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": [
"25",
"50",
"90",
"140"
]
} | [
"B"
] | if the average ( arithmetic mean ) of a and b is 45 and the average of b and c is 70 , what is the value of c − a ? | "the arithmetic mean of a and b = ( a + b ) / 2 = 45 - - a + b = 90 - - 1 similarly for b + c = 140 - - 2 subtracting 1 from 2 we have c - a = 50 ; answer : b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 2000",
"rs . 10,000",
"rs . 15,000",
"rs . 20,000"
]
} | [
"C"
] | a man took a loan from a bank at the rate of 12 % p . a . simple interest . after 3 years he had to pay rs . 5400 interest only for the period . the principal amount borrowed by him was : | "solution principal = rs . ( 100 x 5400 / 12 x 3 ) = rs . 15000 . answer c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"40.5 %",
"48.7 %",
"54.5 %",
"55.6 % %"
]
} | [
"C"
] | the cost price of an article is 55 % of the marked price . calculate the gain percent after allowing a discount of 15 % . | sol . let marked price = rs . 100 . then , c . p . = rs . 55 . s . p = rs . 85 . â ˆ ´ gain % = [ 30 / 55 * 100 ] % = 54.5 % . answer c | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"$ 1",
"$ 27",
"$ 31",
"$ 41"
]
} | [
"A"
] | at an upscale fast - food restaurant , shin can buy 3 burgers , 7 shakes , and one cola for $ 110 . at the same place it would cost $ 164.50 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 = 110 4 b + 10 s + c = 164.5 subtracting the first equation from the second gives us b + 3 s = 54.5 now if we subtract the new equation two times from first or 3 times from... | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"48",
"288",
"12",
"256"
]
} | [
"A"
] | in how many ways 4 boys and 2 girls can be seated in a row so that they are alternate . | "solution : let the arrangement be , b g b g b b 4 boys can be seated in 4 ! ways . girl can be seated in 2 ! ways . required number of ways , = 4 ! * 2 ! = 48 answer : option a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 450",
"rs . 320",
"rs . 550",
"rs . 420"
]
} | [
"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 . 42 per day while the average expenditure per head diminished by re 1 . what was the original expenditure of the mess ? | "solution : let the original average expenditure be rs . x then , 42 ( x - 1 ) - 35 x = 42 . = > 7 x = 84 = > x = 12 therefore original expenditure , = rs . ( 35 × 12 ) = rs . 420 . answer : option d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
". 3",
". 0003",
". 003",
"0.03"
]
} | [
"D"
] | what decimal fraction is 30 ml of a litre ? | "answer required fraction = 30 / 1000 = 3 / 100 = . 03 correct option : d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"7500",
"6500",
"8500",
"9500"
]
} | [
"C"
] | find the simple interest on rs . 68,000 at 16 2 / 3 % per year for 9 months . | "p = rs . 68000 , r = 50 / 3 % p . a and t = 9 / 12 years = 3 / 4 years . simple interest = ( p * r * t ) / 100 = rs . ( 68,000 * ( 50 / 3 ) * ( 3 / 4 ) * ( 1 / 100 ) ) = rs . 8500 answer is c ." | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"300",
"450",
"750",
"800"
]
} | [
"A"
] | a and b undertake to do a piece of work for rs . 600 . a alone can do it in 6 days while b alone can do it in 8 days . with the help of c , they finish it in 3 days . find the share of a | "c ' s 1 day ' s work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 24 a : b : c = ratio of their 1 day ' s work = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 . a ’ s share = rs . ( 600 * 4 / 8 ) = rs . 300 , b ' s share = rs . ( 600 * 3 / 8 ) = rs . 225 . c ' s share = rs . [ 600 - ( 300 + 225 » ) = rs . 75 . answer is a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"2 √ 2",
"2 √ 5",
"6",
"4 √ 2"
]
} | [
"C"
] | twenty four 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 = 24 = > x / 360 * 2 * pi * r + 2 r = 24 = > 2 a / r + 2 r = 24 = > a = r 12 - r ^ 2 = r 12 - r ^ 2 we will now max using derivations max value of a will found at a = 0 i . e 12 - 2 r = 0 r = 6 c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1.2 kg",
"1.5 kg",
"1.7 kg",
"1.9 kg"
]
} | [
"B"
] | when processing flower - nectar into honey bees ' extract , a considerable amount of water gets reduced . how much flower - nectar must be processed to yield 1 kg of honey , if nectar contains 50 % water , and the honey obtained from this nectar contains 25 % water ? | "explanation : flower - nectar contains 50 % of non - water part . in honey this non - water part constitutes 75 % ( 100 - 25 ) . therefore 0.5 x amount of flower - nectar = 0.75 x amount of honey = 0.75 x 1 kg therefore amount of flower - nectar needed = ( 0.75 / 0.51 ) kg = 1.5 kgs answer : b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"0.02",
"0.2",
"2",
"20"
]
} | [
"A"
] | 0.0004 ? = 0.02 | "explanation : required answer = 0.0004 / 0.02 = 0.04 / 2 = 0.02 . answer : option a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"149",
"150",
"151",
"166"
]
} | [
"B"
