Cheukting/mathqa huggingface dataset:
Question (general): a teacher gave the same test to 3 history classes : u , b , and c . the average ( arithmetic mean ) scores for the 3 classes were 65 , 80 , and 77 , respectively . the ratio of the numbers of students in each class who took the test was 4 to 6 to 5 , respectively . what was the average score for the 3 classes combined ?
Options: a ) 74 , b ) 75 , c ) 76 , d ) 77 , e ) 78
Rationale: ans : b ( 75 ) lets say class u indeed has 4 children , b has 6 children and c has 5 children . now , if the average of class u is 65 , hence total marks awarded in the class = 65 * 4 = 260 similarly , class b = 80 * 6 = 480 class c = 77 * 5 = 385 total marks provided = u + b + c = 260 + 480 + 385 = 1125 avg . marks = 1125 / 15 ( total no . of students ) = 75 = b
Answer: b
Question (geometry): a cube of edge 15 cm is immersed completely in a rectangular vessel containing water . if the dimensions of the base of vessel are 20 cm * 15 cm , find the rise in water level ?
Options: a ) 6 cm , b ) 8.25 cm , c ) 11.25 cm , d ) 15.12 cm , e ) 20.62 cm
Rationale: "increase in volume = volume of the cube = 15 * 15 * 15 cm ^ 3 rise in water level = volume / area = 15 * 15 * 15 / 20 * 15 = 11.25 cm answer is c"
Answer: c
Question (general): how many positive integers less than 28 are prime numbers , odd multiples of 5 , or the sum of a positive multiple of 2 and a positive multiple of 4 ?
Options: a ) 27 , b ) 25 , c ) 24 , d ) 22 , e ) 20
Rationale: "9 prime numbers less than 28 : { 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 } 3 odd multiples of 5 : { 5 , 15 , 25 } 11 numbers which are the sum of a positive multiple of 2 and a positive multiple of 4 : { 6 , 8 , 10 , 12 , 14 , 16 , 18 , 20 , 22 , 24 , 26 } notice , that 5 is in two sets , thus total # of integers satisfying the given conditions is 9 + 3 + 11 - 1 = 22 . answer : d ."
Answer: d
Question (general): what are the last two digits of 63 * 35 * 37 * 82 * 71 * 41 * 53 ?
Options: a ) 10 , b ) 30 , c ) 40 , d ) 70 , e ) 80
Rationale: we know that to find the last two digits , we need to find the remainder we get when we divide the product by 100 . remainder of ( 63 * 35 * 37 * 82 * 71 * 41 ) / 100 note that we can simplify this expression by canceling out the 5 and 2 in the numerator and denominator . but before we do that , here is an important note : note : we can not just cancel off the common terms in the numerator and denominator to get the remainder . but , if we want to cancel off to simplify the question , we can do it , provided we remember to multiply it back again . so say , we want to find the remainder when 14 is divided by 10 i . e . 14 / 10 ( remainder 4 ) . but we cancel off the common 2 to get 7 / 5 . the remainder here will be 2 which is not the same as the remainder obtained by dividing 14 by 10 . but if we multiply 2 back by 2 ( the number we canceled off ) , the remainder will become 2 * 2 = 4 which is correct . take another example to reinforce this – what is the remainder when 85 is divided by 20 ? it is 5 . we might rephrase it as – what is the remainder when 17 is divided by 4 ( cancel off 5 from the numerator and the denominator ) . the remainder in this case is 1 . we multiply the 5 back to 1 to get the remainder as 5 which is correct . so keeping this very important point in mind , let ’ s go ahead and cancel the common 5 and 2 . we need the remainder of ( 63 * 7 * 37 * 41 * 71 * 41 * 5 * 2 ) / 10 * 5 * 2 remainder of ( 63 * 7 * 37 * 41 * 71 * 41 ) / 10 now using concept 2 , let ’ s write the numbers in form of multiples of 10 remainder of ( 60 + 3 ) * 7 * ( 30 + 7 ) * ( 40 + 1 ) * ( 70 + 1 ) * ( 40 + 1 ) / 10 remainder of 3 * 7 * 7 * 1 * 1 * 1 / 10 remainder of 147 / 10 = 7 now remember , we had canceled off 10 so to get the actual remainder so we need to multiply by 10 : 7 * 10 = 70 . when 63 * 35 * 37 * 82 * 71 * 41 is divided by 100 , the remainder is 70 . so the last two digits of 63 * 35 * 37 * 82 * 71 * 41 must be 80 . answer ( e )
Answer: e
Question (general): in n is a positive integer less than 200 , and 27 n / 60 is an integer , then n has how many different positive prime factors ?
