Cheukting/mathqa huggingface dataset:
Question (general): there are , in a certain league , 20 teams , and each team face another team for a total of 4 times . how many games are played in the season ?
Options: a ) 450 , b ) 760 , c ) 110 , d ) 180 , e ) 400
Rationale: "by using the formula , t [ n ( n - 1 ) / 2 ] , where t = no . of games between two teams and n = total no . of teams , we get : 760 option b ."
Answer: b
Question (general): if p ( a ) = 2 / 15 , p ( b ) = 4 / 15 , and p ( a â ˆ ª b ) = 12 / 15 find p ( b | a )
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 2 , d ) 4 / 5 , e ) 6
Rationale: "p ( b | a ) = p ( a â ˆ ª b ) / p ( a ) p ( b | a ) = ( 12 / 15 ) / ( 2 / 15 ) = 6 . e"
Answer: e
Question (geometry): the water level in a rectangular swimming pool measuring 20 feet by 25 feet is to be lowered by 6 inches . how many gallons of water must be removed ? ( 1 cu ft = 7.5 gallons )
Options: a ) 100
b ) 250
c ) 1875
d ) 1200
e ) 5625
Rationale: 6 inches = 1 / 2 feet ( there are 12 inches in a foot . ) , so 20 * 25 * 1 / 2 = 250 feet ^ 3 of water must be removed , which equals to 250 * 7.5 = 1875 gallons . answer : c .
Answer: c
Question (gain): a man buys rs . 20 shares paying 9 % dividend . the man wants to have an interest of 12 % on his money . the market value of each share is :
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 18
Rationale: dividend on rs 20 = 9 / 100 * 20 = 9 / 5 is 12 income 100 9 / 5 is an income on rs ( 100 / 12 * 9 / 5 ) = rs 15 answer d
Answer: d
Question (general): a car travels first 160 km at 75 km / hr and the next 160 km at 90 km / hr . what is the average speed for the first 320 km of the tour ?
Options: a ) 71.11 , b ) 71.12 , c ) 71.1 , d ) 71.17 , e ) 81.81
Rationale: "car travels first 160 km at 75 km / hr time taken to travel first 160 km = distancespeed = 160 / 75 car travels next 160 km at 90 km / hr time taken to travel next 160 km = distancespeed = 160 / 90 total distance traveled = 160 + 160 = 2 × 160 total time taken = 160 / 75 + 160 / 90 average speed = total distance traveled / total time taken = 320 / ( 160 / 75 + 160 / 90 ) = 81.81 km / hr answer : e"
Answer: e
Question (general): a , b and c have rs . 500 between them , a and c together have rs . 200 and b and c rs . 360 . how much does c have ?
Options: a ) 60 , b ) 78 , c ) 267 , d ) 29 , e ) 27
Rationale: "a + b + c = 500 a + c = 200 b + c = 360 - - - - - - - - - - - - - - a + b + 2 c = 560 a + b + c = 500 - - - - - - - - - - - - - - - - c = 60 answer : a"
Answer: a
Question (general): if each participant of a chess tournament plays exactly one game with each of the remaining participants , then 190 games will be played during the tournament . what is the number of participants ?
Options: a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22
Rationale: "let n be the number of participants . the number of games is nc 2 = n * ( n - 1 ) / 2 = 190 n * ( n - 1 ) = 380 = 20 * 19 ( trial and error ) the answer is d ."
Answer: d
Question (physics): a certain number of men can finish a piece of work in 10 days . however , if there were 10 less men it will take 10 days more for the work to be finished . how many men were there originally ?
Options: a ) 10 men , b ) 30 men , c ) 40 men , d ) 20 men , e ) none of these
Rationale: "let x be the number of men originally thus , 10 x = ( 10 + 10 ) ( x - 10 ) 10 x = 20 ( x - 10 ) x = 2 ( x - 10 ) x = 20 answer : d"
Answer: d
Question (general): find the average of all numbers between 4 and 34 which are divisible by 5
Options: a ) 20 , b ) 21 , c ) 25 , d ) 30 , e ) 55
Rationale: "explanation : average = ( 5 + 10 + 15 + 20 + 25 + 30 ) / 5 = 105 / 5 = 21 option b"
Answer: b
Question (geometry): how can a cake ( circular ) be cut into 8 pieces by making just 3 cuts ?
