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": [
"40",
"54",
"45",
"39"
]
} | [
"A"
] | a worker makes a toy in every 2 h . if he works for 80 h , then how many toys will he make ? | "answer let number of toys be n . more hours , more toys ( direct proportion ) 2 : 80 : : 1 : n β n = 80 / 2 = 40 toys correct option : a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 72",
"rs . 36",
"rs . 54",
"rs . 60"
]
} | [
"D"
] | the banker ' s gain on a bill due due 1 year hence at 12 % per annum is rs . 7.2 . the true discount is | "solution t . d = [ b . g x 100 / r x t ] = rs . ( 7.2 x 100 / 12 x 1 ) = rs . 60 . answer d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"0.0001",
"0.001",
"0.015",
"0.1"
]
} | [
"C"
] | 0.03 x 0.5 = ? | "explanation : 3 x 5 = 15 . sum of decimal places = 3 0.02 x 0.5 = 0.015 answer - c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 4150",
"rs . 3850",
"rs . 3770",
"rs . 3150"
]
} | [
"D"
] | how much interest can a person get on rs . 7200 at 17.5 % p . a . simple interest for a period of two years and 6 months ? | i = ( 7200 * 2.5 * 17.5 ) / 100 = ( 7200 * 5 * 35 ) / ( 100 * 2 * 2 ) = rs . 3150 answer : d | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"4', '",
"4 β 2', '",
"14', '",
"8 β 2', '"
]
} | [
"C"
] | triangle xyz is an isosceles right triangle . if side xy is longer than side yz , and the area of the triangle is 49 , what is the measure of side xy ? | ans c . . 14 . . xy being larger means it is the hyp . . area = ( 1 / 2 ) * ( yz ) ^ 2 = 4 or yz = 7 * \ sqrt { 2 } . . therefore hyp = xy = 14 | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"10 %",
"20 %",
"25 %",
"30 %"
]
} | [
"B"
] | if the price of sugar rises from rs . 6 per kg to rs . 7.50 per kg , a person , to have no increase in his expenditure on sugar , will have to reduce his consumption of sugar by | "solution let the original consumption = 100 kg and new consumption = x kg . so , 100 x 6 = x Γ 7.50 x = 80 kg . reduction in consumption = 20 % . answer b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"36",
"42",
"44",
"46"
]
} | [
"B"
] | if p and q are positive integers each greater than 1 , and 15 ( p + 1 ) = 29 ( q + 1 ) , what is the least possible value of p + q ? | 17 ( p + 1 ) = 29 ( q + 1 ) - - > ( p + 1 ) / ( q + 1 ) = 29 / 17 - - > the least positive value of p + 1 is 29 , so the least value of p is 28 and the least positive value of q + 1 is 15 , so the least value of q is 14 - - > the least value of p + q is 28 + 14 = 42 . answer : b . | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"18 %",
"20 %",
"21 %",
"23 %"
]
} | [
"B"
] | two kinds of vodka are mixed in the ratio 1 : 2 and 2 : 1 and they are sold fetching the profit 10 % and 20 % respectively . if the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4 / 3 and 5 / 3 times respectively , then the mixture will fetch the profit of | "mixture 1 and 2 having individual profit % of 10 and 20 respectively . individual profits of vodka a for mixture 1 = 1 / 3 * 10 = 3.33 individual profits of vodka b for mixture 1 = 2 / 3 * 10 = 6.77 individual profits for a and b are increased 4 / 3 and 5 / 3 times . means profits of mixtures 1 and 2 will increase too . increased profits of vodka a for mixture 1 = 4 / 3 * 3.33 = 4.44 increased profits of vodka b for mixture 2 = 5 / 3 * 6.77 = 10.55 total increased profits for mixture 1 = 14.99 similarly total increased profits for mixture 2 = 24.42 using allegation formula va : vb = 1 : 1 = [ 24.42 - ( profit of mixture ) ] / [ ( profit of mixture ) - 14.99 ] hence profit of mixture = 19.705 approx = 20 % answer : b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"31.25 %",
"25 %",
"12.5 %",
"0.2083 %"
]
} | [
"A"
] | farm tax is levied on the 40 % of the cultivated land . the tax department collected total $ 3840 through the farm tax from the village of mr . willam . mr . willam paid only $ 480 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 40 % 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 ( 480 / 3840 ) x 100 = 12.5 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 12.5 % x ( 100 / 40 ) = 31.25 % and the answer is not there in the options . the correct answer is ( a ) ." | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"30",
"60",
"80",
"100"
]
} | [
"D"
] | ( 7.5 Γ 7.5 + 37.5 + 2.5 Γ 2.5 ) is equal to : | solution given expression = ( 7.5 Γ 7.5 + 2 Γ 7.5 Γ 2.5 + 2.5 Γ 2.5 ) = ( a 2 + 2 ab + b 2 ) = ( a + b ) 2 = ( 7.5 + 2.5 ) 2 = 102 = 100 . answer d | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"9",
"10",
"8",
"9.5"
]
} | [
"A"
] | the average of 5 quantities is 6 . the average of 3 of them is 4 . what is the average of remaining 2 numbers ? | answer : a | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"35.67 %",
"64.75 %",
"68.00 %",
"69.57 %"
]
} | [
"C"
