * h / 2 = 128 / 2 = 64 m . ans : ( b )
Answer: b
Question (physics): a person crosses a 1080 m long street in 14 minutes . what is his speed in km per hour ?
Options: a ) 4.1 , b ) 4.5 , c ) 4.6 , d ) 5.4 , e ) 5.5
Rationale: "speed = 1080 / ( 12 x 60 ) m / sec = 1.3 m / sec . converting m / sec to km / hr = 1.3 x ( 18 / 5 ) km / hr = 4.6 km / hr . answer : c"
Answer: c
Question (general): if x is a prime number , and x - 1 is the median of the set { x - 1 , 3 x + 3 , 2 x - 4 } , then what is the average ( arithmetic mean ) of the set ?
Options: a ) 2 , b ) 5 / 3 , c ) 3 , d ) 10 / 3 , e ) 14 / 3
Rationale: if x is a prime number , and x - 1 is the median of the set { x - 1 , 3 x + 3 , 2 x - 4 } , then what is the average ( arithmetic mean ) of the set ? a . 2 b . 5 / 3 c . 3 d . 10 / 3 e . 14 / 3 solution : x - 1 is the median of the set , implies if we arrange the set in ascending order , the set would be [ 2 x - 4 , x - 1 , 3 x + 3 ] . this means that : 2 x - 4 < x - 2 < 3 x + 3 solving inequality gives x > - 2 and x < 3 . since x is prime number and the only prime number < 3 is 2 , so put x = 2 . hence set becomes : [ 0 , 1 , 9 ] and avg = 10 / 3 . d
Answer: d
Question (general): the batting average of a particular batsman is 60 runs in 46 innings . if the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs , find his highest score .
Options: a ) 179 , b ) 208 , c ) 210 , d ) 223 , e ) 229
Rationale: "explanation : total runs scored by the batsman = 60 * 46 = 2760 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2760 – 2552 = 208 runs . let the highest score be x , hence the lowest score = x – 150 x + ( x - 150 ) = 208 2 x = 358 x = 179 runs answer a"
Answer: a
Question (physics): the sector of a circle has radius of 21 cm and central angle 135 o . find its perimeter ?
Options: a ) 91.5 cm , b ) 92.2 cm , c ) 28.9 cm , d ) 29.2 cm , e ) 98.2 cm
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 135 / 360 * 2 * 22 / 7 * 21 ) + 2 ( 21 ) = 49.5 + 42 = 91.5 cm answer : a"
Answer: a
Question (general): 8.008 / 1.001
Options: a ) 0.008 , b ) 8 , c ) 0.8 , d ) 80 , e ) 800
Rationale: "answer is 8 , move the decimal forward three places for both numerator and denominator or just multiply both by a thousand . the result is 8008 / 1001 = 8 answer b"
Answer: b
Question (geometry): the radius of a semicircle is 7 . what is the approximate perimeter of the semicircle ?
Options: a ) 36
b ) 25
c ) 15
d ) 28
e ) 37
Rationale: perimeter of a circle = 2 pi * r perimeter of a semicircle = pi * r + 2 r aprox perimiter = 3.14 * 7 + 2 * 7 = 35.98 approximately 36 answer a
Answer: a
Question (physics): a train consists of 12 boggies , each boggy 15 metres long . the train crosses a telegraph post in 18 seconds . due to some problem , one boggies were detached . the train now crosses a telegraph post in
Options: a ) 16.5 sec , b ) 12 sec , c ) 15 sec , d ) 20 sec , e ) none of these
Rationale: length of train = 12 ã — 15 = 180 m . then , speed of train = 180 â  „ 18 = 10 m / s now , length of train = 11 ã — 15 = 165 m â ˆ ´ required time = 165 â  „ 10 = 16.5 sec . answer a
Answer: a
Question (gain): if a sum of money doubles itself in 8 years at simple interest , the ratepercent per annum is
Options: a ) 12 , b ) 12.5 , c ) 13 , d ) 13.5 , e ) 14
Rationale: explanation : let sum = x then simple interest = x rate = ( 100 * x ) / ( x * 8 ) = 12.5 option b
Answer: b
Question (physics): natasha climbs up a hill , and descends along the same way she went up . it takes her 4 hours to reach the top and 2 hours to come back down . if her average speed along the whole journey is 2 kilometers per hour , what was her average speed ( in kilometers per hour ) while climbing to the top ?
