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": [
"4.37 %",
"5 %",
"6 %",
"8.75 %"
]
} | [
"C"
] | the population of a town increased from 1 , 75,000 to 2 , 80,000 in a decade . the average percent increase of population per year is | "solution increase in 10 years = ( 280000 - 175000 ) = 105000 . increase % = ( 105000 / 175000 ã — 100 ) % = 60 % . required average = ( 60 / 10 ) % = 6 % . answer c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"200 %",
"210 %",
"300 %",
"310 %"
]
} | [
"C"
] | if the radius of a circle is diminished by 10 % , then the area is diminished by : | "explanation : let the original radius be r cm . new radius = 2 r area = π r 2 new area = π 2 r 2 = 4 π r 2 increase in area = ( 4 π r 2 − π r 2 ) = 3 π r 2 increase percent = 3 π r 2 / π r 2 ∗ 100 = 300 % option c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"loss of rs . 200",
"loss of rs . 100",
"profit of rs . 100",
"profit of rs . 200"
]
} | [
"D"
] | ravi purchased a refrigerator and a mobile phone for rs . 15000 and rs . 8000 respectively . he sold the refrigerator at a loss of 4 percent and the mobile phone at a profit of 10 percent . overall he make a . | "let the sp of the refrigerator and the mobile phone be rs . r and rs . m respectively . r = 15000 ( 1 - 4 / 100 ) = 15000 - 600 m = 8000 ( 1 + 10 / 100 ) = 8000 + 800 total sp - total cp = r + m - ( 15000 + 8000 ) = - 600 + 800 = rs . 200 as this is positive , an overall profit of rs . 200 was made . answer : d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"2.29",
"2.75",
"4.25",
"4.5"
]
} | [
"C"
] | ( 17 ) 3.75 x ( 17 ) ? = 178 | "solution let ( 17 ) 3.75 * ( 17 ) x = 178 . then , ( 17 ) 3.5 + x = ( 17 ) 8 . ∴ 3.75 + x = 8 ⇔ x = ( 8 - 3.75 ) ⇔ x = 4.25 answer c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"107",
"147",
"10",
"296"
]
} | [
"B"
] | 3 / 8 of 168 * 15 / 5 + x = 549 / 9 + 275 | "explanation : let 3 / 8 of 168 * 15 / 5 + x = 549 / 9 + 275 then , 63 * 15 / 5 + x = 61 + 275 63 * 3 + x = 336 189 + x = 336 x = 147 answer b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"62 kg",
"60 kg",
"70 kg",
"72 kg"
]
} | [
"A"
] | the average weight of 6 students decreases by 3 kg when one of them weighing 80 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 = 3 kg = > ( 80 - x ) / 6 = 3 = > x = 62 answer : a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"227",
"83",
"23",
"827"
]
} | [
"B"
] | find the lcm of 23 , 46,827 | explanation : whenever we have to solve this sort of question , remember the formula . lcm = \ \ begin { aligned } \ \ frac { hcf of denominators } { lcm of numerators } \ \ end { aligned } so answers will be option 2 , please also give attention to the difference in formula of hcf and lcm answer : option b | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"3220",
"4830",
"5120",
"6420"
]
} | [
"C"
] | a metallic sheet is of rectangular shape with dimensions 48 m x 36 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 8 m , the volume of the box ( in m 3 ) is | "solution clearly , l = ( 48 - 16 ) m = 32 m ‹ = › b = ( 36 - 16 ) m = 20 m , ‹ = › h = 8 m . . volume of the box = ( 32 x 20 x 8 ) m 3 = 5120 m 3 . answer c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 45,000",
"rs . 50,000",
"rs . 60,000",
"rs . 15,000"
]
} | [
"D"
] | x and y invested in a business . they earned some profit which they divided in the ratio of 2 : 6 . if x invested rs . 5,000 . the amount invested by y is | solution suppose y invested rs . y then , 5000 / y = 2 / 6 â € ¹ = â € º y = ( 5000 ã — 6 / 2 ) . â € ¹ = â € º y = 15000 . answer d | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"50 %",
"85 %",
"25 %",
"75 %"
]
} | [
"A"
] | the ratio 25 : 50 expressed as percent equals to | "explanation : actually it means 25 is what percent of 50 , which can be calculated as , ( 25 / 50 ) * 100 = 25 * 2 = 50 answer : option a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1628.4",
"1534",
"1492",
"240"
]
} | [
"D"
] | 10 people went to a hotel for combine dinner party 5 of them spent rs . 20 each on their dinner and rest spent 4 more than the average expenditure of all the 10 . what was the total money spent by them . | "solution : let average expenditure of 10 people be x . then , 10 x = 20 * 5 + 5 * ( x + 4 ) ; or , 10 x = 20 * 5 + 5 x + 20 ; or , x = 24 ; so , total money spent = 24 * 10 = rs . 240 . answer : option d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"11 kmph",
"12 kmph",
"14 kmph",
"17 kmph"
]
} | [
"C"
] | a man ' s speed with the current is 20 kmph and speed of the current is 3 kmph . the man ' s speed against the current will be | "explanation : if you solved this question yourself , then trust me you have a all very clear with the basics of this chapter . if not then lets solve this together . speed with current is 20 , speed of the man + it is speed of the current speed in still water = 20 - 3 = 17 now speed against the current will be speed o... | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"4 mph",
"2.5 mph",
"3 mph",
"2 mph"
]
} | [
"D"
