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": [
"0.012",
"0.12",
"0.0012",
"0.00012"
]
} | [
"C"
] | find the quotient : 0.0204 / 17 | 204 / 17 = 12 . dividend contains 4 places of decimal . 0.2040 / 17 = 0.0012 . answer is c . | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"8 %",
"1 %",
"20 %",
"80 %"
]
} | [
"C"
] | the income of a broker remains unchanged though the rate of commission is increased from 4 % to 5 % . the percentage of slump in business is : | "explanation : let the business value changes from x to y . then , 4 % of x = 5 % of y or 4 / 100 Γ x = 5 / 100 Γ y or y = 4 / 5 x change in business = ( x β 4 / 5 x ) = 1 / 5 x percentage slump in business = ( 1 / 5 x Γ 1 / x Γ 100 ) % correct option : c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
". 9",
". 09",
". 009",
". 0009"
]
} | [
"A"
] | . 009 / ? = . 01 | "let . 009 / x = . 01 ; then x = . 009 / . 01 = . 9 / 1 = . 9 answer is a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 15,000",
"rs . 15,500",
"rs . 15,600",
"rs . 28,875"
]
} | [
"D"
] | the length of a room is 5.5 m and width is 3.75 m . find the cost of paying the floor by slabs at the rate of rs . 1400 per sq . metre . | "solution area of the floor = ( 5.5 x 3.75 ) m Β² = 20.635 m Β² cost of paying = rs . ( 1400 x 20.625 ) = rs . 28875 . answer d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"12 kg",
"90 kg",
"72 kg",
"96 kg"
]
} | [
"B"
] | a boat having a length 3 m and breadth 2 m is floating on a lake . the boat sinks by 1.5 cm when a man gets on it . the mass of man is | "solution volume of water displaced = ( 3 x 2 x 0.015 ) m 3 = 0.09 m 3 . mass of man = volume of water displaced Γ density of water = ( 0.09 Γ 1000 ) kg = 90 kg . answer b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1",
"63",
"66",
"67"
]
} | [
"C"
] | what will be the reminder when ( 67 ^ 67 + 67 ) is divided by 68 ? | "( x ^ n + 1 ) will be divisible by ( x + 1 ) only when n is odd ; ( 67 ^ 67 + 1 ) will be divisible by ( 67 + 1 ) ; ( 67 ^ 67 + 1 ) + 66 when divided by 68 will give 66 as remainder . correct option : c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"230 m",
"140 m",
"160 m",
"170 m"
]
} | [
"D"
] | a goods train runs at the speed of 72 kmph and crosses a 350 m long platform in 26 seconds . what is the length of the goods train ? | explanation : speed = [ 72 x ( 5 / 18 ) ] m / sec = 20 m / sec . time = 26 sec . let the length of the train be x metres . then , [ ( x + 350 ) / 26 ] = 20 = > x + 350 = 520 = > x = 170 . answer : d | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"4.37 %",
"5 %",
"6.154 %",
"8.75 %"
]
} | [
"C"
] | the population of a town increased from 1 , 62,500 to 2 , 62,500 in a decade . the average percent increase of population per year is : | "solution increase in 10 year = ( 262500 - 162500 ) = 100000 . increase % = ( 100000 / 162500 x 100 ) % = 61.54 % Γ’ Λ Β΄ required average = ( 61.54 / 10 ) % = 6.154 % answer c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"10 hours",
"12 hours",
"14 hours",
"27 hours"
]
} | [
"D"
] | in a river flowing at 2 km / hr , a boat travels 72 km upstream and then returns downstream to the starting point . if its speed in still water be 6 km / hr , find the total journey time . | explanation : speed of the boat = 6 km / hr speed downstream = ( 6 + 2 ) = 8 km / hr speed upstream = ( 6 - 2 ) = 4 km / hr distance travelled downstream = distance travelled upstream = 72 km total time taken = time taken downstream + time taken upstream = ( 72 / 8 ) + ( 72 / 4 ) = 27 hr . answer : option d | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"456 kms",
"482 kms",
"552 kms",
"556 kms"
]
} | [
"C"
] | the speed of a car increases by 2 kms after every one hour . if the distance travelling in the first one hour was 35 kms . what was the total distance travelled in 12 hours ? | "explanation : total distance travelled in 12 hours = ( 35 + 37 + 39 + . . . . . upto 12 terms ) this is an a . p with first term , a = 35 , number of terms , n = 12 , d = 2 . required distance = 12 / 2 [ 2 Γ 35 + { 12 - 1 ) Γ 2 ] = 6 ( 70 + 23 ) = 552 kms . answer : c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"33.5",
"33.5",
"34.25",
"35"
]
} | [
"C"
] | the average score of a cricketer for 10 matches is 38.9 runs . if the average for the first 6 matches is 42 , then find the average for the last 4 matches . | solution required average = ( 38.9 x 10 ) - ( 42 x 6 ) / 4 = 137 / 4 = 34.25 answer c | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"9 min",
"8 min",
"4 min",
"6 min"
]
} | [
"B"
] | two pipes a and b can fill a tank in 12 and 24 minutes respectively . if both the pipes are used together , how long will it take to fill the tank ? | "explanation : tank can be filled by pipe a in 12 minutes and pipe b in 24 minutes . = > part filled by a in 1 minute = 1 / 12 = > part filled by b in 1 minute = 1 / 24 = > part filled by both in 1 minute = 1 / 12 + 1 / 24 = 3 / 24 = 1 / 8 time taken to fill the entire tank = 8 minutes answer b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"200",
