Cheukting/mathqa huggingface dataset:
Question (gain): a sum of money at simple interest amounts to $ 700 in 3 years and to $ 764 in 4 years . the sum is :
Options: a ) $ 508 , b ) $ 698 , c ) $ 398 , d ) $ 549 , e ) $ 675
Rationale: "a $ 508 s . i . for 1 year = $ ( 764 - 700 ) = $ 64 . s . i . for 3 years = $ ( 64 x 3 ) = $ 192 . principal = $ ( 700 - 192 ) = $ 508 ."
Answer: a
Question (other): how many factors does 34 ^ 2 have ?
Options: a ) 2 , b ) 8 , c ) 20 , d ) 25 , e ) 26
Rationale: "36 ^ 2 = 6 * 6 * 6 * 6 = 2 ^ 4 * 3 ^ 4 total factors = ( 4 + 1 ) * ( 4 + 1 ) = 5 * 4 = 20 answer c ."
Answer: c
Question (general): how many positive integers between 1 and 100 are there such that they are multiples of 15 ?
Options: a ) 5 , b ) 4 , c ) 7 , d ) 1 , e ) 6
Rationale: "multiples of 15 = 15 , 30,45 , - - - - - 90 number of multiples of 15 = > 90 - 15 / 15 + 1 = 6 answer is e"
Answer: e
Question (gain): a man walking at a rate of 10 km / hr crosses a bridge in 3 minutes . the length of the bridge is ?
Options: a ) 500 , b ) 650 , c ) 250 , d ) 111 , e ) 236
Rationale: "speed = 10 * 5 / 18 = 50 / 18 m / sec distance covered in 5 minutes = 50 / 18 * 5 * 60 = 500 m answer is a"
Answer: a
Question (physics): how many paying stones , each measuring 3 * 2 m are required to pave a rectangular court yard 15 m long and 6 m board ?
Options: a ) 99 , b ) 18 , c ) 26 , d ) 15 , e ) 12
Rationale: "15 * 6 = 3 * 2 * x = > x = 15 answer : d"
Answer: d
Question (general): on a partly cloudy day , derek decides to walk back from work . when it is sunny , he walks at a speed of s miles / hr ( s is an integer ) and when it gets cloudy , he increases his speed to ( s + 1 ) miles / hr . if his average speed for the entire distance is 2.8 miles / hr , what fraction w of the total distance did he cover while the sun was shining on him ?
Options: a ) 1 / 4 , b ) 4 / 5 , c ) 1 / 5 , d ) 1 / 6 , e ) 1 / 7
Rationale: if s is an integer and we know that the average speed is 2.8 , s must be = 2 . that meanss + 1 = 3 . this implies that the ratio of time for s = 2 is 1 / 4 of the total time . the formula for distance / rate is d = rt . . . so the distance travelled when s = 2 is 2 t . the distance travelled for s + 1 = 3 is 3 * 4 t or 12 t . therefore , total distance covered while the sun was shining over him is w = 2 / 14 = 1 / 7 . answer : e
Answer: e
Question (other): what number has a 15 : 1 ratio to the number 10 ?
Options: a ) 130 , b ) 100 , c ) 200 , d ) 150 , e ) 120
Rationale: "15 : 1 = x : 10 x = 10 * 15 x = 150 answer : d"
Answer: d
Question (general): if a and b are positive integers and ( 2 ^ a ) ^ b = 2 ^ 7 , what is the value of 2 ^ a * 2 ^ b ?
Options: a ) 16 , b ) 32 , c ) 64 , d ) 256 , e ) 128
Rationale: "2 ^ ab = 2 ^ 7 therefore ab = 7 either a = 1 or 7 or b = 7 or 1 therefore 2 ^ a * 2 ^ b = 2 ^ ( a + b ) = 2 ^ 8 = 256 d"
Answer: d
Question (general): a man is 30 years older than his son . in four years , his age will be twice the age of his son . the present age of this son is
Options: a ) 22 years , b ) 23 years , c ) 24 years , d ) 25 years , e ) 26 years
Rationale: "explanation : let ' s son age is x , then father age is x + 30 . = > 2 ( x + 4 ) = ( x + 30 + 4 ) = > 2 x + 8 = x + 34 = > x = 26 years answer : option e"
Answer: e
Question (general): the sum of the fourth and twelfth term of an arithmetic progression is 20 . what is the sum of the first 17 terms of the arithmetic progression ?
