choices dict | answerKey listlengths 1 1 | question stringlengths 8 751 | rationale stringlengths 8 1.53k | dataset stringclasses 1 value |
|---|---|---|---|---|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"15",
"30",
"40",
"50"
]
} | [
"A"
] | the sum of the squares of three numbers is 125 , while the sum of their products taken two at a time is 50 . their sum is : | "x ^ + y ^ 2 + z ^ 2 = 125 xy + yz + zx = 50 as we know . . ( x + y + z ) ^ 2 = x ^ 2 + y ^ 2 + z ^ 2 + 2 ( xy + yz + zx ) so ( x + y + z ) ^ 2 = 125 + ( 2 * 50 ) ( x + y + z ) ^ 2 = 225 so x + y + z = 15 answer : a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"120 kg",
"130 kg",
"137 kg",
"190 kg"
]
} | [
"C"
] | the average weight of 10 persons increases by 7.2 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ? | "solution total weight increased = ( 10 x 7.2 ) kg = 72 kg . weight of new person = ( 65 + 72 ) kg = 137 kg . answer c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"973",
"6973",
"5994",
"9554"
]
} | [
"C"
] | the difference between the place value and the face value of 6 in the numerical 856973 is | "= ( place value of 6 ) - ( face value of 6 ) = ( 6000 - 6 ) = 5994 answer is c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"17.36 %",
"20 %",
"25 %",
"50 %"
]
} | [
"A"
] | ritesh and co . generated revenue of rs . 1,800 in 2006 . this was 12.5 % of its gross revenue . in 2007 , the gross revenue grew by rs . 2,500 . what is the percentage increase in the revenue in 2007 ? | "explanation : given , ritesh and co . generated revenue of rs . 1,800 in 2006 and that this was 12.5 % of the gross revenue . hence , if 1800 is 12.5 % of the revenue , then 100 % ( gross revenue ) is : = > ( 100 / 12.5 ) Γ 1800 . = > 14,400 . hence , the total revenue by end of 2007 is rs . 14,400 . in 2006 , revenue grew by rs . 2500 . this is a growth of : = > ( 2500 / 14400 ) Γ 100 . = > 17.36 % . answer : a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"76 m', '",
"80 m', '",
"84 m', '",
"88 m', '"
]
} | [
"C"
] | 66 cubic centimetres of silver is drawn into a wire 1 mm in diameter . the length if the wire in meters will be : | explanation : let the length of the wire be h radius = 1 / 2 mm = 120 cm Ο r 2 h = 66 22 / 7 β 1 / 20 β 1 / 20 β h = 66 = > h = 66 β 20 β 20 β 7 / 22 = 8400 cm = 84 m option c | MathQA |
{
"label": [
"A",
"B",
"D",
"E"
],
"text": [
"3",
"2",
"4",
"1"
]
} | [
"E"
] | if a positive integer n has 211 factors , then how many prime factors does n have ? | let the factor be a ^ x * b ^ y . . . . . so ( x + 1 ) ( y + 1 ) . . . . . = 211 . . now 211 is a prime number . . . so only one variable x or y is 210 and the others are 0 . . ( 210 + 1 ) ( 0 + 1 ) . . . so the number becomes a ^ 210 . . thus only one prime factor is there . | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"4586970843",
"4686970743",
"4691100843",
"4586870843"
]
} | [
"C"
] | calculate 469157 x 9999 = ? | "answer 469157 x 9999 = 469157 x ( 10000 - 1 ) = 4691570000 - 469157 = 4691100843 . option : c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"12 h",
"10 h",
"4 h",
"6 h"
]
} | [
"C"
] | the area of a square field is 400 km 2 . how long will it take for a horse to run around at the speed of 20 km / h ? | explanation area of field = 400 km 2 . then , each side of field = β 400 = 20 km distance covered by the horse = perimeter of square field = 20 Γ 4 = 80 km β΄ time taken by horse = distances / peed = 80 / 20 = 4 h answer c | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"3 : 13",
"9 : 13",
"36 : 13",
"13 : 9"
]
} | [
"B"
] | if a and b are in the ratio 3 : 4 , and b and c in the ratio 12 : 13 , then a and c will be in the ratio | solution : ( a / b ) * ( b / c ) = ( 3 / 4 ) * ( 12 / 13 ) ; or , a / b = 36 / 39 = 9 : 13 . answer : option b | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"77', '",
"154', '",
"308', '",
"318', '"
]
} | [
"B"
] | what is the maximum area that can be enclosed by a wire 44 cm long ? | perimeter of circle = 2 * 22 / 7 * r = 44 cm from this r = 7 then area of circle = 22 / 7 * r ^ 2 = 154 answer : b | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"47.095",
"47.752",
"47.932",
"47.95"
]
} | [
"D"
] | 3889 + 12.952 β ? = 3854.002 | explanation let 3889 + 12.952 β x = 3854.002 . then x = ( 3889 + 12.952 ) β 3854.002 = 3901.952 β 3854.002 = 47.95 . answer d | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"277",
"35",
"64",
"72"
]
} | [
"B"
] | ? % of 360 = 126 | "? % of 360 = 126 or , ? = 126 Γ 100 / 360 = 35 answer b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"200', '",
"225', '",
"240', '",
"250', '"
]
} | [
"D"
] | the area of a circle of radius 5 is numerically what percent of its circumference ? | solution required % = [ Ο x ( 5 ) 2 / 2 Ο x 5 x 100 ] % βΉ = βΊ 250 % . answer d | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"9 min",
"10 min",
"12 min",
"7 min"
]
} | [
"A"
] | two fill taps a and b can separately fill a cistern in 45 and 40 minutes respectively . they started to fill a cistern together but tap a is turned off after few minutes and tap b fills the rest part of cistern in 23 minutes . after how many minutes , was tap a turned - off ? | let a was turned off after x min . then , cistern filled by a in x min + cistern filled by b in ( x + 23 ) min = 1 β x / 45 + x + 23 / 40 = 1 β 17 x + 207 = 360 β x = 9 min . answer a | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"$ 21",