Options: a ) 1.5 , b ) 2.5 , c ) 3.75 , d ) 5 , e ) 7.5
Rationale: "let the distance to the top be x , so the total distance traveled by natasha is 2 x . the total time is 4 + 2 = 6 hours the average speed = total distance / total time taken = 2 x / 6 = x / 3 the average speed of the complete journey is 2 km / hour x / 3 = 2 x = 6 km the average speed while climbing = distance / time = 6 / 4 = 1.5 km / h the answer is a ."
Answer: a
Question (general): the average ( arithmetic mean ) of 4 positive integers is 30 . if the average of 2 of these integers is 15 , what is the greatest possible value that one of the other 2 integers can have ?
Options: a ) 55 , b ) 89 , c ) 100 , d ) 109 , e ) 115
Rationale: "a + b + c + d = 120 a + b = 30 c + d = 90 greatest possible = 89 ( just less than 1 ) answer = b"
Answer: b
Question (physics): the length of the bridge , which a train 135 metres long and travelling at 45 km / hr can cross in 30 seconds , is ?
Options: a ) 76 m , b ) 178 m , c ) 240 m , d ) 187 m , e ) 176 m
Rationale: "speed = [ 45 x 5 / 18 ] m / sec = [ 25 / 2 ] m / sec time = 30 sec let the length of bridge be x metres . then , ( 135 + x ) / 30 = 25 / 2 = > 2 ( 135 + x ) = 750 = > x = 240 m . answer : c"
Answer: c
Question (general): carol spends 1 / 4 of her savings on a stereo and 1 / 3 less than she spent on the stereo for a television . what fraction of her savings did she spend on the stereo and television ?
Options: a ) 1 / 4 , b ) 2 / 7 , c ) 5 / 12 , d ) 1 / 2 , e ) 7 / 12
Rationale: "total savings = s amount spent on stereo = ( 1 / 4 ) s amount spent on television = ( 1 - 1 / 3 ) ( 1 / 4 ) s = ( 2 / 3 ) * ( 1 / 4 ) * s = ( 1 / 6 ) s ( stereo + tv ) / total savings = s ( 1 / 4 + 1 / 6 ) / s = 5 / 12 answer : c"
Answer: c
Question (general): jancy had 100 currency notes in all , some of which are of rs 70 denomination and the remaining of rs 50 denomination . the total amount of all these currency notes was rs . 5000 . how much amount ( in rs ) did she have in the denomination of rs 50 ?
Options: a ) 103 , b ) 102 , c ) 100 , d ) 105 , e ) 106
Rationale: let the number of 50 - rupee notes = x then , the number of 70 - rupee notes = ( 100 – x ) 50 x + 70 ( 100 – x ) = 5000 : x = 100 answer : c
Answer: c
Question (general): a line that passes through ( – 1 , – 4 ) and ( 4 , k ) has a slope = k . what is the value of k ?
Options: a ) 3 / 4 , b ) 1 , c ) 4 / 3 , d ) 2 , e ) 7 / 2
Rationale: "slope = ( y 2 - y 1 ) / ( x 2 - x 1 ) = > k = ( k + 4 ) / ( 4 + 1 ) = > 5 k = k + 4 = > k = 1 ans b it is !"
Answer: b
Question (general): a man saves a certain portion of his income during a year and spends the remaining portion on his personal expenses . next year his income increases by 25 % but his savings increase by 100 % . if his total expenditure in 2 years is double his expenditure in 1 st year , what % age of his income in the first year did he save ?
Options: a ) 20 % , b ) 25 % , c ) 28.5 % , d ) 30 % , e ) 32 %
Rationale: "1 st year income = i 1 st year savings = s 1 st year expense = e 1 2 nd year income = 1.25 i 2 nd year savings = 2 s ( 100 % increase ) 2 nd year expense = e 2 e 1 + e 2 = 2 e 1 e 2 = e 1 that means expenses are same during both years . with increase of 25 % income the savings increased by 100 % . or s = . 25 i or s = 25 % of income b is the answer"
Answer: b
Question (general): the contents of a certain box consist of 24 apples and 30 kiwis . how many kiwis must be added to the box so that exactly 30 % of the pieces of fruit in the box will be apples ?
Options: a ) 24 , b ) 26 , c ) 30 , d ) 46 , e ) 50
Rationale: "apples = ( apples + kiwi + x ) * 0.3 24 = ( 30 + 24 + x ) * 0.3 x = 26 . answer : b ."
Answer: b
Question (physics): p and q can complete a work in 80 days and 48 days respectively . p alone started the work and q joined him after 16 days till the completion of the work . how long did the work last ?
