Cheukting/mathqa huggingface dataset:
Question (physics): a room 8 m 47 cm long and 7 m 77 cm broad is to be paved with square tiles . find the least number of square tiles required to cover the floor .
Options: a ) 13636 , b ) 13440 , c ) 13647 , d ) 13431 , e ) 13675
Rationale: "explanation : area of the room = ( 847 x 777 ) cm 2 . size of largest square tile = h . c . f . of 847 cm and 777 cm = 7 cm . area of 1 tile = ( 7 x 7 ) cm 2 . number of tiles required = ( 847 × 777 ) / ( 7 × 7 ) = 13431 answer : option d"
Answer: d
Question (general): if x and y are numbers such that ( x + 8 ) ( y - 8 ) = 0 , what is the smallest possible value of x ^ 2 + y ^ 2
Options: a ) 4 , b ) 24 , c ) 54 , d ) 64 , e ) 94
Rationale: "from ( x + 8 ) ( y - 8 ) = 0 it follows that either , x = - 8 or y = 8 . thus either x ^ 2 = 64 or y ^ 2 = 64 . now , if x ^ 2 = 64 , then the least value of y ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 64 + 0 = 64 . similarly if y ^ 2 = 64 , then the least value of x ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 0 + 64 = 64 . answer : d ."
Answer: d
Question (gain): what will be the compound interest on rs . 50000 after 3 years at the rate of 12 % per annum
Options: a ) rs 20123.20 , b ) rs 20246.4 , c ) rs 20123.40 , d ) rs 20123.50 , e ) none of these
Rationale: "explanation : ( 50000 × ( 1 + 12 / 100 ) 3 ) = > 50000 × 28 / 25 × 28 / 25 × 28 / 25 = > 70246.4 so compound interest will be 70246.4 - 50000 = rs 20246.4 option b"
Answer: b
Question (general): dick and jane each saved $ 1000 in 1989 . in 1990 dick saved 15 percent more than in 1989 , and together he and jane saved a total of $ 2000 . approximately what percent less did jane save in 1990 than in 1989 ?
Options: a ) 3 % , b ) 5 % , c ) 10 % , d ) 15 % , e ) 18 %
Rationale: 1990 dick saved = $ 1150 jane saved = $ 850 ( jane saved $ 150 less than she did the prior year ) jane saved approximately $ 150 / 1000 $ ( 15 % ) less in 1990 answer : d
Answer: d
Question (general): calculate the share of y , if rs . 2690 is divided among x , y and z in the ratio 5 : 7 : 9 ?
Options: a ) 890.7 , b ) 826.7 , c ) 895.7 , d ) 896.7 , e ) 816.7
Rationale: "5 + 7 + 9 = 21 2690 / 21 = 128.1 y ' s share = 7 * 128.1 = 896.7 answer : d"
Answer: d
Question (geometry): the perimeter of an equilateral triangle is 45 . if one of the side is the side of an isoceles triangle of perimeter 40 then what is the lenght of base of isoceles triangle .
Options: a ) 10 units , b ) 20 units , c ) 30 units , d ) 40 units , e ) 15 units
Rationale: "base of isoceles triangle is 40 - 15 - 15 = 10 units . answer : a"
Answer: a
Question (general): a lemonade stand sold only small and large cups of lemonade on tuesday . 3 / 5 of the cups sold were small and the rest were large . if the large cups were sold for 5 / 6 as much as the small cups , what fraction of tuesday ' s total revenue was from the sale of large cups ?
Options: a ) 7 / 16 , b ) 7 / 15 , c ) 10 / 21 , d ) 17 / 35 , e ) 5 / 14
Rationale: "let the total # of cups be 10 . # of small cups sold 3 / 5 * 10 = 6 ; # of large cups sold 10 - 6 = 4 ; let the price of small cup be $ 6 , then the price of larges cup would be 5 / 6 * 6 = $ 5 ; revenue from small cups : 6 * $ 6 = $ 36 ; revenue from large cups cups : 4 * $ 5 = $ 20 ; fraction of total revenue from large cups : 20 / ( 36 + 20 ) = 5 / 14 . answer : e"
Answer: e
Question (gain): after 10 % of the inhabitants of a village disappeared , a panic set in during which 25 % of the remaining inhabitants left the village . at that time , the population was reduced to 4860 . what was the number of original inhabitants ?
