regisss/math_qa huggingface dataset:
Problem: on a scale of map , 0.6 cm represent 6.6 km . if the distance between the points on the map is 80.5 cm , the actual distance between these points is :
Options: a ) 9 km , b ) 72.5 km , c ) 190.75 km , d ) 885.5 km , e ) none of these
Rationale: solution let the actual distance be x km . then , more distance on the map , more is the actual distance ( direct proportion ) ∴ 0.6 : 80.5 : : 6.6 : x ⇔ 0.6 x = 80.5 × 6.6 ⇔ x = ⇔ x = 80.5 x 6.6 / 0.6 = x = 885.5 . answer d
Answer: d
Problem: there are 9 cities numbered 1 to 9 . from how many cities the flight can start so as to reach the city 8 either directly or indirectly such that the path formed is divisible by 3 .
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: start from 1 : 1368 , start from 2 : 2358 , start from 3 : 378 , start from 4 : 48 , start from 5 : 528 , start from 6 : 678 , start from 7 : 78 , why start from 8 ? ? ? , start from 9 : 918 . so flights can start from all 8 other cities . answer : b
Answer: b
Problem: find the sum lend at c . i . at 5 p . c per annum will amount to rs . 740 in 2 years ?
Options: a ) 221 , b ) 287 , c ) 400 , d ) 288 , e ) 671
Rationale: "explanation : 740 = p ( 21 / 20 ) 2 p = 671 answer : e"
Answer: e
Problem: what will be the compound interest on a sum of rs . 25,000 after 3 years at the rate of 12 % p . a . ?
Options: a ) rs . 10123.77 , b ) rs . 10123.21 , c ) rs . 10123.20 , d ) rs . 10123.28 , e ) rs . 10123.21
Rationale: "amount = [ 25000 * ( 1 + 12 / 100 ) 3 ] = 25000 * 28 / 25 * 28 / 25 * 28 / 25 = rs . 35123.20 c . i . = ( 35123.20 - 25000 ) = rs . 10123.20 answer : c"
Answer: c
Problem: what is the value of 5 x ^ 2 − 1.9 x − 3.7 for x = − 0.3 ?
Options: a ) − 4.72 , b ) − 3.82 , c ) − 3.58 , d ) − 2.68 , e ) 0.57
Rationale: "5 x ^ 2 - 1.9 x - 3.7 , x = - 0.3 firstly , 5 x ^ 2 can be written as 5 * x * x - substituting one of the x with - 0.3 we have - 1.5 x - 1.9 x - 3.7 - - - > - 3.4 x - 3.7 - - - > - 3.4 ( - 0.3 ) - 3.7 - - - > 1.02 - 3.7 = - 2.68 answer : d"
Answer: d
Problem: the income of a man increase consistently by 2 % per year . if his present income is rs . 12000 then what will his income be after 1 year ?
Options: a ) 12040 , b ) 12140 , c ) 12240 , d ) 12340 , e ) 12440
Rationale: explanation : income = 12000 x 1.02 = 12240 answer : option c
Answer: c
Problem: find the largest 2 digit number which is exactly divisible by 88 ?
Options: a ) 88 , b ) 89 , c ) 99 , d ) 54 , e ) 90
Rationale: "largest 2 digit number is 99 after doing 99 ÷ 88 we get remainder 11 hence largest 2 digit number exactly divisible by 88 = 99 - 11 = 88 a"
Answer: a
Problem: if greg buys 3 shirts , 6 trousers and 4 ties , the total cost is $ 80 . if greg buys 7 shirts , 2 trousers and 4 ties , the total cost is $ 80 . how much will it cost him to buy 5 trousers , 4 shirts and 4 ties ?