] | how many 3 - digit numbers are divisible by 6 in all ? | solution required numbers are 102 , 018114 , . . . . 996 . this is an a . p with a = 102 , d = 6 . let the number of its terms be n . then a + ( n - 1 ) d ‹ = › 102 + ( n - 1 ) × 6 = 996 ‹ = › n = 150 . answer b | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 500",
"rs . 1800",
"rs . 2000",
"rs . 2500"
]
} | [
"B"
] | a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets rs . 900 more than d , what is b ' s share ? | "let the shares of a , b , c and d be rs . 5 x , rs . 2 x , rs . 4 x and rs . 3 x respectively . then , 4 x - 3 x = 900 x = 900 . b ' s share = rs . 2 x = rs . ( 2 x 900 ) = rs . 1800 . answer = b" | 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 . 90000 . 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 . 90000 = > x + ( x - 3000 ) + ( x + 3000 ) = 90000 = > 3 x = 90000 = > x = 30000 hence , a ' s investment = rs . 33000 b ' s investme... | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"380",
"350",
"334",
"310"
]
} | [
"C"
] | ( 3192 + 6160 ) / 28 | "explanation : as per bodmas rule , first we will solve the equation in bracket then we will go for division = ( 9352 ) / 28 = 334 option c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"2 : 1",
"4 : 9",
"8 : 77",
"4 : 121"
]
} | [
"B"
] | the ratio of radius of a circle and the side of a square is 2 : 3 . find the ratio of their areas : | "radius / side = 2 / 3 â ‡ ’ area of circle / area of square = 4 / 9 answer : b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 312.5",
"rs . 154.75",
"rs . 156.25",
"rs . 158"
]
} | [
"A"
] | the present worth of rs . 338 due in 2 years at 4 % per annum compound interest is | "solution present worth = rs . [ 338 / ( 1 + 4 / 100 ) ² ] = rs . ( 338 x 25 / 26 x 25 / 26 ) = rs . 312.5 answer a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 114.80",
"rs . 86.70",
"rs . 55.40",
"rs . 51.60"
]
} | [
"D"
] | if rs . 64 amount to rs . 83.20 in 2 years , what will rs . 86 amount to in 4 years at the same rate percent per annum ? | "solution p = rs . 64 , s . i . = rs . ( 83.20 - 64 ) = rs . 19.20 , t = 2 years . so , rate = ( 100 x 19.20 / 64 x 2 ) = 15 % . now , p = rs . 86 , r = 15 % , t = 4 years . ∴ s . i . = rs . ( 86 x 15 x 4 / 100 ) rs . 51.60 . answer d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 960",
"rs . 840",
"rs . 296",
"rs . 760"
]
} | [
"C"
] | the banker â € ™ s gain on a sum due 3 years hence at 17 % per annum is rs . 100 . the banker â € ™ s discount is | "solution t . d = ( b . g x 100 / r x t ) = rs . ( 100 x 100 / 17 x 3 ) = rs . 196 . b . d = rs ( 196 + 100 ) = rs . 296 . answer c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"290 / 289",
"1 / 289",
"290 / 90",
"290 / 19"
]
} | [
"A"
] | product of two natural numbers is 17 . then , the sum of reciprocals of their squares is | "explanation : if the numbers are a , b , then ab = 17 , as 17 is a prime number , so a = 1 , b = 17 . 1 / a 2 + 1 / b 2 = 1 / 1 ( 2 ) + 1 / 17 ( 2 ) = 290 / 289 option a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"40.2",
"40.4",
"40.5",
"40.8"
]
} | [
"C"
] | the average of 10 numbers is 40.2 . later it is found that two numbers have been wrongly copied . the first is 15 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 – 13 + 31 – 15 = 405 hence , new average = 405 ⁄ 10 = 40.5 answer c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"q = 300",
"q = 400",
"q = 500",
"q = 600"
]
} | [
"C"
] | there are 200 female managers in a certain company . find the total number of female employees q in the company , if 2 / 5 of all the employees are managers and 2 / 5 of all male employees are managers . | { managers } = { female managers } + { male managers } ; we are told that the total number of managers in the company is 2 / 5 of all the employees , thus { managers } = 2 / 5 ( m + f ) , where m and f are number of female and male employees , respectively . also , we know that 2 / 5 of all male employees are managers ... | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"10 / 9",
"1 / 289",
"290 / 90",
"290 / 19"
]
} | [
"A"
] | product of two natural numbers is 3 . then , the sum of reciprocals of their squares is | "explanation : if the numbers are a , b , then ab = 3 , as 3 is a prime number , so a = 1 , b = 3 . 1 / a 2 + 1 / b 2 = 1 / 1 ( 2 ) + 1 / 3 ( 2 ) = 10 / 9 option a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"7.14",
"7.41",
"4.71",
"4.17"
]
} | [
"D"
] | if the cost price is 96 % of selling price then what is the profit percentage . | "selling price = rs 100 : then cost price = rs 96 : profit = rs 4 . profit = { ( 4 / 96 ) * 100 } % = 4.17 % answer is d ." | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"40",
"44",
"66",
"52"
]
} | [
"C"
] | in a can , there is a mixture of milk and water in the ratio 4 : 5 . if it is filled with an additional 12 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 - 12 ) after adding milk , quantity of milk in the mixture = 6 / 11 t . 6 t / 11 - 12 = 4 / 9 ( t - 12 ) 10 t = 1188 - 528 = > t = 66 . answer : c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"7.3 %",
"10.5 %",
"11 %",
"12.5 %"
]
} | [
"A"