Options: a ) 7000 , b ) 7200 , c ) 7400 , d ) 7600 , e ) 7800
Rationale: let the total number of original inhabitants be x . ( 75 / 100 ) * ( 90 / 100 ) * x = 4860 ( 27 / 40 ) * x = 4860 x = 4860 * 40 / 27 = 7200 the answer is b .
Answer: b
Question (physics): worker a takes 7 hours to do a job . worker b takes 10 hours to do the same job . how long it take both a & b , working together but independently , to do the same job ?
Options: a ) 70 / 17 , b ) 40 / 9 , c ) 50 / 9 , d ) 60 / 9 , e ) 80 / 9
Rationale: "one day work of a = 1 / 7 one day work of b = 1 / 10 so one day work of a and b together = 1 / 7 + 1 / 10 = 17 / 70 so total days required = 70 / 17 answer : a"
Answer: a
Question (physics): in what time will a train 200 meters long cross an electric pole , if its speed is 128 km / hr
Options: a ) 5 seconds , b ) 5.7 seconds , c ) 3 seconds , d ) 2.5 seconds , e ) none of these
Rationale: "explanation : first convert speed into m / sec speed = 128 * ( 5 / 18 ) = 35 m / sec time = distance / speed = 200 / 35 = 5.7 seconds option b"
Answer: b
Question (general): 4 , 12 , 48 , 240 , 1440 , 10080,80640 , 725760 ( . . . )
Options: a ) 7257600 , b ) 10080 , c ) 6200 , d ) 10020 , e ) 12500
Rationale: "explanation : go on multiplying the given numbers by 3 , 4 , 5 , 6 , 7,8 , 9,10 answer : option a"
Answer: a
Question (general): if rs . 10 be allowed as true discount on a bill of rs . 110 at the end of a certain time , then the discount allowed on the same sum due at the end of double the time is ?
Options: a ) 68.33 , b ) 18.33 , c ) 28.33 , d ) 48.33 , e ) 98.33
Rationale: explanation : present worth = amount - truediscount = 110 - 10 = rs . 100 si on rs . 100 for a certain time = rs . 10 si on rs . 100 for doube the time = rs . 20 truediscount on rs . 120 = 120 - 100 = rs . 20 truediscount on rs . 110 = = rs . 18.33 answer : b
Answer: b
Question (physics): a train 120 m long running at 60 kmph crosses a platform in 20 sec . what is the length of the platform ?
Options: a ) 213 , b ) 298 , c ) 350 , d ) 726 , e ) 267
Rationale: "d = 60 * 5 / 18 = 20 = 333 â € “ 120 = 213 answer : a"
Answer: a
Question (physics): two pipes a and b can fill a tank in 12 hours and 15 hours respectively . if both pipe open together in tank , then how much time it take to fill the tank ?
Options: a ) 15 , b ) 18 , c ) 20 / 3 , d ) 19 / 4 , e ) 25 / 4
Rationale: in 1 hour pipe a fill = 1 / 12 in 1 hour pipe b fill = 1 / 15 pipe ( a + b ) in 1 hour = [ 1 / 12 + 1 / 15 ] = 3 / 20 total time taken to fill the tank = 20 / 3 hour answer c
Answer: c
Question (general): when a number is divided by 13 , the remainder is 6 . when the same number is divided by 7 , then remainder is 1 . what is the number ?
Options: a ) 243 , b ) 253 , c ) 312 , d ) 432 , e ) none of these
Rationale: "explanation : take 243 243 ÷ 7 = 34 , remainder = 5 hence this is not the answer take 312 312 ÷ 7 = 44 , remainder = 4 hence this is not the answer take 253 253 ÷ 7 = 36 , remainder = 1 . 253 ÷ 13 = 19 , remainder = 6 this satisfies both the conditions given in the question . hence it is the answer . answer : b"
Answer: b
Question (general): for the past n days , the average ( arithmetic mean ) daily production at a company was 60 units . if today ' s production of 90 units raises the average to 62 units per day , what is the value of n ?