"225",
"93.75",
"320"
]
} | [
"C"
] | if 16 % of 40 % of a number is 6 , then the number is | explanation : let 16 / 100 Γ 40 / 100 Γ a = 6 a = 6 Γ 100 Γ 100 / 16 Γ 40 = 93.75 correct option : c | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"2160",
"2350",
"2000",
"2300"
]
} | [
"A"
] | after spending rs . 5000 on rent , rs . 1500 on milk , rs . 4500 on groceries , rs . 2500 on childrens education rs . 2000 on petrol and rs . 3940 on miscellaneous expenses , mr . kishore saved 10 % of his monthly salary . how much did he save in rs . ? | "explanation : total exp = 5000 + 1500 + 4500 + 2500 + 2000 + 3940 = 19440 exp in % = 100 - 10 = 90 % , 19440 = 90 % saving = 10 % = 19440 x 10 / 90 = rs . 2160 answer : a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"10.22 %",
"20.22 %",
"21.22 %",
"20 %"
]
} | [
"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 10 % 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 90 kg ; profit : ( 120 - 90 ) / 90 * 100 = 20 % answer : d ." | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"250",
"450",
"750",
"800"
]
} | [
"B"
] | a and b undertake to do a piece of work for rs . 1200 . 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 b . | "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 β s share = rs . ( 1200 * 4 / 8 ) = rs . 600 , b ' s share = rs . ( 1200 * 3 / 8 ) = rs . 450 c ' s share = rs . [ 1200 - ( 300 + 225 Β» ) = rs . 150 . answer is b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"67.4 kg",
"57.75 kg",
"58.85 kg",
"49.4 kg"
]
} | [
"C"
] | the average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 65 kg . what is the correct weight ? | "actual total weight is ( 20 Γ£ β 58.4 - 56 + 65 ) = 1177 kgs actual average weight is 1177 / 20 = 58.85 kgs answer is c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"2",
"3",
"4",
"11"
]
} | [
"D"
] | the average ( arithmetic man ) of 3 integers a , b , and c is exactly 4 times 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 = 4 b - - > since a = 0 , then ( 0 + b + c ) / 3 = 4 b - - > c = 11 b - - > c / b = 11 . answer : d . | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"15",
"18",
"20",
"26"
]
} | [
"D"
] | find the average of all the numbers between 17 and 32 which are divisible by 3 . | "sol . average = ( 21 + 24 + 27 + 30 / 4 ) = 102 / 4 = 25.5 answer d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"60",
"45",
"50",
"48"
]
} | [
"D"
] | a ratio between two numbers is 8 : 9 and their l . c . m . is 432 . the first number is | sol . let the required numbers be 8 x and 9 x . then , their l . c . m . is 72 x . β΄ 72 x = 432 β x = 6 . hence , the first number is 48 . answer d | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"32 m 3",
"36 m 3",
"40 m 3",
"44 m 3"
]
} | [
"D"
] | a circular well with a diameter of 2 metres , is dug to a depth of 14 metres . what is the volume of the earth dug out ? | "sol . volume = Ο r 2 h = ( 22 / 7 x 1 x 1 x 14 ) m 3 = 44 m 3 . answer d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"17.64 %",
"33.33 %",
"40 %",
"75 %"
]
} | [
"A"
] | a rectangle having length 140 cm and width 40 cm . if the length of the rectangle is increased by thirty percent then how much percent the breadth should be decreased so as to maintain the same area . | explanation : solution : ( 30 / ( 140 + 30 ) * 100 ) % = 17.64 % answer : a | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 432",
"rs . 425",
"rs . 412",
"rs . 442"
]
} | [
"B"
] | the true discount on a bill of rs . 2360 is rs . 360 . what is the banker ' s discount ? | "explanation : f = rs . 2360 td = rs . 360 pw = f - td = 2360 - 360 = rs . 2000 true discount is the simple interest on the present value for unexpired time = > simple interest on rs . 2000 for unexpired time = rs . 360 banker ' s discount is the simple interest on the face value of the bill for unexpired time = simple interest on rs . 2360 for unexpired time = 360 / 2000 Γ 2360 = 0.18 Γ 2160 = rs . 425 answer : option b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"30 %",
"70 %",
"80 %",
"87.5 %"
]
} | [
"D"
] | in an examination , the percentage of students qualified to the number of students appeared from school a is 70 % . in school b , the number of students appeared is 20 % more than the students appeared from school a and the number of students qualified from school b is 50 % more than the students qualified from school a . what is the percentage of students qualified to the number of students appeared from school b ? | solution let number of students appeared from school a = 100 . then , number of students qualified from school a = 70 . number of students appeared from school b = 120 . number of students qualified from school b = [ 150 / 100 x 70 ] = 105 . required percentage = [ 105 / 120 x 100 ] % = 87.5 % answer d | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"52 kmph .",
"62 kmph .",
"72 kmph .",
"92 kmph ."