] | in an examination , there were 2,000 candidates , out of which 900 candidates were girls and rest were boys . if 32 % of the boys and 32 % of the girls passed , then the total percentage of failed candidates is ? | "girls = 900 , boys = 1100 passed = ( 32 % of 1100 ) + ( 32 % of 900 ) = 352 + 288 = 640 failed = 2000 - 640 = 1360 failed % = [ ( 1360 / 2000 ) x 100 ] % = 68 % . answer : c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"290 / 289",
"1 / 289",
"290 / 90",
"362 / 361"
]
} | [
"D"
] | product of two natural numbers is 19 . then , the sum of reciprocals of their squares is | explanation : if the numbers are a , b , then ab = 19 , as 17 is a prime number , so a = 1 , b = 19 . 1 / a 2 + 1 / b 2 = 1 / 1 ( 2 ) + 1 / 19 ( 2 ) = 362 / 361 option d | 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 r 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 r . hence , answer choice c is the one to go ." | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"10 hours",
"12 hours",
"14 hours",
"15 hours"
]
} | [
"D"
] | in a river flowing at 2 km / hr , a boat travels 40 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 = 40 km total time taken = time taken downstream + time taken upstream = ( 40 / 8 ) + ( 40 / 4 ) = 15 d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"315",
"350",
"325",
"335"
]
} | [
"B"
] | what annual installment will discharge a debt of rs . 1176 due in 3 years at 12 % simple interest ? | "let each installment be rs . x then , ( x + ( ( x * 12 * 1 ) / 100 ) ) + ( x + ( ( x * 12 * 2 ) / 100 ) ) + x = 1176 = ( ( 28 x / 25 ) + ( 31 x / 25 ) + x ) = 1176 Γ― Ζ βΊ ( 28 x + 31 x + 25 x ) = ( 1176 * 25 ) x = ( 1176 * 25 ) / 84 = rs . 350 . therefore , each installment = rs . 350 . answer is b ." | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"230",
"175",
"225",
"315"
]
} | [
"D"
] | what is the compound interest paid on a sum of rs . 1500 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 % 1500 = 1500 * ( 21 / 100 ) = 315 answer d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"20",
"11",
"21",
"41"
]
} | [
"C"
] | the sum of the squares of three numbers is 241 , while the sum of their products taken two at a time is 100 . their sum is : | "x ^ + y ^ 2 + z ^ 2 = 241 xy + yz + zx = 100 as we know . . ( x + y + z ) ^ 2 = x ^ 2 + y ^ 2 + z ^ 2 + 2 ( xy + yz + zx ) so ( x + y + z ) ^ 2 = 241 + ( 2 * 100 ) ( x + y + z ) ^ 2 = 441 so x + y + z = 21 answer : c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1.6 km",
"2 km",
"5.1 km",
"4 km"
]
} | [
"C"
] | the speed of a boat in still water is 18 km / hr and the rate of current is 4 km / hr . the distance travelled downstream in 14 minutes is | "explanation : speed downstreams = ( 18 + 4 ) kmph = 22 kmph . distance travelled = ( 22 x 14 / 60 ) km = 5.1 km option c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 150.50",
"rs . 154.75",
"rs . 156.25",
"rs . 158"
]
} | [
"C"
] | the present worth of rs . 169 due in 2 years at 4 % per annum compound interest is | "solution present worth = rs . [ 169 / ( 1 + 4 / 100 ) Β² ] = rs . ( 169 x 25 / 26 x 25 / 26 ) = rs . 156.25 answer c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"3 .",
"2 .",
"1 / 2 .",
"1 / 4"
]
} | [
"D"
] | two brothers took the gmat exam , the higher score is x and the lower one is y . if the difference between the two scores is 1 / 3 , what is the value of y / x ? | "answer is d : 1 / 4 x - y = ( x + y ) / 3 solving for y / x = 1 / 4" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"4000",
"3050",
"4400",
"4500"
]
} | [
"C"
] | if 15 % of 30 % of 50 % of a number is 99 , then what is the number ? | let the number be a given , 15 / 100 * 30 / 100 * 50 / 100 * a = 99 = > 3 / 20 * 3 / 10 * 1 / 2 * a = 99 = > a = 10 * 20 * 10 * 2 = 4400 . answer : c | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"33 β 2",
"15",
"12",
"22"
]
} | [
"B"
] | if a clock strikes 12 in 33 seconds , it will strike 6 in how many seconds ? | in order to strike 12 , there are 11 intervals of equal time = 33 β 11 = 3 seconds each therefore , to strike 6 it has 5 equal intervals , it requires 5 Γ 3 = 15 sec . answer b | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"15 %",
"25 %",
"0.125 %",
"13.88 %"
]
} | [
"D"
] | farm tax is levied on the 90 % of the cultivated land . the tax department collected total $ 3840 through the farm tax from the village of mr . william . mr . william paid only $ 480 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is : | "this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to ( 480 / 3840 ) x 100 = 12.5 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 12.5 % x ( 100 / 90 ) = 13.88 % the correct answer is ( d ) ." | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 51.75",
"rs 51.50",
"rs 51.25",
"rs 51"
]
} | [
"C"