Options: a ) 30 , b ) 14 , c ) 10 , d ) 9 , e ) 7
Rationale: "( average production for n days ) * n = ( total production for n days ) - - > 60 n = ( total production for n days ) ; ( total production for n days ) + 90 = ( average production for n + 1 days ) * ( n + 1 ) - - > 60 n + 90 = 62 * ( n + 1 ) - - > n = 14 . or as 30 extra units increased the average for n + 1 days by 2 units per day then 30 / ( n + 1 ) = 2 - - > n = 14 . answer : b ."
Answer: b
Question (physics): james took a 3 - hour bike ride . in the second hour he travlled 24 miles , which was 20 percent farther than he traveled the first hour . if he traveled 25 percent farther in the third hour than he did in the second hour , how many miles did jose travel during the entire ride ?
Options: a ) 74.0 , b ) 54.9 , c ) 55.5 , d ) 57.0 , e ) 63.0
Rationale: "let the distance travelled in the first hour be x . thus , 1.2 x = 24 , x = 20 . now , the distance travelled in the 3 rd hour = 24 + 1 / 4 â ˆ — 24 = 30 . = 24 + 20 + 30 = 74 answer : a"
Answer: a
Question (geometry): a rectangular block 6 cm by 12 cm by 15 cm is cut up into an exact number of equal cubes . find the least possible number of cubes .
Options: a ) 30 , b ) 40 , c ) 10 , d ) 20 , e ) 50
Rationale: "explanation : volume of the block = ( 6 x 12 x 15 ) cm 3 = 1080 cm 3 side of the largest cube = h . c . f . of 6 cm , 12 cm , 15 cm = 3 cm . volume of this cube = ( 3 x 3 x 3 ) cm 3 = 27 cm 3 number of cubes = ( 1080 / 27 ) = 40 . answer : b"
Answer: b
Question (physics): a train 360 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 390 m long ?
Options: a ) 40 sec , b ) 60 sec , c ) 45 sec , d ) 48 sec , e ) 50 sec
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 360 + 140 = 750 m required time = 750 * 2 / 25 = 40 sec answer : b"
Answer: b
Question (gain): an empty fuel tank with a capacity of 200 gallons was filled partially with fuel a and then to capacity with fuel b . fuel a contains 12 % ethanol by volume and fuel b contains 16 % ethanol by volume . if the full fuel tank contains 20 gallons of ethanol , how many gallons of fuel a were added ?
Options: a ) 300 , b ) 150 , c ) 100 , d ) 80 , e ) 50
Rationale: "say there are a gallons of fuel a in the tank , then there would be 200 - a gallons of fuel b . the amount of ethanol in a gallons of fuel a is 0.12 a ; the amount of ethanol in 200 - a gallons of fuel b is 0.16 ( 200 - a ) ; since the total amount of ethanol is 20 gallons then 0.12 a + 0.16 ( 200 - a ) = 20 - - > a = 300 . answer : a ."
Answer: a
Question (geometry): the circus sells two kinds of tickets : lower seats for $ 30 and upper seats for $ 20 . on a certain night , the circus sells 80 tickets and gets $ 2100 in revenue from the sales . how many tickets for lower seats did they sell ?
Options: a ) 40
b ) 45
c ) 50
d ) 55
e ) 60
Rationale: let l be the number of lower seat tickets . let u be the number of upper seat tickets . l + u = 80 and u = 80 - l . 30 l + 20 u = 2100 . 30 l + 20 ( 80 - l ) = 2100 10 l + 1600 = 2100 . 10 l = 500 . l = 50 . the answer is c .
Answer: c
Question (general): the average weight of 8 persons increases by 1.5 kg . if a person weighing 65 kg is replaced by a new person , what could be the weight of the new person ?
Options: a ) 76 kg , b ) 77 kg , c ) 76.5 kg , d ) data inadequate , e ) none of these
Rationale: "total weight increases = 8 × 1.5 = 12 kg so the weight of new person = 65 + 12 = 77 kg answer b"
Answer: b
Question (physics): the speed at which a man can row a boat in still water is 26 kmph . if he rows downstream , where the speed of current is 4 kmph , what time will he take to cover 150 metres ?