Options: a ) $ 60 , b ) $ 64 , c ) $ 80 , d ) $ 96 , e ) can not be determined
Rationale: "solution : 3 x + 6 y + 4 z = 80 7 x + 2 y + 4 z = 80 adding both the equations = 10 x + 8 y + 8 z = 160 5 x + 4 y + 4 z = 80 ans c"
Answer: c
Problem: when a number is divided by 6 & then multiply by 12 the answer is 18 what is the no . ?
Options: a ) 4.5 , b ) 5 , c ) 5.6 , d ) 5.7 , e ) 9
Rationale: "if $ x $ is the number , x / 6 * 12 = 18 = > 2 x = 18 = > x = 9 e"
Answer: e
Problem: donovan and michael are racing around a circular 400 - meter track . if donovan runs each lap in 48 seconds and michael runs each lap in 40 seconds , how many laps will michael have to complete in order to pass donovan , assuming they start at the same time ?
Options: a ) 5 , b ) 7 , c ) 8 , d ) 9 , e ) 6
Rationale: "one way of approaching this question is by relative speed method 1 . speed / rate of donovan = distance / time = > 400 / 48 = > 50 / 6 2 . speed / rate of michael = distance / time = > 400 / 40 = > 10 relative speed between them = 10 - 50 / 6 = > 10 / 6 ( we subtract the rates if moving in the same direction and add the rates if moving in the opposite direction ) in order to pass donovan - distance to be covered = 400 , relative rate = 10 / 6 total time taken by micheal to surpass donovan = distance / rate = > 400 * 6 / 10 = > 2400 / 10 = > 240 no . of laps taken by michael = total time / michael ' s rate = > 240 / 40 = > 6 hence correct answer is 6 laps . e"
Answer: e
Problem: a cistern 6 m long and 4 m wide contains water up to a breadth of 1 m 25 cm . find the total area of the wet surface .
Options: a ) 66 m square , b ) 49 m square , c ) 77 m square , d ) 44 m square , e ) 33 m square
Rationale: "area of the wet surface = 2 [ lb + bh + hl ] - lb = 2 [ bh + hl ] + lb = 2 [ ( 4 * 1.25 + 6 * 1.25 ) ] + 6 * 4 = 49 m square answer : b"
Answer: b
Problem: 65 % of the employees of a company are men . 60 % of the men in the company speak french and 40 % of the employees of the company speak french . what is % of the women in the company who do not speak french ?
Options: a ) 4 % , b ) 10 % , c ) 97.14 % , d ) 90.14 % , e ) 20 %
Rationale: "no of employees = 100 ( say ) men = 65 women = 35 men speaking french = 0.60 * 65 = 39 employees speaking french = 0.4 * 100 = 40 therefore women speaking french = 40 - 39 = 1 and women not speaking french = 35 - 1 = 34 % of women not speaking french = 34 / 35 * 100 = 97.14 % answer c"
Answer: c
Problem: a can do a piece of work in 6 days . b can do it in 6 days . with the assistance of c they completed the work in 2 days . find in how many days can c alone do it ?
Options: a ) 8 days , b ) 2 days , c ) 6 days , d ) 7 days , e ) 4 days
Rationale: "c = 1 / 2 - 1 / 6 - 1 / 6 = 1 / 6 = > 6 days answer : c"
Answer: c
Problem: what is the median of a set of consecutive integers if the sum of nth number from the beginning and nth number from the end is 200 ?
Options: a ) 10 , b ) 25 , c ) 50 , d ) 75 , e ) 100
Rationale: "surprisingly no one answered this easy one . property of a set of consecutive integerz . mean = median = ( first element + last element ) / 2 = ( second element + last but one element ) / 2 = ( third element + third last element ) / 2 etc . etc . so mean = median = 200 / 2 = 100 answer is e"
Answer: e
Problem: 57 + 58 = 115 . how many such 2 consecutive numbers are there less than 1500 when added gives a sum which is divisible by 5 ?