"$ 35",
"$ 31",
"$ 41"
]
} | [
"B"
] | at an upscale fast - food restaurant , shin can buy 3 burgers , 7 shakes , and one cola for $ 120 . at the same place it would cost $ 162.50 for 4 burgers , 10 shakes , and one cola . how much would it cost for a meal of one burger , one shake , and one cola ? | "let ' s suppose that the price of a burger is bb , of a shake - ss and that of a cola is cc . we can then construct these equations : 3 b + 7 s + c = 120 4 b + 10 s + c = 162.5 subtracting the first equation from the second gives us b + 3 s = 42.5 now if we subtract the new equation two times from first or 3 times from second we will get b + s + c = 35 . in any case , there is no necessity to know each item ' s price , just the sum . answer : b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 28,000",
"rs . 24,000",
"rs . 30,000",
"rs . 36,000"
]
} | [
"A"
] | jayant opened a shop investing rs . 30,000 . madhu joined him 2 months later , investing rs . 45,000 . they earned a profit of rs . 56,000 after completion of one year . what will be madhu ' s share of profit ? | "30,000 * 12 = 45,000 * 8 1 : 1 madhu ' s share = 1 / 2 * 56,000 i . e . rs . 28,000 answer : a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1.04",
"2.04",
"3.04",
"4.04"
]
} | [
"D"
] | an error 2 % in excess is made while measuring the side of a square . the percentage of error in the calculated area of the square is : | "explanation : 100 cm is read as 102 cm . a 1 = ( 100 Γ 100 ) cm 2 and a 2 = ( 102 Γ 102 ) cm 2 ( a 2 - a 1 ) = [ 1022 - 1002 ] = ( 102 + 100 ) x ( 102 - 100 ) = 404 cm 2 answer : d" | MathQA |
{
"label": [
"A",
"B",
"C",
"E"
],
"text": [
"400",
"500",
"700",
"506"
]
} | [
"C"
] | evaluate 49 / . 07 | "explanation : 49 / . 07 = 4900 / 7 = 700 option c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"10",
"100",
"1000",
"10000"
]
} | [
"D"
] | ( 1000 ) 7 Γ· ( 10 ) 17 = ? | explanation : = ( 103 ) 7 / ( 10 ) 17 = ( 10 ) 21 / ( 10 ) 17 = 10 ( 4 ) = 10000 option d | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"2 kg",
"2.4 kg",
"2.5 kg",
"1.250 kg"
]
} | [
"D"
] | fresh grapes contain 90 % by weight while dried grapes contain 20 % water by weight . what is the weight of dry grapes available from 10 kg of fresh grapes ? | "the weight of non - water in 10 kg of fresh grapes ( which is 100 - 90 = 10 % of whole weight ) will be the same as the weight of non - water in x kg of dried grapes ( which is 100 - 20 = 80 % of whole weight ) , so 10 Γ’ Λ β 0.1 = x Γ’ Λ β 0.8 - - > x = 1.25 answer : d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"0.1402",
"0.001402",
"1.4021",
"0.01402"
]
} | [
"D"
] | 14.02 Γ£ β 0.001 = ? | "14.02 Γ£ β 0.001 = 0.01402 the answer is d ." | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"7",
"14",
"49",
"21"
]
} | [
"C"
] | β ( 49 ) 2 | "explanation β ( 49 ) 2 = ? or , ? = 49 answer c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 105",
"rs . 150",
"rs . 146",
"rs . 135"
]
} | [
"A"
] | if the sales tax be reduced from 4 ( 1 / 2 ) % to 3 ( 1 / 2 ) % , then what difference does it make to a person who purchases a bag with marked price of rs . 10500 ? | "explanation : required difference = ( 4 ( 1 / 2 ) of rs . 10500 ) - ( 3 ( 1 / 2 ) of rs . 10500 ) = ( 9 / 2 β 7 / 2 ) % of rs . 10500 = ( 1 ) x ( 1 / 100 ) x 10500 = rs . 105 answer a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"0.47",
"47",
"470",
"4700"
]
} | [
"C"
] | the value of ( 4.7 Γ 13.26 + 4.7 Γ 9.43 + 4.7 Γ 77.31 ) is | "solution given expression = 4.7 Γ ( 13.26 + 9.43 + 77.31 ) = 4.7 Γ 100 = 470 . answer c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"11",
"13",
"20 3 / 17",
"14"
]
} | [
"B"
] | a is 30 % more efficient than b . how much time will they working together take to complete a job which a alone could have done in 23 days ? | explanation : ratio of times taken by a and b = 100 : 130 = 10 : 13 suppose b takes x days to work the 10 : 13 : : 23 : x = > x = 23 x 13 / 10 = 299 / 10 a β s one day work = 1 / 23 and b β s is 10 / 299 then a + b β s work = 1 / 23 + 10 / 299 = 23 / 299 = 1 / 13 = > 13 days answer : option b | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"91",
"40",
"80",
"90"
]
} | [
"B"
] | the maximum number of student amoung them 1080 pens and 920 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is : | "solution required number of student = h . c . f of 1080 and 920 = 40 . answer b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"2828",
"2850",
"1365",
"1574"
]
} | [
"A"
] | if the product of two numbers is 62216 and their h . c . f . is 22 , find their l . c . m . | "explanation : hcf * lcm = 62216 , because we know product of two numbers = product of hcf and lcm lcm = 62216 / 22 = 2828 option a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"0.21 %",
"21 %",
"0.021 %",
"2.1 %"
]
} | [
"D"
] | present birth rate is 32 per 1000 while death rate is 11 per 1000 . what will be the percentage increase in the rate of population ? | birth rate = 32 / 1000 = 0.032 death rate = 11 / 1000 = 0.011 increase in population = 0.032 - 0.011 = 0.021 = 2.1 % answer : d | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"150",
"151",
"250",
"350"
]
} | [
"B"
] | in a school with 604 students , the average age of the boys is 12 years and that of the girls is 11 years . if the average age of the school is 11 years 9 months , then the number of girls in the school is | "sol . let the number of grils be x . then , number of boys = ( 600 - x ) . then , ( 11 3 / 4 Γ 604 ) β 11 x + 12 ( 604 - x ) β x = 7248 - 7097 β 151 . answer b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 55.50",