]
} | [
"D"
] | a man sitting in a train which is travelling at 20 kmph observes that a goods train , travelling in opposite direction , takes 9 seconds to pass him . if the goods train is 280 m long , find its speed ? | "solution relative speed = ( 280 / 9 ) m / sec = ( 280 / 9 x 18 / 5 ) = 112 kmph . speed of the train = ( 112 - 20 ) kmph = 92 kmph . answer d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"0",
"4905",
"49050",
"490500"
]
} | [
"D"
] | the difference between the place values of two fives in the numerical 86510529 is | "required difference = ( 500000 - 500 ) = 490500 . answer is d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"120 km",
"360 km",
"480 km",
"500 km"
]
} | [
"C"
] | bombay express left delhi for bombay at 14.30 hrs , travelling at a speed of 60 kmph and rajdhani express left delhi for bombay on the same day at 16.30 hrs , travelling at a speed of 80 kmph . how far away from delhi will the two trains meet ? | sol . suppose they meet x hours after 14.30 hrs . then , 60 x = 80 ( x - 2 ) or x = 8 . β΄ required distance = ( 60 x 8 ) km = 480 km . answer c | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"7580",
"7960",
"8290",
"6048"
]
} | [
"D"
] | a leak in the bottom of a tank can empty the full tank in 7 hours . an inlet pipe fills water at the rate of 6 litres a minute . when the tank is full , the inlet is opened and due to the leak , the tank is empty in 12 hours . how many litres does the cistern hold ? | "solution work done by the inlet in 1 hour = ( 1 / 7 - 1 / 12 ) = 5 / 84 work done by the inlet in 1 min . = ( 5 / 84 Γ 1 / 60 ) = 0.000992 volume of 0.000992 part = 6 litres . therefore , volume of whole = ( ( 1 / 0.000992 ) Γ 6 ) βΉ = βΊ 6048 litres . answer d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"35.24",
"36.14",
"36.24",
"36.44"
]
} | [
"D"
] | the mean of 50 observations was 36 . it was found later that an observation 45 was wrongly taken as 23 . the corrected new mean is | "solution correct sum = ( 36 x 50 + 45 - 23 ) = 1822 . Γ’ Λ Β΄ correct mean = 1822 / 50 = 36.44 . answer d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1694 m 2', '",
"1700 m 2', '",
"1598 m 2', '",
"1500 m 2', '"
]
} | [
"A"
] | a circular grass lawn of 35 metres in radius has a path 7 metres wide running around it on the outside . find the area of path . | radius of a circular grass lawn ( without path ) = 35 m β΄ area = Ο r 2 = Ο ( 35 ) 2 radius of a circular grass lawn ( with path ) = 35 + 7 = 42 m β΄ area = Ο r 2 = Ο ( 42 ) 2 β΄ area of path = Ο ( 42 ) 2 β Ο ( 35 ) 2 = Ο ( 422 β 352 ) = Ο ( 42 + 35 ) ( 42 β 35 ) answer a | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1 : 2",
"5 : 9",
"2 : 1",
"11 : 24"
]
} | [
"C"
] | the compounded ratio of ( 2 : 3 ) , ( 6 : 11 ) and ( 11 : 2 ) is : | answer : option c 2 / 3 : 6 / 11 : 11 / 2 = 2 : 1 | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"2 kg",
"2.4 kg",
"3.12 kg",
"10 kg"
]
} | [
"C"
] | fresh grapes contain 90 % by weight while dried grapes contain 20 % water by weight . what is the weight of dry grapes available from 25 kg of fresh grapes ? | the weight of non - water in 25 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 25 Γ’ Λ β 0.1 = x Γ’ Λ β 0.8 - - > x = 3.12 answer : c . | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"2 %",
"4 %",
"6 %",
"8 %"
]
} | [
"B"
] | 2 is what percent of 50 | "explanation : 2 / 50 * 100 = 1 / 25 * 100 = 4 % option b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"3990",
"1540",
"1995",
"3672"
]
} | [
"B"
] | in how many ways can 21 books on english and 19 books on french be placed in a row on a shelf so that two books on french may not be together ? | "in order that two books on french are never together , we must place all books as under x e x e x e x e x e . . . . . x e x where e denotes the position of an english book and x that of a french book . since there are 21 books on english , the number of places marked x are therefore , 22 . now , 19 places out of 22 can be chosen in 22 c 19 = 22 c 3 = ( 22 x 21 x 20 ) / ( 3 x 2 x 1 ) = 1540 ways answer b ." | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 31",
"rs . 32.10",
"rs . 40.40",
"rs . 64.10"
]
} | [
"D"
] | what will be the difference between simple interest and compound interest @ 10 % per annum on a sum of rs . 1000 after 4 years ? | solution s . i . = rs ( 1000 x 10 x 4 / 100 ) = rs . 400 . c . i . = rs . [ 1000 x ( 1 x 10 / 100 ) 4 - 1000 ] = rs . 464.10 β΄ difference = rs . ( 464.10 - 400 ) = rs . 64.10 answer d | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"6 km",
"7 km",
"8 km",
"9 km"
]
} | [
"A"
] | two men start together to walk a certain distance , one at 4 kmph and another at 3 kmph . the former arrives half an hour before the latter . find the distance . | let the distance be x km . then , x / 3 - x / 4 = 1 / 2 ( 4 x - 3 x ) / 12 = 1 / 2 x = 6 km answer : a | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"192",
"200",
"196",
"198"
]
} | [
"A"
] | the citizens of planet nigiet are 8 fingered and have thus developed their decimal system in base 8 . a certain street in nigiet contains 1000 buildings numbered 1 to 1000 in base 8 . how many 3 s are used in numbering these buildings ? express your answer in base 10 | "explanation : number 3 in 1 - 100 comes 20 times . 101 - 200 - > 20 times 201 - 300 - > 20 times 301 - 400 - > 120 times 401 - 500 - > 20 times 501 - 600 - > 20 times 601 - 700 - > 20 times 701 - 800 - > 20 times 801 - 900 - > 20 times 901 - 1000 - > 20 times total times : 300 times ( any no . from 1 to 9 except 0 will occur 300 times ) 8 based planet . . then 3 * 8 ( 2 ) + 0 * 8 ( 1 ) + 0 * 8 ( 0 ) = 192 answer : a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"9",