Options: a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) 500
Rationale: "since 2 + 3 = 5 & 7 + 8 = 15 any combination with these no be will give u desirable result . . . so total no in 100 will be 20 & that ' s why in 1000 , it will be 20 x 15 = 300 . answer : c"
Answer: c
Problem: a is a working partner and b is a sleeping partner in a business . a puts in 60,000 and b 40,000 . a gets 20 % of the profit for managing the business , and the rest is divided in proportion to their capitals . find the share of a in profit of 10000 .
Options: a ) 6800 , b ) 5800 , c ) 4800 , d ) 6500 , e ) none of these
Rationale: "the amount a gets for managing = 20 % of rs . 10000 = 2000 remaining profit = 10000 – 2000 = 8000 this is to be divided in the ratio 3 : 2 . share of a = 3 / 5 of 8000 = 4800 ⇒ total share of a = 4800 + 2000 = 6800 . answer a"
Answer: a
Problem: find the compound interest on $ 15,624 for 9 months at 16 % per annum compounded quarterly .
Options: a ) $ 4152 , b ) $ 1951 , c ) $ 2258 , d ) $ 8978 , e ) $ 8875
Rationale: "p = $ 15625 , n = 9 months = 3 quarters , r = 16 % p . a = 4 % per quarter . amount = $ [ 15625 * ( 1 + ( 4 / 100 ) ^ 3 ) ] = $ ( 15625 * ( 26 / 25 ) * ( 26 / 25 ) * ( 26 / 25 ) ) = $ 17576 . c . i = $ ( 17576 - 15625 ) = $ 1951 . answer ( b )"
Answer: b
Problem: find the probability that a year chosen at random has 53 mondays .
Options: a ) 5 / 28 , b ) 3 / 28 , c ) 1 / 28 , d ) 3 / 28 , e ) 3 / 27
Rationale: "explanation : there are 2 kinds of year leap year - probability = 1 / 4 ( out of 4 years one is a leap year ) non leap year - probability = 3 / 4 so it ' s either this or that now in non leap year , there are 365 days meaning 52 weeks with one day extra that one day can be monday out of 7 possible days . hence the probability = 1 / 7 similarly in leap year , there are 366 days and so 366 / 7 = 52 weeks with 2 days extra now probability of occurrence of monday out of possible 7 days = 2 / 7 so what we essentially want is ( a non leap year and monday ) or ( a leap year and monday ) so it ' ll be [ 3 / 4 * 1 / 7 ] + [ 1 / 4 * 2 / 7 ] = 5 / 28 answer : a"
Answer: a
Problem: a pair of articles was bought for $ 360 at a discount of 10 % . what must be the marked price of each of the article ?
Options: a ) $ 200 , b ) $ 500 , c ) $ 350 , d ) $ 400 , e ) $ 600
Rationale: "s . p . of each of the article = 360 / 2 = $ 180 let m . p = $ x 90 % of x = 360 x = 180 * 100 / 90 = $ 200 answer is a"
Answer: a
Problem: 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
Options: a ) 19828.88 , b ) 19828.8 , c ) 19828.87 , d ) 19828.81 , e ) 19828.82
Rationale: "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"
Answer: b
Problem: if x ^ 2 + y ^ 2 = 18 and xy = 3 , then ( x − y ) ^ 2 =
Options: a ) 8 , b ) 11 , c ) 14 , d ) 12 , e ) 20
Rationale: "but you can not take xy + 3 to mean xy = - 3 . . only if xy + 3 = 0 , it will mean xy = - 3 . . rest your solution is perfect and you will get your correct answer as 18 - 2 * 3 = 12 . . answer d"
Answer: d
Problem: the diameter of a garden roller is 1.4 m and it is 2 m long . how much area will it cover in 5 revolutions ? ( use π = 22 ⁄ 7 )