Options: a ) 18 , b ) 27 , c ) 28 , d ) 12 , e ) 25
Rationale: speed of the boat downstream = 26 + 4 = 30 kmph = 30 * 5 / 18 = 8.33 m / s hence time taken to cover 150 m = 150 / 8.33 = 18 seconds . answer : a
Answer: a
Question (general): a mathematics teacher tabulated the marks secured by 35 students of 8 th class . the average of their marks was 72 . if the marks secured by reema was written as 35 instead of 99 then find the correct average marks up to two decimal places .
Options: a ) 73.41 , b ) 74.31 , c ) 72.43 , d ) 73.43 , e ) 73.82
Rationale: "total marks = 35 x 72 = 2520 corrected total marks = 2520 - 35 + 99 = 2584 correct average = 2584 / 35 = 73.82 answer : e"
Answer: e
Question (general): two employees m and n are paid a total of $ 572 per week by their employer . if m is paid 120 percent of the salary paid to n , how much is n paid per week ?
Options: a ) $ 220 , b ) $ 240 , c ) $ 260 , d ) $ 300 , e ) $ 320
Rationale: "1.2 n + n = 572 2.2 n = 572 n = 260 the answer is c ."
Answer: c
Question (general): if rs . 527 be divided among a , b , c in such a way that a gets 2 / 3 of what b gets and b gets 1 / 4 of what c gets , then their shares are respectively ?
Options: a ) s . 300 , b ) s . 360 , c ) s . 389 , d ) s . 368 , e ) s . 372
Rationale: ( a = 2 / 3 b and b = 1 / 4 c ) = a / b = 2 / 3 and b / c = 1 / 4 a : b = 2 : 3 and b : c = 1 : 4 = 3 : 12 a : b : c = 2 : 3 : 12 a ; s share = 527 * 2 / 17 = rs . 62 b ' s share = 527 * 3 / 17 = rs . 93 c ' s share = 527 * 12 / 17 = rs . 372 . answer : e
Answer: e
Question (gain): the annual interest rate earned by an investment increased by 10 percent from last year to this year . if the annual interest rate earned by the investment this year was 9 percent , what was the annual interest rate last year ?
Options: a ) 1 % , b ) 1.1 % , c ) 8.18 % , d ) 10 % , e ) 10.8 %
Rationale: "9 = 1.1 * x x = 8.18 % answer c )"
Answer: c
Question (other): in what ratio should a variety of rice costing rs . 6 per kg be mixed with another variety of rice costing rs . 8.75 per kg to obtain a mixture costing rs . 7.50 per kg ?
Options: a ) 1 / 68 , b ) 62 / 89 , c ) 12 / 68 , d ) 11 / 84 , e ) 5 / 6
Rationale: "explanation : let us say the ratio of the quantities of cheaper and dearer varieties = x : y by the rule of allegation , x / y = ( 87.5 - 7.50 ) / ( 7.50 - 6 ) = 5 / 6 answer : e"
Answer: e
Question (physics): a driver goes on a trip of 60 kilometers , the first 30 kilometers at 60 kilometers per hour and the remaining distance at 30 kilometers per hour . what is the average speed of the entire trip in kilometers per hour ?
Options: a ) 35 , b ) 36 , c ) 40 , d ) 42 , e ) 45
Rationale: "the time for the first part of the trip was 30 / 60 = 1 / 2 hours . the time for the second part of the trip was 30 / 30 = 1 hour . the total time for the trip was 3 / 2 hours . the average speed for the trip was 60 / ( 3 / 2 ) = 40 kph the answer is c ."
Answer: c
Question (general): a certain meter records voltage between 0 and 10 volts inclusive . if the average value of 3 recordings on the meter was 7 volts , what was the smallest possible recording in volts ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "if average of 3 is 7 so sum of 3 should be 21 3 recording can be from 0 - 10 inclusive to find one smallest other two should be highest so , lets assume three var are a , b , c say a is smallest and give b and c greatest readings say 9 and 9 so a has to be 3 b"
Answer: b
Question (geometry): the perimeter of one square is 48 cm and that of another is 28 cm . find the perimeter and the diagonal of a square which is equal in area to these two combined ?