Options: a ) 2 , b ) 3 , c ) 5 , d ) 6 , e ) 8
Rationale: "( a ) . 27 n / 60 must be an integer . = > 9 n / 20 must be an integer . hence n must be a multiple of 2 * 5 . = > n has 2 different prime integers ."
Answer: a
Question (other): the ratio of the adjacent angles of a parallelogram is 5 : 10 . also , the ratio of the angles of quadrilateral is 5 : 6 : 7 : 12 . what is the sum of the smaller angle of the parallelogram and the second largest angle of the quadrilateral ?
Options: a ) 168 ° , b ) 228 ° , c ) 144 ° , d ) 224 ° , e ) none of these
Rationale: "the measures of the adjacent angles of a parallelogram add up to be 180 ° given so , 5 x + 10 x = 180 ° or , 15 x = 180 ° or , x = 12 ° hence the angles of the parallelogram are 60 ° and 120 ° further it is given we know sum of all the four angles of a quadrilateral is 360 ° so , 5 y + 6 y + 7 y + 12 y = 360 ° or , 5 y + 6 y + 7 y + 12 y = 360 ° or , 30 y = 360 ° or , y = 12 ° hence the angles of the quadrilateral are 60 ° , 72 , 84 ° and 144 ° will be 60 ° + 84 ° = 144 ° answer : c"
Answer: c
Question (general): the population of a city increases by 5 % per year but due to migration it decrease by 1 % per years . what will be the percentage increase in population in 3 years ?
Options: a ) 9 % , b ) 9.27 % , c ) 27 % , d ) 12.48 % , e ) none of these
Rationale: "actual increase in population = 4 % let , earlier population = 100 then the population after 3 years = 100 ( 1 + 4 / 100 ) ^ 3 = 112.4864 ∴ required percentage = 12.48 % answer : d"
Answer: d
Question (general): the sum of the present age of henry and jill is 33 . what is their present ages if 6 years ago henry was twice the age of jill ?
Options: a ) and 20 , b ) and 24 , c ) and 22 , d ) and 29 , e ) of these
Rationale: "let the age of jill 6 years ago be x , age of henry be 2 x x + 6 + 2 x + 6 = 33 x = 7 present ages will be 13 and 20 answer : a"
Answer: a
Question (general): in a division sum , the remainder is 5 and the divisor is 3 times the quotient and is obtained by adding 3 to the thrice of the remainder . the dividend is :
Options: a ) 72 , b ) 76 , c ) 100 , d ) 113 , e ) 112
Rationale: "diver = ( 5 * 3 ) + 3 = 18 3 * quotient = 18 quotient = 6 dividend = ( divisor * quotient ) + remainder dividend = ( 18 * 6 ) + 5 = 113 d"
Answer: d
Question (general): what is the sum of the multiples of 4 between 34 and 135 inclusive ?
Options: a ) 2000 , b ) 2100 , c ) 2150 , d ) 2200 , e ) 2500
Rationale: the fastest way in an ap is to find the average and multiply with total integers . . between 34 and 135 , the smallest multiple of 4 is 36 and largest = 132 . . average = ( 36 + 132 ) / 2 = 84 . . total numbers = ( 132 - 36 ) / 4 + 1 = 24 + 1 = 25 . . sum = 25 * 84 = 2100 ans b
Answer: b
Question (physics): a train sets off at 9 : 00 am at the speed of 70 km / h . another train starts at 9 : 30 am in the same direction at the rate of 80 km / h . at what time will the second train catch the first train ?