] | if the simple interest on a sum of money for 2 years at 5 % per annum is rs . 50 , what will be the compound interest on same values | "explanation : s . i . = p β r β t / 100 p = 50 β 100 / 5 β 2 = 500 amount = 500 ( 1 + 5100 ) 2 500 ( 21 / 20 β 21 / 20 ) = 551.25 c . i . = 551.25 β 500 = 51.25 option c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"130 km",
"120 km",
"100 km",
"124 km"
]
} | [
"D"
] | a bus covered a distance of 250 km , partly at an average speed of 40 kmph and partly at 60 kmph . if the total time taken is 5.2 hours , then the distance covered at 40 kmph is | "let the partial distance covered at 40 kmph be x let the another partial distance covered at 60 kmph be ( 250 - x ) thus , x / 40 - ( 250 - x ) / 60 = 5.2 or , x / 40 + ( 250 - x ) / 60 = 5.2 or , ( 3 x + 500 - 2 x ) / / 120 = 5.2 or 500 + x = 624 x = 124 answer : d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"67 kg",
"77 kg",
"87 kg",
"97 kg"
]
} | [
"B"
] | the average weight of 8 persons increases by 1.5 kg when a person weighting 65 kg is replaced by a new person . what could be the weight of the new person ? | "explanation : let the average weight of 8 persons be β x β years and the age of the new person be β y β years so , ( 8 x β 65 + y ) / 8 = x + 1.5 so , y = 77 kgs 65 + 8 x 1.5 = 77 kgs answer b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1 : 1",
"3 : 2",
"4 : 3",
"5 : 3"
]
} | [
"A"
] | in what ratio must tea at rs . 65 per kg be mixed with tea at rs . 70 per kg so that the mixture must be worth rs . 6 per kg ? | "required ratio = 500 : 500 = 1 : 1 answer a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1738",
"1752",
"1846",
"1648"
]
} | [
"B"
] | in a division sum , the divisor is 12 times the quotient and 6 times the remainder . if the remainder is 24 , what is the divident ? | "solution : dividend = [ divisor * quotient ] + remainder - - - - > ( 1 ) . given divisor = 6 * 24 = 144 . 12 * quotient = 144 = > quotient = 144 / 12 = 12 . substitute these values in the ( 1 ) then we get 1752 as dividend . answer b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"15 %",
"20 %",
"40 %",
"50 %"
]
} | [
"D"
] | the charge for a single room at hotel p is 40 percent less than the charge for a single room at hotel r and 10 percent less than the charge for a single room at hotel g . the charge for a single room at hotel r is what percent greater than the charge for a single room at hotel g ? | "p = 0.6 r = 0.9 g r = 0.9 g / 0.6 = 1.5 * g thus r is 50 % greater than g . the answer is d ." | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 154.50",
"rs . 155.50",
"rs . 156.50",
"rs . 157.50"
]
} | [
"D"
] | if a lends rs . 3500 to b at 10 % p . a . and b lends the same sum to c at 11.5 % p . a . , then the gain of b ( in rs . ) in a period of 3 years is | explanation : we need to calculate the profit of b . it will be , si on the rate b lends - si on the rate b gets gain of b = 3500 Γ 11.5 Γ 3 / 100 β 3500 Γ 10 Γ 3 / 100 = 157.50 option d | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 1200",
"rs . 1500",
"rs . 1980",
"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 . 3300 , 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 = 3000 / 25 = 132 so , a β s amount = 120 Γ 15 = rs . 1980 . answer : option c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 223.20",
"rs . 323.20",
"rs . 423.20",
"rs . 523.20"
]
} | [
"A"
] | a tank is 25 m long 12 m wide and 6 m deep . the cost of plastering its walls and bottom at 30 paise per sq m is | "explanation : area to be plastered = [ 2 ( l + b ) Γ£ β h ] + ( l Γ£ β b ) = [ 2 ( 25 + 12 ) Γ£ β 6 ] + ( 25 Γ£ β 12 ) = 744 sq m cost of plastering = 744 Γ£ β ( 30 / 100 ) = rs . 223.20 answer : a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"475",
"700",
"220",
"400"
]
} | [
"A"
] | a fruit seller had some oranges . he sells 20 % oranges and still has 380 oranges . how many oranges he had originally ? | explanation : he sells 20 % of oranges and still there are 380 oranges remaining = > 80 % of oranges = 380 β ( 80 Γ total oranges ) / 100 = 380 β total oranges / 100 = 4.75 β total oranges = 4.75 Γ 100 = 475 answer : option a | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"7500",
"6500",
"8125",
"9125"
]
} | [
"D"
] | find the simple interest on rs . 73,000 at 16 2 / 3 % per year for 9 months . | "p = rs . 73000 , r = 50 / 3 % p . a and t = 9 / 12 years = 3 / 4 years . simple interest = ( p * r * t ) / 100 = rs . ( 73,000 * ( 50 / 3 ) * ( 3 / 4 ) * ( 1 / 100 ) ) = rs . 9125 answer is d ." | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"33 / 7",
"43 / 7",
"24 / 7",
"19 / 7"
]
} | [
"C"
] | a , b and c can complete a piece of work in 24 , 6 and 12 days respectively . working together , they will complete the same work in : | if a can do a piece of work in n days , then a ' s 1 day ' s work = 1 / n ( a + b + c ) ' s 1 day ' s work = 1 / 24 + 1 / 6 + 1 / 12 = 7 / 24 so , all the three together will complete the job in = 24 / 7 days answer : c | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"30 %",
