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": [
"5865863355",
"5665863355",
"4865863355",
"4665863355"
]
}
|
[
"A"
] |
simplify 586645 * 9999
|
explanation : although it is a simple question , but the trick is to save time in solving this . rather than multiplying it we can do as follows : 586645 * ( 10000 - 1 ) = 5866450000 - 586645 = 5865863355 option a
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 1386",
"rs . 1764",
"rs . 1575",
"rs . 2268"
]
}
|
[
"B"
] |
the true discount on a bill due 9 months hence at 16 % per annum is rs . 189 . the amount of the bill is :
|
"solution 32.5 let p . w . be rs . x . then , s . i . on rs . x at 16 % for 9 months = rs . 189 . ∴ x 16 x 9 / 12 x 1 / 100 = 189 or x = 1575 . ∴ p . w . = rs . 1575 . ∴ sum due = p . w . + t . d . = rs . ( 1575 + 189 ) = rs . 1764 . answer b"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"25 %",
"23 %",
"16.67 %",
"33.33 %"
]
}
|
[
"B"
] |
if the price of petrol increases by 30 , by how much must a user cut down his consumption so that his expenditure on petrol remains constant ?
|
"explanation : let us assume before increase the petrol will be rs . 100 . after increase it will be rs ( 100 + 30 ) i . e 130 . now , his consumption should be reduced to : - = ( 130 − 100 ) / 130 ∗ 100 . hence , the consumption should be reduced to 23 % . answer : b"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"E"
],
"text": [
"50 %",
"125 %",
"25 %",
"30 %"
]
}
|
[
"C"
] |
the ratio 5 : 20 expressed as percent equals to
|
"explanation : actually it means 5 is what percent of 20 , which can be calculated as , ( 5 / 20 ) * 100 = 5 * 5 = 25 option c"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1.12",
"1.2",
"1.25",
"1.3"
]
}
|
[
"B"
] |
if 0.75 : x : : 5 : 8 , then x is equal to :
|
"( x * 5 ) = ( 0.75 * 8 ) x = 6 / 5 x = 1.20 answer = b"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"62 %",
"73 %",
"41 %",
"71 %"
]
}
|
[
"A"
] |
b as a percentage of a is equal to a as a percentage of ( a + b ) . find b as a percentage of a .
|
explanation : according to the question : - = > b / a = a / ( a + b ) . as b is a percent of a , let us assume b = ax . then , equation ( 1 ) can be re - written as = > x = 11 + x . = > x ( 1 + x ) = 1 . = > x 2 + x + 1 = 0 . = > x = − 1 ± 5 / √ 2 thus , x = − 1 + 5 / √ 2 = > 0.62 . = > 62 % . answer : a
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"13000",
"7000",
"10000",
"5000"
]
}
|
[
"D"
] |
a textile manufacturing firm employees 70 looms . it makes fabrics for a branded company . the aggregate sales value of the output of the 70 looms is rs 00000 and the monthly manufacturing expenses is rs 1 , 50000 . assume that each loom contributes equally to the sales and manufacturing expenses are evenly spread over the number of looms . monthly establishment charges are rs 75000 . if one loom breaks down and remains idle for one month , the decrease in profit is :
|
explanation : profit = 5 , 00,000 â ˆ ’ ( 1 , 50,000 + 75,000 ) = rs . 2 , 75,000 . since , such loom contributes equally to sales and manufacturing expenses . but the monthly charges are fixed at rs 75,000 . if one loan breaks down sales and expenses will decrease . new profit : - = > 500000 ã — ( 69 / 70 ) â ˆ ’ 150000 ã — ( 69 / 70 ) â ˆ ’ 75000 . = > rs 2 , 70,000 . decrease in profit = > 2 , 75,000 â ˆ ’ 2 , 70,000 = > rs . 5,000 . answer : d
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 11.81",
"rs . 12",
"rs . 18.94",
"rs . 12.31"
]
}
|
[
"C"
] |
a fruit seller sells mangoes at the rate of rs . 14 per kg and thereby loses 15 % . at what price per kg , he should have sold them to make a profit of 15 % ?
|
"solution 85 : 14 = 115 : x x = ( 14 ã — 115 / 85 ) = rs . 18.94 hence , s . p per kg = rs . 18.94 answer c"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"6 hours",
"5 hours",
"7 hours",
"8 hours"
]
}
|
[
"C"
] |
a truck covers a distance of 392 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 70 km more than that travelled by the truck ?
|
"explanation : speed of the truck = distance / time = 392 / 8 = 49 kmph now , speed of car = ( speed of truck + 18 ) kmph = ( 48 + 18 ) = 66 kmph distance travelled by car = 392 + 70 = 462 km time taken by car = distance / speed = 462 / 66 = 7 hours . answer – c"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 435",
"rs . 350",
"rs . 275",
"rs . 425"
]
}
|
[
"A"
] |
the mean daily profit made by a shopkeeper in a month of 30 days was rs . 350 . if the mean profit for the first fifteen days was rs . 265 , then the mean profit for the last 15 days would be
|
average would be : 350 = ( 265 + x ) / 2 on solving , x = 435 . answer : a
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"427",
"859",
"869",
"856"
]
}
|
[
"D"
] |
the least number which when increased by 8 each divisible by each one of 24 , 32 , 36 and 54 is :
|
"solution required number = ( l . c . m . of 24 , 32 , 36 , 54 ) - 8 = 864 - 8 = 856 . answer d"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"11",
"17",
"13",
"20"
]
}
|
[
"D"
] |
when 242 is divided by a certain divisor the remainder obtained is 11 . when 698 is divided by the same divisor the remainder obtained is 18 . however , when the sum of the two numbers 242 and 698 is divided by the divisor , the remainder obtained is 9 . what is the value of the divisor ?