"rs . 67.50",
"rs . 86.50",
"rs . 105.00"
]
} | [
"D"
] | the sides of a rectangular field are in the ratio 3 : 4 . if the area of the field is 10800 sq . m , the cost of fencing the field @ 25 paise per metre is | "solution let length = ( 3 x ) metres and breadth = ( 4 x ) metres . then , 3 x Γ 4 x = 10800 β 12 x 2 = 10800 β x 2 = 900 β x = 30 . so , length = 90 m and breadth = 120 m . perimeter = [ 2 ( 90 + 120 ) ] m = 420 m . β΄ cost of fencing = rs . ( 0.25 Γ 420 ) = rs . 105.00 . answer d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs 450",
"rs 920",
"rs 550",
"rs . 630"
]
} | [
"D"
] | there were 35 students in a hostel . due to the admission of 7 new students the expenses of the mess were increased by rs . 84 per day while the average expenditure per head diminished by re 1 . what was the original expenditure of the mess ? | explanation : let the original average expenditure be rs . x then , 42 ( x - 1 ) - 35 x = 84 ? 7 x = 126 ? x = 18 therefore original expenditure = rs . ( 35 18 ) = rs . 630 . answer : d | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"45 ( 4 / 11 ) %",
"40 %",
"45 ( 5 / 11 ) %",
"44 ( 5 / 11 ) %"
]
} | [
"B"
] | a batsman scored 100 runs which included 3 boundaries and 8 sixes . what percent of his total score did he make by running between the wickets ? | "explanation : total runs scored = 100 total runs scored from boundaries and sixes = 3 x 4 + 8 x 6 = 60 total runs scored by running between the wickets = 100 - 60 = 40 required % = ( 40 / 100 ) Γ 100 = 40 % answer : option b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"10 %",
"9 1 / 11 %",
"11 1 / 9 %",
"11 %"
]
} | [
"C"
] | the price of an article is cut by 10 % . to restore it to the former value , the new price must be increased by | "explanation : let original price = rs . 100 then , new price = rs . 90 increase on rs . 90 = rs . 100 increase % = ( 10 / 90 Γ 100 ) % = 11 1 / 9 % correct option : c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"0.2",
"0.3",
"0.4",
"0.5"
]
} | [
"C"
] | the function f ( x ) = x + 4 is given . solve the equation : [ 3 . f ( x - 2 ) ] / f ( 0 ) + 4 = f ( 2 x + 1 ) | solution : we calculate f ( 0 ) , f ( x - 2 ) , f ( 2 x + 1 ) , namely f ( 0 ) = 0 + 4 = 4 ; f ( x - 2 ) = x - 2 + 4 = x + 2 ; f ( 2 x + 1 ) = 2 x + 1 + 4 = 2 x + 5 the equation gets this look [ 3 ( x + 2 ) ] / 4 + 4 = 2 x + 5 < = > 3 ( x + 2 ) + 16 = 4 ( 2 x + 5 ) < = > 3 x + 6 + 16 = 8 x + 20 < = > 22 - 20 = 8 x - 3 x < = > 2 = 5 x < = > x = 0.4 answer c | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"276",
"299",
"312",
"400"
]
} | [
"D"
] | the h . c . f . of two numbers is 25 and the other two factors of their l . c . m . are 14 and 16 . the larger of the two numbers is | "solution clearly , the numbers are ( 25 x 14 ) and ( 25 x 16 ) . larger number = ( 25 x 16 ) = 400 . answer d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs 5.30",
"rs 6.44",
"rs 60.44",
"rs 16.44"
]
} | [
"B"
] | a man received a cheque . the amount in rs . has been transposed for paise and vice versa . after spending rs . 5 and 42 paise , he discovered he now had exactly 6 times the value of the correct cheque amount . what amount he should have received ? | explanation : option 4 : - on reversal will be 44 rs 16 ps , after spending 5 rs 42 ps , remaining will be around 40 rs which is not 6 times 16 rs 44 ps . option 3 : - on reversal will lead a smaller value . hence we can eliminate that as well . option 1 : - on reversal is 30 rs 5 paise , after spending 5 rs 42 ps , remaining will be 24 rs 63 paise , 24 rs 63 ps is not 6 times 5 rs 30 paise . option 2 on reversal is 44 rs 06 paise , after spending 5 rs 42 ps , remaining will be 38 rs 64 ps , which is 6 times 6 rs 44 paise . hence rs 6.44 is the answer . we need not even consider option 4 and option 3 as reversed number itself is not 6 times the original number . option 1 when reversed is odd , and when even ( 5 rs 42 ps ) is subtracted from odd , we get a odd number , and an odd number can not be 6 times another number answer : b | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"2",
"3",
"4",
"5"
]
} | [
"A"
] | the unit digit in the product ( 784 x 618 x 917 x 463 ) is | "unit digit in the given product = unit digit in ( 4 x 8 x 7 x 3 ) = 2 answer is a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"25 %",
"19.23 %",
"40 %",
"75 %"
]
} | [
"B"
] | a rectangle having length 105 cm and width 40 cm . if the length of the rectangle is increased by 20 5 percent then how much percent the breadth should be decreased so as to maintain the same area . | explanation : solution : ( 25 / ( 105 + 25 ) * 100 ) % = 19.23 % answer : b | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1040",
"1170",
"1150",
"4160"
]
} | [
"B"
] | in an office , totally there are 5200 employees and 45 % of the total employees are males . 50 % of the males in the office are at - least 50 years old . find the number of males aged below 50 years ? | "number of male employees = 5200 * 45 / 100 = 2340 required number of male employees who are less than 50 years old = 4160 * ( 100 - 50 ) % = 2340 * 50 / 100 = 1170 . answer : b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"80 min .",
"70 min .",
"84 min .",
"55 min ."