] | a trader marked the selling price of an article at 50 % above the cost price . at the time of selling , he allows certain discount and suffers a loss of 1 % . he allowed a discount of : | "sol . let c . p . = rs . 100 . then , marked price = rs . 110 , s . p . = rs . 99 . ∴ discount % = [ 11 / 150 * 100 ] % = 7.3 % answer a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"712.5",
"1234",
"1289",
"1345"
]
} | [
"A"
] | jaclyn buys $ 30 000 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 = 30000 * 9.5 / 100 * ( 18 / 12 ) ^ 1 / 6 = 712.50 answer : a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"12 km",
"15 km",
"18 km",
"24 km"
]
} | [
"A"
] | a software engineer starts from home at 3 pm for every walk on a route which has level road for some distance and a then a hillock . he walks speed of 4 kmph on level ground and then at a speed of 3 kmph on the uphill and then down the hill at a speed of 6 kmph to the level ground and then at a speed of 4 kmph to the h... | time = distance / speed so , let the distance to the level road from home be x km and the distance to the hillock from the level road be y km so , ( x / 4 + y / 3 ) + ( y / 6 + x / 4 ) = 6 x + y = 12 km . answer : a | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"5 %",
"10 %",
"15 %",
"20 %"
]
} | [
"D"
] | a box contains either blue or red flags . the total number of flags in the box is an even number . a group of children are asked to pick up two flags each . if all the flags are used up in the process such that 60 % of the children have blue flags , and 60 % have red flags , what percentage of children have flags of bo... | "solution : let the total number of flags be 100 ( even number ) let the total number of ' blue ' flags alone be ' a ' let the total number of ' red ' flags alone be ' b ' let the total number of ' both ' flags be ' c ' we have given , total number of blue flags = 60 % = 60 = a + c total number of red flags = 55 % = 55... | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 9471",
"rs . 12,628",
"rs . 262.8",
"rs . 241.7"
]
} | [
"D"
] | suganya and suriya are partners in a business . suganya invests rs . 35,000 for 8 months and suriya invests rs . 42,000 for 10 months . out of a profit of rs . 30,570 . suganya ' s share is | solution ratio of their shares = ( 35000 ã — 8 ) : ( 42000 ã — 10 ) = 128 : 125 suganya ' s share = rs . ( 30570 ã — 2 / 253 ) = rs . 241.7 . answer d | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"46.2 %",
"54.54 %",
"55.88 %",
"70 %"
]
} | [
"C"
] | a cricketer scored 136 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 = 136 - ( 12 x 4 + 2 x 6 ) = 136 - ( 60 ) = 76 now , we need to calculate 72 is what percent of 136 . = > 76 / 136 * 100 = 55.88 % answer : c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"45 kg",
"38 kg",
"66 kg",
"36 kg"
]
} | [
"D"
] | the weights of 3 bags are in the ratio 4 : 5 : 6 . if the sum of the weights of the heaviest and the lightest bag is 45 kg more than the weight of the third bag , what is the weight of the lightest bag ? | let the weights of the three boys be 4 k , 5 k and 6 k respectively . 4 k + 6 k = 5 k + 45 = > 5 k = 45 = > k = 9 therefore the weight of the lightest boy = 4 k = 4 ( 9 ) = 36 kg . answer : d | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"8 / 27",
"1 1 / 3",
"2 2 / 3",
"3 / 3"
]
} | [
"C"
] | if a fraction is multiplied by itself and then divided by the reciprocal of the same fraction , the result is 18 26 / 27 . find the fraction . | answer if the required fraction be p according to the question ( p x p ) / ( 1 / p ) = 1826 / 27 ⇒ p 3 = 512 / 27 ∴ p = 8 / 3 = 2 2 / 3 correct option : c | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 22500",
"rs . 25500",
"rs . 26000",
"rs . 28000"
]
} | [
"B"
] | sahil purchased a machine at rs 11000 , then got it repaired at rs 5000 , then gave its transportation charges rs 1000 . then he sold it with 50 % of profit . at what price he actually sold it . | "explanation : question seems a bit tricky , but it is very simple . just calculate all cost price , then get 150 % of cp . c . p . = 11000 + 5000 + 1000 = 17000 150 % of 17000 = 150 / 100 * 17000 = 25500 option b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"900",
"500",
"5750",
"5000"
]
} | [
"C"
] | 6000 - 5000 ÷ 20.00 = ? | "answer given expression = 6000 - 5000 ÷ 20.00 = 6000 - 250 = 5750 correct option : c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"3",
"7",
"1",
"9"
]
} | [
"A"
] | find the remainder when 2 ^ 31 is divided by 5 . | 2 ^ 10 = 1024 . unit digit of 2 ^ 10 x 2 ^ 10 x 2 ^ 10 is 4 [ as 4 x 4 x 4 gives unit digit 4 ] . unit digit of 231 is 8 . now , 8 when divided by 5 , gives 3 as remainder . hence , 231 when divided by 5 , gives 3 as remainder . answer is a . | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"18750 sq . m', '",
"37500 sq . m', '",
"40000 sq . m', '",
"48000 sq . m', '"
]
} | [
"B"
] | the breadth of a rectangular field is 60 % of its length . if the perimeter of the field is 800 m . what is the area of the field ? | solution so length = 250 m ; breadth = 150 m area = ( 250 x 150 ) m ² = 37500 m ² answer b | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"10.22 %",
"20.22 %",
"21.22 %",
"50 %"
]
} | [
"D"