|
"let that divisor be x since remainder is 11 or 18 it means divisor is greater than 18 . now 242 - 11 = 231 = kx ( k is an integer and 234 is divisble by x ) similarly 698 - 18 = 680 = lx ( l is an integer and 689 is divisible by x ) adding both 698 and 242 = ( 231 + 680 ) + 11 + 18 = x ( k + l ) + 29 when we divide this number by x then remainder will be equal to remainder of ( 29 divided by x ) = 9 hence x = 29 - 9 = 20 hence d"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"E"
],
"text": [
"3",
"4",
"5",
"6"
]
}
|
[
"B"
] |
the smallest value of n , for which 2 n + 1 is not a prime number , is
|
"solution ( 2 × 1 + 1 ) = 3 . ( 2 × 2 + 1 ) = 5 . ( 2 × 3 + 1 ) = 7 . ( 2 × 4 + 1 ) = 9 . which is not prime , n = 4 . answer b"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1865113",
"1775123",
"1765013",
"1675123"
]
}
|
[
"C"
] |
( 4300631 ) - ? = 2535618
|
"let 4300631 - x = 2535618 then x = 4300631 - 2535618 = 1765013 answer is c"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 170",
"rs . 140",
"rs . 1.70",
"rs . 4.25"
]
}
|
[
"B"
] |
if 0.5 % of a = 70 paise , then the value of a is ?
|
"answer ∵ 0.5 / 100 of a = 70 / 100 ∴ a = rs . ( 70 / 0.5 ) = rs . 140 correct option : b"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs 200",
"rs 220",
"rs 260",
"rs 280"
]
}
|
[
"A"
] |
the sale price of a trolley bag including the sale tax is rs . 280 . the rate of sale tax is 12 % . if the shopkeeper has made a profit of 25 % , the cost price of the trolley bag is :
|
"explanation : 112 % of s . p . = 280 s . p . = rs . ( 280 x 100 / 112 ) = rs . 250 . c . p . = rs ( 100 / 125 x 250 ) = rs 200 answer : a"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"4.37 %",
"2 %",
"6 %",
"8.75 %"
]
}
|
[
"B"
] |
the population of a town increased from 1 , 25,000 to 1 , 50,000 in a decade . the average percent increase of population per year is :
|
"solution increase in 10 year = ( 150000 - 125000 ) = 25000 . increase % = ( 25000 / 125000 x 100 ) % = 20 % â ˆ ´ required average = ( 20 / 10 ) % = 2 % answer b"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"85",
"93",
"83",
"72"
]
}
|
[
"B"
] |
the sum of digits of a two digit number is 12 , the difference between the digits is 6 . find the number
|
"description : = > x + y = 12 , x - y = 6 adding these 2 x = 18 = > x = 9 , y = 3 . thus the number is 93 answer b"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 72",
"rs . 36",
"rs . 55",
"rs . 50"
]
}
|
[
"C"
] |
the banker ' s gain on a bill due due 1 year hence at 12 % per annum is rs . 6.6 . the true discount is
|
solution t . d = [ b . g x 100 / r x t ] = rs . ( 6.6 x 100 / 12 x 1 ) = rs . 55 . answer c
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"46 kg",
"48 kg",
"70 kg",
"72 kg"
]
}
|
[
"A"
] |
the average weight of 8 students decreases by 5 kg when one of them weighing 86 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 = 5 kg = > ( 86 - x ) / 8 = 5 = > x = 46 answer : a"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"28800",
"24000",
"24936",
"25640"
]
}
|
[
"A"
] |
80 % of the population of a village is 23040 . the total population of the village is ?
|
"answer ∵ 80 % of p = 23040 ∴ p = ( 23040 x 100 ) / 80 = 28800 correct option : a"
|
MathQA
|
{
"label": [
"A",
"C",
"D",
"E"
],
"text": [
"4",
"2",
"6",
"1"
]
}
|
[
"E"
] |
if p is a prime number greater than 5 , what is the remainder when p ^ 2 is divided by 6 .
|
take square of any prime number remainder will be 1 ans e
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"200",
"230",
"140",
"170"
]
}
|
[
"D"
] |
in the annual cultural programme of indra prastha there was this math quiz going on . yudhisthir faced this last question that will bring the champion ' s trophy . what will be thesolution for the given problem ? the function f is defined is defined asf ( 2 x + 3 ) = ( x - 3 ) ( x + 4 ) what is f ( 29 ) ?
|
explanation : f ( 2 x + 3 ) = ( x - 3 ) ( x + 4 ) put x = 13 f ( 2 * 13 + 3 ) = ( 13 - 3 ) * ( 13 + 4 ) = 10 * 17 f ( 29 ) = 170 answer : d
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"4 : 3",
"8 : 7",
"4 : 1",
"6 : 5"
]
}
|
[
"B"
] |
an order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2 . subsequently , the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter . find the ratio of the areas of the carpets in both the cases .
|
"explanation : let the length and breadth of the carpet in the first case be 3 x units and 2 x units respectively . let the dimensions of the carpet in the second case be 7 y , 3 y units respectively . from the data , . 2 ( 3 x + 2 x ) = 2 ( 7 y + 3 y ) = > 5 x = 10 y = > x = 2 y required ratio of the areas of the carpet in both the cases = 3 x * 2 x : 7 y : 3 y = 6 x 2 : 21 y 2 = 6 * ( 2 y ) 2 : 21 y 2 = 6 * 4 y 2 : 21 y 2 = 8 : 7 answer is b"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"18 %",
"20 %",
"17 %",
"18 %"
]
}
|
[
"C"
] |
a shopkeeper labeled the price of his articles so as to earn a profit of 30 % on the cost price . he then sold the articles by offering a discount of 10 % on the labeled price . what is the actual percent profit earned in the deal ?