] | a boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream . if the speed of the boat in still water is 10 mph , the speed of the stream is : | explanation : speed of the boat in still water = 10 mph let speed of the stream be x mph then , speed downstream = ( 10 + x ) mph speed upstream = ( 10 - x ) mph time taken to travel 36 miles upstream - time taken to travel 36 miles downstream = 90 / 60 hours = > 36 / ( 10 − x ) − 36 / ( 10 + x ) = 3 / 2 = > 12 / ( 10 ... | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"23345",
"26695",
"24495",
"25575"
]
} | [
"C"
] | simplify : 99 ^ 48 / 49 * 245 . | "given expression = ( 100 - 1 / 49 ) * 245 = ( 4899 / 49 ) * 245 = 4899 * 5 = 24495 . answer is c ." | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
". 4",
". 04",
". 05",
"0.04"
]
} | [
"B"
] | what decimal fraction is 40 ml of a litre ? | "answer required fraction = 40 / 1000 = 4 / 100 = . 04 correct option : b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"4500",
"4600",
"4680",
"4710"
]
} | [
"A"
] | a company produces on an average 4000 items per month for the first 3 months . how many items it must produce on an average per month over the next 9 months , to average of 4375 items per month over the whole ? | sol . required average = ( 4375 x 12 ) - ( 4000 x 3 ) / 9 ⇔ 52500 - 12000 / 9 ⇔ 40500 / 9 = 4500 . answer a | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"168 °",
"228 °",
"144 °",
"224 °"
]
} | [
"C"
] | the ratio of the adjacent angles of a parallelogram is 5 : 10 . also , the ratio of the angles of quadrilateral is 5 : 6 : 7 : 12 . what is the sum of the smaller angle of the parallelogram and the second largest angle of the quadrilateral ? | "the measures of the adjacent angles of a parallelogram add up to be 180 ° given so , 5 x + 10 x = 180 ° or , 15 x = 180 ° or , x = 12 ° hence the angles of the parallelogram are 60 ° and 120 ° further it is given we know sum of all the four angles of a quadrilateral is 360 ° so , 5 y + 6 y + 7 y + 12 y = 360 ° or , 5 ... | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"9 %",
"9.27 %",
"27 %",
"12.48 %"
]
} | [
"D"
] | the population of a city increases by 5 % per year but due to migration it decrease by 1 % per years . what will be the percentage increase in population in 3 years ? | "actual increase in population = 4 % let , earlier population = 100 then the population after 3 years = 100 ( 1 + 4 / 100 ) ^ 3 = 112.4864 ∴ required percentage = 12.48 % answer : d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs 10000",
"rs 15000",
"rs 16000",
"rs 17000"
]
} | [
"A"
] | a man took a loan at rate of 12 % per annum simple interest . after 3 years he had to pay 3600 interest . the principal amount borrowed by him was . | "explanation : s . i . = p â ˆ — r â ˆ — t / 100 = > p = s . i . â ˆ — 100 / r â ˆ — t = > p = 3600 â ˆ — 100 / 12 â ˆ — 3 = rs 10000 option a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 3240",
"rs . 2520",
"rs . 2880",
"rs . 3360"
]
} | [
"C"
] | a , b and c started a business with a total investment of rs . 72000 . a invests rs . 6000 more than b and b invests rs . 3000 less than c . if the total profit at the end of a year is rs . 8640 , find c ' s share . | "explanation : let c ' s investment = rs . x b ' s investment = rs . ( x - 3000 ) a ' s investment = rs . ( x - 3000 + 6000 ) = rs . ( x + 3000 ) now , ( a + b + c ) ' s investment = rs . 72000 = > x + ( x - 3000 ) + ( x + 3000 ) = 72000 = > 3 x = 72000 = > x = 24000 hence , a ' s investment = rs . 27000 b ' s investme... | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1",
"3",
"5",
"6"
]
} | [
"A"
] | if a is a positive integer , and if the units digit of a ^ 2 is 9 and the units digit of ( a + 1 ) ^ 2 is 4 , what is the units z digit of ( a + 2 ) ^ 2 ? | "i also got a . by punching in numers : z . . . 7 ^ 2 = . . . 9 . . . 8 ^ 2 = . . . 4 . . . 9 ^ 2 = . . . 1 . a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1040",
"2080",
"3120",
"4160"
]
} | [
"C"
] | in an office , totally there are 6400 employees and 65 % of the total employees are males . 25 % 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 = 6400 * 65 / 100 = 4160 required number of male employees who are less than 50 years old = 4160 * ( 100 - 25 ) % = 4160 * 75 / 100 = 3120 . answer : c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"129166",
"121696",
"126196",
"121966"
]
} | [
"D"
] | find the value of ( 75983 * 75983 - 45983 * 45983 / 30000 ) | "given expression = ( 75983 ) 2 - ( 45983 ) 2 / ( 75983 - 45983 ) = ( a - b ) 2 / ( a - b ) = ( a + b ) ( a - b ) / ( a - b ) = ( a + b ) = 75983 + 45983 = 121966 answer is d ." | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 1050",
"rs . 1400",
"rs . 3150",
"rs . 4200"
]
} | [
"C"
] | the cost of painting the 4 walls of a room is rs . 350 . the cost of painting a room 3 times in length , breadth and height will be : | explanation : area of 4 walls of the room = [ 2 ( l + b ) × h ] m 2 area of 4 walls of new room = [ 2 ( 3 l + 3 b ) × 3 h ] m 2 = 9 [ 2 ( l + b ) × h ] m 2 cost of painting the 4 walls of new room = rs . ( 9 × 350 ) = rs . 3150 correct option : c | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"5",
"4",
"1",
"0"
]
} | [
"A"