Options: a ) 12 : 30 , b ) 1 : 00 , c ) 1 : 30 , d ) 2 : 00 , e ) 2 : 30
Rationale: "in thirty minutes the first train travels 35 km . the second train catches the first train at a rate of 80 km / h - 70 km / h = 10 km / h . the second train will catch the first train in 35 / 10 = 3.5 hours , so at 1 : 00 pm . the answer is b ."
Answer: b
Question (geometry): the area of a rectangular plot is 21 times its breadth . if the difference between the length and the breadth is 10 metres , what is its breadth ?
Options: a ) 10 metres , b ) 5 metres , c ) 11 metres , d ) data inadequate , e ) none of these
Rationale: "l × b = 21 × b ∴ l = 21 m and l – b = 10 ∴ b = 21 – 10 = 11 m answer c"
Answer: c
Question (gain): a man took a loan at rate of 12 % per annum simple interest . after 3 years he had to pay 3600 interest . the principal amount borrowed by him was .
Options: a ) rs 10000 , b ) rs 15000 , c ) rs 16000 , d ) rs 17000 , e ) none of these
Rationale: "explanation : s . i . = p â ˆ — r â ˆ — t / 100 = > p = s . i . â ˆ — 100 / r â ˆ — t = > p = 3600 â ˆ — 100 / 12 â ˆ — 3 = rs 10000 option a"
Answer: a
Question (general): a , b and c started a business with a total investment of rs . 72000 . a invests rs . 6000 more than b and b invests rs . 3000 less than c . if the total profit at the end of a year is rs . 8640 , find c ' s share .
Options: a ) rs . 3240 , b ) rs . 2520 , c ) rs . 2880 , d ) rs . 3360 , e ) none of these
Rationale: "explanation : let c ' s investment = rs . x b ' s investment = rs . ( x - 3000 ) a ' s investment = rs . ( x - 3000 + 6000 ) = rs . ( x + 3000 ) now , ( a + b + c ) ' s investment = rs . 72000 = > x + ( x - 3000 ) + ( x + 3000 ) = 72000 = > 3 x = 72000 = > x = 24000 hence , a ' s investment = rs . 27000 b ' s investment = rs . 21000 c ' s investment = rs . 24000 ratio of the capitals of a , b and c = 27000 : 21000 : 24000 = 9 : 7 : 8 a ' s share = rs . [ ( 8 / 24 ) ã — 8640 ] = rs . 2880 answer : option c"
Answer: c
Question (general): ( 3 x + 2 ) ( 2 x - 3 ) = ax ^ 2 + kx + n . what is the value of a - n + k ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 10 , e ) 11
Rationale: "expanding we have 6 x ^ 2 - 9 x + 4 x - 6 6 x ^ 2 - 5 x - 6 taking coefficients , a = 6 , k = - 5 , n = - 6 therefore a - n + k = 6 - ( - 6 ) - 5 = 12 - 5 = 7 the answer is b ."
Answer: b
Question (general): a vendor sells 50 percent of the apples he had and throws away 20 percent of the remainder . the next day , the vendor sells 50 percent of the remaining apples and throws away the rest . in total , what percent of his apples does the vendor throw away ?
Options: a ) 30 , b ) 35 , c ) 40 , d ) 45 , e ) 50
Rationale: "let x be the original number of apples . on day one , the vendor throws away ( 0.2 ) ( 0.5 ) x = 0.1 x . the remaining apples are ( 0.8 ) ( 0.5 ) x = 0.4 x . on day two , the vendor throws away ( 0.5 ) ( 0.4 ) x = 0.2 x . the vendor throws away a total of 0.1 x + 0.2 x = 0.3 x . the vendor throws away 30 percent of the apples . the answer is a ."
Answer: a
Question (physics): a can do a piece of work in 12 days and b alone can do it in 14 days . how much time will both take to finish the work ?