Options: a ) 300 , b ) 120 , c ) 150 , d ) 170 , e ) 270
Rationale: "n th term of a . p . is given by a + ( n - 1 ) d 4 th term = a + 3 d 12 th term = a + 11 d given a + 3 d + a + 11 d = 20 - - > 2 a + 14 d = 20 - - > a + 7 d = 10 sum of n term of a . p = n / 2 [ 2 a + ( n - 1 ) d ] subsitiuing n = 17 . . . we get 17 / 2 [ 2 a + 14 d ] = 17 [ a + 7 d ] = 17 * 10 = 170 . . . answer is d . . ."
Answer: d
Question (gain): a man invests rs . 4,000 at the rate of 5 % per annum . how much more should he invest at the rate of 8 % , so that he can earn a total of 6 % per annum ?
Options: a ) rs . 1200 , b ) rs . 1300 , c ) rs . 1500 , d ) rs . 2000 , e ) none of these
Rationale: "explanation : interest on rs . 4000 at 5 % per annum = ( 4000 × 5 × 1 ) / 100 = rs . 200 let his additional investment at 8 % = x interest on rs . x at 8 % per annum = ( x × 8 × 1 ) / 100 = 2 x / 25 . to earn 6 % per annum for the total , interest = ( 4000 + x ) × 6 × 1 / 100 . = > 200 + 2 x / 25 = ( 4000 + x ) × 6 × 1 / 100 . = > 20000 + 8 x = ( 4000 + x ) × 6 . = > 20000 + 8 x = 24000 + 6 x . = > 2 x = 4000 . = > x = 2000 . answer : d"
Answer: d
Question (general): a cab driver 5 days income was $ 400 , $ 250 , $ 650 , $ 400 , $ 500 . then his average income is ?
Options: a ) $ 400 , b ) $ 420 , c ) $ 440 , d ) $ 460 , e ) $ 480
Rationale: "avg = sum of observations / number of observations avg income = ( 400 + 250 + 650 + 400 + 500 ) / 5 = 440 answer is c"
Answer: c
Question (physics): calculate the time it will take for a train that is 120 meter long to pass a bridge of 160 meter length , if the speed of the train is 40 km / hour ?
Options: a ) 21.2 seconds , b ) 25.2 seconds , c ) 29.2 seconds , d ) 35.2 seconds , e ) 11.2 seconds
Rationale: speed = 40 km / hr = 40 * ( 5 / 18 ) m / sec = 11.1111 m / sec total distance = 120 + 160 = 280 meter time = distance / speed = 280 * ( 1 / 11.1111 ) = 25.2 seconds answer : b
Answer: b
Question (gain): the banker ' s gain on a sum due 6 years hence at 12 % per annum is rs . 540 . what is the banker ' s discount ?
Options: a ) 1240 , b ) 1120 , c ) 1190 , d ) 1290 , e ) none of these
Rationale: "explanation : td = ( bg × 100 ) / tr = ( 540 × 100 ) / ( 6 × 12 ) = ( 90 × 100 ) / 12 = ( 15 × 100 ) 2 / = rs . 750 bg = bd – td = > 540 = bd - 750 = > bd = 540 + 750 = 1290 answer : option d"
Answer: d
Question (geometry): if the difference between the length and breadth of a rectangle is 23 m and its perimeter is 246 m , what is its area ?
Options: a ) 2510 , b ) 3650 , c ) 2530 , d ) 2515 , e ) 2520
Rationale: "length = breadth + 23 . therefore , 4 × breadth + 2 × 23 = 246 m ⇒ breadth = 50 m length = 50 + 23 = 73 m area = 73 × 50 = 3650 m 2 answer is b ."
Answer: b
Question (physics): a and b can together finish a work in 30 days . they worked together for 20 days and then b left . after another 20 days , a finished the remaining work . in how many days a alone can finish the job ?