]
} | [
"C"
] | a man is walking at a speed of 10 km per hour . after every kilometre , he takes rest for 7 minutes . how much time will be take to cover a distance of 7 kilometres ? | "rest time = number of rest Γ£ β time for each rest = 6 Γ£ β 7 = 42 minutes total time to cover 7 km = ( 7 Γ’ Β β 10 Γ£ β 60 ) minutes + 42 minutes = 84 minutes answer c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"800",
"300",
"700",
"400"
]
} | [
"B"
] | if 90 % of a = 30 % of b and b = x % of a , then the value of x is ? | "0.9 a = 0.3 b so b = 3 a means 300 % of a answer : b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"4.5",
"4.2",
"4.7",
"4.8"
]
} | [
"B"
] | the average of 6 number is 3.95 . the average of two of them is 3.8 , while the average of the other two is 3.85 . what is the average of the remaining two number ? | solution : sum of the remaining two numbers = ( 3.95 Γ 6 ) - [ ( 3.8 Γ 2 ) + ( 3.85 Γ 2 ) ] = 23.70 - ( 7.6 + 7.7 ) = 23.70 - 15.3 = 8.4 . β΄ required average = 8.4 / 2 = 4.2 answer b | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 150.50",
"rs . 154.75",
"rs . 156.25",
"rs . 625"
]
} | [
"D"
] | the present worth of rs . 676 due in 2 years at 4 % per annum compound interest is | solution present worth = rs . [ 676 / ( 1 + 4 / 100 ) Β² ] = rs . ( 676 x 25 / 26 x 25 / 26 ) = rs . 625 answer d | MathQA |
{
"label": [
"A",
"B",
"D",
"E"
],
"text": [
"20",
"37",
"43",
"50"
]
} | [
"A"
] | set x consists of 5 integers and has median of 20 and a range of 20 . what is the value of the greatest possible integer that can be present in the set ? | "note that both median and range do not restrict too many numbers in the set . range is only concerned with the smallest and greatest . median only cares about the middle . quick check of each option starting from the largest : ( e ) 50 range of 20 means the smallest integer will be 30 . so 20 can not lie in between and hence can not be the median . ( d ) 43 range of 20 means the smallest integer will be 23 . so 20 can not lie in between and hence can not be the median . ( c ) 40 range of 20 means the smallest integer will be 20 . 20 can lie in between such as : 20 , 20 , 20 , 20 , 20 this is possible . hence it is the greatest such number . answer ( a )" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"18",
"750",
"24",
"120"
]
} | [
"A"
] | how many plants will be there in a circular bed whose outer edge measure 30 cms , allowing 4 cm 2 for each plant ? | "circumference of circular bed = 30 cm area of circular bed = ( 30 ) 2 β 4 Ο space for each plant = 4 cm 2 β΄ required number of plants = ( 30 ) 2 β 4 Ο Γ· 4 = 17.89 = 18 ( approx ) answer a" | MathQA |
{
"label": [
"A",
"C",
"D",
"E"
],
"text": [
"112 %",
"96 %",
"80 %",
"64 %"
]
} | [
"A"
] | mary ' s income is 60 % more than tim ' s income and tim ' s income is 30 % less than juan ' s income . what % of juan ' s income is mary ' s income . | "even i got 96 % j = 100 t = 100 * 0.7 = 70 m = 70 * 1.6 = 112 if mary ' s income is x percent of j m = j * x / 100 x = m * 100 / j = 112 * 100 / 100 = 112 ans : a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"28.5",
"27.675",
"30",
"34 %"
]
} | [
"D"
] | a shopkeeper sold an article offering a discount of 5 % and earned a profit of 27.3 % . what would have been the percentage of profit earned if no discount had been offered ? | "giving no discount to customer implies selling the product on printed price . suppose the cost price of the article is 100 . then printed price = 100 Γ£ β ( 100 + 27.3 ) / ( 100 Γ’ Λ β 5 ) = 100 Γ£ β 127.3 / 95 = 134 hence , required % profit = 134 Γ’ β¬ β 100 = 34 % answer d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"230 m",
"240 m",
"260 m",
"270 m"
]
} | [
"D"
] | a goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds . what is the length of the goods train ? | "speed = ( 72 x ( 5 / 18 ) ) m / sec = 20 m / sec . time = 26 sec . let the length of the train be x metres . then , ( ( x + 250 ) / 26 ) = 20 x + 250 = 520 x = 270 . d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"4 hrs",
"4.5 hrs",
"5.4 hrs",
"6 hrs ."