Options: a ) 21
b ) 787
c ) 37
d ) 26
e ) 01
Rationale: explanation : cut the cake using three mutually perpendicular planes . it leaves 8 pieces , one each in each octant . answera
Answer: a
Question (gain): the bankers discount of a certain sum of money is rs . 72 and the true discount on the same sum for the same time is rs . 60 . the sum due is :
Options: a ) rs . 360 , b ) rs . 432 , c ) rs . 540 , d ) rs . 1080 , e ) rs . 1280
Rationale: "sum = ( b . d * t . d ) / ( b . d - t . d ) ( 72 * 60 ) / 72 - 60 ; 360 answer : a"
Answer: a
Question (physics): the length of a room is 5.5 m and width is 3.75 m . find the cost of paying the floor by slabs at the rate of rs . 1000 per sq . metre .
Options: a ) rs . 15,000 , b ) rs . 15,500 , c ) rs . 15,600 , d ) rs . 20,625 , e ) none
Rationale: "solution area of the floor = ( 5.5 x 3.75 ) m ² = 20.635 m ² cost of paying = rs . ( 1000 x 20.625 ) = rs . 20625 . answer d"
Answer: d
Question (general): find the value of x in [ ( 17.28 / x ) / ( 3.6 * 0.2 ) ] = 2
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: ( 17.28 / x ) = 2 * 3.6 * 0.2 x = ( 17.28 / 1.44 ) = ( 1728 / 14 ) = 12 . option b
Answer: b
Question (general): set a contains all the even numbers between 22 and 70 inclusive . set b contains all the even numbers between 62 and 110 inclusive . what is the difference between the sum of elements of set b and the sum of the elements of set a ?
Options: a ) 600 , b ) 800 , c ) 1000 , d ) 1200 , e ) 1400
Rationale: "each term in set b is 40 more than the corresponding term in set a . the difference of the sums = 25 * 40 = 1000 . the answer is c ."
Answer: c
Question (general): a person travels from p to q a speed of 40 km / hr and returns by increasing his speed by 50 % . what is his average speed for both the trips ?
Options: a ) 27 , b ) 87 , c ) 48 , d ) 77 , e ) 51
Rationale: "speed on return trip = 150 % of 40 = 60 km / hr . average speed = ( 2 * 40 * 60 ) / ( 40 + 60 ) = 48 km / hr . answer : c"
Answer: c
Question (general): the average of 5 numbers is 6.8 . if one of the numbers is multiplied by a factor of 2 , the average of the numbers increases to 9.2 . what number is multiplied by 2 ?
Options: a ) 12.0 , b ) 30.0 , c ) 30.9 , d ) 40.0 , e ) 60.0
Rationale: the average of 5 numbers is 6.8 the sum of 5 numbers will be 6.8 x 5 = 34 the average of 5 number after one of the number is multiplied by 2 is 9.2 the sum of the numbers will now be 9.2 x 5 = 46 so the sum has increased by 46 - 34 = 12 let the number multiplied by 2 be n then , 2 n = n + 12 or n = 12 answer : - a
Answer: a
Question (gain): the sale price sarees listed for rs . 345 after successive discount is 12 % and 25 % is ?
Options: a ) 321 , b ) 276 , c ) 342 , d ) 228 , e ) 245
Rationale: "explanation : 345 * ( 88 / 100 ) * ( 75 / 100 ) = 228 answer : d"
Answer: d
Question (geometry): the length and breadth of the floor of the room are 20 feet and 10 feet respectively . square tiles of 2 feet length of different colours are to be laid on the floor . black tiles are laid in the first row on all sides . if white tiles are laid in the one - third of the remaining and blue tiles in the rest , how many blue tiles will be there ?
Options: a ) 16
b ) 24
c ) 32
d ) 48
e ) none of these
Rationale: area left after laying black tiles = [ ( 20 – 4 ) × ( 10 – 4 ) ] sq . ft . = 96 sq . ft . area under white tiles = ( 1 ⁄ 3 × 96 ) sq . ft = 32 sq . ft . area under blue tiles = ( 96 – 32 ) sq . ft = 64 sq . ft . number of blue tiles = 64 / 2 × 2 = 16 . answer a
Answer: a
Question (other): in a group of 89 students , 36 are taking history , and 32 are taking statistics . if 59 students are taking history or statistics or both , then how many students are taking history but not statistics ?