Options: a ) 40 , b ) 50 , c ) 54 , d ) 60 , e ) none of these
Rationale: "( a + b ) ' s 20 days work = ( 1 / 30 * 20 ) = 2 / 3 . remaining work = ( 1 - 2 / 3 ) = 1 / 3 . now , 1 / 3 work is done by a in 20 days . whole work will be done by a in ( 20 * 3 ) = 60 days . correct option : d"
Answer: d
Question (general): how many numbers between 190 and 580 are divisible by 4,5 and 6 ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: every such number must be divisible by l . c . m of 4 , 5,6 i . e , 60 . such numbers are 240,300 , 360,420 , 480,540 . clearly , there are 6 such numbers answer : a
Answer: a
Question (physics): a 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 24 sec . what is the length of the platform ?
Options: a ) 389 m , b ) 350 m , c ) 187.5 m , d ) 299 m , e ) 219.5 m
Rationale: "speed = 300 / 24 = 25 / 2 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 39 = 25 / 2 = > x = 187.5 m . answer : c"
Answer: c
Question (gain): what percent is 3 % of 5 % ?
Options: a ) 60 % , b ) 50 % , c ) 75 % , d ) 45 % , e ) 30 %
Rationale: "required percentage = 3 % / 5 % * 100 = 3 / 5 * 100 = 60 % answer is a"
Answer: a
Question (general): when positive integer x is divided by positive integer y , the result is 59.32 . what is the sum t of all possible 2 - digit remainders for x / y ?
Options: a ) 560 , b ) 616 , c ) 672 , d ) 728 , e ) 784
Rationale: "ans b 616 . . . remainders = . 32 = 32 / 100 = 8 / 25 = 16 / 50 and so on . . so two digit remainders are 16 + 24 + 32 + . . . . + 96 . . t = 8 ( 2 + 3 + 4 . . . . + 12 ) = 616 . b"
Answer: b
Question (geometry): perimeter of an equilateral and isosceles is 45 and 40 respectively . at least one of the sides of isosceles is equal to the equilateral . what ' s the base of isosceles triangle ?
Options: a ) 7
b ) 8
c ) 9
d ) 10
e ) 11
Rationale: 10 units as other 2 sides will be 15,15 units . answer : d
Answer: d
Question (general): kamal obtained 76 , 60 , 82 , 67 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 65 , b ) 69 , c ) 74 , d ) 75 , e ) none
Rationale: "sol . average = 76 + 60 + 82 + 67 + 85 / 5 ) = ( 375 / 5 ) = 74 . answer c"
Answer: c
Question (physics): a train covers a distance of 12 km in 10 min . if it takes 16 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 320 m , b ) 188 m , c ) 120 m , d ) 178 m , e ) 189 m
Rationale: "speed = ( 12 / 10 * 60 ) km / hr = ( 72 * 5 / 18 ) m / sec = 20 m / sec . length of the train = 20 * 16 = 320 m . answer : a"
Answer: a
Question (physics): if 12 men and 16 boys can do a piece of work in 5 days and 13 men together will 24 boys can do it in 4 days . compare the daily work done by a man with that of a boy .
Options: a ) 2 : 9 , b ) 2 : 1 , c ) 2 : 7 , d ) 2 : 5 , e ) 2 : 2
Rationale: "12 m + 16 b - - - - - 5 days 13 m + 24 b - - - - - - - 4 days 60 m + 80 b = 52 m + 96 b 8 m = 16 b = > 1 m = 2 b m : b = 2 : 1 answer : b"
Answer: b
Question (general): what least value should be replaced by * in 223 * 431 so the number become divisible by 9
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "explanation : trick : number is divisible by 9 , if sum of all digits is divisible by 9 , so ( 2 + 2 + 3 + * + 4 + 3 + 1 ) = 15 + * should be divisible by 9 , 15 + 3 will be divisible by 9 , so that least number is 3 . answer : option a"
Answer: a
Question (gain): the cost price of a radio is rs . 1340 and it was sold for rs . 1210 , find the loss % ?