] | a shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 20 % while buying and by 20 % while selling . what is his percentage profit ? | "the owner buys 100 kg but actually gets 120 kg ; the owner sells 100 kg but actually gives 80 kg ; profit : ( 120 - 80 ) / 80 * 100 = ~ 50 % answer : d ." | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1.5 kg",
"2 kg",
". 5 kg",
"1 kg"
]
} | [
"D"
] | in 1 kg mixture of iron and manganese 20 % of manganese . how much iron should be added so that the proportion of manganese becomes 10 % | explanation : by the rule of alligation , we have percentage concentration of manganese in the mixture : 20 percentage concentration of manganese in pure iron : 0 percentage concentration of manganese in the final mixture 10 10 - 0 = 10 20 - 10 = 10 = > quantity of the mixture : quantity of iron = 10 : 10 = 1 : 1 given... | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"800",
"500",
"2800",
"1600"
]
} | [
"C"
] | find the value of 3.5 x [ ( 3.6 x 0.48 x 2.50 ) / ( 0.12 x 0.09 x 0.5 ) ] | answer 3.5 x [ ( 3.6 x 0.48 x 2.50 ) / ( 0.12 x 0.09 x 0.5 ) ] = 3.5 x [ ( 36 x 48 x 250 ) / ( 12 x 9 x 5 ) ] = 3.5 x 4 x 4 x 50 = 2800 correct option : c | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 21136.36",
"rs . 31136.36",
"rs . 51136.36",
"rs . 61136.36"
]
} | [
"C"
] | a man sells a car to his friend at 12 % loss . if the friend sells it for rs . 54000 and gains 20 % , the original c . p . of the car was : | "explanation : s . p = rs . 54,000 . gain earned = 20 % c . p = rs . [ 100 / 120 ã — 54000 ] = rs . 45000 this is the price the first person sold to the second at at loss of 12 % . now s . p = rs . 45000 and loss = 12 % c . p . rs . [ 100 / 88 ã — 45000 ] = rs . 51136.36 correct option : c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"343",
"232",
"216",
"484"
]
} | [
"A"
] | how many cubes of 4 cm edge can be cut out of a cube of 28 cm edge | "explanation : number of cubes = ( 28 x 28 x 28 ) / ( 4 x 4 x 4 ) = 343 answer : a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 500",
"rs . 1500",
"rs . 2200",
"rs . 2500"
]
} | [
"C"
] | a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets rs . 1100 more than d , what is b ' s share ? | "let the shares of a , b , c and d be rs . 5 x , rs . 2 x , rs . 4 x and rs . 3 x respectively . then , 4 x - 3 x = 1100 x = 1100 . b ' s share = rs . 2 x = rs . ( 2 x 1100 ) = rs . 2200 . answer = c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"10 min",
"20 min",
"30 min",
"40 min"
]
} | [
"C"
] | a motorcyclist x drives along a circular fence at a rate of 2 rounds per hour and another motor cyclist y at a rate of 4 rounds per hour . after how long they will cross each other for the first time ? | explanation : since x and y move in the same direction they cross each other when there is a difference of two round between the two . relative speed of x and y = 4 - 2 = 2 . time taken to complete one round at this speed = 1 / 2 hour = 30 minutes answer : c | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"140,90",
"180,60",
"160,90",
"150,80"
]
} | [
"D"
] | a third of arun â € ™ s marks in mathematics exceed a half of his marks in english by 10 . if he got 230 marks in two subjects together how many marks did he got in english ? | "let arun â € ™ s marks in mathematics and english be x and y then ( 1 / 3 ) x - ( 1 / 2 ) y = 10 2 x - 3 y = 60 â € ¦ â € ¦ > ( 1 ) x + y = 230 â € ¦ â € ¦ . > ( 2 ) solving ( 1 ) and ( 2 ) x = 150 and y = 80 answer is d ." | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 200",
"rs . 250",
"rs . 300",
"rs . 780"
]
} | [
"D"
] | the cost of 3 pens and 5 pencils is rs . 260 . also the cost of one pen and one pencil is in the ratio of 5 : 1 respectively . what is the cost of one dozen pens ? | explanation : let the cost of one pen is ‘ 5 x ’ and pencil is ‘ x ’ 3 x 5 x + 5 x = rs . 260 15 x + 5 x = rs . 260 x = 260 / 20 = 13 : . cost of 1 pen = 5 x = 5 x 13 = 65 : . cost of 12 pens , i . e . ( one dozen ) = 65 x 12 = rs . 780 answer : option d | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"100",
"120",
"91.2",
"180"
]
} | [
"C"
] | one side of a rectangular field is 16 m and one of its diagonal is 17 m . find the area of the field . | "solution other side = √ ( 17 ) 2 - ( 16 ) 2 = √ 289 - 256 = √ 33 = 5.7 m . ∴ area = ( 16 x 5.7 ) m 2 = 91.2 m 2 . answer c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"2436",
"2801",
"- 2801",
"- 660"
]
} | [
"D"
] | - 24 x 29 + 36 = ? | "given exp . = - 24 x ( 30 - 1 ) + 36 = - ( 24 x 30 ) + 24 + 36 = - 720 + 60 = - 660 answer is d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"648",
"1800",
"2700",
"10800"
]
} | [
"B"
] | running at the same constant rate , 6 identical machines can produce a total of 270 bottles per minute . at this rate , how many bottles could 10 such machines produce in 4 minutes ? | "let the number of required bottles be x machine 6 : 10 time 1 : 4 = : : 270 : x therefore 6 x 1 x x = 10 x 4 x 270 = > x = ( 10 x 4 x 270 ) / ( 6 ) = > x = 1800 answer : option b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"0.98",
"9.4",
"0.094",
"94"
]
} | [
"A"