Options: a ) 9 , b ) 19 , c ) 27 , d ) 26 , e ) 31
Rationale: "number of students taking history = h = 36 number of students taking statistics = s = 32 total number of students = t = 89 number of students taking history or statistics or both = b = 59 number of students taking neither history nor statistics = n = 89 - 59 = 30 letxbe the number of students taking both history and statistics . then t = h + s + n - x or 89 = 36 + 32 + 30 - x or x = 9 now , number of students taking only history will be h - x or 36 - 9 = 27 answer : - c"
Answer: c
Question (gain): the workforce of company x is 60 % female . the company hired 22 additional male workers , and as a result , the percent of female workers dropped to 55 % . how many employees did the company have after hiring the additional male workers ?
Options: a ) 160 , b ) 220 , c ) 264 , d ) 360 , e ) 420
Rationale: "let ' s xx be total quantity of employees 0.6 x = females before adding men 0.55 ( x + 22 ) = females after adding men as quantity of women does n ' t change we can make an equation : 0.6 x = 0.55 ( x + 22 ) 0.05 x = 12.1 x = 242 - this is quantity of employees before adding 22 men so after adding it will be 264 answer is c"
Answer: c
Question (gain): a fruit seller sells mangoes at the rate of rs . 8 per kg and thereby loses 20 % . at what price per kg , he should have sold them to make a profit of 5 %
Options: a ) rs 8.5 , b ) rs 9.5 , c ) rs 10.5 , d ) rs 11.5 , e ) none of these
Rationale: explanation : 80 : 8 = 105 : x x = ( 8 × 105 / 80 ) = rs 10.5 option c
Answer: c
Question (physics): two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 21 seconds . the ratio of their speeds is ?
Options: a ) 3 / 6 , b ) 3 / 2 , c ) 2 / 3 , d ) 3 / 5 , e ) 5 / 2
Rationale: "let the speeds of the two trains be x m / sec and y m / sec respectively . then , length of the first train = 27 x meters , and length of the second train = 17 y meters . ( 27 x + 17 y ) / ( x + y ) = 21 = = > 27 x + 17 y = 21 x + 21 y = = > 6 x = 4 y = = > x / y = 2 / 3 . answer : c"
Answer: c
Question (general): if n = 9 ^ 11 – 9 , what is the units digit of n ?
Options: a ) 0 , b ) 1 , c ) 4 , d ) 6 , e ) 8
Rationale: always divide the power ( incase 11 ) by 4 and use the remainder as the new power . the question now becomes 9 ^ 3 - 9 . now 9 ^ 3 has last digit 9 . , we subtract 9 from 9 , thus 9 - 9 = 0 is the answer . option a
Answer: a
Question (physics): two trains each 210 m in length each , are running on two parallel lines in opposite directions . if one goes at the speed of 90 km / h while the other travels at 85 km / h . how long will it take for them to pass each other completely .
Options: a ) 3 sec , b ) 2.6 sec , c ) 3.6 sec , d ) 8.6 sec , e ) 7.6 sec
Rationale: "explanation : d = 210 m + 210 m = 420 m rs = 90 + 85 = 175 * 5 / 18 = 243 / 5 t = 420 * 5 / 243 = 8.6 sec answer : option d"
Answer: d
Question (physics): b completes a work in 8 days . a alone can do it in 10 days . if both work together , the work can be completed in how many days ?
Options: a ) 3.75 days , b ) 4.44 days , c ) 5 days , d ) 6.44 days , e ) 7 days
Rationale: "1 / 8 + 1 / 10 = 9 / 40 40 / 9 = 4.44 days answer : b"
Answer: b
Question (gain): a sum fetched a total simple interest of rs . 1000 at the rate of 10 p . c . p . a . in 4 years . what is the sum ?
Options: a ) 2500 , b ) 2800 , c ) 3500 , d ) 1900 , e ) 1500
Rationale: sol . principal = rs . [ 100 * 1000 / 10 * 4 ] = rs . [ 100000 / 40 ] = rs . 2500 . answer a
Answer: a
Question (general): p and q are the only two applicants qualified for a short - term research project that pays 360 dollars in total . candidate p has more experience and , if hired , would be paid 50 percent more per hour than candidate q would be paid . candidate q , if hired , would require 10 hours more than candidate p to do the job . candidate p ’ s hourly wage is how many dollars greater than candidate q ’ s hourly wage ?
Options: a ) $ 3 , b ) $ 6 , c ) $ 9 , d ) $ 12 , e ) $ 15
Rationale: "let q ' s hourly wage be x , then p ' s hourly wage is 1.5 x let t be the number of hours that q needs , then p needs t - 10 hours to do the job . since they both are paid an equal total amount of $ 360 : x * t = 1.5 x * ( t - 10 ) t = 30 hours and q ' s hourly wage is 360 / 30 = $ 12 p ' s hourly wage is 360 / ( t - 10 ) = $ 18 which is $ 6 per hour more . the answer is b ."