] | a certain number when divided by 899 leaves the remainder 63 . find the remainder when the same number is divided by 29 . | "sol . ( a ) number = 899 q + 63 , where q is quotient = 31 × 29 q + ( 58 + 5 ) = 29 [ 31 q + 2 ] + 5 ∴ remainder = 5 answer a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"250 kg",
"275 kg",
"300 kg",
"266.66 kg"
]
} | [
"D"
] | an ore contains 25 % of an alloy that has 90 % iron . other than this , in the remaining 75 % of the ore , there is no iron . how many kilograms of the ore are needed to obtain 60 kg of pure iron ? | solution : let there is 100 kg of ore . 25 % ore contains 90 % off iron that means 25 kg contains ; 25 * 90 / 100 = 22.5 kg iron . 22.5 kg iron contains 100 kg of ore . then , 1 kg of iron contains = 25 / 100 kg ore ; hence , 60 kg iron contains = 100 * 60 / 22.5 = 266.66 kg ore . answer : option d | MathQA |
{
"label": [
"A",
"B",
"D",
"E"
],
"text": [
"32",
"37",
"20",
"50"
]
} | [
"D"
] | set x consists of 10 integers and has median of 10 and a range of 10 . 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 an... | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"34",
"92",
"68",
"88"
]
} | [
"B"
] | a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 720 sq . feet , how many feet of fencing will be required ? | "explanation we have : l = 20 ft and lb = 720 sq . ft . so , b = 36 ft . length of fencing = ( l + 2 b ) = ( 20 + 72 ) ft = 92 ft . answer b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"0.045374",
"4.5388",
"453.88",
"473.88"
]
} | [
"A"
] | [ ( 3.241 x 14 ) / 100 ] = ? | "answer multiplying 3.241 x 14 = 4.5374 now divide 4.5374 by 100 so , 4.5374 ÷ 100 = 0.045374 ∴ shift the decimal two places to the left as 100 correct option : a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"36",
"45",
"123",
"63"
]
} | [
"A"
] | 365 : 90 : : 623 : ? | "365 - - - 3 * 6 * 5 . . . . 90 623 - - - 6 * 2 * 3 . . . . 36 answer a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"− 220",
"− 100",
"100",
"− 80"
]
} | [
"D"
] | if the average ( arithmetic mean ) of a and b is 110 , and the average of b and c is 150 , what is the value of a − c ? | "question : a - c = ? ( a + b ) / 2 = 110 = = = > a + b = 220 ( b + c ) / 2 = 150 = = = > b + c = 300 ( a + b ) - ( b + c ) = 220 - 300 = = = > a + b - b - c = - 80 = = = > a - c = - 80 answer : d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1200",
"120",
"360",
"168"
]
} | [
"D"
] | average age of students of an adult school is 46 years . 120 new students whose average age is 32 years joined the school . as a result the average age is decreased by 4 years . find the number of students of the school after joining of the new students . | "explanation : let the original no . of students be x . according to situation , 46 x + 120 * 32 = ( x + 120 ) 36 ⇒ x = 48 so , required no . of students after joining the new students = x + 120 = 168 . answer : d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"600",
"680",
"582",
"560"
]
} | [
"C"
] | if the product of two numbers is 51216 and their h . c . f . is 33 , find their l . c . m . | "explanation : hcf * lcm = 51216 , because we know product of two numbers = product of hcf and lcm lcm = 51216 / 88 = 582 option c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"35.22",
"36.12",
"36.22",
"36.42"
]
} | [
"D"
] | the mean of 50 observations was 36 . it was found later that an observation 44 was wrongly taken as 23 . the corrected new mean is | "solution correct sum = ( 36 x 50 + 44 - 23 ) = 1821 . â ˆ ´ correct mean = 1821 / 50 = 36.42 . answer d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 8000",
"rs . 8400",
"rs . 7500",
"rs . 7800"
]
} | [
"A"
] | what sum of money put at c . i amounts in 2 years to rs . 8820 and in 3 years to rs . 9261 ? | "explanation : 8820 - - - - 441 100 - - - - ? = > 5 % x * 105 / 100 * 105 / 100 = 8820 x * 1.1025 = 8820 x = 8820 / 1.1025 = > 8000 answer is a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"2 √ 2', '",
"2 √ 5', '",
"5', '",
"7', '"
]
} | [
"D"
] | twenty eight meters of wire is available to fence off a flower bed in the form of a circular sector . what must the radius of the circle in meters be , if we wish to have a flower bed with the greatest possible surface area ? | area of sector , a = x / 360 * pi * r ^ 2 circumference of the sector = 28 = > x / 360 * 2 * pi * r + 2 r = 28 = > 2 a / r + 2 r = 28 = > a = r 14 - r ^ 2 = r 14 - r ^ 2 we will now max using derivations max value of a will found at a = 0 i . e 14 - 2 r = 0 r = 7 d | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"15",
"18",
"20",
"22"
]
} | [
"B"
] | find the average of all the numbers between 6 and 30 which are divisible by 4 . | "sol . average = ( 8 + 12 + 16 + 20 + 24 + 28 / 6 ) = 108 / 6 = 18 answer b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"80",
"100",
"75",
"90"
]
} | [
"B"
] | if 60 % of 3 / 5 of a number is 36 , then the number is ? | "let the number be x . then 60 % of 3 / 5 of x = 36 60 / 100 * 3 / 5 * x = 36 x = ( 36 * 25 / 9 ) = 100 required number = 100 . correct option : b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"2 : 3",
"3 : 2",
"4 : 5",
"5 : 3"
]
} | [
"B"