]
} | [
"A"
] | a thief runs away from a with a speed of 20 km / hr . a police from a station 60 km away started chasing him after 1 hr . with a speed of 40 km / hr . time taken by the police to catch the thief is : | explanation : solution : distance traveled by the thief in 1 hr . = 20 km . total distance of them after 1 hr = ( 60 + 20 ) km = 80 km . their relative speed = ( 40 - 20 ) = 20 km / hr . time taken to catch the thief = 80 / 20 = 4 hrs . answer : a | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"0.47",
"47",
"470",
"4700"
]
} | [
"C"
] | the value of ( 4.7 Γ 13.26 + 4.7 Γ 9.43 + 4.7 Γ 77.31 ) is : | solution given expression = 4.7 Γ ( 13.26 + 9.43 + 77.31 ) = 4.7 Γ 100 = 470 . answer c | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"2902",
"14000",
"8402",
"16800"
]
} | [
"B"
] | ( 500 + 200 ) Γ 4 Γ ( 3 + 2 ) = ? | "( 500 + 200 ) Γ 4 Γ ( 3 + 2 ) = ? or , ? = 700 Γ 4 Γ 5 = 14000 answer b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"31 kg",
"32 kg",
"33 kg",
"34 kg"
]
} | [
"C"
] | the average weight of a , b and c is 45 kg . if the average weight of a and b be 40 kg and that of b and c be 44 kg , then the weight of b is : | "explanation : let a , b , c represent their respective weights . then , we have : a + b + c = ( 45 x 3 ) = 135 β¦ . ( i ) a + b = ( 40 x 2 ) = 80 β¦ . ( ii ) b + c = ( 44 x 2 ) = 88 β¦ . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 168 β¦ . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 33 . b β s weight = 33 kg . answer : c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"16.089",
"16.35",
"16.89",
"16.944"
]
} | [
"D"
] | 48.95 - 32.006 = ? | "48.950 - 32.006 - - - - - - - - - 16.944 answer is d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"2",
"3 / 2",
"4",
"5"
]
} | [
"B"
] | the average ( arithmetic man ) of 3 integers a , b , and c is exactly half the median . if a < b < c and a = 0 , what is the value of c / b ? | the average of three integers a , b , and c is exactly twice the median - - > ( a + b + c ) / 3 = 1 b / 2 - - > since a = 0 , then ( 0 + b + c ) / 3 = 1 b / 2 - - > c = 3 b / 2 - - > c / b = 3 / 2 . answer : b . | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"76",
"1936",
"1304",
"1296"
]
} | [
"B"
] | find β ? / 11 = 4 ? | answer let β n / 11 = 4 then β n = 11 x 4 = 44 β΄ n = 44 x 44 = 1936 . correct option : b | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"2436",
"2801",
"- 2801",
"- 2071"
]
} | [
"D"
] | - 84 * 29 + 365 = ? | "= > - 84 * ( 30 - 1 ) + 365 ; = > - ( 84 * 30 ) + 84 + 365 ; = > - 2520 + 449 = - 2071 . correct option : d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"20 %",
"18 %",
"36 %",
"64 %"
]
} | [
"A"
] | if the area of a circle decreases by 36 % , then the radius of a circle decreases by | "if area of a circle decreased by x % then the radius of a circle decreases by ( 100 β 10 β 100 β x ) % = ( 100 β 10 β 100 β 36 ) % = ( 100 β 10 β 64 ) % = 100 - 80 = 20 % answer a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"20 %",
"25 %",
"18 %",
"50 %"
]
} | [
"D"
] | if the given two numbers are respectively 7 % and 14 % of a third number , then what percentage is the first of the second ? | "here , l = 7 and m = 14 therefore , first number = l / m x 100 % of second number = 7 / 14 x 100 % of second number = 50 % of second number answer : d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 170",
"rs . 160",
"rs . 1.70",
"rs . 4.25"
]
} | [
"B"
] | if 0.5 % of a = 80 paise , then the value of a is ? | "answer β΅ 0.5 / 100 of a = 80 / 100 β΄ a = rs . ( 80 / 0.5 ) = rs . 160 correct option : b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"4 km",
"6 km",
"6.8 km",
"7.2 km"
]
} | [
"B"
] | if john covers a certain distance in 1 hr . 24 min . by covering two third of the distance at 4 kmph and the rest at 5 kmph , then find the total distance | explanation : let the total distance be y km . then , ( 2 / 3 ) y / 4 + ( 1 / 3 ) y / 5 = 7 / 5 y / 6 + y / 15 = 7 / 5 7 y = 42 y = 6 km answer b | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs 14000",
"rs 25000",
"rs 16000",
"rs 17000"
]
} | [
"B"
] | a man took a loan at rate of 12 % per annum simple interest . after 3 years he had to pay 9000 interest . the principal amount borrowed by him was . | explanation : s . i . = p Γ’ Λ β r Γ’ Λ β t / 100 = > p = s . i . Γ’ Λ β 100 / r Γ’ Λ β t = > p = 9000 Γ’ Λ β 100 / 12 Γ’ Λ β 3 = rs 25000 option b | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1677",
"1683",
"2523",
"3363"
]
} | [
"B"
] | the least number which when divided by 5 , 67 and 8 leaves a remainder 3 , but when divided by 9 leaves no remainder , is : | solution l . c . m . of 5 , 6 , 7 , 8 = 840 . so , required number is of the form 840 k + 3 . least value of k for which ( 840 k + 3 ) is divisible by 9 is k = 2 . so , required number = ( 840 Γ 2 + 3 ) = 1683 . answer b | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 537600",
"rs . 180000",
"rs . 201600",
"rs . 504000"
]
} | [
"A"
] | the monthly incomes of a and b are in the ratio 5 : 2 . b ' s monthly income is 12 % more than c ' s monthly income . if c ' s monthly income is rs . 16000 , then find the annual income of a ? | b ' s monthly income = 16000 * 112 / 100 = rs . 17920 b ' s monthly income = 2 parts - - - - > rs . 17920 a ' s monthly income = 5 parts = 5 / 2 * 17920 = rs . 44800 a ' s annual income = rs . 44800 * 12 = rs . 537600 answer : a | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"161",
"154",
"216",
"158"
]
} | [
"A"