|
explanation : let the cp of the article = rs . 100 . then labeled price = rs . 130 . sp = rs . 130 - 10 % of 130 = rs . 130 - 13 = rs . 117 . gain = rs . 117 – rs . 100 = rs . 17 therefore , gain / profit percent = 17 % . answer : option c
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"100 m",
"120 m",
"140 m",
"160 m"
]
}
|
[
"C"
] |
a train covers a distance of 12 km in 10 minutes . if it takes 7 seconds to pass a telegraph post , then the length of the train is
|
"explanation : speed = 12 / 10 x 60 km / hr = 72 x 5 / 18 m / sec = 20 m / sec . length of the train = ( speed x time ) = ( 20 x 7 ) m = 140 m answer : option c"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"296', '",
"252', '",
"344', '",
"388', '"
]
}
|
[
"C"
] |
the sum of four consecutive even numbers is 36 . find the sum of the squares of these numbers ?
|
let the four numbers be x , x + 2 , x + 4 and x + 6 . = > x + x + 2 + x + 4 + x + 6 = 36 = > 4 x + 12 = 36 = > x = 6 the numbers are 6 , 8 , 10 and 12 . sum of their squares = 62 + 82 + 102 + 122 = 36 + 64 + 100 + 144 = 344 . answer : c
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"48 hours",
"51 hours",
"36 hours",
"56 hours"
]
}
|
[
"D"
] |
speed of a boat in standing water is 8 kmph and the speed of the stream is 2 kmph . a man rows to place at a distance of 210 km and comes back to the starting point . the total time taken by him is :
|
"sol . speed upstream = 6 kmph ; speed downstream = 10 kmph . ∴ total time taken = [ 210 / 6 + 210 / 10 ] hours = 56 hours . answer d"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 880",
"rs . 890",
"rs . 1200",
"rs . 900"
]
}
|
[
"C"
] |
if the compound interest on a certain sum of money for 4 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 4 yrs = ( 3000 x 10 x 4 ) / 100 = 1200 / - answer : c ."
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"3",
"2",
"1 / 2",
"1 / 3"
]
}
|
[
"D"
] |
two brothers took the gmat exam , the higher score is u and the lower one is v . if the difference between the two scores is equal to their average , what is the value of v / u ?
|
answer is d : 1 / 3 u - v = ( u + v ) / 2 solving for v / u = 1 / 3 d
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"2.09 %",
"20.9 %",
"209 %",
"0.209 %"
]
}
|
[
"C"
] |
2.09 can be expressed in terms of percentage as
|
"explanation : while calculation in terms of percentage we need to multiply by 100 , so 2.09 * 100 = 209 answer : option c"
|
MathQA
|
{
"label": [
"A",
"B",
"D",
"E"
],
"text": [
"3",
"1 / 2",
"- 1 / 2",
"- 1"
]
}
|
[
"A"
] |
if | x | = 4 x - 1 , then x = ?
|
"answer : a approach : substituted option a i . e x = 1 . inequality satisfied ."
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"12.50 %",
"13.50 %",
"5 %",
"14.50 %"
]
}
|
[
"C"
] |
an uneducated retailer marks all his goods at 40 % 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 . 140 . s . p . = 75 % of rs . 140 = rs . 105 . ∴ gain % = 5 % . answer c
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"800",
"3200",
"900",
"1600"
]
}
|
[
"B"
] |
find the value of 4 x [ ( 3.6 x 0.48 x 2.50 ) / ( 0.12 x 0.09 x 0.5 ) ]
|
"answer 4 x [ ( 3.6 x 0.48 x 2.50 ) / ( 0.12 x 0.09 x 0.5 ) ] = 4 x [ ( 36 x 48 x 250 ) / ( 12 x 9 x 5 ) ] = 4 x 4 x 4 x 50 = 3200 correct option : b"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"16000",
"18000",
"20000",
"30000"
]
}
|
[
"D"
] |
a courtyard is 18 meter long and 12 meter board is to be paved with bricks of dimensions 12 cm by 6 cm . the total number of bricks required is :
|
"explanation : number of bricks = courtyard area / 1 brick area = ( 1800 ã — 1200 / 12 ã — 6 ) = 30000 option d"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"9 %",
"9.27 %",
"22.50 %",
"12 %"
]
}
|
[
"C"
] |
the population of a city increases by 8 % 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 = 7 % let , earlier population = 100 then the population after 3 years = 100 ( 1 + 7 / 100 ) ^ 3 = 122.5043 ∴ required percentage = 22.50 % answer : c"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"546",
"674",
"672",
"960"
]
}
|
[
"A"
] |
in an office in singapore there are 60 % female employees . 50 % of all the male employees are computer literate . if there are total 62 % employees computer literate out of total 1300 employees , then the no . of female employees who are computer literate ?
|
"solution : total employees , = 1300 female employees , 60 % of 1300 . = ( 60 * 1300 ) / 100 = 780 . then male employees , = 520 50 % of male are computer literate , = 260 male computer literate . 62 % of total employees are computer literate , = ( 62 * 1300 ) / 100 = 806 computer literate . thus , female computer literate = 806 - 260 = 546 . answer : option a"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"12 kg",
"120 kg",
"72 kg",
"96 kg"
]
}
|
[
"B"
] |
a boat having a length 4 m and breadth 3 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 3 x 0.01 ) m 3 = 0.12 m 3 . ∴ mass of man = volume of water displaced x density of water = ( 0.12 x 1000 ) kg = 120 kg . answer : b"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"20 kg",
"25 kg",
"30 kg",
"35 kg"
]
}
|
[
"B"
] |
when the price of sugar was increased by 32 % , a family reduced its consumption in such a way that the expenditure on sugar was only 10 % more than before . if 30 kg were consumed per month before , find the new monthly consumption .