"49 %",
"90 %",
"100 %"
]
} | [
"B"
] | in a restaurant , the profit is 120 % of the cost . if the cost increases by 12 % but the selling price remains constant , approximately what percentage of the selling price is the profit ? | "explanation : let c . p . = rs . 100 . then , profit = rs . 120 , s . p . = rs . 220 . new c . p . = 112 % of rs . 100 = rs . 112 new s . p . = rs . 220 . profit = rs . ( 220 - 112 ) = rs . 108 . required percentage = ( 108 / 220 * 100 ) % = 49 % appox answer : b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1998",
"2001",
"2002",
"2003"
]
} | [
"C"
] | the year next to 1991 having the same calendar as that of 1990 is β | we go on counting the odd days from 1991 onward still the sum is divisible by 7 . the number of such days are 14 upto the year 2001 . so , the calender for 1991 will be repeated in the year 2002 . answer c | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"16.32",
"16.9",
"12.25",
"13.21"
]
} | [
"A"
] | the simple interest on rs . 34 for 8 months at the rate of 6 paise per rupeeper month is | "sol . s . i . = rs . [ 34 * 6 / 100 * 8 ] = rs . 16.32 answer a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"41 / 45",
"15 / 14",
"4 / 5",
"5 / 4"
]
} | [
"A"
] | jack and jill are marathon runners . jack can finish a marathon ( 41 km ) in 4.5 hours and jill can run a marathon in 4.1 hours . what is the ratio of their average running speed ? ( jack : jill ) | "average speed of jack = distance / time = 41 / ( 9 / 2 ) = 82 / 9 average speed of jill = 41 / ( 4.1 ) = 10 ratio of average speed of jack to jill = ( 82 / 9 ) / 10 = 82 / 90 = 41 / 45 answer a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"73.41",
"74.31",
"73.42",
"73.43"
]
} | [
"C"
] | a mathematics teacher tabulated the marks secured by 35 students of 8 th class . the average of their marks was 72 . if the marks secured by reema was written as 46 instead of 96 then find the correct average marks up to two decimal places . | "total marks = 35 x 72 = 2520 corrected total marks = 2520 - 46 + 96 = 2570 correct average = 2570 / 35 = 73.42 answer : c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"18",
"750",
"21",
"120"
]
} | [
"C"
] | how many plants will be there in a circular bed whose outer edge measure 33 cms , allowing 4 cm 2 for each plant ? | "circumference of circular bed = 33 cm area of circular bed = ( 33 ) 2 Γ’ Β β 4 Γ― β¬ space for each plant = 4 cm 2 Γ’ Λ Β΄ required number of plants = ( 33 ) 2 Γ’ Β β 4 Γ― β¬ Γ£ Β· 4 = 21.65 = 21 ( approx ) answer c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs 25",
"rs 30",
"rs 35",
"rs 40"
]
} | [
"A"
] | find the simple interest on the rs . 2000 at 25 / 4 % per annum for the period from 4 th feb 2005 to 18 th april 2005 | explanation : one thing which is tricky in this question is to calculate the number of days . always remember that the day on which money is deposited is not counted while the day on which money is withdrawn is counted . so lets calculate the number of days now , time = ( 24 + 31 + 18 ) days = 73 / 365 years = 1 / 5 years p = 2000 r = 25 / 4 % s . i . = = 2000 Γ 254 Γ 5 Γ 100 = 25 answer : a | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"6.09 %",
"6.10 %",
"6.12 %",
"6.14 %"
]
} | [
"A"
] | effective annual rate of interest corresponding to nominal rate of 6 % per annum compounded half yearly will be | explanation : let the amount rs 100 for 1 year when compounded half yearly , n = 2 , rate = 6 / 2 = 3 % amount = 100 ( 1 + 3 / 100 ) 2 = 106.09 effective rate = ( 106.09 - 100 ) % = 6.09 % option a | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"12 kg",
"10 kg",
"20 kg",
"72 kg"
]
} | [
"A"
] | the average weight of 5 students decreases by 12 kg when one of them weighing 72 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 = 12 kg = > ( 72 - x ) / 5 = 12 = > x = 12 answer : a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"3002",
"3013",
"3024",
"3036"
]
} | [
"B"
] | find the least multiple of 23 , which when divided by 1821 and 24 leaves remainders 710 and 13 respectively . | solution here ( 18 - 7 ) = 11 , ( 21 - 10 ) = 11 and ( 24 - 13 ) = 11 . l . c . m . of 1821 and 24 is 504 . let required number be 504 k - 11 . least value of k for which ( 504 k - 11 ) is divisible 23 is k = 6 . so , required number = 504 Γ 6 - 11 = 3024 - 11 = 3013 . answer b | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 380",
"rs . 215",
"rs . 190",
"rs . 395"
]
} | [
"C"
] | a trader sells 20 meters of cloth for rs . 4500 at the profit of rs . 10 per metre of cloth . what is the cost price of one metre of cloth ? | "sp of 1 m of cloth = 4500 / 20 = rs . 225 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 225 - rs . 10 = rs . 215 . answer : c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 22000",
"rs . 24000",
"rs . 26000",
"rs . 28000"
]
} | [
"B"