] | 1 , 13 , 35 , 67 , 109 , ____ | "1 , 13 , 35 , 67 , 109 , . . . . . 13 = 1 + 12 35 = 13 + 22 67 = 35 + 32 109 = 67 + 42 so 109 + 52 = 161 answer : a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 179.50",
"rs . 1700",
"rs . 175.50",
"rs . 180"
]
} | [
"A"
] | tea worth rs . 126 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . if the mixture is worth rs . 157 per kg , the price of the third variety per kg will be | solution since first second varieties are mixed in equal proportions , so their average price = rs . ( 126 + 135 / 2 ) = rs . 130.50 so , the mixture is formed by mixing two varieties , one at rs . 130.50 per kg and the other at say , rs . x per kg in the ratio 2 : 2 , i . e . , 1 : 1 . we have to find x . x - 157 / 22.50 = 1 = Γ’ β¬ ΒΊ x - 157 = 22.50 = Γ’ β¬ ΒΊ x = 179.50 . hence , price of the third variety = rs . 179.50 per kg . answer a | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"400",
"400",
"445",
"465"
]
} | [
"B"
] | there were 35 students in a hostel . due to the admission of 7 new students , the expenses of mess were increased by 42 per day while the average expenditure per head diminished by 1 . what was the original expenditure of the mess ? | let the original average expenditure be ` x . then , 42 ( x β 1 ) β 35 x = 42 β 7 x = 84 β x = 12 . β΄ original expenditure = ( 35 Γ 12 ) = 420 . answer b | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"2",
"4",
"6",
"8"
]
} | [
"B"
] | two concentric circles form a ring . the inner and outer circumferences of ring are ( 352 / 7 ) m and ( 518 / 7 ) m respectively . find the width of the ring . | "let the inner and outer radii be r and r meters . then 2 ( 22 / 7 ) r = ( 352 / 7 ) = r = ( ( 352 / 7 ) x ( 7 / 22 ) x ( 1 / 2 ) ) = 8 m . 2 ( 22 / 7 ) r = ( 528 / 7 ) = r = ( ( 528 / 7 ) x ( 7 / 22 ) x ( 1 / 2 ) ) = 12 m . therefore , width of the ring = ( r - r ) = ( 12 - 8 ) m = 4 m . answer is b ." | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"30",
"33.6",
"18",
"20"
]
} | [
"C"
] | find the average of all prime numbers between 12 and 24 . | "sol . there are five prime numbers between 12 and 24 . they are 13 , 17 , 19 , 23 Γ’ Λ Β΄ required average = [ 13 + 17 + 19 + 23 / 4 ] = 72 / 4 = 18 answer c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"2000",
"4000",
"5000",
"6000"
]
} | [
"D"
] | 3 partners a , b , c start a business . twice a β s capital is equal to thrice b β s capital and b β s capital is 4 times c β s capital . out of a total profit of rs . 16500 at the end of the year , b β share is : | sol . let c = x . then , b = 4 x and 2 a = 3 * 4 x = 12 x or a = 6 x . β΄ a : b : c = 6 x : 4 x : x = 6 : 4 : 1 . so , b β s capital = rs . [ 16500 * 4 / 11 ] = rs . 6000 . answer d | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"60",
"30",
"300",
"600"
]
} | [
"D"
] | mike and his friend are going on a road trip and hoping to miss traffic . if they are driving at a rate of 6 miles per minute , what is their speed in kilometers per hour ? [ 1 km = 0.6 miles ] | to calculate the equivalent of kilometres in a mile 6 miles = 6 * ( 0.6 ) ^ - 1 = 10 kilometres in 1 hour there are 60 minutes speed in kmph = 10 * 60 = 600 correct answer - d | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"62 kg",
"60 kg",
"70 kg",
"72 kg"
]
} | [
"B"
] | the average weight of 10 students decreases by 6 kg when one of them weighing 120 kg is replaced by a new student . the weight of the student is | "explanation : let the weight of student be x kg . given , difference in average weight = 6 kg = > ( 120 - x ) / 10 = 6 = > x = 60 answer : b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1 : 4",
"3 : 2",
"2 : 3",
"2 : 5"
]
} | [
"B"
] | if a and b get profits of rs . 6000 and rs . 4000 respectively at the end of year the ratio of their investments are ? | "profit = investment * time so , 6000 = i 1 * 1 = 6000 4000 = i 2 * 1 = 4000 i 1 / i 2 = 6000 / 4000 = 3 / 2 answer : b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 258",
"rs . 358",
"rs . 458",
"rs . 558"
]
} | [
"D"
] | a tank is 25 m long 12 m wide and 6 m deep . the cost of plastering its walls and bottom at 75 paise per sq m is | "explanation : area to be plastered = [ 2 ( l + b ) Γ h ] + ( l Γ b ) = [ 2 ( 25 + 12 ) Γ 6 ] + ( 25 Γ 12 ) = 744 sq m cost of plastering = 744 Γ ( 75 / 100 ) = rs . 558 answer : d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"8 kg .",
"10.8 kg .",
"7 kg .",
"18.0 kg"
]
} | [
"C"
] | if the weight of 12 meters long rod is 14 kg . what is the weight of 6 meters long rod ? | "answer β΅ weight of 12 m long rod = 14 kg β΄ weight of 1 m long rod = 14 / 12 kg β΄ weight of 6 m long rod = 14 x 6 / 12 = 7 kg option : c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"32.5 %",
"40 %",
"60 %",
"65 %"
]
} | [
"C"
] | solution a is made up of alcohol and water mixed in the ratio of 21 : 4 by volume ; solution b is made up of alcohol and water mixed in the ratio of 2 : 3 by volume . if solution a and solution b are mixed in the ratio of 5 : 6 by volume , what percent of the resultant mixture is alcohol ? | let mixture after mixing a and b is 110 ml ( number assumed for calculation because of 5 : 6 ) now solution a is 50 ml and solu b is 60 ml further in a 100 ml a contains 84 ml alch so 50 ml contain 42 ml in mix b 100 ml solution contain 40 ml alc , 60 ml of b , it will be 24 ml alcohol . so 42 + 24 = 66 in 110 ml solution which is 60 % answer : c | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"32256",
"24000",
"24936",
"25600"