Options: a ) a ) 3.2222 , b ) b ) 5 , c ) c ) 6.46 , d ) d ) 8.3333 , e ) e ) 9
Rationale: this question can be solved by different methods . we need to conserve time in exams so solving this problem using equations is the good idea . time taken to finish the job = xy / ( x + y ) = 12 x 14 / ( 12 + 14 ) = 150 / 25 = 6.46 days answer : c
Answer: c
Question (gain): a jar full of whisky contains 40 % alcohol . a part of this whisky is replaced by another containg 19 % alcohol and now the percentage of alcohol was found to be 26 % . what quantity of whisky is replaced ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 2 / 5 , d ) 3 / 5 , e ) 4 / 5
Rationale: let us assume the total original amount of whiskey = 10 ml - - - > 4 ml alcohol and 6 ml non - alcohol . let x ml be the amount removed - - - > total alcohol left = 4 - 0.4 x new quantity of whiskey added = x ml out of which 0.19 is the alcohol . thus , the final quantity of alcohol = 4 - 0.4 x + 0.19 x - - - - > ( 4 - 0.21 x ) / 10 = 0.26 - - - > x = 20 / 3 ml . per the question , you need to find the x ml removed as a ratio of the initial volume - - - > ( 20 / 3 ) / 10 = 2 / 3 . hence , b is the correct answer .
Answer: b
Question (other): two numbers are in the ratio 3 : 4 . if their l . c . m . is 96 . what is sum of the numbers ?
Options: a ) 48 , b ) 56 , c ) 76 , d ) 84 , e ) 85
Rationale: "explanation : let the numbers be 3 x and 4 x lcm of 3 x and 4 x = 12 x ( since lcm of 3 and 4 is 12 . hence lcm of 3 x and 4 x is 12 x ) given that lcm of 3 x and 4 x is 96 = > 12 x = 96 = > x = 96 / 12 = 8 sum of the numbers = 3 x + 4 x = 7 x = 7 x 8 = 56 answer : option b"
Answer: b
Question (general): x ^ y + y ^ x = 2408 find the values of x ?
Options: a ) 2407 , b ) 2408 , c ) 2409 , d ) 2405 , e ) 32
Rationale: 2407 ^ 1 + 1 ^ 2407 = 2408 answer : a
Answer: a
Question (physics): the speed of a boat in still water in 20 km / hr and the rate of current is 6 km / hr . the distance travelled downstream in 12 minutes is :
Options: a ) 10.6 , b ) 5.2 , c ) 10.8 , d ) 5.4 , e ) 5.0
Rationale: "speed downstream = ( 20 + 6 ) = 26 kmph time = 24 minutes = 12 / 60 hour = 1 / 5 hour distance travelled = time × speed = 1 / 5 × 26 = 5.20 km answer is b ."
Answer: b
Question (gain): 15 litres of mixture contains 20 % alcohol and the rest water . if 5 litres of water be mixed with it , the percentage of alcohol in the new mixture would be ?
Options: a ) 16.67 % , b ) 23 % , c ) 15 % , d ) 19.75 % , e ) 21.23 %
Rationale: "alcohol in the 15 litres of mix . = 20 % of 15 litres = ( 20 * 15 / 100 ) = 3 litres water in it = 15 - 3 = 12 litres new quantity of mix . = 15 + 5 = 20 litres quantity of alcohol in it = 3 litres percentage of alcohol in new mix . = 3 * 100 / 20 = 15 % answer is c"
Answer: c
Question (general): alok ordered 16 chapatis , 5 plates of rice , 7 plates of mixed vegetable and 6 ice - cream cups . the cost of each chapati is rs . 6 , that of each plate of rice is rs . 45 and that of mixed vegetable is rs . 70 . the amount that alok paid the cashier was rs . 1111 . find the cost of each ice - cream cup ?
Options: a ) 25 , b ) 66 , c ) 77 , d ) 50 , e ) 91
Rationale: "let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 1111 96 + 225 + 490 + 6 x = 1111 6 x = 300 = > x = 50 . answer : d"
Answer: d
Question (general): the average of 3 numbers is 48 . the average of two of these numbers is 56 % . what is the third number ?
Options: a ) 64 , b ) 32 , c ) 46 , d ) 75 , e ) 47
Rationale: b 32 the total of three numbers must be 48 x 3 = 144 . the total of two numbers must be 56 x 2 = 112 . therefore , 144 - 112 = 32 .