"6",
"4",
"3"
]
} | [
"D"
] | if 3 x β 5 y = 5 and x / x + y = 5 / 7 , then what is the value of x β y ? | 3 x β 5 y = 5 . . . ( i ) and xx + y = 57 xx + y = 57 β 7 x = 5 x + 5 y β 2 x = 5 y . . . ( ii ) from ( i ) and ( ii ) , x = 5 and y = 2 β΄ x β y = 3 answer d | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"4500",
"7500",
"5000",
"8000"
]
} | [
"D"
] | the difference between compound interest and simple interest on a certain amount of money at 5 % per annum for 2 years is 20 . 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 20 , the sum = 400 Γ 20 = 8000 answer d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"25 %",
"9.09 %",
"40 %",
"75 %"
]
} | [
"B"
] | a rectangle having length 150 cm and width 40 cm . if the length of the rectangle is increased by fifteen percent then how much percent the breadth should be decreased so as to maintain the same area . | "explanation : solution : ( 15 / ( 150 + 15 ) * 100 ) % = 9.09 % answer : b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 40000",
"rs . 36000",
"rs . 50000",
"rs . 45000"
]
} | [
"A"
] | ajay spends 45 % of his monthly income on household items , 25 % of his monthly income on buying cloths , 7.5 % of his monthly income on medicines and saves the remaining amount which is rs . 9000 . find his monthly income . | "let the monthly income of ajay be rs . x savings of ajay = x - ( 45 + 25 + 7.5 ) / 100 * x = 22.5 / 100 x 22.5 / 100 x = 9000 x = 40000 . answer : a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"0.44202",
"0.44204",
"0.442022",
"0.442025"
]
} | [
"D"
] | the average of numbers 0.44204 , 0.44203 , 0.44202 and 0.44201 is ? | "answer average = ( 0.44204 + 0.44203 + 0.44202 + 0.44201 ) / 4 = 1.7681 / 4 = 0.442025 correct option : d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"$ 1166",
"$ 1168",
"$ 1166.6",
"$ 1167"
]
} | [
"D"
] | 3 people decided to put a down payment on a car for 3500 dollars . how much money do they each have to pay , given that that they have to pay the same amount , and they can not use any bills below $ 1 ? | to keep the amount exact when dividing for 3 , we have to work backwards through division . dividing 3500 by 3 will give us 1166.66 then by subtracting . 66 , we get 1166 , and we multiply it by 3 to get 3498 . to get enough for the down payment , we add 3 to 3498 . dividing the result by 3 gives us our answer . correct option : d | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"15.502 %",
"25.7014 %",
"12.502 %",
"21.7014 %"
]
} | [
"D"
] | farm tax is levied on the 60 % of the cultivated land . the tax department collected total $ 3840 through the farm tax from the village of mr . willam . mr . willam paid only $ 500 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is : | "only trick n this question is to ignore 60 % information as farm tax is levied uniformly in the village and that includes mr william ' s land . what percentage of tax mr william paid ? this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to ( 500 / 3840 ) x 100 = 13.02083 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 13.02083 % x ( 100 / 60 ) = 21.7014 % and the answer is not there in the options . the correct answer is ( d ) ." | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"20 %",
"18 %",
"24 %",
"64 %"
]
} | [
"C"
] | if the area of a circle decreases by 42 % , 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 42 ) % = ( 100 β 10 β 58 ) % = 100 - 76 = 24 % answer c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 960",
"rs . 840",
"rs . 520",
"rs . 760"
]
} | [
"C"
] | the banker Γ’ β¬ β’ s gain on a sum due 3 years hence at 10 % per annum is rs . 120 . the banker Γ’ β¬ β’ s discount is | "solution t . d = ( b . g x 100 / r x t ) = rs . ( 120 x 100 / 10 x 3 ) = rs . 400 . b . d = rs ( 400 + 120 ) = rs . 520 . answer c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"37.5 %",
"38.5 %",
"42 %",
"27.5 %"
]
} | [
"A"
] | the cost price of an article is 64 % of the marked price . calculate the gain percent after allowing a discount of 12 % . | "sol . let marked price = rs . 100 . then , c . p . = rs . 64 . s . p = rs . 88 . β΄ gain % = [ 24 / 64 * 100 ] % = 37.5 % . answer a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"16.2",
"12",
"5",
"500"
]
} | [
"B"
] | 45 x ? = 60 % of 900 | "answer let 45 x a = ( 60 x 900 ) / 100 β΄ a = ( 60 x 9 ) / 45 = 12 correct option : b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"350 m",
"240 m",
"440 m",
"640 m"
]
} | [
"D"
] | a thief is spotted by a policeman from a distance of 160 meters . when the policeman starts the chase , the thief also starts running . if the speed of the thief be 8 km / hr and that of the policeman 10 km / hr , how far the thief will have run before he is overtaken ? | "relative speed of the policeman = ( 10 - 8 ) km / hr = 2 km / hr . time taken by police man to cover ( 160 m / 1000 ) x 1 / 2 hr = 2 / 25 hr . in 2 / 25 hr / s , the thief covers a distance of 8 x 2 / 25 km = 16 / 25 km = 640 m answer is d ." | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"8000",
"10000",
"12000",
"9000"
]
} | [
"A"