]
} | [
"D"
] | 90 % of the population of a village is 23040 . the total population of the village is ? | "answer β΅ 90 % of p = 23040 β΄ p = ( 23040 x 100 ) / 90 = 25600 correct option : d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"40.2",
"40.4",
"40.6",
"40.8"
]
} | [
"B"
] | the average of 10 numbers is 40.2 . later it is found that two numbers have been wrongly copied . the first is 16 greater than the actual number and the second number added is 13 instead of 31 . find the correct average . | "sum of 10 numbers = 402 corrected sum of 10 numbers = 402 β 13 + 31 β 16 = 404 hence , new average = 404 β 10 = 40.4 answer b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"25.5",
"16.7",
"25",
". 25"
]
} | [
"B"
] | 1 / 0.06 is equal to | "explanation : 1 / 0.06 = ( 1 * 100 ) / 6 = 100 / 6 = 16.7 option b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"2.6 kg",
"4 kg",
"3.4 kg",
"1.8 kg"
]
} | [
"A"
] | how many kg of sugar must be added to 30 kg of 2 % solution of sugar and water to increase it to a 10 % solution ? | explanation : solution : amount of sugar in 30 kg solution = ( 2 / 100 * 30 ) kg = 0.6 kg . let x kg of sugar be added . then , ( 0.6 + x ) / ( 30 + x ) = 10 / 100 60 + 100 x = 300 + 10 x x = 240 / 90 = 8 / 3 = 2.6 answer : a | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"4500",
"7500",
"5000",
"7200"
]
} | [
"D"
] | the difference between compound interest and simple interest on a certain amount of money at 5 % per annum for 2 years is 18 . find the sum : | "sol . ( d ) let the sum be 100 . therefore , si = 100 Γ 5 Γ 2100 = 10100 Γ 5 Γ 2100 = 10 and ci = 100 ( 1 + 5100 ) 2 β 100100 ( 1 + 5100 ) 2 β 100 β΄ = 100 Γ 21 Γ 2120 Γ 20 β 100 = 414 = 100 Γ 21 Γ 2120 Γ 20 β 100 = 414 difference of ci and si = 41 β 4 - 10 = 1 β 4 if the difference is 1 β 4 , the sum = 100 = > if the difference is 18 , the sum = 400 Γ 18 = 7200 answer d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"220 km",
"120 km",
"100 km",
"140 km"
]
} | [
"A"
] | a bus covered a distance of 250 km , partly at an average speed of 40 kmph and partly at 60 kmph . if the total time taken is 6 hours , then the distance covered at 40 kmph is | "let the partial distance covered at 40 kmph be x let the another partial distance covered at 60 kmph be ( 250 - x ) thus , x / 40 - ( 250 - x ) / 60 = 6 or , x / 40 + ( 250 - x ) / 60 = 6 or , ( 3 x + 500 - 2 x ) / / 120 = 6 or 500 + x = 720 x = 220 answer : a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"45 kmph",
"25 kmph",
"30 kmph",
"50 kmph"
]
} | [
"D"
] | a train 125 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is ? | "explanation : speed of the train relative to man = ( 125 / 10 ) m / sec = ( 25 / 2 ) m / sec . [ ( 25 / 2 ) x ( 18 / 5 ) ] km / hr = 45 km / hr . let the speed of the train be ' s ' km / hr . then , relative speed = ( s - 5 ) km / hr . s - 5 = 45 = > s = 50 km / hr . answer is d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"600",
"700",
"800",
"960"
]
} | [
"D"
] | if 4 ( p ' s capital ) = 6 ( q ' s capital ) = 10 ( r ' s capital ) , then out of the total profit of rs 4960 , r will receive | "explanation : let p ' s capital = p , q ' s capital = q and r ' s capital = r then 4 p = 6 q = 10 r = > 2 p = 3 q = 5 r = > q = 2 p / 3 r = 2 p / 5 p : q : r = p : 2 p / 3 : 2 p / 5 = 15 : 10 : 6 r ' s share = 4960 * ( 6 / 31 ) = 160 * 6 = 960 . answer : option d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"70 kg",
"72 kg",
"75 kg",
"80 kg"
]
} | [
"C"
] | the average weight of 3 packets a , b and c is 84 kg . another packet d added into the group and the average now becomes 80 kg . if another packet e , whose weight is 3 kg more than that of d , replaces a then the average weight of b , c , d and e becomes 79 kg . the weight of a is : | explanation : a + b + c = ( 84 x 3 ) = 252 kg , a + b + c + d = ( 80 x 4 ) = 320 kg . d = ( 320 - 252 ) = 68 , e = ( 68 + 3 ) = 7 l . b + c + d + e = ( 79 x 4 ) = 316 . ( a + b + c + d ) - ( b + c + d + e ) = ( 320 - 316 ) kg = 4 kg . a - e = 4 = a = ( 4 + e ) = 75 kg answer : c | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"12.75",
"85",
"204",
"250"
]
} | [
"B"
] | the difference between a number and its two - fifth is 510 . what is 10 % of that number ? | "explanation : let the number be x . then , x - 2 / 5 x = 510 x = ( 510 * 5 ) / 3 = 850 10 % of 850 = 85 . answer is b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"80 kmph",
"60 kmph",
"86 kmph",
"90 kmph"
]
} | [
"C"
] | a train travels 240 km in 3 hours and 450 km in 5 hours . find the average speed of train . | "as we know that speed = distance / time for average speed = total distance / total time taken thus , total distance = 240 + 450 = 690 km thus , total speed = 8 hrs or , average speed = 690 / 8 or , 86 kmph . answer : c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"18 %",
"21 %",
"20 %",
"26.1 %"
]
} | [
"D"
] | mahesh marks an article 15 % above the cost price of rs . 540 . what must be his discount percentage if he sells it at rs . 459 ? | "cp = rs . 540 , mp = 540 + 15 % of 540 = rs . 621 sp = rs . 459 , discount = 621 - 459 = 162 discount % = 162 / 621 * 100 = 26.1 % answer : d" | MathQA |
{
"label": [
"B",
"C",
"D",
"E"
],
"text": [
"256",
"48",
"525",
"425"
]
} | [
"C"