|
since , expenditure = price × consumption ∴ 110 % of 30 = 132 ⁄ 100 × new consumption ⇒ 110 ⁄ 100 × 30 = 132 ⁄ 100 × new consumption ⇒ new consumption = 25 kg answer b
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 2000",
"rs . 10,500",
"rs . 15,500",
"rs . 22,500"
]
}
|
[
"D"
] |
a man took a loan from a bank at the rate of 8 % 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 / 8 x 3 ) = rs . 22,500 . answer d
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"12 kg",
"60 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 cm when a man gets on it . the mass of man is :
|
"solution volume of water displaced = ( 3 × 2 × 0.01 ) m 3 = 0.06 m 3 . ∴ mass of man = volume of water displaced × density of water = ( 0.06 × 100 ) kg = 60 kg . answer b"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"78 kg",
"60 kg",
"64 kg",
"70 kg"
]
}
|
[
"A"
] |
zinc and copper are melted together in the ratio 9 : 11 . what is the weight of melted mixture , if 35.1 kg of zinc has been consumed in it ?
|
"sol . for 9 kg zinc , mixture melted = ( 9 + 11 ) kg . for 35.1 kg zinc , mixture , melted = [ 20 / 9 x 35.1 ] kg = 78 kg . answer a"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"6",
"12",
"24",
"120"
]
}
|
[
"C"
] |
the largest natural number which exactly divides the product of any 4 consecutive natural numbers is
|
sol . required number = 1 × 2 × 3 × 4 = 24 . answer c
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"3327",
"3237",
"3927",
"2337"
]
}
|
[
"C"
] |
9873 + x = 13800 , then x is ?
|
"answer x = 13800 - 9873 = 3927 option : c"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"45 ( 4 / 11 ) %",
"45 %",
"53 ( 11 / 13 ) %",
"44 ( 5 / 11 ) %"
]
}
|
[
"C"
] |
a batsman scored 130 runs which included 3 boundaries and 8 sixes . what percent of his total score did he make by running between the wickets ?
|
"explanation : total runs scored = 130 total runs scored from boundaries and sixes = 3 x 4 + 8 x 6 = 60 total runs scored by running between the wickets = 130 - 60 = 70 required % = ( 70 / 130 ) × 100 = 700 / 13 = 53 ( 11 / 13 ) % answer : option c"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"50",
"60",
"80",
"320"
]
}
|
[
"A"
] |
a number exceeds 20 % of itself by 40 . the number is
|
"explanation : let the answer be ' a ' then a − 20 / 100 a = 40 ⇒ 5 a − a = 200 ⇒ a = 50 ⇒ a = 50 correct option : a"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"120,50",
"180,60",
"180,90",
"120,40"
]
}
|
[
"A"
] |
a third of arun â € ™ s marks in mathematics exceed a half of his marks in english by 15 . if he got 170 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 = 15 2 x - 3 y = 90 â € ¦ â € ¦ > ( 1 ) x + y = 170 â € ¦ â € ¦ . > ( 2 ) solving ( 1 ) and ( 2 ) x = 120 and y = 50 answer is a .
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"178",
"176",
"175",
"96"
]
}
|
[
"A"
] |
a train passes a man standing on a platform in 8 seconds and also crosses the platform which is 267 metres long in 20 seconds . the length of the train ( in metres ) is :
|
explanation : let the length of train be l m . acc . to question ( 267 + l ) / 20 = l / 8 2136 + 8 l = 20 l l = 2136 / 12 = 178 m answer a
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"160",
"180",
"200",
"240"
]
}
|
[
"D"
] |
a number whose fifth part increased by 6 is equal to its fourth part diminished by 6 is ?
|
"answer let the number be n . then , ( n / 5 ) + 6 = ( n / 4 ) - 6 â ‡ ’ ( n / 4 ) - ( n / 5 ) = 12 â ‡ ’ ( 5 n - 4 n ) / 20 = 12 â ˆ ´ n = 240 option : d"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1 : 4",
"1 : 25",
"1 : 52",
"1 : 522"
]
}
|
[
"A"
] |
a cube of edge 6 cm is cut into cubes each of edge 3 cm . the ratio of the total surface area of one of the small cubes to that of the large cube is equal to :
|
"sol . required ratio = 6 * 3 * 3 / 6 * 6 * 6 = 1 / 4 = 1 : 4 . answer a"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 120",
"rs . 160",
"rs . 240",
"rs . 330"
]
}
|
[
"D"
] |
a sum of rs . 1870 has been divided among a , b and c such that a gets of what b gets and b gets of what c gets . b ’ s share is :
|
"explanation let c ’ s share = rs . x then , b ’ s share = rs . x / 4 , a ’ s share = rs . ( 2 / 3 x x / 4 ) = rs . x / 6 = x / 6 + x / 4 + x = 1870 = > 17 x / 12 = 1870 = > 1870 x 12 / 17 = rs . 1320 hence , b ’ s share = rs . ( 1320 / 4 ) = rs . 330 . answer d"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"0.1484",
"14.84",
"1.484",
"2.762"
]
}
|
[
"C"
] |
by how much is 12 % of 24.2 more than 10 % of 14.2 ?
|
"answer required difference = ( 12 x 24.2 ) / 100 - ( 10 x 14.2 ) / 100 = 2.904 - 1.42 = 1.484 . correct option : c"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"60 kg",
"63 kg",
"50 kg",
"77 kg"
]
}
|
[
"B"
] |
how many kilograms of sugar costing rs . 9 per kg must be mixed with 27 kg of sugar costing rs . 7 per kg so that there may be gain of 10 % by selling the mixture at rs . 9.24 per kg ?