] | arun borrowed a sum of money from jayant at the rate of 8 % per annum simple interest for the first 4 years , 10 % per annum for the next 6 years and 12 % per annum for the period beyond 10 years . if he pays a total of 12160 as interest only at the end of 15 years , how much money did he borrow ? | let the principal = p then p Γ 8 Γ 4 / 100 + p Γ 10 Γ 6 / 100 + p Γ 12 Γ 5 / 100 = 12160 β 152 p = 12160 Γ 100 or 12160 Γ 100 / 152 = 8000 answer a | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"12.50 %",
"27.50 %",
"14 %",
"14.50 %"
]
} | [
"B"
] | an uneducated retailer marks all his goods at 50 % above the cost price and thinking that he will still make 15 % profit , offers a discount of 15 % on the marked price . what is his actual profit on the sales ? | "sol . let c . p . = rs . 100 . then , marked price = rs . 150 . s . p . = 85 % of rs . 150 = rs . 127.5 . β΄ gain % = 27.50 % . answer b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"11 kmph",
"12 kmph",
"18 kmph",
"17 kmph"
]
} | [
"C"
] | a man ' s speed with the current is 20 kmph and speed of the current is 1 kmph . the man ' s speed against the current will be | explanation : speed with current is 20 , speed of the man + it is speed of the current speed in s Ι΅ ll water = 20 - 1 = 19 now speed against the current will be speed of the man - speed of the current = 19 - 1 = 18 kmph answer : c | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"120 %",
"0.120 %",
"1.20 %",
"0.209 %"
]
} | [
"A"
] | 1.20 can be expressed in terms of percentage as | "explanation : while calculation in terms of percentage we need to multiply by 100 , so 1.20 * 100 = 120 answer : option a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"31 kg",
"32 kg",
"33 kg",
"35 kg"
]
} | [
"D"
] | 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 45 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 = ( 45 x 2 ) = 90 β¦ . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 170 β¦ . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 35 . b β s weight = 35 kg . answer : d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"64",
"72",
"80",
"85"
]
} | [
"D"
] | a cricketer whose bowling average is 12.4 runs per wicket takes 5 wickets for 26 runs and thereby decreases his average by 0.4 . the number of wickets taken by him till the last match was : | "let the number of wickets taken till the last match be x . then , 12.4 x + 26 / x + 5 = 12 β 12.4 x + 26 = 12 x + 60 β 0.4 x = 34 β x = 34 β 0.4 = 340 β 4 = 85 . answer d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"151",
"149",
"151.25",
"148"
]
} | [
"C"
] | the mean of 20 values was 150 . it was detected on rechecking that one value 160 was wrongly copied as 135 for the computation of the mean . find the correct mean . | corrected mean = 150 Γ 20 β 135 + 160 / 20 = 3000 β 135 + 160 / 20 = 3025 / 20 = 151.25 answer c | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 120",
"rs . 160",
"rs . 240",
"rs . 300"
]
} | [
"C"
] | a sum of rs . 1360 has been divided among a , b and c such that a gets of what b gets and b gets of what c gets . b β s share is : | "explanation let c β s share = rs . x then , b β s share = rs . x / 4 , a β s share = rs . ( 2 / 3 x x / 4 ) = rs . x / 6 = x / 6 + x / 4 + x = 13660 = > 17 x / 12 = 13660 = > 13660 x 12 / 17 = rs . 960 hence , b β s share = rs . ( 960 / 4 ) = rs . 240 . answer c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs 10",
"rs 20",
"rs 24",
"rs 28"
]
} | [
"B"
] | rs . 120 are divided among a , b , c such that a ' s share is rs . 20 more than b ' s and rs . 20 less than c ' s . what is b ' s share | explanation : let c = x . then a = ( x οΏ½ 20 ) and b = ( x οΏ½ 40 ) . x + x - 20 + x - 40 = 120 or x = 60 . a : b : c = 40 : 20 : 60 = 2 : 1 : 3 . b ' s share = rs . 120 * ( 1 / 6 ) = rs . 20 answer : b | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1 / 5",
"1 / 10",
"7 / 20",
"3 / 5"
]
} | [
"B"
] | 3 / 5 of all married couples have more than one child . 1 / 2 of all married couples have more than 3 children . what fraction of all married couples have 2 or 3 children ? | "plug in simple numbers . take 100 couples for example . 3 / 5 of 100 couples have more than one child = 60 couples . 1 / 2 of 100 couples have more than 3 kids = 50 couples . this implies that 50 couples are a subset of 60 couples and the complement of 60 couples within those 100 couples , which equals 40 couples have either one or no kids at all . we need to find couples that have 2 or 3 kids , so essentially , it is 60 - 50 = 10 . fraction will be 10 / 100 = 1 / 10 . option b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"7450",
"14900",
"7400",
"6875"
]
} | [
"D"
] | vijay sells a cupboard at 12 % below cost price . had he got rs . 1650 more , he would have made a profit of 12 % . what is the cost price of the cupboard ? | "explanation : cost price = 1650 / ( 0.12 + 0.12 ) = 2086 / 0.24 = rs . 6875 answer d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"132 Β°",
"228 Β°",
"156 Β°",
"224 Β°"
]
} | [
"A"
] | the ratio of the adjacent angles of a parallelogram is 4 : 11 . 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 Β° given so , 4 x + 11 x = 180 Β° or , 15 x = 180 Β° or , x = 12 Β° hence the angles of the parallelogram are 48 Β° and 132 Β° further it is given we know sum of all the four angles of a quadrilateral is 360 Β° so , 5 y + 6 y + 7 y + 12 y = 360 Β° or , 5 y + 6 y + 7 y + 12 y = 360 Β° or , 30 y = 360 Β° or , y = 12 Β° hence the angles of the quadrilateral are 60 Β° , 72 , 84 Β° and 144 Β° will be 48 Β° + 84 Β° = 132 Β° answer : a | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs 10123.20",