Options: a ) 5 days , b ) 10 days , c ) 14 days , d ) 22 days , e ) 40 days
Rationale: explanation : work done by p in 1 day = 1 / 80 work done by q in 1 day = 1 / 48 work done by p in 16 days = 16 ã — ( 1 / 80 ) = 1 / 5 remaining work = 1 â € “ 1 / 5 = 4 / 5 work done by p and q in 1 day = 1 / 80 + 1 / 48 = 1 / 30 number of days p and q take to complete the remaining work = ( 4 / 5 ) / ( 1 / 30 ) = 24 total days = 16 + 24 = 40 answer : option e
Answer: e
Question (other): what is the square root of 83,521 ?
Options: a ) 476 , b ) 489 , c ) 289 , d ) 511 , e ) 311
Rationale: "1 ) checking the last digits in the answer options a , c , e are out since last digit of the square is known to be 1 . 2 ) c = 489 ^ 2 and e = 511 ^ 2 c = ( 300 - 11 ) ^ 2 and e = ( 300 + 11 ) ^ 2 since we need the answer less than 90000 = > e is out . thus we have c as the ans ."
Answer: c
Question (physics): two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 9 hours and 16 hours respectively . the ratio of their speeds is
Options: a ) 4 : 9 , b ) 4 : 3 , c ) 4 : 12 , d ) 4 : 8 , e ) 4 : 5
Rationale: "let us name the trains as a and b . then , ( a ' s speed ) : ( b ' s speed ) = b : a = 16 : 9 = 4 : 3 . answer : b"
Answer: b
Question (general): every student in a room is either a junior or a senior . there is at least one junior and at least one senior in the room . if 2 / 3 of the juniors is equal to 1 / 2 of the seniors , what fraction of the students in the room are juniors ?
Options: a ) 3 / 20 , b ) 1 / 3 , c ) 3 / 7 , d ) 2 / 7 , e ) 7 / 2
Rationale: "let total number of juniors = j total number of seniors = s ( 2 / 3 ) j = ( 1 / 2 ) s = > s = 4 / 3 j total number of students = j + s = ( 7 / 3 ) j fraction of the students in the room are juniors = j / ( j + s ) = j / [ ( 7 / 3 ) j ] = 3 / 7 answer c"
Answer: c
Question (general): a meal cost $ 34.50 and there was no tax . if the tip was more than 10 pc but less than 15 pc of the price , then the total amount paid should be :
Options: a ) 40 - 42 , b ) 39 - 41 , c ) 38 - 40 , d ) 37 - 39 , e ) 36 - 37
Rationale: 10 % ( 34.5 ) = 3.45 15 % ( 34.5 ) = 5.175 total amount could have been 34.5 + 3.45 and 34.5 + 5.175 = > could have been between 37.95 and 39.675 = > approximately between 38 and 40 answer is c .
Answer: c
Question (general): in an examination , questions were asked in 5 sections . out of the total students , 5 % candidates cleared the cut - off in all the sections and 5 % cleared none . of the rest , 25 % cleared only one section and 20 % cleared 4 sections . if 24.5 % of the entire candidates cleared two sections and 300 candidates cleared 3 sections . find out how many candidates appeared at the examination ?
Options: a ) 1000 , b ) 1200 , c ) 1500 , d ) 2000 , e ) 1800
Rationale: solution : passed in none = 5 % passed in all = 5 % passed in four = 20 % 0 f 90 % = 18 % passed in three = 24.5 % passed in three = ( 100 - 5 - 5 - 22.5 - 24.5 - 18 ) = 25 % . but given 300 students passed in three . hence , 25 % = 300 . so , 100 % = 1200 . 1200 students must have appeared . answer : option b
Answer: b
Question (physics): a carpenter worked alone for 1 day on a job that would take him 4 more days to finish . he and another carpenter completed the job in 2 more days . how many days would it have taken the second carpenter to do the complete job working alone ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 14 , e ) 24
Rationale: "a carpenter worked only 1 day on something that takes him 4 more days . means ; carpenter finishes his work in 5 days . let his buddy finish the same task in x days . respective rates per day : 1 / 5 and 1 / x to complete 1 work : first guy worked for 3 days @ rate = 1 / 5 per day . second one worked for 2 days @ rate = 1 / x per day expression : days * rate = work 3 * 1 / 5 + 2 * 1 / x = 1 3 x + 10 = 5 x 2 x = 10 x = 5 days . ans : a"
Answer: a
Question (general): g ( x ) is defined as the product of all even integers k such that 0 < k ≤ x . for example , g ( 14 ) = 2 × 4 × 6 × 8 × 10 × 12 × 14 . if g ( z ) is divisible by 4 ^ 11 , what is the smallest possible value for z ?