Options: a ) 18 % , b ) 9 % , c ) 22 % , d ) 24 % , e ) 21
Rationale: "1340 - - - - 130 100 - - - - ? = > 9 % answer : b"
Answer: b
Question (probability): the probability that a number selected at random from the first 50 natural numbers is a composite number is ?
Options: a ) 17 / 65 , b ) 17 / 25 , c ) 17 / 28 , d ) 17 / 65 , e ) 17 / 39
Rationale: "the number of exhaustive events = ⁵ ⁰ c ₁ = 50 . we have 15 primes from 1 to 50 . number of favourable cases are 34 . required probability = 34 / 50 = 17 / 25 . answer : b"
Answer: b
Question (general): if x : y = 4 : 7 , find the value of ( 6 x + 2 y ) : ( 5 x – y )
Options: a ) 7 : 13 , b ) 38 : 7 , c ) 3 : 13 , d ) 2 : 3 , e ) 38 : 13
Rationale: explanation : given : x / y = 4 / 7 ( 6 x + 2 y ) : ( 5 x – y ) = ( 6 * 4 + 2 * 7 ) : ( 5 * 4 – 7 ) 38 : 13 answer : e
Answer: e
Question (gain): ritesh and co . generated revenue of rs . 2,500 in 2006 . this was 12.5 % of its gross revenue . in 2007 , the gross revenue grew by rs . 2,500 . what is the percentage increase in the revenue in 2007 ?
Options: a ) 12.5 % , b ) 20 % , c ) 25 % , d ) 50 % , e ) none of these
Rationale: "explanation : given , ritesh and co . generated revenue of rs . 2,500 in 2006 and that this was 12.5 % of the gross revenue . hence , if 2500 is 12.5 % of the revenue , then 100 % ( gross revenue ) is : = > ( 100 / 12.5 ) × 2500 . = > 20,000 . hence , the total revenue by end of 2007 is rs . 10,000 . in 2006 , revenue grew by rs . 2500 . this is a growth of : = > ( 2500 / 20000 ) × 100 . = > 12.5 % . answer : a"
Answer: a
Question (general): according to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . how many 15 - ounce cans of the concentrate are required to prepare 200 6 - ounce servings of orange juice ?
Options: a ) 25 , b ) 34 , c ) 50 , d ) 20 , e ) 100
Rationale: "orange juice concentrate : water : : 1 : 3 total quantity of orange juice = 200 * 6 = 1200 oz so orange juice concentrate : water : : 300 oz : 900 oz no . of 15 oz can = 300 oz / 15 oz = 20 answer d , 20 cans"
Answer: d
Question (gain): the difference between compound interest and simple interest on an amount of $ 15,000 for 2 years is $ 96 . what is the rate of interest per annum ?
Options: a ) 6 % , b ) 7 % , c ) 9 % , d ) 8 % , e ) 5 %
Rationale: "[ 15000 x ( 1 + r / 100 ) ^ 2 - 15000 ] - [ ( 15000 x r x 2 ) / 100 ] = 96 = = > 15000 [ ( 1 + r / 100 ) ^ 2 - 1 - 2 r / 100 ] = 96 = = > 15000 [ ( ( 100 + r ) ^ 2 - 10000 - ( 200 x r ) ) / 10000 ] = 96 = = > r ^ 2 = ( 96 x 2 ) / 3 = 64 = = > r = 8 . rate = 8 % answer d ) 8 %"
Answer: d
Question (general): if x + y = 14 , x - y = 60 , for integers of x and y , x = ?
Options: a ) 37 , b ) 35 , c ) 25 , d ) 20 , e ) 42
Rationale: "x + y = 14 x - y = 60 2 x = 74 x = 37 answer is a"
Answer: a
Question (physics): if in a race of 100 m , a covers the distance in 20 seconds and b in 25 seconds , then a beats b by :
Options: a ) 20 m , b ) 16 m , c ) 11 m , d ) 10 m , e ) 15 m
Rationale: "explanation : the difference in the timing of a and b is 5 seconds . hence , a beats b by 5 seconds . the distance covered by b in 5 seconds = ( 100 * 5 ) / 25 = 20 m hence , a beats b by 20 m . answer a"
Answer: a
Question (physics): the speed of a car is 90 km in the first hour and 30 km in the second hour . what is the average speed of the car ?