Answer: b
Question (physics): find the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 17 cm
Options: a ) 178 cm 2 , b ) 323 cm 2 , c ) 285 cm 2 , d ) 167 cm 2 , e ) 197 cm 2
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 17 ) = 323 cm 2 answer : b"
Answer: b
Question (gain): a cylinder of height h is 7 / 8 of water . when all of the water is poured into an empty cylinder whose radius is 25 percent larger than that of the original cylinder , the new cylinder is 3 / 5 full . the height of the new cylinder is what percent of h ?
Options: a ) 25 % , b ) 50 % , c ) 69 % , d ) 80 % , e ) 100 %
Rationale: "basically we can disregard the radius is 25 % information , as we are only asked about the height of the original and the new cylinder . this is becausethe new cylinder is 3 / 5 fullmeans the same as that it ' s height is 3 / 5 . original cylinder 7 / 8 new cylinder 3 / 5 so 3 / 5 / 7 / 8 = 3 / 5 * 8 / 7 = 0.69 or 69 % . answer c"
Answer: c
Question (general): linda spent 3 / 4 of her savings on furniture and the rest on a tv . if the tv cost her $ 250 , what were her original savings ?
Options: a ) $ 500 , b ) $ 600 , c ) $ 700 , d ) $ 800 , e ) $ 1000
Rationale: "if linda spent 3 / 4 of her savings on furnitute , the rest 4 / 4 - 3 / 4 = 1 / 4 on a tv but the tv cost her $ 250 . so 1 / 4 of her savings is $ 250 . so her original savings are 4 times $ 250 = $ 1000 correct answer e"
Answer: e
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 7 % . what was its profit on the items sold in february ?
Options: a ) 27.5 % , b ) 30 % , c ) 35 % , d ) 39.5 % , 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 = 0.93 * 150 x = 139.5 x hence total profit = 39.5 % option d"
Answer: d
Question (general): bill made a profit of 10 % by selling a product . if he had purchased that product for 10 % less and sold it at a profit of 30 % , he would have received $ 56 more . what was his original selling price ?
Options: a ) $ 880 , b ) $ 950 , c ) $ 1100 , d ) $ 1240 , e ) $ 1360
Rationale: "let p be the original purchase price of the product . bill originally sold the product for 1.1 * p . in the second scenario , the purchase price is 0.9 * p . a 30 % profit means the selling price would be 1.3 * 0.9 * p = 1.17 * p thus , according to the information in the question , 1.17 p - 1.1 p = 56 0.07 = 56 p = 800 the original selling price was 800 * 1.1 = 880 . the correct answer is a ."
Answer: a
Question (physics): a train speeds past a pole in 10 seconds and a platform 100 m long in 30 seconds . its length is ?
Options: a ) 188 m , b ) 876 m , c ) 251 m , d ) 50 m , e ) 45 m
Rationale: "let the length of the train be x meters and its speed be y m / sec . they , x / y = 10 = > y = x / 10 x + 100 / 30 = x / 10 x = 50 m . answer : d"
Answer: d
Question (general): suraj has a certain average of runs for 16 innings . in the 17 th innings he scores 112 runs thereby increasing his average by 6 runs . what is his average after the 17 th innings ?
Options: a ) 18 , b ) 25 , c ) 16 , d ) 72 , e ) 27
Rationale: "to improve his average by 6 runs per innings he has to contribute 16 x 6 = 96 runs for the previous 16 innings . thus , the average after the 17 th innings = 112 - 96 = 16 . answer : c"
Answer: c
Question (gain): a man can row downstream at the rate of 16 km / hr and upstream at 8 km / hr . find man ' s rate in still water and the rate of current ?
Options: a ) 12,4 , b ) 6,3 , c ) 9,3 , d ) 6,6 , e ) none of these
Rationale: "explanation : rate of still water = 1 / 2 ( 16 + 8 ) = 12 km / hr rate of current = 1 / 2 ( 16 - 8 ) = 4 km / hr answer : option a"
Answer: a
Question (general): the average of squares of first 11 consecutive even numbers is :
Options: a ) 164 , b ) 174 , c ) 184 , d ) 194 , e ) 204
Rationale: 2 ( n + 1 ) ( 2 n + 1 ) / 3 ( 2 * 12 * 23 ) / 3 = 2 * 4 * 23 = 184 answer : c
Answer: c
Question (geometry): the length of a rectangular plot is 10 mtr more than its width . the cost of fencing the plot along its perimeter at the rate of rs . 6.5 mtr is rs . 1430 . the perimeter of the plot is ?