] | a and b together have $ 1210 . if of a ' s amount is equal to of b ' s amount , what is the ratio between a and b ? | "( 4 / 15 ) a = ( 2 / 5 ) b a = ( ( 2 / 15 ) * ( 15 / 4 ) ) b a = ( 3 / 2 ) b a / b = 3 / 2 a : b = 3 : 2 option b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 80",
"rs . 85",
"rs . 88",
"rs . 100"
]
} | [
"C"
] | a trader sells 45 meters of cloth for rs . 4500 at the profit of rs . 12 per metre of cloth . what is the cost price of one metre of cloth ? | sp of 1 m of cloth = 4500 / 45 = rs . 100 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 100 - rs . 12 = rs . 88 . answer : c | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
". 5",
". 05",
". 05",
"0.05"
]
} | [
"B"
] | what decimal fraction is 50 ml of a litre ? | "answer required fraction = 50 / 1000 = 5 / 100 = . 05 correct option : b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"8.5 km / hr",
"9 km / hr",
"10 km / hr",
"12.5 km / hr"
]
} | [
"C"
] | a man ' s speed with the current is 15 km / hr and the speed of the current is 2.5 km / hr . the man ' s speed against the current is | sol . man ' s rate in still in water = ( 15 - 2.5 ) km / hr = 12.5 km / hr . man ' s rate against the current = ( 12.5 - 2.5 ) km / hr = 10 km / hr . answer c | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1",
"3",
"7",
"9"
]
} | [
"D"
] | ab + cd = jjj , where ab and cd are two - digit numbers and jjj is a 3 digit number ; a , b , c , and d are distinct positive integers . in the addition problem above , what is the value of c ? | ab and cd are two digit integers , their sum can give us only one three digit integer of a kind of jjj it ' s 111 . so , a = 1 . 1 b + cd = 111 now , c can not be less than 9 , because no to digit integer with first digit 1 ( mean that it ' s < 20 ) can be added to two digit integer less than 90 to have the sum 111 ( i... | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"140",
"121",
"110",
"160"
]
} | [
"D"
] | 8 friends went to a hotel and decided to pay the bill amount equally . but 7 of them could pay rs . 80 each as a result 8 th has to pay rs . 70 extra than his share . find the amount paid by him . | "explanation : average amount paid by 7 persons = rs . 80 increase in average due to rs . 70 paid extra by the 8 th men = rs . 70 / 7 = rs . 10 therefore , average expenditure of 8 friends = rs . 80 + rs . 10 = rs . 90 therefore , amount paid by the 11 th men = rs . 90 + rs . 70 = rs . 160 correct option : d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"20 %",
"25 %",
"33.33 %",
"18 %"
]
} | [
"A"
] | a milk man has 15 liters of milk . if he mixes 5 liters of water , which is freely available , in 20 liters of pure milk . if the cost of pure milk is rs . 18 per liter , then the profit of the milkman , when he sells all the mixture at cost price is : | "explanation : when the water is freely available and all the water is sold at the price of the milk , then the water gives the profit on the cost of 20 liters of milk . therefore , profit percentage = 20 % . answer : a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1 : 3",
"2 : 3",
"3 : 5",
"4 : 5"
]
} | [
"C"
] | find the ratio in which rice at rs . 10.0 a kg be mixed with rice at rs . 5.70 a kg to produce a mixture worth rs . 6.30 a kg ? | "solution required ratio = 60 : 100 = 3 : 5 answer c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"2 : 3",
"4 : 3",
"6 : 7",
"7 : 2"
]
} | [
"D"
] | 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 4 hours and 49 hours respectively . the ratio of their speeds is : | "let us name the trains as a and b . then , ( a ' s speed ) : ( b ' s speed ) = â ˆ š b : â ˆ š a = â ˆ š 49 : â ˆ š 4 = 7 : 2 . answer d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"412",
"502",
"512",
"522"
]
} | [
"C"
] | find 62976 ÷ ? = 123 | "answer let 62976 / n = 123 then n = 62976 / 123 = 512 . option : c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 360",
"rs . 120",
"rs . 240",
"rs . 300"
]
} | [
"B"
] | x alone can do a piece of work in 15 days and y alone can do it in 10 days . x and y undertook to do it for rs . 720 . with the help of z they finished it in 5 days . how much is paid to z ? | solution : in one day x can finish 1 / 15 th of the work . in one day y can finish 1 / 10 th of the work . let us say that in one day z can finish 1 / zth of the work . when all the three work together in one day they can finish 1 / 15 + 1 / 10 + 1 / z = 1 / 5 th of the work . therefore , 1 / z = 1 / 30 . ratio of thei... | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"3.64",
"1.75",
"3.52",
"2.72"
]
} | [
"A"
] | the weights of one liter vegetable ghee packet of two brands ‘ a ’ and ‘ b ’ are 950 gm and 850 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 = 950 gm 1 l b = 850 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 950 * 3 * ( 4 / 5 ) = 2280 if we have 2 part... | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"148",
"152",
"156",
"145"
]
} | [
"D"