Options: a ) 13 √ 4 , b ) 13 √ 2 , c ) 23 √ 2 , d ) 13.9 √ 2 , e ) 13 √ 9
Rationale: "4 a = 48 4 a = 28 a = 12 a = 7 a 2 = 144 a 2 = 49 combined area = a 2 = 193 = > a = 13.9 d = 13.9 √ 2 answer : d"
Answer: d
Question (physics): two bullet train s 140 m and 160 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time ( in seconds ) which they take to cross each other , is :
Options: a ) 15.8 sec . , b ) 12.8 sec . , c ) 11.8 sec . , d ) 10.8 sec . , e ) 08.8 sec .
Rationale: "d 10.8 sec . relative speed = ( 60 + 40 ) km / hr = 100 x 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = ( 140 + 160 ) m = 300 m . required time = 300 x 9 / 250 = 54 / 5 = 10.8 sec ."
Answer: d
Question (general): 18 times a positive integer is more than its square by 80 , then the positive integer is
Options: a ) 13 , b ) 10 , c ) 11 , d ) 12 , e ) 14
Rationale: "explanation : let the number be x . then , 18 x = x 2 + 80 = > x 2 - 18 x + 80 = 0 = > ( x - 10 ) ( x - 8 ) = 0 = > x = 10 or 8 answer : b"
Answer: b
Question (general): if | x + 3 | = 15 , what is the sum of all the possible values of x ?
Options: a ) - 16 , b ) - 12 , c ) - 8 , d ) - 3 , e ) 11
Rationale: "there will be two cases x + 3 = 15 or x + 3 = - 15 = > x = 12 or x = - 18 sum of both the values will be - 18 + 15 = - 3 answer : d"
Answer: d
Question (geometry): a box has 12 shapes ; 3 circles , 5 squares , and 4 triangles . how many groups of 3 shapes can be made with at least 1 triangle ?
Options: a ) 46
b ) 64
c ) 164
d ) 146
e ) 56
Rationale: the problem asks for a combination , since order does n ' t matter . now , selecting r items from a set of n gives the combination formula : ncr = n ! / r ! ( n - r ) ! n = 12 r = 3 so , total groups is 12 c 3 = 12 ! / ( 3 ! ( 12 - 3 ) ! ) = 220 , and n = 12 - 4 = 8 r = 3 for groups without a triangle is 8 c 3 = 8 ! / ( 3 ! ( 8 - 3 ) ! ) = 56 , so , groups with at least 1 triangle = 220 - 56 = 164 answer : c
Answer: c
Question (gain): how many liters of water must be evaporated from 50 liters of a 3 - percent sugar solution to get a 5 - percent solution ?
Options: a ) 35 , b ) 22.5 , c ) 27 , d ) 16 2 / 3 , e ) 15
Rationale: "how many liters of water must be evaporated from 50 liters of a 3 - percent sugar solution to get a 5 - percent solution ? 3 % of a 50 liter solution is 1.5 l . so you are trying to determine how many liters must a solution be for the 1.5 l to represent 5 % of the solution . set up an inequality and solve for x : 1.5 / x = 1 / 5 x = 7.5 since you need a 15 l solution , you must evaporate 22.5 of the original 50 l solution to get a 5 % solution . answer is b ."
Answer: b
Question (general): we bought 85 hats at the store . blue hats cost $ 6 and green hats cost $ 7 . the total price was $ 540 . how many green hats did we buy ?
Options: a ) a ) 36 , b ) b ) 30 , c ) c ) 40 , d ) d ) 42 , e ) e ) 44
Rationale: "let b be the number of blue hats and let g be the number of green hats . b + g = 85 . b = 85 - g . 6 b + 7 g = 540 . 6 ( 85 - g ) + 7 g = 540 . 510 - 6 g + 7 g = 540 . g = 540 - 510 = 30 . the answer is b ."