|
"explanation : let the rate of second quality be rs x per kg . step 1 : s . p of 1 kg of mixture = rs . 9.24 gain = 10 % c . p of 1 kg of mixture = [ 100 / ( 100 + 10 ) × 9.24 ] . = > rs . 8.40 . thus , the mean price = rs . 8.40 . step 2 : c . p of 1 kg of sugar of 1 st kind = 900 p c . p of 1 kg of sugar of 2 nd kind = 700 p mean price = 840 p by the rule of alligation , we have : c . p . of 1 kg of c . p . of 1 kg of sugar of 1 st sugar of 2 nd kind ( 900 p ) kind ( 700 p ) \ / mean price ( 840 p ) / \ 840 - 700 : 900 - 840 ( 140 ) ( 60 ) = > required ratio = 140 : 60 = 7 : 3 . step 3 : let , x kg of sugar of 1 st kind be mixed with 27 kg of 2 nd kind , then = > 7 : 3 = x : 27 . = > 7 / 3 = x / 27 . = > x = ( 7 / 3 ) x 27 . = > x = 63 . answer : b"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 692.80",
"rs . 820",
"rs . 1170",
"rs . 1385"
]
}
|
[
"C"
] |
average monthly income of a family of 4 earning members was rs . 735 . one of the earning members died and therefore , the average income came down to rs 590 . the income of the deceased was ?
|
"answer income of the deceased = total income of 4 members - total income of remaining 3 members . = 735 x 4 - 590 x 3 rs . = 1170 rs . correct option : c"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"144",
"288",
"36",
"256"
]
}
|
[
"C"
] |
in how many ways 3 boys and 3 girls can be seated in a row so that they are alternate .
|
"solution : let the arrangement be , b g b g b g b 34 boys can be seated in 3 ! ways . girl can be seated in 3 ! ways . required number of ways , = 3 ! * 3 ! = 36 . answer : option c"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"95",
"99",
"26",
"73"
]
}
|
[
"B"
] |
what two - digit number is less than the sum of the square of its digits by 13 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 - 13 thus 2 xy + 5 = x ^ 2 + y ^ 2 - 13 x ^ 2 + y ^ 2 - 2 xy = 16 ( 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 99 thus the answer is b
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"20 %",
"25 %",
"55 %",
"65 %"
]
}
|
[
"A"
] |
the ratio 4 : 20 expressed as percent equals to
|
explanation : actually it means 4 is what percent of 20 , which can be calculated as , ( 4 / 20 ) * 100 = 4 * 5 = 20 answer : option a
|
MathQA
|
{
"label": [
"B",
"C",
"D",
"E"
],
"text": [
"$ 81.90",
"$ 8190.03",
"$ 819.00",
"$ 8.19"
]
}
|
[
"D"
] |
jack takes a loan of $ 120000 with 12 % annual interest : the interest is paid once , at the end of the year . jill takes a loan of $ 120000 with 12 % annual interest , compounding monthly at the end of each month . at the end of one full year , compared to jack ' s loan interest , approximately how much more does jill have to repay ?
|
jack ' s interest = $ 120,000 * 0.12 = $ 14400 or $ 1,200 each month . jills ’ s interest , 12 % / 12 = 1 % each month : for the 1 st month = $ 120,000 * 0.01 = $ 1,200 ; for the 2 nd month = $ 1,200 + 1 % of 1,200 = $ 1,212 , so we would have interest earned on interest ( very small amount ) ; for the 3 rd month = $ 1,212 + 1 % of 1,212 = ~ $ 1,224 ; for the 4 th month = $ 1,224 + 1 % of 1,224 = ~ $ 1,236 ; . . . for the 12 th month = $ 1,320 + 1 % of 1,320 = ~ $ 1,332 . the difference between jack ' s interest and jill ’ s interest = ~ ( 12 + 24 + . . . + 132 ) = $ 792 . answer : d .
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"E"
],
"text": [
"700",
"900",
"705",
"506"
]
}
|
[
"B"
] |
evaluate 45 / . 05
|
"explanation : 45 / . 05 = 4500 / 5 = 900 option b"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"2000",
"2573",
"1600",
"2950"
]
}
|
[
"C"
] |
solve for x and check : - 200 x = 1600
|
"solution : dividing each side by - 200 , we obtain ( - 200 x / - 200 ) = ( 1600 / - 200 ) therefore : x = - 8 check : - 200 x = 1600 ( - 200 * - 8 ) = 1600 1600 = 1600 answer : c"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"2 / 5",
"3 / 5",
"1 / 6",
"1"
]
}
|
[
"D"
] |
what is difference between biggest and smallest fraction among 2 / 3 , 3 / 4 , 4 / 5 and 5 / 3
|
"explanation : 2 / 3 = . 66 , 3 / 4 = . 75 , 4 / 5 = . 8 and 5 / 3 = 1.66 so biggest is 5 / 3 and smallest is 2 / 3 their difference is 5 / 3 - 2 / 3 = 3 / 3 = 1 option d"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"12.4",
"14",
"16",
"18.6"
]
}
|
[
"C"
] |
the average of 10 numbers is calculated as 15 . it is discovered later on that while calculating the average one number , namely 36 was wrongly read as 26 . the correct average is :
|
explanation : sum of numbers = ( 10 × × 15 - 26 + 36 ) = 160 correct average = 160 / 10 = 16 correct option : c
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"600",
"750",
"1000",
"1250"
]
}
|
[
"D"
] |
a man walking at the rate of 5 km / hr crosses a bridge in 15 minutes . the length of the bridge ( in metres ) is
|
"explanation : speed = ( 5 × 5 / 18 ) m / sec = 25 / 18 m / sec . distance covered in 15 minutes = ( 25 / 18 × 15 × 60 ) m = 1250 m . answer : d"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1 : 5",
"9 : 25",
"5 : 1",
"25 : 9"
]
}
|
[
"C"
] |
two interconnected , circular gears travel at the same circumferential rate . if gear a has a diameter of 10 centimeters and gear b has a diameter of 50 centimeters , what is the ratio of the number of revolutions that gear a makes per minute to the number of revolutions that gear b makes per minute ?