Options: a ) 22 , b ) 24 , c ) 28 , d ) 32 , e ) 44
Rationale: g ( z ) = 4 ^ 11 = 2 ^ 22 . so we have to find a product with atleast 22 2 ' s in it . in option 1 22 the total no of 2 ' s = [ 22 / 2 ] + [ 22 / 4 ] + [ 22 / 8 ] + [ 22 / 16 ] = 11 + 5 + 2 + 1 = 19 in option 2 24 the total no of 2 ' s = [ 24 / 2 ] + [ 24 / 4 ] + [ 24 / 8 ] + [ 24 / 16 ] = 12 + 6 + 3 + 1 = 22 . hence b
Answer: b
Question (other): if 12 ounces of a strong vinegar solution are diluted with 50 ounces of water to form a 7 - percent vinegar solution , what was the concentration of the original solution ?
Options: a ) 19.3 % , b ) 17 % , c ) 36.17 % , d ) 15.5 % , e ) 12.5 %
Rationale: let x be the quantity of non - vinegar in the strong vinegar solution thus vinegar quantity will be 12 - x when 50 ounces of water were added the percentage of vinegar becomes 7 % , thus ( 12 - x ) / 62 = 7 / 100 from this equation x = 7.66 answer ( 12 - 7.66 ) / 12 = 36.17 % answer : c
Answer: c
Question (general): if ( a + b ) = 5 , ( b + c ) = 6 and ( c + d ) = 3 , what is the value of ( a + d ) ?
Options: a ) 16 . , b ) 8 . , c ) 7 . , d ) 2 . , e ) - 2 .
Rationale: "given a + b = 5 b + c = 6 c + d = 3 ( a + b ) - ( b + c ) + ( c + d ) = ( a + d ) = > 5 - 6 + 3 = 2 . option d . . ."
Answer: d
Question (physics): on a map the distance between two mountains is 312 inches . the actual distance between the mountains is 136 km . ram is camped at a location that on the map is 25 inch from the base of the mountain . how many km is he from the base of the mountain ?
Options: a ) 10.89 , b ) 14.81 , c ) 14.8 , d ) 14.82 , e ) 14.12
Rationale: "explanation : since 312 inch = 136 km so 1 inch = 136 / 312 km so 25 inch = ( 136 ã — 25 ) / 312 = 10.89 km answer : a"
Answer: a
Question (other): a garrison of 400 men had a provision for 31 days . after 27 days 200 persons re - enforcement leave the garrison . find the number of days for which the remaining ration will be sufficient ?
Options: a ) 65 days , b ) 45 days , c ) 8 days , d ) 16 days , e ) 18 days
Rationale: 400 - - - 31 400 - - - 4 200 - - - ? 400 * 4 = 200 * x = > x = 8 days . answer : c
Answer: c
Question (general): a salesman commission is 10 % on all sales upto $ 5000 and 5 % on all sales exceeding this . he remits $ 15000 to his parent company after deducting his commission . find the total sales ?
Options: a ) 15456 , b ) 14758 , c ) 15789 , d ) 13250 , e ) 12450
Rationale: "let his total sales be x total sales - commission = $ 15000 x - [ ( 10 % of 5000 ) + 5 % of ( x - 5000 ) ] = 15000 95 x / 100 = 15000 x = 15789 approximately answer is c"
Answer: c
Question (general): ( 7.5 × 7.5 + 3.75 + 2.5 × 2.5 ) is equal to
Options: a ) 30 , b ) 60 , c ) 80 , d ) 100 , e ) 90
Rationale: "solution given expression = ( 7.5 x 7.5 + 2 × 7.5 × 2.5 + 2.5 × 2.5 ) ² = ( a ² + 2 ab + b ² ) = ( a + b ) ² = ( 7.5 + 2.5 ) ² = 10 ² = 100 . answer d"
Answer: d
Question (general): a merchant has selected two items to be placed on sale , one of which currently sells for 40 percent less than the other . if he wishes to raise the price of the cheaper item so that the two items are equally priced , by what percentage must he raise the price of the less expensive item ?
Options: a ) 40 % , b ) 50 % , c ) 60 % , d ) 30 % , e ) 20 %
Rationale: "expensive item = $ 100 ; cheap item = $ 60 ; we must increase $ 60 to $ 100 , so by $ 40 , which is approximately 60 % increase : ( 100 - 60 ) / 60 = 2 / 3 = ~ 0.66 . answer : c ."
Answer: c
Question (physics): a owes b rs . 50 . he agrees to pay b over a number of consecutive days on a monday , paying single note or rs . 10 or rs . 20 on each day . in how many different ways can a repay b .