] | subtracting 2 % of a from a is equivalent to multiplying a by how much ? | answer let a - 2 % of a = ab . ⇒ ( 98 x a ) / 100 = ab ∴ b = 0.98 correct option : a | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 4,900",
"rs . 5,000",
"rs . 5,100",
"rs . 5266"
]
} | [
"D"
] | mr . karan borrowed a certain amount at 6 % per annum simple interest for 9 years . after 9 years , he returned rs . 8110 / - . find out the amount that he borrowed . | "explanation : let us assume mr . karan borrowed amount is rs . a . ( the principal ) by formula of simple interest , s . i . = prt / 100 where p = the principal , r = rate of interest as a % , t = time in years s . i . = ( p * 6 * 9 ) / 100 = 54 p / 100 amount = principal + s . i . 8110 = p + ( 54 p / 100 ) 8110 = ( 1... | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"210",
"280",
"360",
"720"
]
} | [
"D"
] | the banker â € ™ s discount of a certain sum of money is rs . 60 and the true discount on the same sum for the same time is rs . 54 . the sum due is | "sol . sum = b . d . * t . d . / b . d . - t . d . = rs . [ 60 * 54 / 60 - 54 ] = rs . [ 72 * 60 / 6 ] = rs . 720 answer d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"79698",
"80578",
"500578",
"81268"
]
} | [
"C"
] | 517 x 517 + 483 x 483 = ? | "= ( 517 ) ^ 2 + ( 483 ) ^ 2 = ( 500 + 17 ) ^ 2 + ( 500 - 17 ) ^ 2 = 2 [ ( 500 ) ^ 2 + ( 17 ) ^ 2 ] = 2 [ 250000 + 289 ] = 2 x 250289 = 500578 answer is c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"4",
"5 1 / 2",
"6",
"8"
]
} | [
"A"
] | a can finish a work in 12 days and b can do the same work in 15 days . b worked for 10 days and left the job . in how many days , a alone can finish the remaining work ? | "b ' s 10 day ' s work = ( 1 / 15 * 10 ) = 2 / 3 remaining work = ( 1 - 2 / 3 ) = 1 / 3 now , 1 / 18 work is done by a in 1 day 1 / 3 work is done by a in ( 12 * 1 / 3 ) = 4 days . correct option : a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"277",
"36",
"64",
"72"
]
} | [
"B"
] | ? % of 360 = 129.6 | "? % of 360 = 129.6 or , ? = 129.6 × 100 / 360 = 36 answer b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 4480",
"rs . 5275",
"rs . 6275",
"rs . 6725"
]
} | [
"A"
] | the owner of a furniture shop charges his customer 25 % more than the cost price . if a customer paid rs . 5600 for a computer table , then what was the cost price of the computer table ? | "cp = sp * ( 100 / ( 100 + profit % ) ) = 5600 ( 100 / 125 ) = rs . 4480 . answer : a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"54",
"55",
"56",
"57"
]
} | [
"A"
] | the true discount on a bill of rs . 270 is rs . 45 . the banker ' s discount is | solution p . w = rs . ( 270 - 45 ) = rs . 225 s . i on rs . 270 = rs . ( 45 / 225 x 270 ) = rs . 54 . answer a | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"45 kg",
"50 kg",
"53 kg",
"55 kg"
]
} | [
"A"
] | the average weight of a class of 24 students is 35 kg . if the weight of the teacher be included , the average rises by 400 g . the weight of the teacher is | "solution weight of the teacher = ( 35.4 × 25 - 35 × 24 ) kg = 45 kg . answer a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 55.50', '",
"rs . 67.50', '",
"rs . 86.50', '",
"rs . 98.00', '"
]
} | [
"D"
] | the sides of a rectangular field are in the ratio 3 : 4 . if the area of the field is 9408 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 × 4 x = 9408 ⇔ 12 x 2 = 9408 ⇔ x 2 = 784 ⇔ x = 28 . so , length = 84 m and breadth = 112 m . perimeter = [ 2 ( 84 + 112 ) ] m = 392 m . ∴ cost of fencing = rs . ( 0.25 × 392 ) = rs . 98.00 . answer d | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"$ 60",
"$ 70",
"$ 75",
"$ 96"
]
} | [
"B"
] | if greg buys 3 shirts , 4 trousers and 2 ties , the total cost is $ 90 . if greg buys 7 shirts , 2 trousers and 2 ties , the total cost is $ 50 . how much will it cost him to buy 3 trousers , 5 shirts and 2 ties ? | "solution : 3 x + 4 y + 2 z = 90 7 x + 2 y + 2 z = 50 adding both the equations = 10 x + 6 y + 4 z = 140 5 x + 3 y + 2 z = 70 ans b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"3.6 kg",
"3.696 kg",
"36 kg",
"36.9 kg"
]
} | [
"B"
] | a hollow iron pipe is 21 cm long and its external diameter is 8 cm . if the thickness of the pipe is 1 cm and iron weighs 8 g / cm 3 , then the weight of the pipe is | "explanation : external radius = 4 cm , internal radius = 3 cm . volume of iron = [ ( 22 / 7 ) × ( 42 - 32 ) × 21 ] cm 3 = 462 cm 3 weight of iron = ( 462 x 8 ) gm = 3696 gm = 3.696 kg answer : b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1 / 2",
"2 / 3",
"1 / 5",
"1 / 6"
]
} | [
"B"
] | in a throw of dice what is the probability of ge æ « ng number greater than 2 | explanation : number greater than 2 is 3 , 4 , 5 & 6 , so only 4 number total cases of dice = [ 1,2 , 3,4 , 5,6 ] so probability = 4 / 6 = 2 / 3 answer : b | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"3 : 1",
"3 : 2",
"3 : 5",
"2 : 1"
]
} | [
"D"
] | if the volume of two cubes are in the ratio 64 : 8 , the ratio of their edges is : | "explanation : let the edges be a and b of two cubes , then a 3 / b 3 = 64 / 8 = > ( a / b ) 3 = ( 4 / 2 ) 3 a / b = 2 / 1 = > a : b = 2 : 1 option d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"0.01",