Answer: b
Question (general): if â € œ * â €  is called â € œ + â €  , â € œ / â €  is called â € œ * â €  , â € œ - â €  is called â € œ / â €  , â € œ + â €  is called â € œ - â €  . 80 / 40 â € “ 10 * 20 + 10 = ?
Options: a ) 185 , b ) 160 , c ) 170 , d ) 145 , e ) 225
Rationale: "explanation : given : 80 / 40 â € “ 10 * 20 + 10 = ? substituting the coded symbols for mathematical operations , we get , 80 * 40 / 20 + 20 â € “ 10 = ? 80 * 2 + 20 â € “ 10 = ? 160 + 20 â € “ 10 = ? 180 â € “ 10 = 170 answer : c"
Answer: c
Question (gain): a , b and c enter into a partnership . a invests 3 times as much as b invests and 2 / 3 of what c invests . at the end of the year , the profit earned is rs . 66000 . what is the share of c ?
Options: a ) rs . 15250 , b ) rs . 13375 , c ) rs . 16750 , d ) rs . 18000 , e ) none of these
Rationale: "explanation : let the investment of c be rs . x . the inverstment of b = rs . ( 2 x / 3 ) the inverstment of a = rs . ( 3 × ( 2 / 3 ) x ) = rs . ( 2 x ) ratio of capitals of a , b and c = 2 x : 2 x / 3 : x = 6 : 2 : 3 c ' s share = rs . [ ( 3 / 11 ) × 66000 ] = rs . 18000 answer : option d"
Answer: d
Question (physics): a factory has three types of machines , each of which works at its own constant rate . if 7 machine as and 11 machine bs can produce 525 widgets per hour , and if 8 machine as and 22 machine cs can produce 600 widgets per hour , how many widgets could one machine a , one machine b , and one machine c produce in one 8 - hour day ?
Options: a ) 400 , b ) 475 , c ) 550 , d ) 625 , e ) 600
Rationale: "let machine a produce a widgets per hour . b produce b widgets per hour and c produce c widgets per hour . 7 a + 11 b = 525 - - - ( 1 ) 8 a + 22 c = 600 - - - ( 2 ) dividing ( 2 ) by 2 4 a + 11 c = 300 . . . . . ( 3 ) adding ( 1 ) ( 3 ) 11 a + 11 b + 11 c = 825 a + b + c = 75 per hour so for eight hrs = 75 * 8 = 600 = answer = e"
Answer: e
Question (gain): find number which is 70 % less than 60 .
Options: a ) 18 , b ) 22 , c ) 28 , d ) 26 , e ) 98
Rationale: "explanation : 70 % less is 30 % of the given number therefore , 30 % of 60 is 18 . answer : a"
Answer: a
Question (other): a person want to give his money of $ 1000 to his 4 children a , b , c , d in the ratio 2 : 4 : 3 : 1 . what is the a + d share ?
Options: a ) $ 100 , b ) $ 200 , c ) $ 300 , d ) $ 500 , e ) $ 600
Rationale: "a ' s share = 1000 * 2 / 10 = $ 200 d ' s share = 1000 * 1 / 10 = $ 100 a + d = $ 300 answer is c"
Answer: c
Question (physics): mariah has decided to hire three workers . to determine whom she will hire , she has selected a group of 14 candidates . she plans to have one working interview with 3 of the 14 candidates every day to see how well they work together . how many days will it take her to have working interviews with all the different combinations of job candidates ?
Options: a ) 720 , b ) 120 , c ) 300 , d ) 30 , e ) 333
Rationale: "333 . answer e"
Answer: e
Question (physics): an athlete runs 200 metres race in 20 seconds . what is his speed ?