Options: a ) 40 m 2 , b ) 44 m 2 , c ) 48 m 2 , d ) 36 m 2 , e ) none of these
Rationale: "required area covered in 5 revolutions = 5 × 2 π rh = 5 × 2 × 22 ⁄ 7 × 0.7 × 2 = 44 m 2 answer b"
Answer: b
Problem: what is the dividend . divisor 16 , the quotient is 8 and the remainder is 4
Options: a ) 127 , b ) 128 , c ) 130 , d ) 131 , e ) 132
Rationale: "e = d * q + r e = 16 * 8 + 4 e = 128 + 4 e = 132"
Answer: e
Problem: harold and millicent are getting married and need to combine their already - full libraries . if harold , who has 1 / 2 as many books as millicent , brings 1 / 3 of his books to their new home , then millicent will have enough room to bring 1 / 4 of her books to their new home . what fraction of millicent ' s old library capacity is the new home ' s library capacity ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 4 / 5 , e ) 5 / 12
Rationale: "because we see h willbring 1 / 3 of his booksto the new home - - > try to pick a number that isdivisible by 3 . before : assume h = 30 books h = 1 / 2 m - - > m = 60 books after : h ' = 1 / 3 h = 10 books m ' = 1 / 4 m = 15 books total = 25 books m ' = 25 = 5 / 12 * 60 ratio : 5 / 12 ans : e"
Answer: e
Problem: if a , b and c together can finish a piece of work in 4 days . a alone in 36 days and b in 18 days , then c alone can do it in ?
Options: a ) 1 , b ) 7 , c ) 8 , d ) 9 , e ) 6
Rationale: "c = 1 / 4 - 1 / 36 – 1 / 18 = 1 / 6 = > 6 days ' answer : e"
Answer: e
Problem: in a coconut grove , ( x + 1 ) trees yield 60 nuts per year , x trees yield 120 nuts per year and ( x – 1 ) trees yield 180 nuts per year . if the average yield per year per tree be 100 , find x .
Options: a ) 2 , b ) 4 , c ) 5 , d ) 6 , e ) none of the above
Rationale: "( x + 1 ) × 60 + x × 120 + ( x − 1 ) × 180 / ( x + 1 ) + x + ( x − 1 ) = 100 ⇒ 360 x − 120 / 3 x = 100 ⇒ 60 x = 120 ⇒ x = 2 answer a"
Answer: a
Problem: three numbers are in the ratio 3 : 4 : 5 and their l . c . m . is 2400 . their h . c . f is ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60
Rationale: "let the numbers be 3 x , 4 x and 5 x their l . c . m . = 60 x 60 x = 2400 x = 40 the numbers are 3 * 40 , 4 * 40 , 5 * 40 hence required h . c . f . = 40 answer is c"
Answer: c
Problem: the area of a circular field is 17.56 hectares . find the cost of fencing it at the rate of rs . 3 per metre approximately
Options: a ) 4457
b ) 4567
c ) 4235
d ) 4547
e ) 4675
Rationale: explanation : area = ( 17.56 x 10000 ) m 2 = 175600 m 2 . π r 2 = 175600 ⇔ ( r ) 2 = ( 175600 x ( 7 / 22 ) ) ⇔ r = 236.37 m . circumference = 2 π r = ( 2 x ( 22 / 7 ) x 236.37 ) m = 1485.78 m . cost of fencing = rs . ( 1485.78 x 3 ) = rs . 4457 . answer : option a
Answer: a
Problem: a certain no . whendivided by 35 leaves a remainder 25 , what is the remainder if the same no . be dividedby 15 ?
Options: a ) 2 , b ) 4 , c ) 7 , d ) 8 , e ) 9
Rationale: explanation : 35 + 25 = 60 / 15 = 4 ( remainder ) b
Answer: b
Problem: . on dividing a number by 357 , we get 36 as remainder . on dividing the same number 17 , what will be the remainder ?