"1 , 000,000",
"0.001",
"1,000"
]
} | [
"B"
] | if 10,000 microns = 1 decimeter , and 10,000 , 000,000 angstroms = 1 decimeter , how many angstroms equal 1 micron ? | given that 10,000 microns = 1 decimeter = 10,000 , 000,000 angstroms so , 1 micron = 10,000 , 000,000 / 10,000 = 1 , 000,000 answer : b | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"630",
"735",
"825",
"600"
]
} | [
"B"
] | what is the compound interest paid on a sum of rs . 3500 for the period of 2 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 total % of interest = 10 + 11 = 21 total interest = 21 % 3500 = 3500 * ( 21 / 100 ) = 735 answer b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"180 km",
"190 km",
"220 km",
"230 km"
]
} | [
"A"
] | a boat takes 19 hours for travelling downstream fro poin a to point b and coming back to a point c midway between a and b . if the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph , what is the distance between a and b ? | sol . speed downstream = ( 14 + 4 ) km / hr = 18 km / hr ; speed upstream = ( 14 - 4 ) km / hr = 10 km / hr . let the distance between a and b be x km . then , x / 18 + ( x / 2 ) / 10 = 19 ⇔ x / 18 + x / 20 = 19 ⇒ x = 180 km . answer a | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"3 : 4",
"4 : 3",
"17 : 16",
"16 : 17"
]
} | [
"B"
] | if 15 % of a is the same as 20 % of b , then a : b is : | "expl : 15 % of a i = 20 % of b = 15 a / 100 = 20 b / 100 = 4 / 3 = 4 : 3 answer : b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"12 kg",
"60 kg",
"72 kg",
"80 kg"
]
} | [
"D"
] | a boat having a length 4 m and breadth 2 m is floating on a lake . the boat sinks by 1 cm when a man gets on it . the mass of the man is : | "explanation : volume of water displaced = ( 4 x 2 x 0.01 ) m 3 = 0.08 m 3 . ∴ mass of man = volume of water displaced x density of water = ( 0.08 x 1000 ) kg = 80 kg . answer : d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"574580",
"574200",
"584250",
"576460"
]
} | [
"B"
] | 5800 * 99 | "explanation : 5800 * ( 100 - 1 ) = 580000 - 5800 = 574200 option b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 960",
"rs . 250",
"rs . 300",
"rs . 150"
]
} | [
"A"
] | the cost of 3 pens and 5 pencils is rs . 340 . also the cost of one pen and one pencil is in the ratio of 4 : 1 respectively . what is the cost of one dozen pens ? | "explanation : let the cost of one pen is ‘ 4 x ’ and pencil is ‘ x ’ 3 x 4 x + 5 x = rs . 340 12 x + 5 x = rs . 340 x = 340 / 17 = 20 : . cost of 1 pen = 4 x = 4 x 20 = 80 : . cost of 12 pens , i . e . ( one dozen ) = 80 x 12 = rs . 960 answer : option a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs 18221.76",
"rs 18123.30",
"rs 18123.40",
"rs 18123.50"
]
} | [
"A"
] | what will be the compound interest on rs . 45000 after 3 years at the rate of 12 % per annum | "explanation : ( 45000 × ( 1 + 12 / 100 ) 3 ) = > 45000 × 28 / 25 × 28 / 25 × 28 / 25 = > 63221.76 so compound interest will be 63221.76 - 45000 = rs 18221.76 option a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"3 : 1",
"3 : 2",
"3 : 5",
"3 : 7"
]
} | [
"A"
] | if the volume of two cubes are in the ratio 27 : 1 , the ratio of their edges is : | "explanation : let the edges be a and b of two cubes , then a 3 / b 3 = 27 / 1 = > ( a / b ) 3 = ( 3 / 1 ) 3 a / b = 3 / 1 = > a : b = 3 : 1 option a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"2 km",
"4 km",
"5 km",
"2.25 km"
]
} | [
"D"
] | a man can row 4 kmph is still water . if the river is running at 2 kmph it takes 90 min to row to a place and back . how far is the place | explanation : speed in still water = 4 kmph speed of the stream = 2 kmph speed upstream = ( 4 - 2 ) = 2 kmph speed downstream = ( 4 + 2 ) = 6 kmph total time = 90 minutes = 90 ⁄ 60 hour = 3 ⁄ 2 hour let l be the distance . then ( l / 6 ) + ( l / 2 ) = 32 = > l + 3 l = 9 = > 4 l = 9 = > l = 9 ⁄ 4 = 2.25 km . answer : op... | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1360",
"1450",
"1600",
"947"
]
} | [
"D"
] | the simple interest and the true discount on a certain sum for a given time and at a given rate are rs . 85 and rs . 78 respectively . the sum is : | sol . sum = s . i . * t . d . / ( s . i ) - ( t . d . ) = 85 * 78 / ( 85 - 78 ) = rs . 947 . answer d | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"4 hours",
"5 hours",
"6 hours",
"7 hours"
]
} | [
"C"
] | two workers a and b are engaged to do a work . a working alone takes 8 hours more to complete the job than if both worked together . if b worked alone , he would need 4 1 / 2 hours more to complete the job than they both working together . what time would they take to do the work together ? | let a and be together take x hours to complete the work . then , a alone takes ( x + 8 ) hrs and b alone takes ( x + 9 / 2 ) hrs to complete the work . then , 1 / ( x + 8 ) + 1 / ( x + 9 / 2 ) = 1 / x , 1 / ( x + 8 ) + 2 / ( 2 x + 9 ) = 1 / x x ( 4 x + 25 ) = ( x + 8 ) ( 2 x + 9 ) 2 x ^ 2 = 72 , x ^ 2 = 36 , x = 6 corr... | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1 : 2",
"2 : 1",
"2 : 3",
"3 : 2"
]
} | [
"D"