Options: a ) 2 , b ) 8 , c ) 9 , d ) 6 , e ) 5
Rationale: he can pay by all 10 rupee notes = 1 way 3 ten rupee + 1 twenty rupee = 4 ! 3 ! × 1 ! 4 ! 3 ! × 1 ! = 4 ways 1 ten rupee + 2 twenty rupee notes = 3 ! 2 ! × 1 ! 3 ! 2 ! × 1 ! = 3 ways total ways = 1 + 4 + 3 = 8 answer : b
Answer: b
Question (general): if two positive numbers are in the ratio 1 / 12 : 1 / 9 , then by what percent is the second number more than the first ?
Options: a ) 70 % , b ) 90 % , c ) 33.33 % , d ) 50 % , e ) 65 %
Rationale: "given ratio = 1 / 12 : 1 / 9 = 9 : 12 let first number be 9 x and the second number be 12 x . the second number is more than first number by 3 x . required percentage = 3 x / 9 x * 100 = 33.33 % . answer : c"
Answer: c
Question (gain): a and b invests rs . 10000 each , a investing for 6 months and b investing for all the 12 months in the year . if the total profit at the end of the year is rs . 4500 , find their shares ?
Options: a ) 1500,6000 , b ) 4500,3000 , c ) 3500,3000 , d ) 1500,3000 , e ) 2500,3000
Rationale: "the ratio of their profits a : b = 6 : 12 = 1 : 2 share of a in the total profit = 1 / 3 * 4500 = rs . 1500 share of b in the total profit = 2 / 3 * 4500 = rs . 3000 answer : d"
Answer: d
Question (general): a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 32.49 , the number of the member is the group is :
Options: a ) 57 , b ) 67 , c ) 77 , d ) 87 , e ) 97
Rationale: "explanation : money collected = ( 32.49 x 100 ) paise = 3249 paise . ∴ number of members = √ ( 3249 ) = 57 . answer : a"
Answer: a
Question (general): q ' = 3 q - 3 , what is the value of ( 6 ' ) ' ?
Options: a ) 120 , b ) 150 , c ) 180 , d ) 210 , e ) 240
Rationale: ( 6 ' ) ' = ( 3 * 6 - 3 ) ' = 15 ' = 15 * 15 - 15 = 210 answer d
Answer: d
Question (general): in 1979 approximately 1 / 3 of the 38.3 million airline passengers traveling to or from the united states used kennedy airport . if the number of such passengers that used miami airport was 1 / 2 the number that used kennedy airport and 4 times the number that used logan airport , approximately how many millions of these passengers used logan airport that year ?
Options: a ) 18.6 , b ) 9.3 , c ) 6.2 , d ) 3.1 , e ) 1.6
Rationale: number of passengers using kennedy airport = 38 / 3 = ~ 12.67 passengers using miami airport = 12.67 / 2 = ~ 6.3 passengers using logan airport = 6.3 / 4 = ~ 1.58 so e
Answer: e
Question (general): when n is divided by 24 , the remainder is 3 . find thee difference between previous remainder and the remainder when 9 n is divided by 7 ?
Options: a ) 2 , b ) 7 , c ) 5 , d ) 3 , e ) 6
Rationale: "let n = 3 ( leaves a remainder of 3 when divided by 24 ) 9 n = 9 ( 3 ) = 27 , which leaves a remainder of 6 when divided by 7 . difference = 6 - 3 = 3 . answer d"
Answer: d
Question (general): the initial price of an article is rs . 6000 which increases 40 % increse in its price in the first year , a 20 % decrease in the second year and a 20 % increase in the next year . what is the final price of the article ?
Options: a ) rs . 5392 , b ) rs . 6392 , c ) rs . 8392 , d ) rs . 7392 , e ) rs . 9392
Rationale: "the initial price of the article is rs . 6000 . in the 1 st year , price of the article = 6000 + 2400 = rs . 8400 . in the 2 nd year , price = 8400 - 20 % of 8400 = 8400 - 1680 = rs . 6720 . in the 3 rd year , price = 6720 + 10 % of 6720 = 6720 + 672 = rs . 7392 required price = = rs . 7392 . answer : d"
Answer: d
Question (physics): a and b can finish a work in 16 days while a alone can do the same work in 20 days . in how many days b alone will complete the work ?
Options: a ) 76 days , b ) 48 days , c ) 80 days , d ) 31 days , e ) 22 days
Rationale: "b = 1 / 16 – 1 / 20 = 1 / 80 = > 80 days answer : c"
Answer: c