] | sahil purchased a machine at rs 10000 , 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 . = 10000 + 5000 + 1000 = 16000 150 % of 16000 = 150 / 100 * 16000 = 24000 option b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"761200",
"761400",
"761800",
"761500"
]
} | [
"A"
] | simplify : 896 x 896 - 204 x 204 | "( 896 ) ^ 2 - ( 204 ) ^ 2 = ( 896 + 204 ) ( 896 - 204 ) = 1100 x 692 = 761200 . answer is a ." | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1.2 kg",
"1.5 kg",
"1.7 kg",
"1.9 kg"
]
} | [
"A"
] | 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 40 % water ? | "explanation : flower - nectar contains 50 % of non - water part . in honey this non - water part constitutes 60 % ( 100 - 40 ) . therefore 0.5 x amount of flower - nectar = 0.60 x amount of honey = 0.60 x 1 kg therefore amount of flower - nectar needed = ( 0.60 / 0.51 ) kg = 1.2 kgs answer : a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 9471",
"rs . 12,628",
"rs . 18,040",
"rs . 18,942"
]
} | [
"C"
] | 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 . 31,570 . suganya ' s share is | "solution ratio of their shares = ( 35000 Γ 8 ) : ( 42000 Γ 10 ) = 2 : 3 . suganya ' s share = rs . ( 31570 Γ 2 / 5 ) = rs . 12628 . answer c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"2736900",
"2738800",
"150000",
"2716740"
]
} | [
"C"
] | 500 x 223 + 500 x 77 = ? | "= 8796 x ( 223 + 77 ) ( by distributive law ) = 500 x 300 = 150000 answer is c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"2",
"4",
"8",
"16"
]
} | [
"B"
] | in the rectangular coordinate system , points ( 4 , 0 ) and ( β 4 , 0 ) both lie on circle c . what is the maximum possible value of the radius of c | "it takes 3 distinct points to define a circle . only 2 are given here . the two points essentially identify a single chord of the circle c . since no other information is provided , however , the radius of the circle can essentially be anything . all this information tell us is that the radius isgreater 4 b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"300 kmph",
"360 kmph",
"600 kmph",
"720 kmph"
]
} | [
"D"
] | an aeroplane covers a certain distance at a speed of 240 kmph in 5 hours . to cover the same distance in 1 2 / 3 hours , it must travel at a speed of : | "explanation : distance = ( 240 x 5 ) = 1200 km . speed = distance / time speed = 1200 / ( 5 / 3 ) km / hr . [ we can write 1 2 / 3 hours as 5 / 3 hours ] required speed = 1200 x 3 / 5 km / hr = 720 km / hr . answer : option d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"11",
"14",
"18",
"23"
]
} | [
"B"
] | when 242 is divided by a certain divisor the remainder obtained is 6 . when 698 is divided by the same divisor the remainder obtained is 13 . however , when the sum of the two numbers 242 and 698 is divided by the divisor , the remainder obtained is 5 . what is the value of the divisor ? | "let that divisor be x since remainder is 6 or 13 it means divisor is greater than 13 . now 242 - 6 = 236 = kx ( k is an integer and 234 is divisble by x ) similarly 698 - 13 = 685 = lx ( l is an integer and 689 is divisible by x ) adding both 698 and 242 = ( 236 + 685 ) + 6 + 13 = x ( k + l ) + 19 when we divide this number by x then remainder will be equal to remainder of ( 19 divided by x ) = 5 hence x = 19 - 5 = 14 hence b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"10 hours",
"12 hours",
"14 hours",
"21 hours"
]
} | [
"D"
] | in a river flowing at 2 km / hr , a boat travels 56 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 = 56 km total time taken = time taken downstream + time taken upstream = ( 56 / 8 ) + ( 56 / 4 ) = 21 hr . answer : option d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"60",
"45",
"20",
"15"
]
} | [
"C"
] | a ratio between two numbers is 5 : 4 and their l . c . m . is 80 . the first number is | "sol . let the required numbers be 5 x and 4 x . then , their l . c . m . is 20 x . β΄ 20 x = 80 β x = 4 . hence , the first number is 20 . answer c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 18 , 828.80",
"rs . 19 , 828.80",
"rs . 18 , 028.80",
"rs . 17 , 828.80"
]
} | [
"B"
] | the compound interest earned by sunil on a certain amount at the end of two years at the rate of 8 % p . a . was rs . 2828.80 . find the total amount that sunil got back at the end of two years in the form of principal plus interest earned . | "let the sum be rs . p p { [ 1 + 8 / 100 ] 2 - 1 } = 2828.80 p ( 8 / 100 ) ( 2 + 8 / 100 ) = 2828.80 [ a 2 - b 2 = ( a - b ) ( a + b ) ] p = 2828.80 / ( 0.08 ) ( 2.08 ) = 1360 / 0.08 = 17000 principal + interest = rs . 19828.80 answer : b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"0.64202",
"0.64204",
"0.642022",
"0.642025"
]
} | [
"D"
] | the average of numbers 0.64204 , 0.64203 , 0.64202 and 0.64201 is ? | "answer average = ( 0.64204 + 0.64203 + 0.64202 + 0.64201 ) / 4 = 2.5681 / 4 = 0.642025 correct option : d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1601249",