] | six women can do a work in 10 days . ten men can complete the same work in 4 days . what is the ratio between the capacity of a man and a woman ? | "explanation : ( 6 ã — 10 ) women can complete the work in 1 day . â ˆ ´ 1 woman ' s 1 day ' s work = 1 / 60 ( 10 ã — 4 ) men can complete the work in 1 day . â ˆ ´ 1 man ' s 1 day ' s work = 1 / 40 so , required ratio = 1 / 60 : 1 / 40 = 3 : 2 answer : d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"50 kg",
"60 kg",
"70 kg",
"80 kg"
]
} | [
"B"
] | a boat having a length 3 m and breadth 2 m is floating on a lake . the boat sinks by 1 cm when a man gets into it . the mass of the man is : | explanation : in this type of question , first we will calculate the volume of water displaces then will multiply with the density of water . volume of water displaced = 3 * 2 * 0.01 = 0.06 m cube mass of man = volume of water displaced * density of water = 0.06 * 1000 = 60 kg option b | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"6 hours",
"5 hours",
"5.5 hours",
"8 hours"
]
} | [
"C"
] | a truck covers a distance of 296 km at a certain speed in 8 hours . how much time would a car take at an average speed which is 18 kmph more than that of the speed of the truck to cover a distance which is 6.5 km more than that travelled by the truck ? | explanation : speed of the truck = distance / time = 296 / 8 = 37 kmph now , speed of car = ( speed of truck + 18 ) kmph = ( 37 + 18 ) = 55 kmph distance travelled by car = 296 + 6.5 = 302.5 km time taken by car = distance / speed = 302.5 / 55 = 5.5 hours . answer – c | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"290 / 289",
"26 / 25",
"290 / 90",
"290 / 19"
]
} | [
"B"
] | product of two natural numbers is 5 . then , the sum of reciprocals of their squares is | "explanation : if the numbers are a , b , then ab = 5 , as 17 is a prime number , so a = 1 , b = 5 . 1 / a 2 + 1 / b 2 = 1 / 1 ( 2 ) + 1 / 5 ( 2 ) = 26 / 25 option b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"62 kg",
"60 kg",
"70 kg",
"72 kg"
]
} | [
"D"
] | the average weight of 5 students decreases by 4 kg when one of them weighing 92 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 = 4 kg = > ( 92 - x ) / 5 = 4 = > x = 72 answer : d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1.6 km",
"2 km",
"3.6 km",
"6.75 km"
]
} | [
"D"
] | the speed of a boat in still water is 24 km / hr and the rate of current is 3 km / hr . the distance travelled downstream in 15 minutes is | "explanation : speed downstreams = ( 24 + 3 ) kmph = 27 kmph . distance travelled = ( 27 x 15 / 60 ) km = 6.75 km option d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"3.5 : 6",
"14 : 24",
"7 : 12",
"2.3 : 4"
]
} | [
"C"
] | the ratio of two quantities is 7 to 12 . if each of the quantities is divided by 3 , what is the ratio of these 2 new quantities ? | "if both sides of a ratio are divided by the same number there is no change in the ratio . 5 : 6 means 7 x : 12 x . . . the ratio starts as 7 / ( 1 ) : 12 / ( 1 ) . so when you diveide by three it becomes 7 / ( 3 ) : 12 / ( 3 ) . . so if the xs are equal the ratio does not change . . answer : c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 880",
"rs . 890",
"rs . 895",
"rs . 2100"
]
} | [
"D"
] | if the compound interest on a certain sum of money for 7 years at 10 % per annum be rs . 993 , what would be the simple interest ? | "let p = principal a - amount we have a = p ( 1 + r / 100 ) 3 and ci = a - p atq 993 = p ( 1 + r / 100 ) 3 - p ? p = 3000 / - now si @ 10 % on 3000 / - for 7 yrs = ( 3000 x 10 x 7 ) / 100 = 2100 / - answer : d ." | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1",
"0",
"2",
"- 1"
]
} | [
"C"
] | a set s = { x , - 8 , - 5 , - 2 , 2 , 6 , 9 , y } with elements arranged in increasing order . if the median and the mean of the set are the same , what is the value of | x | - | y | ? | "median of the set = ( - 2 + 2 ) / 2 = 0 as per statement , mean of the set = 0 mean of the set | y | - | x | + 17 - 15 = 0 ( where x is negative n y is positive ) | y | - | x | = - 2 so the absolute difference between two numbers is 2 answer c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"12.5 %",
"40 %",
"120 %",
"125 %"
]
} | [
"C"
] | the ratio 6 : 5 expressed as a percent equals | "solution 6 : 5 = 6 / 5 = ( 6 / 5 x 100 ) % . = 120 % . answer c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"77.77 %', '",
"75 %', '",
"67.5 %', '",
"87.5 %', '"
]
} | [
"B"
] | the volume of the sphere q is ( 37 / 64 ) % less than the volume of sphere p and the volume of sphere r is ( 19 / 27 ) % less than that of sphere q . by what is the surface area of sphere r less than the surface area of sphere p ? | explanation : let the volume of sphere p be 64 parts . therefore volume of sphere q = > 64 − ( 37 / 64 ) % of 64 . = > 64 − 37 = 27 parts . the volume of r is : - = > 27 − ( 19 / 27 ) × 27 . = > 27 − 19 = 8 parts . volume ratio : = > p : q : r = 64 : 27 : 8 . radius ratio : = > p : q : r = 4 : 3 : 2 . the surface area ... | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"31 , 20",
"30 , 19",
"29 , 18",
"28 , 17"
]
} | [
"D"