Answer: b
Question (gain): by selling an article for $ 180 , a person gains $ 30 . what is the gain % ?
Options: a ) 25 % , b ) 30 % , c ) 50 % , d ) 20 % , e ) 10 %
Rationale: "s . p . = $ 180 gain = $ 30 c . p . = 180 - 30 = 150 gain % = 30 / 150 * 100 = 20 % answer is d"
Answer: d
Question (other): two vessels p and q contain 62.5 % and 87.5 % of alcohol respectively . if 2 litres from vessel p is mixed with 6 litres from vessel q , the ratio of alcohol and water in the resulting mixture is ?
Options: a ) 13 : 1 , b ) 13 : 3 , c ) 13 : 8 , d ) 13 : 5 , e ) 13 : 2
Rationale: quantity of alcohol in vessel p = 62.5 / 100 * 2 = 5 / 4 litres quantity of alcohol in vessel q = 87.5 / 100 * 6 = 21 / 4 litres quantity of alcohol in the mixture formed = 5 / 4 + 21 / 4 = 13 / 2 = 6.5 litres as 8 litres of mixture is formed , ratio of alcohol and water in the mixture formed = 6.5 : 1.5 = 13 : 3 . answer : b
Answer: b
Question (general): what is 2 / 5 of 5 / 9 of 1 / 2 ?
Options: a ) 1 / 4 , b ) 1 / 9 , c ) 9 / 16 , d ) 5 / 8 , e ) 16 / 9
Rationale: "2 / 5 * 5 / 9 * 1 / 2 = 1 / 9 answer : b"
Answer: b
Question (physics): john completes a piece of work in 10 days , rose completes the same work in 40 days . if both of them work together , then the number of days required to complete the work is ?
Options: a ) 5 days , b ) 8 days , c ) 10 days , d ) 12 days , e ) 14 days
Rationale: "if a can complete a work in x days and b can complete the same work in y days , then , both of them together can complete the work in x y / x + y days . that is , the required no . of days = 10 × 40 / 50 = 8 days b )"
Answer: b
Question (physics): at a time a , do 20 % less work than b . if a do any work in 15 / 2 hour , then in how many hour b will finish work ?
Options: a ) 5 hour , b ) 11 / 2 hour , c ) 6 hour , d ) 13 / 2 hour , e ) 8 hour
Rationale: let b will finish a work in x hour . then , in x hour a , 80 / 100 = 4 / 5 work do ratio of work done by a and b = inverse ratio of time taken 4 / 5 : 1 = 2 / 15 : 1 / x 4 / 5 * 1 / x = 1 * 2 / 15 = 4 / 5 x = 2 / 15 ; x = 6 . time = 6 hour answer c
Answer: c
Question (physics): worker a takes 8 hours to do a job . worker b takes 10 hours to do the same job . how long it take both a & b , working together but independently , to do the same job ?
Options: a ) 20 / 9 , b ) 40 / 9 , c ) 50 / 9 , d ) 60 / 9 , e ) 80 / 9
Rationale: "one day work of a = 1 / 8 one day work of b = 1 / 10 so one day work of a and b together = 1 / 8 + 1 / 10 = 9 / 40 so total days required = 40 / 9 answer : b"
Answer: b
Question (general): if a is a positive integer , and if the units digit of a ^ 2 is 9 and the units digit of ( a + 1 ) ^ 2 is 4 , what is the units z digit of ( a + 2 ) ^ 2 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) c . 14
Rationale: "i also got a . by punching in numers : z . . . 7 ^ 2 = . . . 9 . . . 8 ^ 2 = . . . 4 . . . 9 ^ 2 = . . . 1 . a"
Answer: a
Question (general): 106 ã — 106 + 94 ã — 94 = ?
Options: a ) 20072 , b ) 20062 , c ) 10072 , d ) 20172 , e ) 10272
Rationale: "explanation : ( a + b ) 2 + ( a â ˆ ’ b ) 2 = 2 ( a 2 + b 2 ) ( reference : basic algebraic formulas ) 1062 + 942 = ( 100 + 6 ) 2 + ( 100 â ˆ ’ 6 ) 2 = 2 ( 1002 + 62 ) = 2 ( 10000 + 36 ) = 20072 . answer : option a"
Answer: a
Question (general): in an office , totally there are 6400 employees and 65 % of the total employees are males . 25 % of the males in the office are at - least 50 years old . find the number of males aged below 50 years ?