Options: a ) 23 , b ) 38 , c ) 37 , d ) 36 , e ) 28
Rationale: "speed = distance / time = 200 / 20 = 10 m / s = 10 * 18 / 5 = 36 km / hr answer : d"
Answer: d
Question (general): a certain meter records voltage between 0 and 10 volts inclusive . if the average value of 3 recordings on the meter was 6 volts , what was the smallest possible recording in volts ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "if average of 3 is 6 so sum of 3 should be 18 3 recording can be from 0 - 10 inclusive to find one smallest other two should be highest so , lets assume three var are a , b , c say a is smallest and give b and c greatest readings say 8 and 8 so a has to be 2 a"
Answer: a
Question (general): what is the remainder when 7777 * 8888 * 101010 is divided by 33
Options: a ) 110 , b ) 220 , c ) 330 , d ) 440 , e ) 550
Rationale: "7777 / 33 = = > remainder = 22 8888 / 33 = = > remainder = 11 101010 / 33 = = > remainder = 30 = 22 * 11 * 30 = 7260 / 33 = = > remainder = 220 answer : b"
Answer: b
Question (general): find the last digit in the product 287 x 287 + 269 x 269 - 2 x 287 x 269 ?
Options: a ) 5 , b ) 6 , c ) 8 , d ) 9 , e ) 4
Rationale: explanation : given exp . = a 2 + b 2 - 2 ab , where a = 287 and b = 269 = ( a - b ) 2 = ( 287 - 269 ) 2 = ( 182 ) = 324 answer is e
Answer: e
Question (general): at a monthly meeting , 2 / 3 of the attendees were males and 3 / 4 of the male attendees arrived on time . if 5 / 6 of the female attendees arrived on time , what fraction of the attendees at the monthly meeting did not arrive on time ?
Options: a ) 1 / 3 , b ) 1 / 4 , c ) 3 / 8 , d ) 2 / 9 , e ) 5 / 18
Rationale: "males who did not arrive on time are 1 / 4 * 2 / 3 = 1 / 6 of the attendees . females who did not arrive on time are 1 / 6 * 1 / 3 = 1 / 18 of the attendees . the fraction of all attendees who did not arrive on time is 1 / 6 + 1 / 18 = 2 / 9 the answer is d ."
Answer: d
Question (general): the sum of the ages of 4 children born at the intervals of 4 years each is 36 years . what is the age of the youngest child ?
Options: a ) 3 , b ) 18 , c ) 10 , d ) 99 , e ) 38
Rationale: "let x = the youngest child . each of the other four children will then be x + 4 , x + 8 , x + 12 we know that the sum of their ages is 36 . so , x + ( x + 4 ) + ( x + 8 ) + ( x + 12 ) = 36 therefore the youngest child is 3 years old answer : a"
Answer: a
Question (general): a school has 4 section of chemistry in class x having 50 , 35 , 45 and 42 students . the mean marks obtained in chemistry test are 50 , 60 , 55 and 45 respectively for the 4 sections . determine the overall average of marks per student .
Options: a ) 50.12 , b ) 52.12 , c ) 51.12 , d ) 53.12 , e ) none of the above
Rationale: "required average marks = 50 ã — 50 + 35 ã — 60 + 45 ã — 55 + 42 ã — 45 / 50 + 35 + 45 + 42 = 2500 + 2100 + 2475 + 1890 / 172 = 8965 â  „ 172 = 52.12 answer b"
Answer: b
Question (general): what is the least integer that is a sum of 4 different prime numbers each greater than 10 ?
Options: a ) 60 , b ) 62 , c ) 64 , d ) 66 , e ) 68
Rationale: the sum of the four smallest primes greater than 10 is 11 + 13 + 17 + 19 = 60 . the answer is a .
Answer: a
Question (geometry): what is the smallest positive integer that can be multiplied by 605 to make it a perfect square ?
Options: a ) 2 , b ) 3 , c ) 5 , d ) 7 , e ) 11
Rationale: "605 is multiplied by 5 gives 3025 its a square root of 55 answer is 5 - option c"
Answer: c
Question (other): set a consists of the integers from 1 to 12 , inclusive , while set b consists of the integers from 5 to 15 , inclusive . how many distinct integers do belong to the both sets at the same time ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 15 , e ) 9
Rationale: "a = { 1,2 , 3,4 , 5,6 , 7 , 8 , 9 , 10 , 11 , 12 } b = { 5,6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 } common elements = { 5,6 , 7 , 8 , 9 , 10 , 11 , 12 } = 8 elements answer : option a ."
Answer: a