Options: a ) 50 kmph , b ) 60 kmph , c ) 75 kmph , d ) 85 kmph , e ) 90 kmph
Rationale: "explanation : s = ( 90 + 30 ) / 2 = 60 kmph b )"
Answer: b
Question (general): suzie ’ s discount footwear sells all pairs of shoes for one price and all pairs of boots for another price . on monday the store sold 22 pairs of shoes and 16 pairs of boots for $ 580 . on tuesday the store sold 8 pairs of shoes and 32 pairs of boots for $ 800 . how much more do pairs of boots cost than pairs of shoes at suzie ’ s discount footwear ?
Options: a ) $ 10.50 , b ) $ 12.50 , c ) $ 11.50 , d ) $ 16.50 , e ) $ 9.50
Rationale: "let x be pair of shoes and y be pair of boots . 22 x + 16 y = 580 . . . eq 1 8 x + 32 y = 800 . . . . eq 2 . now multiply eq 1 by 2 and sub eq 2 . 44 x = 1160 8 x = 800 . 36 x = 360 = > x = 10 . sub x in eq 2 . . . . we get 80 + 32 y = 800 . . . then we get 32 y = 720 then y = 22.50 differenece between x and y is 12.50 answer : b"
Answer: b
Question (physics): the speed of a boat in still water in 65 km / hr and the rate of current is 15 km / hr . the distance travelled downstream in 25 minutes is :
Options: a ) 55.55 km , b ) 44.44 km , c ) 33.33 km , d ) 22.22 km , e ) 11.11 km
Rationale: "explanation : speed downstream = ( 65 + 15 ) = 80 kmph time = 25 minutes = 25 / 60 hour = 5 / 12 hour distance travelled = time × speed = ( 2 / 5 ) × 80 = 33.33 km answer : option c"
Answer: c
Question (general): ( √ 27 + √ 243 ) / √ 48 = ?
Options: a ) 2 √ 2 , b ) 2 √ 3 , c ) 3 √ 2 , d ) 3 √ 3 , e ) 3
Rationale: "( √ 27 + √ 243 ) / √ 48 = ( 3 √ 3 + 9 √ 3 ) / 4 √ 3 = 12 √ 3 / 4 √ 3 = 3 . hence , the correct answer is e ."
Answer: e
Question (physics): two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 21 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ?
Options: a ) 2887 , b ) 444 , c ) 877 , d ) 278 , e ) 178
Rationale: "1 h - - - - - 5 ? - - - - - - 60 12 h rs = 16 + 21 = 37 t = 12 d = 37 * 12 = 444 answer : b"
Answer: b
Question (geometry): the volume of a cube is 1728 cc . find its surface ?
Options: a ) 864
b ) 209
c ) 278
d ) 276
e ) 280
Rationale: a 3 = 1728 = > a = 12 6 a 2 = 6 * 12 * 12 = 864 answer : a
Answer: a
Question (gain): you hold some gold in a vault as an investment . over the past year the price of gold increases by 50 % . in order to keep your gold in the vault , you must pay 8 % of the total value of the gold per year . what percentage has the value of your holdings changed by over the past year .
Options: a ) 35 % , b ) 36 % , c ) 37 % , d ) 38 % , e ) 40 %
Rationale: "( 100 % + 50 % ) * ( 100 % - 8 % ) = 150 * 0.92 = 138 % an increase of 38 % your gold holdings have increased in value by 38 % . the answer is d"
Answer: d
Question (gain): 18 litres of mixture contains 20 % alcohol and the rest water . if 3 litres of water be mixed with it , the percentage of alcohol in the new mixture would be ?
Options: a ) 16.67 % , b ) 17.14 % , c ) 18.3 % , d ) 19.75 % , e ) 21.23 %
Rationale: "alcohol in the 18 litres of mix . = 20 % of 18 litres = ( 20 * 18 / 100 ) = 3.6 litres water in it = 18 - 3.6 = 14.4 litres new quantity of mix . = 18 + 3 = 21 litres quantity of alcohol in it = 3.6 litres percentage of alcohol in new mix . = 3.6 * 100 / 21 = 17.14 % answer is b"
Answer: b
Question (geometry): two isosceles triangles have equal vertical angles and their areas are in the ratio 4 : 9 . find the ratio of their corresponding heights .