Options: a ) 1040 , b ) 2080 , c ) 3120 , d ) 4160 , e ) none of these
Rationale: "number of male employees = 6400 * 65 / 100 = 4160 required number of male employees who are less than 50 years old = 4160 * ( 100 - 25 ) % = 4160 * 75 / 100 = 3120 . answer : c"
Answer: c
Question (general): the ratio of a to b is 4 to 5 , where a and b are positive . if x equals a increased by 75 percent of a , and m equals b decreased by 80 percent of b , what is the value of m / x ?
Options: a ) 1 / 7 , b ) 3 / 4 , c ) 4 / 5 , d ) 5 / 4 , e ) 3 / 2
Rationale: "a / b = 4 / 5 m / x = ( 1 / 5 ) * 5 / ( 7 / 4 ) * 4 = 1 / 7 the answer is a ."
Answer: a
Question (general): 9 . the least number which should be added to 28523 so that the sum is exactly divisible by 3 , 5 , 7 and 8 is
Options: a ) 41 , b ) 42 , c ) 32 , d ) 37 , e ) 39
Rationale: lcm of 3 , 5 , 7 and 8 = 840 28523 ÷ 840 = 33 remainder = 803 hence the least number which should be added = 840 - 803 = 37 answer : option d
Answer: d
Question (general): find the value of ( 75983 * 75983 - 45983 * 45983 / 30000 )
Options: a ) 129166 , b ) 121696 , c ) 126196 , d ) 121966 , e ) none of them
Rationale: "given expression = ( 75983 ) 2 - ( 45983 ) 2 / ( 75983 - 45983 ) = ( a - b ) 2 / ( a - b ) = ( a + b ) ( a - b ) / ( a - b ) = ( a + b ) = 75983 + 45983 = 121966 answer is d ."
Answer: d
Question (general): what is the value of 10 ^ 6 - 6 ^ 4 ?
Options: a ) 9 , 97,111 , b ) 9 , 97,322 , c ) 9 , 98,704 , d ) 9 , 98,851 , e ) 9 , 98,900
Rationale: "as 10 ^ n will always have last digit as 0 and 6 ^ n will always as last digit 6 . . hence difference of such sum should always be ending with 4 and there is only on option . . answer c"
Answer: c
Question (physics): the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 1250 resolutions ?
Options: a ) 1277 m , b ) 1760 m , c ) 1278 m , d ) 1288 m , e ) 1378 v
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 1250 resolutions . = 1250 * 2 * 22 / 7 * 22.4 = 176000 cm = 1760 m answer : b"
Answer: b
Question (gain): a man gains 20 % by selling an article for a certain price . if the sells it at double the price , the percentage of profit will be
Options: a ) 740 % , b ) 540 % , c ) 640 % , d ) 140 % , e ) 240 %
Rationale: "explanation : let c . p . = rs . x . then , s . p . = rs . ( 12 % of x ) = rs . 6 x / 5 new s . p . = 2 * 6 x / 5 = rs . 12 x / 5 profit = 12 x / 5 - x = rs . 7 x / 5 profit = 7 x / 5 * 1 / x * 100 = 140 % . answer : d"
Answer: d
Question (gain): the salary of a worker is first increased by 10 % and afterwards reduced by 10 % . what is the net change in the worker ' s salary ?
Options: a ) 1 % increase , b ) 1 % decrease , c ) 2 % increase , d ) 2 % decrease , e ) no change
Rationale: "let x be the original salary . the final salary is 0.9 ( 1.1 x ) = 0.99 x the answer is b ."
Answer: b
Question (general): alok ordered 16 chapatis , 5 plates of rice , 7 plates of mixed vegetable and 6 ice - cream cups . the cost of each chapati is rs . 6 , that of each plate of rice is rs . 45 and that of mixed vegetable is rs . 70 . the amount that alok paid the cashier was rs . 1051 . find the cost of each ice - cream cup ?