Options: a ) 126 , b ) 156 , c ) 190 , d ) 321 , e ) 220
Rationale: "sol . let width = x , length = ( 10 + x ) perimeter = 2 ( x + ( 10 + x ) ) = 2 ( 2 x = 10 ) & 2 ( 2 x + 10 ) * 6.5 = 1430 x = 50 required perimeter = 2 ( 50 + 60 ) = 220 e"
Answer: e
Question (general): rahul played weel in this season . his current batting averagge is 51 . if he score 69 runs in today match . his batting average will become 54 . how many matches had he played in this season .
Options: a ) 8 , b ) 10 , c ) 9 , d ) 6 , e ) 5
Rationale: 51 x + 69 = 54 ( x + 1 ) = > 3 x = 15 = > x = 5 answer : e
Answer: e
Question (general): 1852 - 1230 ÷ 10.00 = ?
Options: a ) 62.2 , b ) 2000 , c ) 1700 , d ) 1729 , e ) none
Rationale: "answer given expression = 1852 - 1230 ÷ 10.00 = 1852 - 123 = 1729 correct option : d"
Answer: d
Question (gain): last year a certain bond price with a face value of 5000 yielded 8 % of its face value in interest . if that interest was approx 6.5 of the bond ' s selling price approx what was the bond ' s selling price ?
Options: a ) 4063 , b ) 5325 , c ) 5351 , d ) 6000 , e ) 6154
Rationale: "interest = 0.08 * 5000 = 0.065 * selling price - - > selling price = 0.08 * 5000 / 0.065 - - > selling price = ~ 6,154 answer : e ."
Answer: e
Question (general): mixture contains alcohol and water in the ratio 4 : 3 . if 8 liters of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture .
Options: a ) 10 , b ) 99 , c ) 27 , d ) 4 , e ) 29
Rationale: "let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 32 x = 4 ( 3 x + 5 ) 20 x = 20 x = 1 quantity of alcohol = ( 4 x 1 ) litres = 4 litres . answer : d"
Answer: d
Question (general): mary ' s income is 60 % more than tim ' s income and tim ' s income is 50 % less than juan ' s income . what % of juan ' s income is mary ' s income .
Options: a ) 124 % , b ) b . 120 % , c ) 96 % , d ) 80 % , e ) 64 %
Rationale: "even i got 96 % j = 100 t = 100 * 0.5 = 50 m = 50 * 1.6 = 80 if mary ' s income is x percent of j m = j * x / 100 x = m * 100 / j = 80 * 100 / 100 = 80 ans : d"
Answer: d
Question (physics): laxmi and prasanna set on a journey . laxmi moves northwards at a speed of 40 kmph and prasanna moves southward at a speed of 38 kmph . how far will be prasanna from laxmi after 60 minutes ?
Options: a ) 11 , b ) 50 , c ) 78 , d ) 27 , e ) 18
Rationale: "explanation : we know 60 min = 1 hr total northward laxmi ' s distance = 40 kmph x 1 hr = 40 km total southward prasanna ' s distance = 38 kmph x 1 hr = 38 km total distance between prasanna and laxmi is = 40 + 38 = 78 km . answer : c"
Answer: c
Question (gain): a grocer has 400 pounds of coffee in stock , 20 percent of which is decaffeinated . if the grocer buys another 100 pounds of coffee of which 70 percent is decaffeinated , what percent , by weight , of the grocer ’ s stock of coffee is decaffeinated ?
Options: a ) 28 % , b ) 30 % , c ) 32 % , d ) 34 % , e ) 36 %
Rationale: "1 . 20 % of 400 = 80 pounds of decaffeinated coffee 2 . 70 % of 100 = 70 pounds of decaffeinated coffee 3 . wt have 150 pounds of decaffeinated out of 500 pounds , that means 150 / 500 * 100 % = 30 % . the correct answer is b ."