"rs 10123.30",
"rs 10123.40",
"rs 10123.50"
]
} | [
"A"
] | what will be the compound interest on rs . 25000 after 3 years at the rate of 12 % per annum | "explanation : ( 25000 Γ ( 1 + 12 / 100 ) 3 ) = > 25000 Γ 28 / 25 Γ 28 / 25 Γ 28 / 25 = > 35123.20 so compound interest will be 35123.20 - 25000 = rs 10123.20 option a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"10 : 20",
"2 : 4",
"1 : 2",
"4 : 8"
]
} | [
"C"
] | if there are 10 apples and 20 oranges , what is the ratio of apples to oranges ? | a ratio should be reduced to the lowest common denominator . 10 : 20 means 10 x : 20 x which can be written as 1 ( 10 ) : 2 ( 10 ) . . . answer : c | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"94",
"99",
"26",
"73"
]
} | [
"A"
] | what two - digit number is less than the sum of the square of its digits by 10 and exceeds their doubled product by 5 ? | "let the digits be x and y . the number would be 10 x + y . we are given that 2 xy + 5 = 10 x + y = x ^ 2 y ^ 2 - 10 thus 2 xy + 5 = x ^ 2 + y ^ 2 - 10 x ^ 2 + y ^ 2 - 2 xy = 15 ( x - y ) ^ 2 = 16 ( x - y ) = 4 or - 4 substituting the values of ( x - y ) in the equation 2 xy + 5 = 10 x + y x comes out to be 1 or 9 . . . thus the two numbers can be 15 or 94 thus the answer is a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"7580",
"7960",
"8290",
"1440"
]
} | [
"D"
] | a leak in the bottom of a tank can empty the full tank in 3 hours . an inlet pipe fills water at the rate of 6 litres a minute . when the tank is full , the inlet is opened and due to the leak , the tank is empty in 12 hours . how many litres does the cistern hold ? | "solution work done by the inlet in 1 hour = ( 1 / 3 - 1 / 12 ) = 1 / 4 work done by the inlet in 1 min . = ( 1 / 4 Γ 1 / 60 ) = 0.004167 volume of 0.004167 part = 6 litres . therefore , volume of whole = 0.004167 x 6 βΉ = βΊ 1440 litres . answer d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"6000",
"8000",
"8960",
"2000"
]
} | [
"C"
] | a courtyard is 24 meter long and 14 meter board is to be paved with bricks of dimensions 25 cm by 15 cm . the total number of bricks required is : | "explanation : number of bricks = courtyard area / 1 brick area = ( 2400 Γ£ β 1400 / 25 Γ£ β 15 ) = 8960 option c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"16000",
"18078",
"11076",
"11456"
]
} | [
"C"
] | a courtyard is 18 meter long and 12 meter board is to be paved with bricks of dimensions 15 cm by 13 cm . the total number of bricks required is : | "explanation : number of bricks = courtyard area / 1 brick area = ( 1800 Γ£ β 1200 / 15 Γ£ β 13 ) = 11076 option c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs 62.10",
"rs 63.10",
"rs 64.10",
"rs 65.10"
]
} | [
"C"
] | what will be the difference between simple and compound interest @ 10 % per annum on the sum of rs 1000 after 4 years | explanation : s . i . = 1000 β 10 β 4 / 100 = 400 c . i . = [ 1000 ( 1 + 10 / 100 ) 4 β 1000 ] = 464.10 so difference between simple interest and compound interest will be 464.10 - 400 = 64.10 option c | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 962",
"rs . 672",
"rs . 546",
"rs . 876"
]
} | [
"D"
] | the cost of the paint is rs . 36.50 per kg . if 1 kg of paint covers 16 sq . ft , how much will it cost to paint outside of a cube having 8 feet each side | "explanation : surface area of a cube = 6 x 82 = 384 sq . ft quantity of paint required = ( 384 / 16 ) = 24 kg cost of painting = 36.5 x 24 = rs . 876 answer : d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"10.6 kg",
"10.8 kg",
"11 kg",
"13 kg"
]
} | [
"D"
] | the average weight of 19 students is 15 kg . by the admission of a new student the average weight is reduced to 14.9 kg . the weight of the new student is ? | "answer weight of new student = total weight of all 20 students - total weight of initial 19 students = ( 20 x 14.9 - 19 x 15 ) kg = 13 kg . correct option : d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"3 : 15",
"1 : 2",
"3 : 20",
"20 : 3"
]
} | [
"A"
] | if 0.3 of a number is equal to 0.06 of another number , the ratio of the numbers i | "sol . 0.3 a = 0.06 b Γ’ β‘ β a / b = 0.06 / 0.30 = 6 / 30 = 3 / 15 . Γ’ Λ Β΄ a : b = 3 : 15 . answer a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 9471",
"rs . 12,628",
"rs . 912.54",
"rs . 18,942"
]
} | [
"C"
] | suganya and suriya are partners in a business . suganya invests rs . 32,000 for 8 months and suriya invests rs . 28,000 for 10 months . out of a profit of rs . 30,570 . suganya ' s share is | "solution ratio of their shares = ( 32000 Γ£ β 8 ) : ( 28000 Γ£ β 10 ) = 32 : 35 . suganya ' s share = rs . ( 31570 Γ£ β 2 / 67 ) = rs . 912.54 . answer c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"12.50 %",
"13.50 %",
"14 %",
"23.75 %"
]
} | [
"D"
] | an uneducated retailer marks all his goods at 65 % above the cost price and thinking that he will still make 25 % profit , offers a discount of 25 % on the marked price . what is his actual profit on the sales ? | "sol . let c . p . = rs . 100 . then , marked price = rs . 165 . s . p . = 75 % of rs . 165 = rs . 123.75 . β΄ gain % = 23.75 % . answer d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"130",
"140",
"110",
"120"
]
} | [
"D"