|
"same circumferential rate means that a point on both the gears would take same time to come back to the same position again . hence in other words , time taken by the point to cover the circumference of gear a = time take by point to cover the circumference of gear b time a = 2 * pi * 25 / speed a time b = 2 * pi * 5 / speed b since the times are same , 50 pi / speed a = 10 pi / speed b speeda / speed b = 50 pi / 30 pi = 5 / 1 correct option : c"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 80",
"rs . 86",
"rs . 90",
"rs . 95"
]
}
|
[
"B"
] |
a trader sells 45 meters of cloth for rs . 4500 at the profit of rs . 14 per metre of cloth . what is the cost price of one metre of cloth ?
|
"sp of 1 m of cloth = 4500 / 45 = rs . 100 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 105 - rs . 14 = rs . 86 . answer : b"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"5 : 2",
"7 : 3",
"9 : 2",
"13 : 4"
]
}
|
[
"B"
] |
the age of father 10 years ago was thirce the age of his son . 10 years hence , father ’ s age will be twice that of his son . the ration of their present ages is :
|
solution let the ages of father and son 10 year ago be 3 x and x years respectively . then , ( 3 x + 10 ) + 10 = 2 [ ( x + 10 ) + 10 ⇔ 3 x + 20 = 2 x + 40 ⇔ x = 20 . ∴ required ratio = ( 3 x + 10 ) : ( x + 10 ) = 70 : 30 : 7 : 3 . answer b
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"100', '",
"120', '",
"150', '",
"180', '"
]
}
|
[
"B"
] |
one side of a rectangular field is 15 m and one of its diagonal is 17 m . find the area of the field .
|
solution other side = √ ( 17 ) 2 - ( 15 ) 2 = √ 289 - 225 = √ 64 = 8 m . ∴ area = ( 15 x 8 ) m 2 = 120 m 2 . answer b
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs 840",
"rs 1320",
"rs 1620",
"rs 1890"
]
}
|
[
"D"
] |
if 4 men working 10 hours a day earn rs . 1400 per week , then 9 men working 6 hours a day will earn how much per week ?
|
"explanation : ( men 4 : 9 ) : ( hrs / day 10 : 6 ) : : 1400 : x hence 4 * 10 * x = 9 * 6 * 1400 or x = 9 * 6 * 1400 / 4 * 10 = 1890 answer : d"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"350",
"370",
"390",
"430"
]
}
|
[
"B"
] |
average expenditure of a person for the first 3 days of a week is rs . 330 and for the next 4 days is rs . 420 . average expenditure of the man for the whole week is :
|
"explanation : assumed mean = rs . 330 total excess than assumed mean = 4 × ( rs . 420 - rs . 350 ) = rs . 280 therefore , increase in average expenditure = rs . 280 / 7 = rs . 40 therefore , average expenditure for 7 days = rs . 330 + rs . 40 = rs . 370 correct option : b"
|
MathQA
|
{
"label": [
"A",
"B",
"D",
"E"
],
"text": [
"32",
"37",
"43",
"50"
]
}
|
[
"E"
] |
set x consists of 10 integers and has median of 30 and a range of 30 . what is the value of the greatest possible integer that can be present in the set ?
|
"note that both median and range do not restrict too many numbers in the set . range is only concerned with the smallest and greatest . median only cares about the middle . quick check of each option starting from the largest : ( e ) 50 range of 20 means the smallest integer will be 30 . so 20 can not lie in between and hence can not be the median . ( d ) 43 range of 20 means the smallest integer will be 23 . so 20 can not lie in between and hence can not be the median . ( c ) 40 range of 20 means the smallest integer will be 20 . 20 can lie in between such as : 20 , 20 , 20 , 20 , 20 , 20 , 20 , 20 , 20 , 40 , 50 this is possible . hence it is the greatest such number . answer ( e )"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"15 %",
"20 %",
"23 %",
"30 %"
]
}
|
[
"C"
] |
if the price of sugar rises from rs . 10 per kg to rs . 13 per kg , a person , to have no increase in the expenditure on sugar , will have to reduce his consumption of sugar by
|
"sol . let the original consumption = 100 kg and new consumption = x kg . so , 100 x 10 = x × 13 = x = 77 kg . ∴ reduction in consumption = 23 % . answer c"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"80 kmph",
"69 kmph",
"70 kmph",
"90 kmph"
]
}
|
[
"B"
] |
a train travels 290 km in 4.5 hours and 400 km in 5.5 hours . find the average speed of train .
|
"as we know that speed = distance / time for average speed = total distance / total time taken thus , total distance = 290 + 400 = 690 km thus , total speed = 10 hrs or , average speed = 690 / 10 or , 69 kmph . answer : b"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1584', '",
"1854', '",
"1458', '",
"1485', '"
]
}
|
[
"A"
] |
the radius of a cylinder is 12 m , height 21 m . the lateral surface area of the cylinder is :
|
lateral surface area = 2 π rh = 2 × 22 / 7 × 12 × 21 = 44 × 36 = 1584 m ( power 2 ) answer is a .
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"10 %",
"50 %",
"25 %",
"17.6 %"
]
}
|
[
"D"
] |
a retailer buys a radio for rs 225 . his overhead expenses are rs 30 . he sellis the radio for rs 300 . the profit percent of the retailer is
|
"explanation : cost price = ( 225 + 30 ) = 255 sell price = 300 gain = ( 45 / 255 ) * 100 = 17.6 % . answer : d"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"41",
"910",
"1001",
"1911"
]
}
|
[
"A"
] |
the maximum numbers of students among them 451 pens and 410 toys can be distributed in such a way that each student gets the same number of pens and same number of toys is
|
"olution required number of students . = h . c . f of 451 and 410 . â € ¹ = â € º 41 . answer a"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"120 m .",
"80 m .",
"150 m .",
"100 m ."