] | the ratio of ducks and frogs in a pond is 37 : 39 respectively . the average number of ducks and frogs in the pond is 142 . what is the number of frogs in the pond ? | "solution : ratio of ducks and frogs in pond , = 37 : 39 . average of ducks and frogs in pond , = 142 . so , total number of ducks and frogs in the pond , = 2 * 142 = 284 . therefore , number of frogs , = ( 284 * 39 ) / 76 = 145 . answer : option d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"4",
"4 √ 2",
"8",
"6"
]
} | [
"D"
] | triangle xyz is an isosceles right triangle . if side xy is longer than side yz , and the area of the triangle is 9 , what is the measure of side xy ? | "ans d . . 6 . . xy being larger means it is the hyp . . area = ( 1 / 2 ) * ( yz ) ^ 2 = 9 or yz = 3 * \ sqrt { 2 } . . therefore hyp = xy = 6" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"328",
"348",
"358",
"362"
]
} | [
"C"
] | after distributing the sweets equally among 25 children , 8 sweets remain . had the number of children been 28 , 22 sweets would have been left after equal distribution . what was the total number of sweets ? | explanation : let the total number of sweets be ( 25 x + 8 ) . then , ( 25 x + 8 ) - 22 is divisible by 28 ( 25 x - 14 ) is divisible by 28 28 x - ( 3 x + 14 ) is divisible by 28 ( 3 x + 14 ) is divisible by 28 x = 14 . therefore total number of sweets = ( 25 x 14 + 8 ) = 358 . answer : c | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"45 ( 4 / 11 ) %",
"60 %",
"45 ( 5 / 11 ) %",
"44 ( 5 / 11 ) %"
]
} | [
"B"
] | a batsman scored 150 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 = 150 total runs scored from boundaries and sixes = 3 x 4 + 8 x 6 = 60 total runs scored by running between the wickets = 150 - 60 = 90 required % = ( 90 / 150 ) × 100 = 60 % answer : option b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"44 %",
"69 %",
"144 %",
"40 %"
]
} | [
"B"
] | if the radius of a circle is increased by 30 % then the area is increased by : | "initially a = pi * r 2 now r 2 = 130 / 100 r then area = pi * ( 130 r / 100 ) 2 area = 169 r / 100 that is area increases from 100 to 169 = increase in area = 69 % answer : b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"15 m', '",
"22.5 m', '",
"25 m', '",
"30 m', '"
]
} | [
"D"
] | the length of a rectangle hall is 5 m more than its breadth . the area of the hall is 750 m 2 . the length of the hall is : | solution let breadth = x metres . then , length = ( x + 5 ) metres . then x ( x + 5 ) = 750 ⇔ x 2 + 5 x − 750 = 0 ⇔ ( x + 30 ) ( x + 25 ) = 0 ⇔ x = 25 . ∴ length = ( x + 5 ) = 30 m . answer d | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"114",
"120",
"134",
"144"
]
} | [
"D"
] | p , q , r enter into a partnership & their share are in the ratio 1 / 2 : 1 / 3 : 1 / 4 , after two months , p withdraws half of the capitals & after 10 months , a profit of rs 378 is divided among them . what is q ' s share ? | explanation : the ratio of their initial investment = 1 / 2 : 1 / 3 : 1 / 4 = 6 : 4 : 3 let ' s take the initial investment of p , q and r as 6 x , 4 x and 3 x respectively a : b : c = ( 6 x * 2 + 3 x * 10 ) : 4 x * 12 : 3 x * 12 = ( 12 + 30 ) : 4 * 12 : 3 * 12 = ( 4 + 10 ) : 4 * 4 : 12 = 14 : 16 : 12 = 7 : 8 : 6 b ' s... | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 660",
"rs . 675",
"rs . 860",
"rs . 960"
]
} | [
"B"
] | a man buys an item at rs . 750 and sells it at the loss of 10 percent . then what is the selling price of that item | "explanation : here always remember , when ever x % loss , it means s . p . = ( 100 - x ) % of c . p when ever x % profit , it means s . p . = ( 100 + x ) % of c . p so here will be ( 100 - x ) % of c . p . = 90 % of 750 = 90 / 100 * 750 = 675 option b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"60",
"50",
"66",
"54"
]
} | [
"A"
] | entry fee in an examination was re . 1 . later , this was reduced by 25 % which increased the sale by 20 % . the percentage increase in the number of visitors is | sol . let the total original sale be rs . 100 . then , original number of visitors = 100 . new number of visitors = 120 / 0.75 = 160 . ∴ increase % = 60 % . answer a | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"18.20",
"18.33",
"18",
"18.3"
]
} | [
"B"
] | 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 | "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 = ( 110 x 20 / 120 ) = rs . 18.33 answer : b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"5336",
"4306",
"4236",
"4336"
]
} | [
"A"
] | in a division sum , the divisor is 10 times the quotient and 5 times the remainder . if the remainder is 46 , the dividend is | sol . divisor = ( 5 × 46 ) = 230 . also , 10 × q = 230 ⇒ q = 23 . and , r = 46 . dividend = ( 230 × 23 + 46 ) = 5336 . answer a | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"19', '",
"750', '",
"24', '",
"120', '"
]
} | [
"A"
] | how many plants will be there in a circular bed whose outer edge measure 31 cms , allowing 4 cm 2 for each plant ? | circumference of circular bed = 31 cm area of circular bed = ( 31 ) 2 â „ 4 ï € space for each plant = 4 cm 2 â ˆ ´ required number of plants = ( 31 ) 2 â „ 4 ï € ã · 4 = 19.11 = 19 ( approx ) answer a | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 49.17",
"rs . 51.03",
"rs . 54.17",
"rs . 55.33"
]
} | [
"D"