"1607249",
"1701249",
"1708249"
]
} | [
"D"
] | calculate 1307 x 1307 = ? | "answer 1307 x 1307 = ( 1307 ) 2 = ( 1300 + 7 ) 2 = ( 1300 ) 2 + ( 7 ) 2 + 2 x 1300 x 7 = 1690000 + 49 + 18200 = 1708249 option : d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1 / 35",
"3 / 35",
"5 / 37",
"4 / 63"
]
} | [
"D"
] | the hcf and lcm of two numbers m and n are respectively 6 and 210 . if m + n = 80 , then 1 / m + 1 / n is equal to | "answer we have , m x n = 6 x 210 = 1260 Γ’ Λ Β΄ 1 / m + 1 / n = ( m + n ) / mn = 80 / 1260 = 4 / 63 correct option : d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"4",
"4 β 2",
"12",
"8 β 2"
]
} | [
"C"
] | triangle xyz is an isosceles right triangle . if side xy is longer than side yz , and the area of the triangle is 36 , what is the measure of side xy ? | "ans c . . 12 . . xy being larger means it is the hyp . . area = ( 1 / 2 ) * ( yz ) ^ 2 = 36 or yz = 3 * \ sqrt { 2 } . . therefore hyp = xy = 12" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"3",
"4",
"5",
"6"
]
} | [
"D"
] | in a coconut grove , ( x + 3 ) trees yield 60 nuts per year , x trees yield 120 nuts per year and ( x β 3 ) trees yield 180 nuts per year . if the average yield per year per tree be 100 , find x . | "( x + 3 ) Γ 60 + x Γ 120 + ( x β 3 ) Γ 180 / ( x + 3 ) + x + ( x β 3 ) = 100 β 360 x β 360 / 3 x = 100 β 60 x = 360 β x = 6 answer d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"30",
"4",
"9",
"8"
]
} | [
"C"
] | find the average of all prime numbers between 4 and 15 . | sol . there are four prime numbers between 4 and 15 . they are 5 , 7 , 11 , 13 Γ’ Λ Β΄ required average = [ 5 + 7 + 11 + 13 / 4 ] = 36 / 4 = 9 answer c | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"0.33",
"33",
"0.033",
"0.0033"
]
} | [
"B"
] | if the digits 33 in the decimal 0.00033 repeat indefinitely , what is the value of ( 10 ^ 5 - 10 ^ 3 ) ( 0.00033 ) ? | 99 * 0.33 = 32.67 approx . 33 answer : b | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"3 : 4",
"3 : 5",
"4 : 5",
"5 : 7"
]
} | [
"A"
] | two whole numbers whose sum is 72 can not be in the ratio | "sol . the sum of the ratio terms must divide 72 . so , the ratio can not be 3 : 4 . answer a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"300",
"345",
"325",
"335"
]
} | [
"A"
] | what annual installment will discharge a debt of rs . 1008 due in 3 years at 12 % simple interest ? | "let each installment be rs . x then , ( x + ( ( x * 12 * 1 ) / 100 ) ) + ( x + ( ( x * 12 * 2 ) / 100 ) ) + x = 1008 = ( ( 28 x / 25 ) + ( 31 x / 25 ) + x ) = 1008 Γ― Ζ βΊ ( 28 x + 31 x + 25 x ) = ( 1008 * 25 ) x = ( 1008 * 25 ) / 84 = rs . 300 . therefore , each installment = rs . 300 . answer is a ." | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"0.045388",
"4.5388",
"0.03242",
"473.88"
]
} | [
"C"
] | [ ( 3.242 x 10 ) / 100 ] = ? | "answer multiplying 3.242 x 10 = 3.242 now divide 3.242 by 100 so , 3.242 Γ· 100 = 0.03242 β΄ shift the decimal two places to the left as 100 correct option : c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 340",
"rs . 400",
"rs . 450",
"rs . 475"
]
} | [
"B"
] | rs . 1210 were divided among a , b , c so that a : b = 5 : 4 and b : c = 9 : 10 . then , c gets : | "solution a : b = 5 : 4 , b : c = 9 : 10 = ( 9 x 4 / 9 ) : ( 10 x 4 / 90 = 4 : 40 / 9 β΄ a : b : c = 5 : 4 : 40 / 9 = 45 : 36 : 40 . sum of ratio terms = ( 45 + 36 + 40 ) = 121 β΄ c β s share = rs . ( 1210 x 40 / 121 ) = rs . 400 . answer b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"22666",
"20000",
"25000",
"22235"
]
} | [
"A"
] | sheela deposits rs . 3400 in bank savings account . if this is 15 % of her monthly income . what is her monthly income in ? | "explanation : 15 % of income = rs . 3400 100 % of income = 3400 x 100 / 15 = rs . 22666 answer : a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"720",
"180",
"75",
"65"
]
} | [
"C"
] | the number of degrees that the hour hand of a clock moves through between noon and 2.30 in the afternoon of the same day is | "explanation : the hour hand moves from pointing to 12 to pointing to half way between 2 and 3 . the angle covered between each hour marking on the clock is 360 / 12 = 30 . since the hand has covered 2.5 of these divisions the angle moved through is 75 . answer : c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"2 : 1",
"1 : 2",
"6 : 13",
"13 : 6"
]
} | [
"D"
] | mr . kutty has only hens and sheep . if the total number of their heads is 38 and the total number of legs is 100 then what is the ratio between the numbers of hens and sheep ? | let the total number of hens and sheep be x and y respectively . i . e . , x + y = 38 and 2 x + 4 y = 100 β΄ ratio = 13 : 6 answer d | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"256",
"258",
"268",
"358"
]
} | [
"B"