Options: a ) 4 / 5
b ) 5 / 4
c ) 3 / 2
d ) 5 / 7
e ) 2 / 3
Rationale: we are basically given that the triangles are similar . in two similar triangles , the ratio of their areas is the square of the ratio of their sides and also , the square of the ratio of their corresponding heights . therefore , area / area = height ^ 2 / height ^ 2 = 4 / 9 - - > height / height = 2 / 3 . answer : e .
Answer: e
Question (general): in a certain company , the ratio of male to female employees is 7 : 8 . if 3 more men were hired , this ratio would increase to 8 : 9 . how many male employees are there in the company ?
Options: a ) 6 , b ) 21 , c ) 27 , d ) 189 , e ) 192
Rationale: another approach is to use two variables . let m = present number of males let f = present number of females the ratio of male to female employees is 7 : 8 so , m / f = 7 / 8 cross multiply to get 7 f = 8 m if 3 more men were hired , this ratio would increase to 8 : 9 so , ( m + 3 ) / f = 8 / 9 cross multiply to get 9 ( m + 3 ) = 8 f expand : 9 m + 27 = 8 f we now have a system of two equations and two variables : 7 f = 8 m 9 m + 27 = 8 f solve to get : m = 189 and f = 216 answer : d
Answer: d
Question (general): a guy was asked to specify his age in years . he said , “ take my age 5 years hence , multiply it by 5 and subtract 5 times of my age 5 years ago and you will know my age . ” what was the age of that guy ?
Options: a ) 18 , b ) 15 , c ) 33 , d ) 39 , e ) 50
Rationale: current age of the guy = a years . then , 5 ( a + 5 ) – 5 ( a – 5 ) = a ( 5 a + 25 ) – ( 5 a – 25 ) = a a = 50 e
Answer: e
Question (other): of 60 children , 30 are happy , 10 are sad , and 20 are neither happy nor sad . there are 17 boys and 43 girls . if there are 6 happy boys and 4 sad girls , how many boys are neither happy nor sad ?
Options: a ) 5 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "venn diagrams are useful for multiple values of a single variable e . g . state of mind - happy / sad / neither . when you have two or more variables such as here where you have gender - boy / girl too , it becomes unwieldy . in this case , either use the table or logic . table method is shown above ; here is how you will use logic : there are 6 happy boys . there are 4 sad girls but total 10 sad children . so rest 6 sad children must be sad boys . we have 6 happy boys and 6 sad boys . total we have 17 boys . so 17 - 6 - 6 = 5 boys must be neither happy nor sad . answer ( a )"
Answer: a
Question (physics): ram , who is half as efficient as krish , will take 27 days to complete a task if he worked alone . if ram and krish worked together , how long will they take to complete the task ?
Options: a ) 16 days , b ) 12 days , c ) 9 days , d ) 6 days , e ) 18 days
Rationale: number of days taken by ram to complete task = 27 since ram is half as efficient as krish , amount of work done by krish in 1 day = amount of work done by ram in 2 days if total work done by ram in 27 days is 27 w amount of work done by ram in 1 day = w amount of work done by krish in 1 day = 2 w total amount of work done by krish and ram in a day = 3 w total amount of time needed by krish and ram to complete task = 27 w / 3 w = 9 days answer c
Answer: c
Question (gain): what is the compound interest on rs : 60,000 for 4 months at the rate of 5 % per annum
Options: a ) 1058.24 , b ) 2006.24 , c ) 1006.13 , d ) 1015.24 , e ) 1014.24
Rationale: "it is monthly compound rate = 5 / 12 % per month 60000 * ( 1 + 5 / 1200 ) ^ 4 - 60000 = 1006.13 answer : c"
Answer: c
Question (physics): two persons a and b can complete a piece of work in 40 days and 60 days respectively . if they work together , what part of the work will be completed in 6 days ?