] | if 10 litres of an oil of rs . 50 per litres be mixed with 5 litres of another oil of rs . 66 per litre then what is the rate of mixed oil per litre ? | "50 * 10 = 500 66 * 5 = 330 830 / 15 = 55.33 answer : d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"50 kmph",
"60 kmph",
"65 kmph",
"36 kmph"
]
} | [
"D"
] | a car takes 6 hours to cover a distance of 324 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ? | "time = 6 distence = 324 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 324 / 9 = 36 kmph d )" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1187.5",
"1234",
"1289",
"1345"
]
} | [
"A"
] | jaclyn buys $ 50 000 worth of debentures in a company . she earns 9.5 % p . a . simple interest , paid to her quarterly ( that is , every 3 months ) . if the agreed period of the debenture was 18 months : calculate the amount of interest jaclyn will earn for each quarter | "explanation : i = ( p x r x t ) / 100 answer : a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1 / 6",
"1 / 8",
"1 / 9",
"1 / 12"
]
} | [
"C"
] | what is the probability of getting a sum 9 from two throws of a dice ? | "in two throws of a dice , n ( s ) = ( 6 x 6 ) = 36 . let e = event of getting a sum = { ( 3 , 6 ) , ( 4 , 5 ) , ( 5 , 4 ) , ( 6 , 3 ) } . p ( e ) = n ( e ) / n ( s ) = 4 / 36 = 1 / 9 . answer : c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"14 : 5",
"15 : 5",
"16 : 5",
"19 : 6"
]
} | [
"D"
] | if x : y = 1 : 4 , then find the value of ( 7 x + 3 y ) : ( 2 x + y ) | explanation : let x = 1 k and y = 4 k , so = 7 ( k ) + 3 ( 4 k ) / 2 ( k ) + 1 ( 4 k ) = 19 k / 6 k = 19 : 6 option d | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"986000",
"968000",
"978000",
"987000"
]
} | [
"A"
] | evaluate : 986 x 237 + 986 x 863 | "986 x 137 + 986 x 863 = 986 x ( 137 + 863 ) = 986 x 1000 = 986000 . answer is a ." | MathQA |
{
"label": [
"A",
"B",
"C",
"E"
],
"text": [
"90",
"91",
"94",
"95"
]
} | [
"C"
] | how many zeros are the end of 380 ! ? | 380 ! has 380 / 5 + 380 / 5 ^ 2 + 380 / 5 ^ 3 = 76 + 15 + 3 = 94 trailing zeros ( take only the quotient into account ) . answer : c . | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"4 / 5",
"4 / 7",
"5",
"5 / 7"
]
} | [
"A"
] | the difference between a positive proper fraction and its reciprocal is 9 / 20 . the fraction is ? | "let the required fraction be x . then 1 - x = 9 x 20 1 - x 2 = 9 x 20 20 - 20 x 2 = 9 x 20 x 2 + 9 x - 20 = 0 20 x 2 + 25 x - 16 x - 20 = 0 5 x ( 4 x + 5 ) - 4 ( 4 x + 5 ) = 0 ( 4 x + 5 ) ( 5 x - 4 ) = 0 x = 4 / 5 option a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"0.003",
"0.0005",
"0.025",
"0.005"
]
} | [
"C"
] | double of quarter of 5 percent written as a decimal is : | "explanation : solution : ( 2 ) * ( 1 / 4 ) * 5 % = 0.025 answer : c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1 / 20",
"3 / 50",
"1 / 75",
"1 / 25"
]
} | [
"B"
] | what will be the fraction of 6 % | "explanation : 6 * 1 / 100 = 3 / 50 . option b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"25",
"40",
"90",
"140"
]
} | [
"B"
] | if the average ( arithmetic mean ) of a and b is 40 and the average of b and c is 60 , what is the value of c − a ? | "- ( a + b = 80 ) b + c = 120 c - a = 40 b . 40" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1 / 14",
"3 / 35",
"5 / 37",
"2 / 35"
]
} | [
"A"
] | the hcf and lcm of two numbers m and n are respectively 5 and 210 . if m + n = 75 , then 1 / m + 1 / n is equal to | "answer we have , m x n = 5 x 210 = 1050 â ˆ ´ 1 / m + 1 / n = ( m + n ) / mn = 75 / 1050 = 1 / 14 correct option : a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"22.8 kg",
"25.6 kg",
"19 kg",
"26.5 kg"
]
} | [
"C"
] | if 11.25 m of a uniform steel rod weighs 42.75 kg . what will be the weight of 5 m of the same rod ? | "explanation : let the required weight be x kg . then , less length , less weight ( direct proportion ) = > 11.25 : 5 : : 42.75 : x = > 11.25 x x = 5 x 42.75 = > x = ( 5 x 42.75 ) / 11.25 = > x = 19 answer : c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 6000",
"rs . 7935",
"rs . 8265.63",
"rs . 3967.5"
]
} | [
"C"
] | simple interest on a certain sum of money for 2 years at 12 % per annum is half the compound interest on rs . 6000 for 2 years at 15 % per annum . the sum placed on simple interest is | "solution c . i . = rs [ 6000 x ( 1 + 15 / 100 ) â ² - 4000 ] rs . ( 4000 x 115 / 100 x 115 / 100 - 6000 ) = rs . 7935 . sum = rs . [ 3967.5 x 100 / 4 x 12 ] = rs . 8265.63 . answer c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"6893",
"6993",
"6093",
"693"
]
} | [
"D"
] | what is the difference between the largest and the smallest number written with 7 , 7 , 0 , 7 ? | "7770 7077 - - - - - - - - - - - - - 693 answer : d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"3 / 4 ∏', '",
"4 / 3 ∏', '",
"5 ∏', '",
"5 / 9 ∏', '"
]
} | [
"B"
] | the volume of the greatest sphere that can be cut off from a cylindrical log of wood of base radius 1 cm and height 5 cm is : | sol . required volume = volume of a sphere of radius 1 cm = [ 4 / 3 ∏ * 1 * 1 * 1 ] cm ³ = 4 / 3 ∏ cm ³ answer b | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"18",
"750",
"23",
"120"
]
} | [
"C"