] | 88 % of 370 + 24 % of 210 - ? = 118 | "let 88 % of 370 + 240 % of 210 - x = 118 then , x = ( 88 / 100 * 370 ) + ( 24 / 100 * 210 ) - 118 - 325.60 + 50.40 - 118 = 376 - 118 = 258 correct option : b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 500",
"rs . 515",
"rs . 550",
"rs . 600"
]
} | [
"A"
] | the sale price of an article including the sales tax is rs . 616 . the rate of sales tax is 10 % . if the shopkeeper has made a profit of 12 % , then the cost price of the article is | "solution 110 % of s . p . = 616 βΉ = βΊ s . p . = ( 616 x 100 / 110 ) . βΉ = βΊ rs . 560 . c . p . βΉ = βΊ rs . ( 100 / 112 x 560 ) βΉ = βΊ rs . 500 . answer a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 692",
"rs . 768",
"rs . 876",
"rs . 972"
]
} | [
"C"
] | the cost of the paint is rs . 36.50 per kg . if 1 kg of paint covers 16 squares feet , how much will it cost to paint outside of a cube having 8 feet each side ? | "solution surface area of the cube = ( 6 Γ 82 ) sq . ft = 384 sq . ft . quantity of paint required = ( 384 / 16 ) kg βΉ = βΊ 24 kg . cost of painting = rs . ( 36.50 Γ 24 ) = rs . 876 . answer c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"820",
"340",
"420",
"209"
]
} | [
"B"
] | 300 + 5 Γ 8 = ? | 300 + 5 Γ 8 = ? or , ? = 300 + 40 = 340 answer b | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"25.5",
"2.5",
"40",
". 25"
]
} | [
"C"
] | 1 / 0.025 is equal to | "explanation : 1 / 0.025 = ( 1 * 1000 ) / 25 = 1000 / 25 = 40 option c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"32 m 3",
"25.1 m 3",
"40 m 3",
"44 m 3"
]
} | [
"B"
] | a circular well with a diameter of 2 metres , is dug to a depth of 8 metres . what is the volume of the earth dug out ? | "solution volume = Ο r 2 h βΉ = βΊ ( 22 / 7 Γ 1 Γ 1 Γ 8 ) m 3 βΉ = βΊ 25.1 m 3 . answer b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"31",
"36",
"41",
"51"
]
} | [
"D"
] | the average age of 36 students in a group is 14 years . when teacher β s age is included to it , the average increases by one . what is the teacher β s age in years ? | "sol . age of the teacher = ( 37 Γ 15 β 36 Γ 14 ) years = 51 years . answer d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"125",
"70",
"40",
"25"
]
} | [
"C"
] | 1 β 5 of a number is equal to 5 β 8 of the second number . if 35 is added to the first number then it becomes 4 times of second number . what is the value of the second number ? | let x be the first number and y be the second number . 1 β 5 x = 5 β 8 y \ x β y = 25 β 8 . . . . . . ( i ) x + 35 = 4 y or , 25 β 8 y + 35 = 4 y \ y = 40 answee c | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"9 %",
"9.27 %",
"25.97 %",
"12 %"
]
} | [
"C"
] | the population of a city increases by 9 % 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 = 8 % let , earlier population = 100 then the population after 3 years = 100 ( 1 + 8 / 100 ) ^ 3 = 125.97 β΄ required percentage = 25.97 % answer : c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 512",
"rs . 552",
"rs . 612",
"rs . 622"
]
} | [
"C"
] | find compound interest on rs . 7500 at 4 % per annum for 2 years , compounded annually . | "solution amount = rs [ 7500 x ( 1 + 4 / 100 ) Β² ] = rs . ( 7500 x 26 / 25 x 26 / 25 ) = rs . 8112 . c . i = rs ( 8112 - 7500 ) = rs . 612 . answer c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"632",
"731",
"533",
"434"
]
} | [
"A"
] | a number is 4 less than 6 times the other number . if the sum of both the number is 38 , what are the numbers ? | that numbers are x , 6 x - 4 so sum = x + 6 x - 4 = 38 7 x = 42 = = > x = 6 another no is 32 answer is 6 , 32 answer : a | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"50",
"30",
"125",
"25"
]
} | [
"D"
] | if the l . c . m of two numbers is 750 and their product is 18750 , find the h . c . f of the numbers . | "h . c . f = ( product of the numbers ) / ( their l . c . m ) = 18750 / 750 = 25 . answer : d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1",
"9000",
"9001",
"90001"
]
} | [
"C"
] | if the largest 3 digit number is subtracted from the smallest 5 digit number , then the remainder is | solution required remainder = ( 10000 - 999 ) = 9001 answer c | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"9 %",
"9.10 %",
"27 %",
"12 %"
]
} | [
"B"
] | the population of a city increases by 7 % 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 = 6 % let , earlier population = 100 then the population after 3 years = 100 ( 1 + 6 / 100 ) ^ 3 = 119.1016 β΄ required percentage = 9.1016 % answer : b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1 β 55",
"54 β 55",
"45 β 55",
"3 β 55"
]
} | [
"B"
] | in a box carrying one dozen of oranges , one - third have become bad . if 3 oranges are taken out from the box at random , what is the probability that at least one orange out of the 3 oranges picked up is good ? | n ( s ) = 12 c 3 = 12 Γ 11 Γ 10 / 3 Γ 2 = 2 Γ 11 Γ 10 = 220 no . of selection of 3 oranges out of the total 12 oranges = 12 c 3 = 2 Γ 11 Γ 10 = 220 no . of selection of 3 bad oranges out of the total 4 bad oranges = 4 c 3 = 4 \ n ( e ) = no . of desired selection of oranges = 220 β 4 = 216 \ p ( e ) = n ( e ) / n ( s ) = 216 / 220 = 54 / 55 answer b | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"18 %",