] | 10 friends went to a hotel and decided to pay the bill amount equally . but 9 of them could pay rs . 50 each as a result 10 th has to pay rs . 180 extra than his share . find the amount paid by him . | "explanation : average amount paid by 9 persons = rs . 50 increase in average due to rs . 50 paid extra by the 10 th men = rs . 180 / 9 = rs . 20 therefore , average expenditure of 10 friends = rs . 50 + rs . 20 = rs . 70 therefore , amount paid by the 10 th men = rs . 70 + rs . 50 = rs . 120 correct option : d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1.05",
"1.16",
"1.2",
"1.3"
]
} | [
"A"
] | if 0.75 : x : : 5 : 7 , then x is equal to : | "explanation : ( x * 5 ) = ( 0.75 * 7 ) x = 5.25 / 5 = 1.05 answer : a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"4 kmph",
"5 kmph",
"6 kmph",
"7 kmph"
]
} | [
"B"
] | a man rows 750 m in 675 seconds against the stream and returns in 7 and half minutes . his rowing speed in s Ι΅ ll water is | explanation : rate upstream = ( 750 / 675 ) = 10 / 9 m / sec rate downstream ( 750 / 450 ) m / sec = 5 / 3 m / sec rate in still water = ( 1 / 2 ) * [ ( 10 / 9 ) + ( 5 / 3 ) ] m / sec . = 25 / 18 m / sec = ( 25 / 18 ) * ( 18 / 5 ) kmph = 5 kmph answer : b | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 1200",
"rs . 1500",
"rs . 2100",
"rs . 2000"
]
} | [
"C"
] | a alone can finish a work in 10 days which b alone can finish in 15 days . if they work together and finish it , then out of a total wages of rs . 3500 , a will get : | "explanation : ratio of working days of a : b = 10 : 15 therefore , their wages ratio = reverse ratio = 15 : 10 therefore , a will get 15 units of ratio total ratio = 25 1 unit of ratio = 3500 / 25 = 140 so , a β s amount = 120 Γ 15 = rs . 2100 . answer : option c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"160",
"200",
"250",
"350"
]
} | [
"A"
] | in a school with 640 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 = ( 640 - x ) . then , ( 11 3 / 4 Γ 640 ) β 11 x + 12 ( 640 - x ) β x = 7680 - 7520 β 160 . answer a | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 22000",
"rs . 24500",
"rs . 26500",
"rs . 28500"
]
} | [
"D"
] | sahil purchased a machine at rs 13000 , 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 . = 13000 + 5000 + 1000 = 19000 150 % of 19000 = 150 / 100 * 19000 = 28500 option d | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"12.5 %",
"40 %",
"180 %",
"125 %"
]
} | [
"C"
] | the ratio 9 : 5 expressed as a percent equals | "solution 9 : 5 = 9 / 5 = ( 9 / 5 x 100 ) % . = 180 % . answer c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"10",
"4 β 2",
"8",
"8 β 2"
]
} | [
"A"
] | triangle xyz is an isosceles right triangle . if side xy is longer than side yz , and the area of the triangle is 25 , what is the measure of side xy ? | "ans a . . 10 . . xy being larger means it is the hyp . . area = ( 1 / 2 ) * ( yz ) ^ 2 = 25 or yz = 5 * \ sqrt { 2 } . . therefore hyp = xy = 10" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"0.09",
"0.9",
"9",
"90"
]
} | [
"A"
] | what is 15 % of 2 / 3 of 0.4 ? | "the best way to solve these questions is to convert every term into fraction ( 15 / 100 ) * ( 2 / 3 ) * ( 4 / 10 ) = 120 / 3000 = 0.04 option a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"8 hours",
"10 hours",
"12 hours",
"24 hours"
]
} | [
"C"
] | a can do a piece of work in 4 hours ; b and c together can do it in 3 hours , while a and c together can do it in 2 hours . how long will b alone take to do it ? | "a ' s 1 hour ' s work = 1 / 4 ; ( b + c ) ' s 1 hour ' s work = 1 / 3 ; ( b + c ) ' s 1 hour ' s work = 1 / 2 ( a + b + c ) ' s 1 hour ' s work = ( 1 / 4 + 1 / 3 ) = 7 / 12 b ' s 1 hour ' s work = ( 7 / 12 - 1 / 2 ) = 1 / 12 b alone will take 12 hours to do the work . answer = c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 49.17",
"rs . 51.03",
"rs . 58.66",
"rs . 55.33"
]
} | [
"C"
] | if 10 litres of an oil of rs . 55 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 ? | 55 * 10 = 550 66 * 5 = 330 880 / 15 = 58.66 answer : c | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 8400",
"rs . 11,900",
"rs . 13,600",
"rs . 14,700"
]
} | [
"D"
] | a , b , c subscribe rs . 50,000 for a business . a subscribes rs . 4000 more than b and b rs . 5000 more than c . out of a total profit of rs . 35,000 , a receives : | explanation : let c = x . then , b = x + 5000 and a = x + 5000 + 4000 = x + 9000 . so , x + x + 5000 + x + 9000 = 50000 3 x = 36000 x = 12000 a : b : c = 21000 : 17000 : 12000 = 21 : 17 : 12 . a ' s share = rs . ( 35000 x 21 / 50 ) = rs . 14,700 . answer is d | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"22.4",
"22",
"20",
"19.2"
]
} | [
"A"
] | a trader mixes 80 kg of tea at 15 per kg with 20 kg of tea at cost price of 20 per kg . in order to earn a profit of 40 % , what should be the sale price of the mixed tea ? | c . p . of mixture = 80 Γ 15 + 20 Γ 20 / 80 + 20 = 16 β΄ s . p . = ( 100 + 40 ) / 100 Γ 16 = 22.4 answer a | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 49.17",
"rs . 58",
"rs . 54.17",
"rs . 55.33"
]
} | [
"B"
] | if 10 litres of an oil of rs . 54 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 ? | "54 * 10 = 540 66 * 5 = 330 870 / 15 = 58 answer : b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"160",
"180",
"200",
"220"
]
} | [
"C"
] | a number whose fifth part increased by 5 is equal to its fourth part diminished by 5 , is | "x / 5 + 5 = x / 4 - 5 = > x / 5 - x / 4 = 10 x / 20 = 10 = > x = 200 answer : c ." | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"- 12",
"- 3",
"0",
"2"