] | how many plants will be there in a circular bed whose outer edge measure 34 cms , allowing 4 cm 2 for each plant ? | "circumference of circular bed = 34 cm area of circular bed = ( 34 ) 2 â „ 4 ï € space for each plant = 4 cm 2 â ˆ ´ required number of plants = ( 34 ) 2 â „ 4 ï € ã · 4 = 22.98 = 23 ( approx ) answer c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"15 : 12', '",
"15 : 14', '",
"15 : 16', '",
"15 : 22', '"
]
} | [
"C"
] | if the ratio of the areas of two squares is 225 : 256 , then the ratio of their perimeters is : | explanation : a 2 / b 2 = 225 / 256 = 15 / 16 < = > 4 a / 4 b = 4 ∗ 15 / 4 ∗ 16 = 15 / 16 = 15 : 16 option c | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"4 : 3",
"3 : 4",
"5 : 6",
"7 : 9"
]
} | [
"D"
] | two vessels a and b contain spirit and water in the ratio 5 : 2 and 7 : 6 respectively . find the ratio in which these mixture be mixed to obtain a new mixture in vessel c containing spirit and water in the ration 8 : 5 ? | let the c . p . of spirit be re . 1 litre . spirit in 1 litre mix . of a = 5 / 7 litre , c . p . of 1 litre mix . in a = re . 5 / 7 spirit in 1 litre mix . of b = 7 / 13 litre , c . p . of 1 litre mix . in b = re . 7 / 13 spirit in 1 litre mix . of c = 8 / 13 litre , mean price = re . 8 / 13 . by the rule of alligation... | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"81",
"81.5",
"82",
"84.5"
]
} | [
"B"
] | 3 math classes : x , y , and z , take an algebra test . the average score in class x is 83 . the average score in class y is 76 . the average score in class z is 85 . the average score of all students in classes x and y together is 79 . the average score of all students in classes y and z together is 81 . what is the a... | explanation : let the number of students in classes x , y and z be a , b and c respectively . then total of x = 83 a total of y = 76 b total of z = 85 c and , ( 83 a + 76 b ) / ( a + b ) = 79 . i . e 4 a = 3 b . also , ( 76 b + 85 c ) / ( b + c ) = 81 . i . e 4 c = 5 b . hence , b = ( 4 / 3 ) a , c = ( 5 / 4 ) b = ( 5 ... | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"4.37 %",
"7.3 %",
"7.6 %",
"8.75 %"
]
} | [
"B"
] | the population of a town increased from 1 , 34,000 to 2 , 32,500 in a decade . the average percent increase of population per year is : | "explanation : increase in 10 years = ( 232500 - 134000 ) = 98500 . increase % = ( 98500 / 134000 x 100 ) % = 73 % . required average = ( 73 / 10 ) % = 7.3 % . answer : option b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"4.5 %",
"5.5 %",
"6.5 %",
"8.75 %"
]
} | [
"A"
] | the population of a town increased from 1 , 33,400 to 1 , 93,500 in a decade . the average percent increase of population per year is : | "explanation : increase in 10 years = ( 193500 - 133400 ) = 60100 . increase % = ( 60100 / 133400 x 100 ) % = 45 % . required average = ( 45 / 10 ) % = 4.5 % . answer : option a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"276",
"299",
"312",
"322"
]
} | [
"D"
] | the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 13 and 14 . the larger of the two numbers is | "solution clearly , the numbers are ( 23 x 13 ) and ( 23 x 14 ) . larger number = ( 23 x 14 ) = 322 . answer d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"63.07 kmph",
"54.28 kmph",
"62.02 kmph",
"64.02 kmph"
]
} | [
"B"
] | a car during its journey travels 1 hour at a speed of 40 kmph , another 30 minutes at a speed of 60 kmph , and 2 hours at a speed of 60 kmph . the average speed of the car is | first car travels 1 hrs at speed of 40 kmph distance = 40 x 1 = 40 m then car travels 30 min at a speed of 60 kmph distance = 30 min at speed of 60 kmph distance = 60 x 1 / 2 = 30 m at last it travels 2 hours at speed of 60 kmph distance = 60 x 2 = 120 m total distance = 40 + 30 + 120 = 190 total time = 1 + 1 / 2 + 2 =... | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"160",
"180",
"220",
"225"
]
} | [
"A"
] | a , b , c hired a car for rs . 520 and used it for 7,8 and 11 hours respectively . hire charges paid by b were : | sol . a : b : c = 7 : 8 : 11 . hire charges paid by b = rs . [ 520 * 8 / 26 ] = rs . 160 answer a | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"14,15",
"15,16",
"17,18",
"18,19"
]
} | [
"C"
] | the difference between the squares of two consecutive numbers is 35 . the numbers are | "explanation : let the numbers be a and ( a + 1 ) ( a + 1 ) 2 − a 2 = 35 ⇒ a 2 + 2 a + 1 − a 2 = 35 ⇒ 2 a = 34 ⇒ 2 a = 34 or a = 17 the numbers are 17 & 18 . correct option : c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"900",
"930",
"990",
"993"
]
} | [
"D"
] | what is the compound interest paid on a sum of rs . 3000 for the period of 3 years at 10 % per annum . | "solution = interest % for 1 st year = 10 interest % for 2 nd year = 10 + 10 % of 10 = 10 + 10 * 10 / 100 = 11 interest % for 3 rd year = 10 + 10 % ( 10 + 11 ) = 10 + 2.1 = 12.1 total % of interest = 10 + 11 + 12.1 = 33.1 total interest = 33.1 % 3000 = 3000 * ( 33.1 / 100 ) = 993 answer d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1560",
"1561",
"1559",
"1557"
]
} | [
"B"