]
}
|
[
"A"
] |
a runs twice as fast as b and gives b a start of 60 m . how long should the racecourse be so that a and b might reach in the same time ?
|
ratio of speeds of a and b is 2 : 1 b is 60 m away from a but we know that a covers 1 meter ( 2 - 1 ) more in every second than b the time taken for a to cover 60 m is 60 / 1 = 60 m so the total time taken by a and b to reach = 2 * 60 = 120 m answer : a
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"20 , 35,45",
"28 , 49,63",
"16 , 28,36",
"16 , 28,46"
]
}
|
[
"B"
] |
the present ages of 3 persons are in the proportion of 4 : 7 : 9 . 8 years ago , the sum of their ages was 116 . find their present ages .
|
let the present ages of three persons be 4 k , 7 k and 9 k respectively . ( 4 k - 8 ) + ( 7 k - 8 ) + ( 9 k - 8 ) = 116 20 k = 140 k = 7 therefore , then present ages are 28 , 49,63 . answer : b
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"81 min",
"108 min",
"144 min",
"192 min"
]
}
|
[
"C"
] |
one pipe can fill a tank three times as fast as another pipe . if together the two pipes can fill the tank in 86 minutes , then the slower pipe alone will be able to fill the tank in
|
"solution let the slower pipe alone fill the tank in x minutes . then , faster pipes will fill it in x / 3 minutes . therefore , 1 / x + 3 / x = 1 / 36 ‹ = › 4 / x = 1 / 36 ‹ = › x = 144 min . answer c"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 600",
"rs . 500",
"rs . 400",
"rs . 300"
]
}
|
[
"A"
] |
the banker ' s gain of a certain sum due 2 years hence at 10 % per annum is rs . 24 . what is the present worth ?
|
"explanation : t = 2 years r = 10 % td = ( bg × 100 ) / tr = ( 24 × 100 ) / ( 2 × 10 ) = 12 × 10 = rs . 120 td = ( pw × tr ) / 100 ⇒ 120 = ( pw × 2 × 10 ) / 100 ⇒ 1200 = pw × 2 pw = 1200 / 2 = rs . 600 answer : option a"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"960",
"1060",
"1,200",
"1020"
]
}
|
[
"D"
] |
the profit earned by selling an article for 912 is equal to the loss incurred when the same article is sold for 448 . what should be the sale price of the article for making 50 per cent profit ?
|
"let the profit or loss be x and 912 – x = 448 + x or , x = 464 ⁄ 2 = 232 \ cost price of the article = 912 – x = 448 + x = 680 \ sp of the article = 680 × 150 ⁄ 100 = 1020 answer d"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"25",
"60",
"90",
"140"
]
}
|
[
"B"
] |
if the average ( arithmetic mean ) of a and b is 30 and the average of b and c is 60 , what is the value of c − a ?
|
- ( a + b = 60 ) b + c = 120 c - a = 60 b . 60
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1.9732",
"1.0025",
"1.5693",
"1.0266"
]
}
|
[
"A"
] |
given that 268 x 74 = 19732 , find the value of 2.68 x . 74 .
|
"solution sum of decimals places = ( 2 + 2 ) = 4 . therefore , = 2.68 × . 74 = 1.9732 answer a"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"10 %",
"11 %",
"12 %",
"10.5 %"
]
}
|
[
"B"
] |
on a sum of money , the simple interest for 2 years is rs . 660 , while the compound interest is rs . 696.30 , the rate of interest being the same in both the cases . the rate of interest is
|
"solution difference in c . i and s . i for 2 years = rs ( 696.30 - 660 ) = rs . 36.30 . s . i for one years = rs 330 . s . i on rs . 330 for 1 year = rs . 36.30 rate = ( 100 x 36.30 / 330 x 1 ) % = 11 % . answer b"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"5 hours",
"4 hours",
"3 hours",
"2 hours"
]
}
|
[
"C"
] |
a boat can travel with a speed of 22 km / hr in still water . if the speed of the stream is 5 km / hr , find the time taken by the boat to go 81 km downstream
|
"explanation : speed of the boat in still water = 22 km / hr speed of the stream = 5 km / hr speed downstream = ( 22 + 5 ) = 27 km / hr distance travelled downstream = 81 km time taken = distance / speed = 81 / 27 = 3 hours . answer : option c"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"22.2 %",
"36 %",
"80 %",
"122.2 %"
]
}
|
[
"D"
] |
the cost price of an article is 36 % of the marked price . calculate the gain percent after allowing a discount of 20 % .
|
"sol . let marked price = rs . 100 . then , c . p . = rs . 36 . s . p = rs . 80 . â ˆ ´ gain % = [ 44 / 36 * 100 ] % = 122.2 % . answer d"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"18 %",
"21 %",
"25.9 %",
"19 %"
]
}
|
[
"C"
] |
mahesh marks an article 15 % above the cost price of rs . 540 . what must be his discount percentage if he sells it at rs . 460 ?
|
cp = rs . 540 , mp = 540 + 15 % of 540 = rs . 621 sp = rs . 460 , discount = 621 - 460 = 161 discount % = 161 / 621 * 100 = 25.9 % answer : c
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1 / 5",
"1 / 6",
"1 / 7",
"3 / 10"
]
}
|
[
"D"
] |
a can finish a work in 10 days and b can do same work in half the time taken by a . then working together , what part of same work they can finish in a day ?