] | the difference of two numbers is 11 and one fifth of their sum is 9 . the numbers are : | "x − y = 11 , x + y = 5 × 9 x − y = 11 , x + y = 45 , y = 17 , x = 28 answer : d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1100",
"800",
"1400",
"1200"
]
} | [
"C"
] | a , band c enter into partnership . a invests 3 times as much as b and b invests two - third of what c invests . at the end of the year , the profit earned is rs . 7700 . what is the share of b ? | "let c ' s capital = rs . x . then , b ' s capital = rs . ( 2 / 3 ) x a ’ s capital = rs . ( 3 x ( 2 / 3 ) . x ) = rs . 2 x . ratio of their capitals = 2 x : ( 2 / 3 ) x : x = 6 : 2 : 3 . hence , b ' s share = rs . ( 7700 x ( 2 / 11 ) ) = rs . 1400 . answer is c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"450",
"451",
"460",
"462"
]
} | [
"D"
] | find the number which is nearest to 457 and is exactly divisible by 11 . | "solution on dividing 457 by 11 , remainder is 6 . required number is either 451 or 462 nearest to 456 is = 462 . answer d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"20.0015",
"20.0105",
"20.0115",
"20.0114"
]
} | [
"D"
] | 12.1212 + 17.0005 - 9.1103 = ? | solution given expression = ( 12.1212 + 17.0005 ) - 9.1103 = ( 29.1217 - 9.1103 ) = 20.0114 . answer d | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1.9432",
"1.0025",
"1.5693",
"1.0266"
]
} | [
"A"
] | given that 268 x 74 = 19432 , find the value of 2.68 x . 74 . | "solution sum of decimals places = ( 2 + 2 ) = 4 . therefore , = 2.68 × . 74 = 1.9432 answer a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"144 m 2",
"120 m 2",
"108 m 2",
"158 m 2"
]
} | [
"A"
] | the floor of a rectangular room is 20 m long and 12 m wide . the room is surrounded by a veranda of width 2 m on all its sides . the area of the veranda is : | "area of the outer rectangle = 24 ã — 16 = 384 m 2 area of the inner rectangle = 20 ã — 12 = 240 m 2 required area = ( 304 â € “ 180 ) = 144 m 2 answer a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"7.2 kg .",
"10.8 kg .",
"12.4 kg .",
"18.0 kg"
]
} | [
"B"
] | if the weight of 13 meters long rod is 23.4 kg . what is the weight of 6 meters long rod ? | "answer ∵ weight of 13 m long rod = 23.4 kg ∴ weight of 1 m long rod = 23.4 / 13 kg ∴ weight of 6 m long rod = 23.4 x 6 / 13 = 10.8 kg option : b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"6",
"4",
"8",
"8"
]
} | [
"A"
] | if x and y are the two digits of the number 653 xy such that this number is divisible by 80 , then x + y = ? | "80 = 2 x 5 x 8 since 653 xy is divisible by 2 and 5 both , so y = 0 . now , 653 x is divisible by 8 , so 13 x should be divisible by 8 . this happens when x = 6 . x + y = ( 6 + 0 ) = 6 . answer : a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 18.95",
"rs 16",
"rs . 21",
"rs . 25.71"
]
} | [
"C"
] | the average earning of a mechanic for the first - 4 days of a week is rs . 18 and for the last 4 days is rs . 22 . if he earns rs . 13 on the fourth day , his average earning for the whole week is ? | answer total earning for the week = sum of earning of first four days + sum of earning of last four days - earning of 4 th day = 4 x 18 + 4 x 22 - 13 = rs . 147 â ˆ ´ average earning = 147 / 7 = rs . 21 correct option : c | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1",
"2",
"4",
"6"
]
} | [
"C"
] | what is the unit digit in the product ( 3 ^ 68 x 6 ^ 59 x 7 ^ 71 ) ? | "unit digit in 3 ^ 4 = 1 = > unit digit in ( 3 ^ 4 ) ^ 16 = 1 therefore , unit digit in 3 ^ 65 = unit digit in [ ( 3 ^ 4 ) ^ 16 x 3 ] = ( 1 x 3 ) = 3 unit digit in 6 ^ 59 = 6 unit digit in 7 ^ 4 = 1 = > unit digit in ( 7 ^ 4 ) ^ 17 is 1 unit digit in 7 ^ 71 = unit digit in [ ( 7 ^ 4 ) ^ 17 x 7 ^ 3 ] = ( ( 1 x 3 ) = 3 t... | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"58 kg",
"60 kg",
"64 kg",
"70 kg"
]
} | [
"C"
] | zinc and copper are melted together in the ratio 9 : 11 . what is the weight of melted mixture , if 28.8 kg of zinc has been consumed in it ? | sol . for 9 kg zinc , mixture melted = ( 9 + 11 ) kg . for 28.8 kg zinc , mixture , melted = [ 20 / 9 x 28.8 ] kg = 64 kg . answer c | MathQA |
{
"label": [
"A",
"B",
"D",
"E"
],
"text": [
"1",
"2",
"3 / 7",
"3 / 4"
]
} | [
"D"
] | joe has candys on his pocket , 4 of those candies have lemon flavor , and 3 have caramel flavor . if joe take one , what is the probability that he picks one caramel flavor ? | the total number of candies is 7 and the number of candies with lemon flavor is 3 then , in one chance the probability to pick one candie with lemon flavor is 3 / 7 answer d | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"- 12",
"- 3",
"0",
"2"
]
} | [
"C"
] | if x and y are integers such that | y + 3 | ≤ 3 and 2 y – 3 x + 6 = 0 , what is the least possible value w of the product xy ? | "how to deal with inequalities involving absolute values ? first example shows us the so callednumber case in this case we have | y + 3 | ≤ 3 which is generalized | something | ≤ some number . first we solve as if there were no absolute value brackets : y + 3 ≤ 3 y ≤ 0 so y is 0 or negative second scenario - remove the... | MathQA |
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