] | there are 7 thieves . they stole diamonds from a diamond merchant and ran away . while running , night sets in and they decide to rest in the jungle . when everybody was sleeping , two of them woke up and decided to divide the diamonds equally among themselves . but when they divided the diamonds equally , one diamond ... | we need a number that is a multiple of 7 that will give a remainder of 1 when divided by 2 , 3 , 4 , 5 , and 6 . the least common multiple of these numbers is 60 . so , we need a multiple of 7 that is 1 greater than a multiple of 60 . answer b | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"35 %",
"20 %",
"17 %",
"18 %"
]
} | [
"A"
] | a shopkeeper labeled the price of his articles so as to earn a profit of 50 % on the cost price . he then sold the articles by offering a discount of 10 % on the labeled price . what is the actual percent profit earned in the deal ? | "explanation : let the cp of the article = rs . 100 . then labeled price = rs . 150 . sp = rs . 150 - 10 % of 150 = rs . 150 - 15 = rs . 135 . gain = rs . 135 â € “ rs . 100 = rs . 35 therefore , gain / profit percent = 35 % . answer : option a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1 / 4",
"1 / 5",
"1 / 3",
"1 / 8"
]
} | [
"C"
] | what will be the fraction of 33.33 % | "explanation : it will 33.33 * 1 / 100 = 1 / 3 answer : option c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"168 °",
"228 °",
"156 °",
"224 °"
]
} | [
"C"
] | the ratio of the adjacent angles of a parallelogram is 6 : 9 . also , the ratio of the angles of quadrilateral is 5 : 6 : 7 : 12 . what is the sum of the smaller angle of the parallelogram and the second largest angle of the quadrilateral ? | "the measures of the adjacent angles of a parallelogram add up to be 180 ° given so , 6 x + 9 x = 180 ° or , 15 x = 180 ° or , x = 12 ° hence the angles of the parallelogram are 72 ° and 108 ° further it is given we know sum of all the four angles of a quadrilateral is 360 ° so , 5 y + 6 y + 7 y + 12 y = 360 ° or , 5 y... | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"66 , 78",
"70 , 82",
"94 , 106",
"84 , 96"
]
} | [
"D"
] | the h . c . f . of two numbers is 12 and their difference is 12 . the numbers are | "solution out of the given numbers , the two with h . c . f . 12 and difference 12 are 84 and 96 answer d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"4 / 9",
"2 4 / 9",
"3 4 / 9",
"4 4 / 9"
]
} | [
"D"
] | worker a takes 8 hours to do a job . worker b takes 10 hours to do a job . how long should it take both a and b , working together to do same job . | "explanation : in this type of questions , first we need to calculate 1 hours work , then their collective work as , a ' s 1 hour work is 1 / 8 b ' s 1 hour work is 1 / 10 ( a + b ) ' s 1 hour work = 1 / 8 + 1 / 10 = 9 / 40 so both will finish the work in 40 / 9 hours = 4 4 / 9 option d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"35.67 %",
"64.75 %",
"68.57 %",
"70.20 %"
]
} | [
"D"
] | in an examination , there were 2,000 candidates , out of which 900 candidates were girls and rest were boys . if 28 % of the boys and 32 % of the girls passed , then the total percentage of failed candidates is ? | girls = 900 , boys = 1100 passed = ( 28 % of 1100 ) + ( 32 % of 900 ) = 308 + 288 = 596 failed = 2000 - 596 = 1404 failed % = [ ( 1404 / 2000 ) x 100 ] % = 70.2 % . answer : d | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"46.2 %",
"54.54 %",
"63 %",
"56.52 %"
]
} | [
"D"
] | a cricketer scored 138 runs which included 12 boundaries and 2 sixes . what percent of his total score did he make by running between the wickets . | explanation : number of runs made by running = 138 - ( 12 x 4 + 2 x 6 ) = 138 - ( 60 ) = 78 now , we need to calculate 72 is what percent of 138 . = > 78 / 138 * 100 = 56.52 % answer : d | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"35000",
"40000",
"50000",
"60000"
]
} | [
"D"
] | p and q invested in a shop . the profits were divided in the ratio of 2 : 3 respectively . if p invested rs . 40,000 , the amount invested by q is : | "suppose q invested rs . y . then , 40000 / y = 2 / 3 or y = [ 40000 x 3 / 2 ] = 60000 . answer d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"11",
"21",
"28",
"42"
]
} | [
"B"
] | a is twice as good a workman as b and together they finish a piece of work in 14 days . the number of days taken by a alone to finish the work is : | "( a ' s 1 day ' s work ) : ( b ' s 1 day ' s work ) = 2 : 1 ( a + b ) ' s 1 day ' s work = 1 / 14 divide 1 / 14 in the ratio 2 : 1 a ' s 1 day ' s work = ( 1 / 14 x 2 / 3 ) = 1 / 21 hence , a alone can finish the work in 21 days . correct option : b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"49.5 kmph",
"49.0 kmph",
"48.5 kmph",
"48.0 kmph"
]
} | [
"D"
] | nick took a bus from home to market , that travels at 80 kmph . while walking back at 8 kmph , halfway through , he suddenly realized he was getting late and he cycled back the remaining distance in 60 kmph . find the average speed . | let the distance be 2 x ( one way ) time taken by bus = 2 x / 80 , by walking = x / 8 , by cycling = x / 60 hours : . average speed = total distance / total time = 8 x / x / 40 + x / 8 + x / 60 = 8 * 60 / 1.5 + 7.5 + 1 = 12.0 answer : d | MathQA |
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