Options: a ) 25 , b ) 40 , c ) 77 , d ) 99 , e ) 91
Rationale: "let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 1051 96 + 225 + 490 + 6 x = 1051 6 x = 240 = > x = 40 . answer : b"
Answer: b
Question (general): the cost of painting the 4 walls of a room is rs . 350 . the cost of painting a room 3 times in length , breadth and height will be :
Options: a ) rs . 1050 , b ) rs . 1400 , c ) rs . 3150 , d ) rs . 4200 , e ) none
Rationale: explanation : area of 4 walls of the room = [ 2 ( l + b ) × h ] m 2 area of 4 walls of new room = [ 2 ( 3 l + 3 b ) × 3 h ] m 2 = 9 [ 2 ( l + b ) × h ] m 2 cost of painting the 4 walls of new room = rs . ( 9 × 350 ) = rs . 3150 correct option : c
Answer: c
Question (general): a number is doubled and 5 is added . if the resultant is trebled , it becomes 123 . what is that number ?
Options: a ) 12 , b ) 29 , c ) 27 , d ) 18 , e ) 99
Rationale: "explanation : let the number be x . therefore , 3 ( 2 x + 5 ) = 123 6 x + 15 = 123 6 x = 108 x = 18 answer : d"
Answer: d
Question (general): a certain number when divided by 899 leaves the remainder 63 . find the remainder when the same number is divided by 29 .
Options: a ) 5 , b ) 4 , c ) 1 , d ) 0 , e ) can not be determined
Rationale: "sol . ( a ) number = 899 q + 63 , where q is quotient = 31 × 29 q + ( 58 + 5 ) = 29 [ 31 q + 2 ] + 5 ∴ remainder = 5 answer a"
Answer: a
Question (physics): kelsey travelled for 10 hours . he covered the first half of the distance at 25 kmph and remaining half of the distance at 40 kmph . find the distance travelled by kelsey ?
Options: a ) 583 km , b ) 400 km , c ) 670 km , d ) 360 km , e ) 234 km
Rationale: let the distance travelled be x km . total time = ( x / 2 ) / 25 + ( x / 2 ) / 40 = 10 = > x / 50 + x / 80 = 10 = > ( 8 x + 5 x ) / 400 = 10 = > x = 400 km answer : b
Answer: b
Question (gain): a gambler has won 40 % of his 30 poker games for the week so far . if , all of a sudden , his luck changes and he begins winning 80 % of the time , how many more games must he play to end up winning 60 % of all his games for the week ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 35 , e ) 40
Rationale: "let x be the number of additional games the gambler needs to play . 0.4 ( 30 ) + 0.8 x = 0.6 ( x + 30 ) 0.2 x = 6 x = 30 the answer is c ."
Answer: c
Question (gain): lola has $ 240.00 in her checking account . she spent $ 180.00 . what percentage does she have left in her account ?
Options: a ) 75 % , b ) 50 % , c ) 40 % , d ) 55 % , e ) none of these
Rationale: explanation : amount left : 240 - 180 = 60 amount left percentage = ( 60 / 240 x 100 ) % = 25 % answer : e
Answer: e
Question (geometry): the length of the rectangular field is double its width . inside the field there is square shaped pond 5 m long . if the area of the pond is 1 / 8 of the area of the field . what is the length of the field ?
Options: a ) 54
b ) 32
c ) 75
d ) 20
e ) 11
Rationale: a / 8 = 5 * 5 = > a = 5 * 5 * 8 x * 2 x = 5 * 5 * 8 x = 10 = > 2 x = 20 answer : d
Answer: d
Question (geometry): if the length of a rectangle is halved and its breadth is tripled , what is the percentage change in its area ?
Options: a ) 30
b ) 40
c ) 50
d ) 60
e ) 70
Rationale: length is halved . i . e . , length is decreased by 50 % breadth is tripled i . e . , breadth is increased by 200 % formula for change in area is : = ( - x + y - xy / 100 ) % = ( − 50 + 200 − 50 × 200 / 100 ) % = 50 % i . e . , area is increased by 50 % answer is c .
Answer: c