Answer: b
Question (general): the value of ( 34.31 * 0.5 * 1.567 ) / ( 0.0673 * 23.25 * 7.57 ) is close to
Options: a ) 2 , b ) 1.15 , c ) 2.05 , d ) 2.27 , e ) 2.35
Rationale: "( 34.31 * 0.5 * 1.567 ) / ( 0.0673 * 23.25 * 7.57 ) = 26.882 / 11.845 = 2.27 answer : d"
Answer: d
Question (general): the average age of 15 students of a class is 15 years . out of these , the average age of 5 students is 14 years and that of the other 9 students is 16 years . the age of the 15 th student is
Options: a ) 9 years , b ) 11 years , c ) 14 years , d ) 21 years , e ) 25 years
Rationale: "solution age of the 15 th student = [ 15 x 15 - ( 14 x 5 + 16 x 9 ) ] = ( 225 - 214 ) = 11 years . answer b"
Answer: b
Question (gain): the population of a town is 10000 . it increases annually at the rate of 20 % p . a . what will be its population after 2 years ?
Options: a ) 14300 , b ) 14400 , c ) 14500 , d ) 14600 , e ) 15400
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 10000 × 120 / 100 × 120 / 100 = 14400 b )"
Answer: b
Question (general): what is the decimal equivalent of ( 1 / 4 ) ^ 3 ?
Options: a ) 0.0016 , b ) 0.0625 , c ) 0.16 , d ) 0.25 , e ) 0.0156
Rationale: ( 1 / 4 ) ^ 3 = 1 / 64 = 0.0156 answer : e
Answer: e
Question (general): a student took 6 courses last year and received an average ( arithmetic mean ) grade of 100 points . the year before , the student took 5 courses and received an average grade of 40 points . to the nearest tenth of a point , what was the student ’ s average grade for the entire two - year period ?
Options: a ) 79 , b ) 89 , c ) 95 , d ) 72.72 , e ) 97.2
Rationale: "let the 6 courses that were taken last year be a 1 , a 2 , a 3 , a 4 , a 5 , a 6 a 1 + a 2 + a 3 + a 4 + a 5 + a 6 = 100 * 6 = 600 the year before , the 5 courses be b 1 , b 2 , b 3 , b 4 , b 5 b 1 + b 2 + b 3 + b 4 + b 5 = 40 * 5 = 200 student ' s average = ( 600 + 200 ) / 11 = 72.72 answer d"
Answer: d
Question (gain): at what price must an article costing rs . 66.5 be marked in order that after deducting 5 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 87.5 , b ) 89.5 , c ) 82.3 , d ) 82.1 , e ) 92.4
Rationale: "cp = 66.5 sp = 66.5 * ( 125 / 100 ) = 83.125 mp * ( 95 / 100 ) = 59.375 mp = 87.5 answer : a"
Answer: a
Question (probability): three 6 faced dice are thrown together . the probability that all the three show the same number on them is - .
Options: a ) 1 / 36 , b ) 1 / 216 , c ) 1 / 48 , d ) 1 / 55 , e ) 1 / 90
Rationale: "it all 3 numbers have to be same basically we want triplets . 111 , 222 , 333 , 444 , 555 and 666 . those are six in number . further the three dice can fall in 6 * 6 * 6 = 216 ways . hence the probability is 6 / 216 = 1 / 36 answer a"
Answer: a
Question (general): the smallest number which when diminished by 7 , is divisible 12 , 16 , 18 , 21 and 28 is :
Options: a ) 1008 , b ) 1015 , c ) 1022 , d ) 1032 , e ) none of these
Rationale: "explanation required number = ( l . c . m . of 12,16 , 18 , 21 , 28 ) + 7 = 1008 + 7 = 1015 answer b"
Answer: b
Question (general): the average of first 15 even numbers is ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 16 , e ) 14
Rationale: "sum of 15 even numbers = 15 * 16 = 240 average = 240 / 15 = 16 answer : d"
Answer: d
Question (general): in 100 litres mixture milk and water are in the ratio 3 : 2 . after adding how many liters of water its ratio will become 3 : 4
Options: a ) 48 , b ) 50 , c ) 62 , d ) 78 , e ) 100
Rationale: milk quantity = 3 / 5 * 60 = 36 water quantity = 100 - 36 = 64 new ratio of m : w = 36 : 64 + x = 3 : 4 192 + 3 x = 144 x = 48 answer is a
Answer: a
Question (gain): a sum fetched a total simple interest of 4034.25 at the rate of 9 % . p . a . in 5 years . what is the sum ?
Options: a ) 5768 , b ) 8925 , c ) 8965 , d ) 6474 , e ) 8723
Rationale: "principal = ( 100 x 4034.25 ) / ( 9 x 5 ) = 403425 / 45 = 8965 . answer c"
Answer: c