] | he number of times a bucket of capacity 4 liters to be used to fill up a tank is less than number of ties another bucket of capacity 3 liters used for the same purpose by 4 . what is the capacity of the tank ? | 4 x = 3 ( x + 4 ) , where x may be number of times 4 l bucket is used . 4 x = 3 ( x + 4 ) - - > 1 . x = 12 , substitute x to lhs or rhs of 1 , which gets you the capacity , and it is 48 . answer : c | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"18",
"750",
"24",
"19"
]
} | [
"C"
] | how many plants will be there in a circular bed whose outer edge measure 35 cms , allowing 4 cm 2 for each plant ? | "circumference of circular bed = 35 cm area of circular bed = ( 35 ) 2 Γ’ Β β 4 Γ― β¬ space for each plant = 4 cm 2 Γ’ Λ Β΄ required number of plants = ( 35 ) 2 Γ’ Β β 4 Γ― β¬ Γ£ Β· 4 = 24.36 = 24 ( approx ) answer c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"3.84",
"1.75",
"3.28",
"2.72"
]
} | [
"C"
] | the weights of one liter vegetable ghee packet of two brands β a β and β b β are 900 gm and 700 gm respectively . if they are mixed in the ratio of 3 : 2 by volumes to form a mixture of 4 liters , what is the weight ( in kg ) of the mixture ? | "here ' s how i did it . my notes from reading the problem were : 1 l a = 900 gm 1 l b = 700 gm we are mixing five parts ( 3 parts a plus 2 parts b , 5 parts total ) to get 4 l , so 5 x = 4 - - - > x = 4 / 5 . each part is 4 / 5 of a liter . so if we have 3 parts a , we have 900 * 3 * ( 4 / 5 ) = 2160 if we have 2 parts b , we have 700 * 2 * ( 4 / 5 ) = 1120 2160 + 1120 = 3280 solving for units gives us 3.28 so the answer is c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"13",
"15",
"19",
"24"
]
} | [
"C"
] | the product of two numbers is 266 and their difference is 5 . what is the bigger number ? | "explanation : let the two numbers be a and b , here a > b ab = 266 b = 266 / a - - - - - - - - - - - - - - - - - ( i ) given , a β b = 5 - - - - - - - - - - - ( ii ) substitute from ( i ) in ( ii ) , we get a β 266 / a = 5 a 2 β 5 a + 266 = 0 ( a β 19 ) ( a β 14 ) = 0 therefore , a = 19 or a = 14 hence , bigger number = a = 19 answer : c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"75200",
"79970",
"75460",
"24580"
]
} | [
"B"
] | the difference between the place values of 8 and 3 in the number 587435 is | sol . = ( place value of 8 ) β ( place value of 3 ) = ( 80000 - 30 ) = 79970 answer b | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"25",
"50",
"90",
"140"
]
} | [
"C"
] | if the average ( arithmetic mean ) of a and b is 35 and the average of b and c is 80 , what is the value of c β a ? | "- ( a + b = 70 ) b + c = 160 c - a = 90 c . 90" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 7000",
"rs . 8000",
"rs . 8600",
"rs . 9000"
]
} | [
"C"
] | the salary of a , b , c , d , e is rs . 8000 , rs . 5000 , rs . 14000 , rs . 7000 , rs . 9000 per month respectively , then the average salary of a , b , c , d , and e per month is | answer average salary = 8000 + 5000 + 14000 + 7000 + 9000 / 5 = rs . 8600 correct option : c | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"3",
"- 3",
"1 / 3",
"- 1 / 3"
]
} | [
"B"
] | the value of log 5 ( 1 / 125 ) is : | "log 5 ( 1 / 125 ) = log 5 ( 1 / 5 ) ^ 3 = 3 log 5 ( 1 / 5 ) = 3 ( log 5 1 - log 5 5 ) = 3 ( 0 - 1 ) = - 3 answer : b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"37800",
"37600",
"37200",
"37500"
]
} | [
"A"
] | find the l . c . m . of 72 , 108 and 2100 . | 72 = 2 ^ 3 x 3 ^ 2 , 108 = 3 ^ 3 x 2 ^ 2 , 2100 = 2 ^ 2 x 5 ^ 2 x 3 x 7 . l . c . m . = 2 ^ 3 x 3 ^ 3 x 5 ^ 2 x 7 = 37800 . answer is a . | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"18 kmph",
"22 kmph",
"16 kmph",
"20 kmph"
]
} | [
"B"
] | in a stream running at 3 kmph , a motor boat goes 10 km upstream and back again to the starting point in 57 minutes . find the speed of motor boat in still water ? | "explanation : let the speed of motor boat instill water be x kmph then , speed in downstream = ( x + 3 ) km and . speed in upstream = ( x - 3 ) kmph time taken to row 10 km & back = ( 10 / x + 3,10 / x - 3 ) 10 / x + 3 + 10 / x - 3 = 57 / 60 11 x 2 - 240 x - 44 = 0 ( x - 22 ) ( 11 x + 2 ) = 0 x = 22 or x = - 2 / 11 then x = 22 kmph answer : option b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"40",
"44",
"48",
"22"
]
} | [
"D"
] | in a can , there is a mixture of milk and water in the ratio 4 : 5 . if it is filled with an additional 4 litres of milk the can would be full and ratio of milk and water would become 6 : 5 . find the capacity of the can ? | "let the capacity of the can be t litres . quantity of milk in the mixture before adding milk = 4 / 9 ( t - 4 ) after adding milk , quantity of milk in the mixture = 6 / 11 t . 6 t / 11 - 4 = 4 / 9 ( t - 4 ) 10 t = 396 - 176 = > t = 22 . answer : d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1240",
"1120",
"1190",
"1634"
]
} | [
"D"
] | the banker ' s gain on a sum due 6 years hence at 12 % per annum is rs . 684 . what is the banker ' s discount ? | "explanation : td = ( bg Γ 100 ) / tr = ( 684 Γ 100 ) / ( 6 Γ 12 ) = rs . 950 bg = bd β td = > 684 = bd - 950 = > bd = 684 + 950 = 1634 answer : option d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 4000",
"rs . 4500",
"rs . 4300",
"rs . 4200"
]
} | [
"D"
] | two mixers and one t . v . cost rs . 7000 , while two t . v . s and a mixer cost rs , 9800 . the value of one t . v . is : | explanation : let c . p . of a mixer be rs . x and that of a t . v . be rs . y . then , 2 x + y = 7000 and 2 y + x = 9800 . multiplying 2 nd equatien by 2 and subtracting first from it , we get 3 y = 19600 - 7000 = 12600 or y = 4200 c . p . of a t . v . = rs . 4200 answer : d | MathQA |
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