]
} | [
"C"
] | if x and y are integers such that | y + 3 | β€ 3 and 2 y β 3 x + 6 = 0 , what is the least possible value e 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 | β€ 3 which is generalized | something | β€ some number . first we solve as if there were no absolute value brackets : y + 3 β€ 3 y β€ 0 so y is 0 or negative second scenario - remove the absolute value brackets . put a negative sign around the other side of the inequality , andflip the sign : y + 3 > = - 3 y > = - 6 therefore we have a possible range for y : - 6 = < y < = 0 ok , so far so good , we ' re half way through . what about x ? here ' s the formula : 2 y β 3 x + 6 = 0 , rewrite it as 2 y + 6 = 3 x . you can say that 2 y + 6 is a multiple of 3 ( = 3 x ) . so all values which must be integer must also satisfy this constraint . i ' m just saying that , so it ' s easier to evaluate all the possible numbers ( - 6 , - 3 , 0 ) . if you plug in y = 0 , x will be 2 and xy = 0 as the lowest possible value e . hence , answer choice c is the one to go . | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"3",
"4",
"8",
"9"
]
} | [
"C"
] | in a coconut grove , ( x + 4 ) trees yield 60 nuts per year , x trees yield 120 nuts per year and ( x β 4 ) trees yield 180 nuts per year . if the average yield per year per tree be 100 , find x . | ( x + 4 ) Γ 60 + x Γ 120 + ( x β 4 ) Γ 180 / ( x + 4 ) + x + ( x β 4 ) = 100 β 360 x β 480 / 3 x = 100 β 60 x = 480 β x = 8 answer c | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"17 %",
"10 %",
"21 %",
"16 %"
]
} | [
"A"
] | weights of two friends ram and shyam are in the ratio 2 : 5 . if ram ' s weight is increased by 10 % and total weight of ram and shyam become 82.8 kg , with an increases of 15 % . by what percent did the weight of shyam has to be increased ? | "solution : given ratio of ram and shayam ' s weight = 2 : 5 hence , ( x - 15 ) / ( 15 - 10 ) = 2 / 5 or , x = 17 % . answer : option a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"4691130840",
"4686970743",
"4691100843",
"4586870843"
]
} | [
"A"
] | calculate 469160 x 9999 = ? | "answer 469160 x 9999 = 469160 x ( 10000 - 1 ) = 4691600000 - 469160 = 4691130840 . option : a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"12",
"13",
"32",
"34"
]
} | [
"D"
] | two unbiased coins are tossed . what is probability of getting at most one tail ? | "explanation : total 4 cases = [ hh , tt , th , ht ] favourable cases = [ hh , th , ht ] please note we need atmost one tail , not atleast one tail . so probability = 3 / 4 answer : d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"724",
"804",
"814",
"844"
]
} | [
"C"
] | what is the least number of square tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad ? | "solution length of largest tile = h . c . f . of 1517 cm & 902 cm = 41 cm . area of each tile = ( 41 x 41 ) cm 2 β΄ required number of tiles = [ 1517 x 902 / 41 x 41 ] = 814 . answer c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"- 3",
"- 1",
"- 1 / 3",
"0"
]
} | [
"A"
] | line m lies in the xy - plane . the y - intercept of line m is - 5 , and line m passes through the midpoint of the line segment whose endpoints are ( 2 , 4 ) and ( 6 , - 8 ) . what is the slope of line m ? | "ans : a solution : line m goes through midpoint of ( 2 , 4 ) and ( 6 , - 8 ) . midpoint is ( 4 , - 2 ) as we can see that the y axis of intercept point is ( 0 , - 5 ) means line m is parallel to x axis slope m = - 3 ans : a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"30",
"40",
"60",
"50"
]
} | [
"A"
] | a train traveling with constant speed crosses a 90 m long platform in 12 seconds and a 120 m long platform in 15 seconds . find the length of the train and its speed . | let the length of the train be x m and its speed be y m / sec . then , x / y = 12 = > y = x / 12 ( x + 90 ) / 12 = x + 120 / 15 = > x = 30 m . answer : a | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"678.6 m 3",
"36 m 3",
"40 m 3",
"44 m 3"
]
} | [
"A"
] | a circular well with a diameter of 6 metres , is dug to a depth of 24 metres . what is the volume of the earth dug out ? | "solution volume = Ο r 2 h βΉ = βΊ ( 22 / 7 Γ 3 Γ 3 Γ 24 ) m 3 βΉ = βΊ 678.6 m 3 . answer a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"35.2",
"36.1",
"36.5",
"41.5"
]
} | [
"D"
] | the mean of 50 observations was 41 . it was found later that an observation 48 was wrongly taken as 23 . the corrected new mean is | "sol . therefore correct sum = ( 41 Γ 50 + 48 β 23 ) = 2075 . therefore correct mean = 2075 / 50 = 41.5 . answer d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"50",
"74",
"78",
"80"
]
} | [
"A"
] | ashok secured average of 70 marks in 6 subjects . if the average of marks in 5 subjects is 74 , how many marks did he secure in the 6 th subject ? | "explanation : number of subjects = 6 average of marks in 6 subjects = 70 therefore total marks in 6 subjects = 70 * 6 = 420 now , no . of subjects = 5 total marks in 5 subjects = 74 * 5 = 370 therefore marks in 6 th subject = 420 β 370 = 50 answer a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 3000",
"rs . 3600",
"rs . 2000",
"rs . 4000"
]
} | [
"C"
] | p , q and r have rs . 5000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ? | "let the amount with r be rs . r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 5000 - r ) = > 3 r = 10000 - 2 r = > 5 r = 10000 = > r = 2000 . answer : c" | MathQA |
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