"20 %",
"21 %",
"35 %"
]
} | [
"D"
] | two kinds of vodka are mixed in the ratio 1 : 2 and 2 : 1 and they are sold fetching the profit 10 % and 35 % respectively . if the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4 / 3 and 5 / 3 times respectively , then the mixture will fetch the profit of | answer : d . | MathQA |
{
"label": [
"A",
"B",
"C",
"E"
],
"text": [
"1400",
"1500",
"1505",
"1506"
]
} | [
"B"
] | evaluate 75 / . 05 | "explanation : 75 / . 05 = 7500 / 5 = 1500 option b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"32', '",
"64', '",
"25', '",
"16', '"
]
} | [
"B"
] | each side of a rectangular field diminished by 40 % . by how much per cent is the area of the field diminished ? | solution : let the original length of the rectangle be 20 unit and breadth be 10 unit . then original area = length * breadth = 20 * 10 = 200 square unit . 40 % decrease in each side , then length = ( 20 - 40 % of 20 ) = 12 unit . breadth = ( 10 - 40 % of 10 ) = 6 unit . now , area = 12 * 6 = 72 square unit . decrease in area = 200 - 72 = 128 square unit . % decrease in area = ( 128 / 200 ) * 100 = 64 % mind calculation method : let the original area be 100 square unit . 100 = = = 40 % β ( decrease in length ) = = = > 60 = = = 40 % β = = = ( decrease in breadth ) = = = > 36 . diminished in area = 100 - 36 = 64 % answer : option b | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 72",
"rs . 92",
"rs . 162.50",
"rs . 116.50"
]
} | [
"C"
] | a 13 % stock yields 8 % . the market value of the stock is : | "solution to obtain rs . 8 , investment = rs . 100 . to obtain rs . 13 , investment = rs . ( 100 / 8 x 13 ) = rs . 162.50 β΄ market value of rs . 100 stock = rs . 162.50 answer c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"0.1602",
"0.001602",
"1.6021",
"0.01602"
]
} | [
"A"
] | 16.02 Γ£ β 0.01 = ? | "16.02 Γ£ β 0.01 = 0.1602 the answer is a ." | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs 6.56",
"rs 9.56",
"rs 10.56",
"rs 11.56"
]
} | [
"A"
] | a fruit seller sells mangoes at the rate of rs . 5 per kg and thereby loses 20 % . at what price per kg , he should have sold them to make a profit of 5 % | "explanation : 80 : 5 = 105 : x x = ( 5 Γ 105 / 80 ) = rs 6.56 option a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1 : 5', '",
"1 : 25', '",
"1 : 125', '",
"1 : 625', '"
]
} | [
"B"
] | a cube of edge 5 cm is cut into cubes of each edge 1 cm . the ratio of the total surface area of one of the small cubes to that of the large cube is equal to | solution required ratio = ( 6 x 1 x 1 / 6 x 5 x 5 ) βΉ = βΊ 1 / 25 βΉ = βΊ 1 : 125 . answer b | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"76",
"76.5",
"85",
"80"
]
} | [
"C"
] | the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ? | "explanation : total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 65 + 20 ) kg = 85 kg . answer : c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"7",
"5",
"4",
"6"
]
} | [
"C"
] | 248 : 3 : : 328 : ? | "248 - - - - 24 / 8 . . . 3 328 - - - 32 / 8 . . . 4 answer c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"15 %",
"25 %",
"0.125 %",
"0.2083 %"
]
} | [
"B"
] | farm tax is levied on the 50 % of the cultivated land . the tax department collected total $ 3840 through the farm tax from the village of mr . willam . mr . willam paid only $ 480 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 50 % 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 ( 480 / 3840 ) x 100 = 12.5 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 12.5 % x ( 100 / 50 ) = 25 % and the answer is not there in the options . the correct answer is ( b ) . | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"79698",
"80578",
"80698",
"180578"
]
} | [
"D"
] | 317 x 317 + 283 x 283 = ? | "= ( 317 ) ^ 2 + ( 283 ) ^ 2 = ( 300 + 17 ) ^ 2 + ( 300 - 17 ) ^ 2 = 2 [ ( 300 ) ^ 2 + ( 17 ) ^ 2 ] = 2 [ 90000 + 289 ] = 2 x 90289 = 180578 answer is d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"40",
"50",
"70",
"60"
]
} | [
"C"
] | in a group of 100 people , 50 like reading books , 20 like both reading books and listening songs . how many like listening songs ? | make a venn diagram , and enter your data . let the number of people who like listening songs be x x + 20 + 30 = 100 x = 50 so number who like listening songs = 20 + 50 = 70 answer c | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"71",
"69",
"72",
"75"
]
} | [
"A"
] | kamal obtained 76 , 60 , 72 , 65 and 82 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ? | "sol . average = 76 + 60 + 72 + 65 + 82 / 5 ) = ( 355 / 5 ) = 71 . answer a" | MathQA |
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