|
"explanation : please note in this question , we need to answer part of work for a day rather than complete work . it was worth mentioning here because many do mistake at this point in hurry to solve the question so lets solve now , a ' s 1 day work = 1 / 10 b ' s 1 day work = 1 / 5 [ because b take half the time than a ] ( a + b ) ' s one day work = ( 1 / 10 + 1 / 5 ) = 3 / 10 so in one day 3 / 10 work will be done answer : d"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"14",
"42",
"28",
"12"
]
}
|
[
"B"
] |
two sets of 6 consecutive positive integers have exactly one integer in common . the sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set ?
|
"a = ( 1,2 , 3,4 , 5,6 ) , sum of this = 21 b = ( 6 , 7,8 , 9,10 , 11,12 ) , sum of this = 63 , the differenct between 63 - 21 = 42 hence , 42 is the answer i . e . b"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"56.25",
"60",
"52.5",
"5.25"
]
}
|
[
"A"
] |
what is the sum of the first 15 terms of an a . p whose 11 th and 7 th terms are 5.25 and 3.25 respectively
|
a + 10 d = 5.25 , a + 6 d = 3.25 , 4 d = 2 , d = ½ a + 5 = 5.25 , a = 0.25 = ¼ , s 15 = 15 / 2 ( 2 * ¼ + 14 * ½ ) = 15 / 2 ( 1 / 2 + 14 / 2 ) = 15 / 2 * 15 / 2 = 225 / 4 = 56.25 answer : a
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"10",
"15",
"20",
"25"
]
}
|
[
"A"
] |
in a class , 30 students pass in english and 20 students in math , while some students among these pass in both . how many more students do only english as compared to those doing only maths ?
|
let us consider tht x student are tohse who passed in both english and maths . . . so first we remove x student from both of them therefore , english = 30 - x maths = 20 - x now , number of students more in english = ( 30 - x ) - ( 20 - x ) = 30 - x - 20 + x = 10 answer : a
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"70",
"7",
"0.7",
"0.07"
]
}
|
[
"D"
] |
0.0007 ? = 0.01
|
"explanation : required answer = 0.0007 / 0.01 = 0.07 / 1 = 0.07 . answer : option d"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"84 m",
"88 m",
"42 m",
"137 m"
]
}
|
[
"C"
] |
33 cubic centimetres of silver is drawn into a wire 1 mm in diameter . the length of the wire in metres will be :
|
"sol . let the length of the wire b h . radius = 1 / 2 mm = 1 / 20 cm . then , 22 / 7 * 1 / 20 * 1 / 20 * h = 33 ⇔ = [ 33 * 20 * 20 * 7 / 22 ] = 4200 cm = 42 m . answer c"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"0.000196",
"0.00196",
"19.6",
"196"
]
}
|
[
"A"
] |
0.014 × 0.014 = ?
|
"solution sum of decimals places = 6 . 14 × 14 = 196 . = s 0.014 × 0.014 = 0.000196 answer a"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"3 / 4",
"1 / 4",
"3 / 8",
"7 / 8"
]
}
|
[
"D"
] |
three unbiased coins are tossed . what is the probability of getting at most two heads ?
|
explanation : here s = { ttt , tth , tht , htt , thh , hth , hht , hhh } let e = event of getting at most two heads . then e = { ttt , tth , tht , htt , thh , hth , hht } . p ( e ) = n ( e ) / n ( s ) = 7 / 8 . answer is d
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 15,000",
"rs . 15,500",
"rs . 12,375",
"rs . 16,500"
]
}
|
[
"C"
] |
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 . 600 per sq . metre .
|
"solution area of the floor = ( 5.5 x 3.75 ) m ² = 20.635 m ² cost of paying = rs . ( 600 x 20.625 ) = rs . 12,375 . answer c"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"16",
"1.6",
"0.16",
"0.016"
]
}
|
[
"B"
] |
if 204 ÷ 12.75 = 16 , then 2.04 ÷ 1.275 = ?
|
explanation : ( 204 / 12.75 ) = 16 ⇒ ( 20.4 ) / ( 1.275 ) = 16 ( ∵ divided numerator and denominator by 10 ) ⇒ 2.04 / 1.275 = 1.6 ( ∵ divided lhs and rhs by 10 ) answer : option b
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"82 m",
"50 m",
"75 m",
"80 m"
]
}
|
[
"C"
] |
two trains of equal length are running on parallel lines in the same directions at 46 km / hr . and 36 km / hr . the faster trains pass the slower train in 54 seconds . the length of each train is :
|
"explanation : the relative speed of train is 46 - 36 = 10 km / hr = ( 10 x 5 ) / 18 = 25 / 9 m / s 10 × 518 = 259 m / s in 54 secs the total distance traveled is 54 x 25 / 9 = 150 m . therefore the length of each train is = 150 / 2 = 75 m . answer c"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"22.8 kg",
"26.6 kg",
"28 kg",
"26.5 kg"
]
}
|
[
"B"
] |
if 11.25 m of a uniform steel rod weighs 42.75 kg . what will be the weight of 7 m of the same rod ?
|
"explanation : let the required weight be x kg . then , less length , less weight ( direct proportion ) = > 11.25 : 7 : : 42.75 : x = > 11.25 x x = 7 x 42.75 = > x = ( 7 x 42.75 ) / 11.25 = > x = 26.6 answer : b"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"144 m 2",
"140 m 2",
"108 m 2",
"158 m 2"
]
}
|
[
"B"
] |
the floor of a rectangular room is 19 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 = 23 ã — 16 = 368 m 2 area of the inner rectangle = 19 ã — 12 = 228 m 2 required area = ( 368 â € “ 228 ) = 140 m 2 answer b"
|
MathQA
|
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"761200",
"761400",
"761800",
"210000"
]
}
|
[
"D"
] |
simplify : 500 x 500 - 200 x 200
|
"( 500 ) ^ 2 - ( 200 ) ^ 2 = ( 500 + 200 ) ( 500 - 200 ) = 700 x 300 = 210000 . answer is d ."
|
MathQA
|
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