Options: a ) 1 / 8 , b ) 1 / 3 , c ) 1 / 6 , d ) 1 / 2 , e ) 1 / 4
Rationale: "a ' s one day ' s work = 1 / 40 b ' s one day ' s work = 1 / 60 ( a + b ) ' s one day ' s work = 1 / 40 + 1 / 60 = 1 / 24 the part of the work completed in 6 days = 6 ( 1 / 24 ) = 1 / 4 . answer : e"
Answer: e
Question (gain): at what price must an article costing rs . 95 be marked in order that after deducting 5 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 130 , b ) 125 , c ) 145 , d ) 135 , e ) 144
Rationale: "cp = 95 sp = 47.50 * ( 125 / 100 ) = 118.125 mp * ( 95 / 100 ) = 118.125 mp = 125 answer : b"
Answer: b
Question (general): a “ sophie germain ” prime is any positive prime number p for which 2 p + 1 is also prime . the product of all the possible units digits of sophie germain primes greater than 9 is
Options: a ) 3 , b ) 7 , c ) 21 , d ) 189 , e ) 267
Rationale: "in that case , the sophie prime numbers greater than 9 are 11,23 , 47,59 , . . which yields units digit as 1 , 3,7 and 9 product would be 1 x 3 x 7 x 9 = 189 answer should be d"
Answer: d
Question (general): a man performs 1 / 2 of the total journey by rail , 1 / 3 by bus and the remaining 3 km on foot . his total journey is
Options: a ) 18 km , b ) 10 km , c ) 12 km , d ) 24 km , e ) 25 km
Rationale: "explanation : let the journey be x km then , 1 x / 2 + 1 x / 3 + 3 = x 5 x + 18 = 6 x x = 18 km answer : option a"
Answer: a
Question (physics): the sum of all consecutive odd integers from − 27 to 37 , inclusive , is
Options: a ) 110 , b ) 135 , c ) 150 , d ) 165 , e ) 235
Rationale: "the sum of the odd numbers from - 27 to + 27 is 0 . let ' s add the remaining numbers . 29 + 31 + 33 + 35 + 37 = 5 ( 33 ) = 165 the answer is d ."
Answer: d
Question (general): if 20 % of a number is equal to one - third of another number , what is the ratio of first number to the second number ?
Options: a ) 2 : 5 , b ) 1 : 4 , c ) 5 : 3 , d ) 6 : 11 , e ) 2 : 3
Rationale: "let 20 % of a = 1 / 3 b then 20 a / 100 = 1 b / 3 a / 5 = b / 3 a / b = 5 / 3 a : b = 5 : 3 answer is c"
Answer: c
Question (general): a person travels from p to q a speed of 60 km / hr and returns by increasing his speed by 50 % . what is his average speed for both the trips ?
Options: a ) 33 , b ) 75 , c ) 48 , d ) 99 , e ) 21
Rationale: speed on return trip = 150 % of 60 = 90 km / hr . average speed of trip = 60 + 90 / 2 = 150 / 2 = 75 km / hr answer : b
Answer: b
Question (general): ( 1.1 + 1.1 + 1.1 + 1.1 ) x 1.1 x 1.1 = ? = ? x 0.121
Options: a ) 54 , b ) 33 , c ) 44 , d ) 22 , e ) 26
Rationale: "explanation : ? = ( 1.1 + 1.1 + 1.1 + 1.1 ) x 1.1 x 1.1 / 0.121 = ( 4.4 x 1.1 x 1.1 ) / 0.121 = 44 answer : option c"
Answer: c
Question (general): how much is 85 % of 40 is greater than 4 / 5 of 25 ?
Options: a ) 22 , b ) 14 , c ) 88 , d ) 12 , e ) 66
Rationale: "( 85 / 100 ) * 40 – ( 4 / 5 ) * 25 = 14 answer : b"
Answer: b
Question (general): ( 23341379 x 72 ) = ?
Options: a ) 1680579288 , b ) 1223441288 , c ) 2142579288 , d ) 2142339288 , e ) none of these
Rationale: "explanation : 23341379 x 72 = 23341379 ( 70 + 2 ) = ( 23341379 x 70 ) + ( 23341379 x 2 ) = 1633896530 + 46682758 = 1680579288 . answer : option a"
Answer: a