Options: a ) 0 , b ) 3 , c ) 5 , d ) 8 , e ) 2
Rationale: let x be the number and y be the quotient . then , x = 357 x y + 36 = ( 17 x 21 x y ) + ( 17 x 2 ) + 2 = 17 x ( 21 y + 2 ) + 2 ) required remainder = 2 . answer : option e
Answer: e
Problem: there is a point p on the circle . a and b started running in two constant different speeds . a in clockwise and b in anti - clockwise . first time 500 m in clockwise from p then 400 anti - clockwise . if b is yet to complete one round , what is the circumference of the circle ?
Options: a ) 700 , b ) 800 , c ) 900 , d ) 1000 , e ) 1100
Rationale: let the speeds of a & b be u and v resp . and let circumference be c . let their first meeting be after time t then ut + vt = c and ut = 500 ∴ vt = c − 500 and u / v = 500 / ( c − 500 ) for their second meeting after time t , ut + vt = 2 c and vt = 400 ∴ ut = 2 c − 400 and u / v = ( 2 c − 400 ) / 400 hence 500 / ( c − 500 ) = ( 2 c − 400 ) / 400 simplifying , 100000 = ( c − 200 ) ( c − 500 ) = c ² − 700 c + 100000 → c = 700 answer : a
Answer: a
Problem: carina has 55 ounces of coffee divided into 5 - and 10 - ounce packages . if she has 2 more 5 - ounce packages than 10 - ounce packages , how many 10 - ounce packages does she have ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: lets say 5 and 10 ounce packages be x and y respectively . given that , 5 x + 10 y = 55 and x = y + 2 . what is the value of y . substituting the x in first equation , 5 y + 10 + 10 y = 55 - > y = 45 / 15 . = 3 e
Answer: e
Problem: how many two - digit numbers yield a remainder of 2 when divided by both 5 and 16 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "easier to start with numbers that are of the form 16 p + 2 - - - > 18,34 , 50,66 , 82,96 . out of these , there is only one number ( 82 ) is also of the form 5 q + 2 . thus 1 is the answer . b is the correct answer ."
Answer: b
Problem: a computer manufacturer produces a certain electronic component at a cost of $ 50 per component . shipping costs for delivering the components are $ 8 per unit . further , the manufacturer has costs of $ 16,000 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 200 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ?
Options: a ) 135 , b ) 129 , c ) 131 , d ) 138 , e ) 141
Rationale: "$ 16000 is a fixed cost each component is $ 58 ( $ 50 to produce , $ 8 to ship ) manufacturer will be producing and selling 200 components so therefore the equation to find price would be 200 * p = 16000 + ( 200 * 50 ) + ( 200 * 8 ) p = ( 16000 + 10000 + 1600 ) / 200 p = 138 answer : d"
Answer: d
Problem: the area of an isosceles trapezoid with sides of length 5 and bases of length 8 and 14 is ?
Options: a ) 22 , b ) 32 , c ) 44 , d ) 55 , e ) 56
Rationale: "we can divide the trapezoid into two triangles and a rectangle sides of triangle , t 1 - - > h 1 = 5 , b 1 = 3 , s 1 = root ( 25 - 9 ) = 4 = s 2 of triangle t 2 area of triangle = ( 1 / 2 ) * 4 * 3 = 6 side of the rectangle = 8 * 4 = 32 total area of the trapezoid = 32 + 6 + 6 = 44 answer : c"
Answer: c
Problem: a rope of which a calf is tied is increased from 15 m to 18 m , how much additional grassy ground shall it graze ?
Options: a ) 1218 , b ) 1212 , c ) 1210 , d ) 3 . 11.14 , e ) 291.1
Rationale: "π ( 182 – 152 ) = 311.14 answer : d"
Answer: d
Problem: the radius of a circle is increased by 1 % . find how much % does its area increases ?
Options: a ) 2.21 %
b ) 2.07 %
c ) 2.08 %
d ) 2.01 %
e ) 2.11 %
Rationale: r = 100 r = 101 r 2 = 10000 r 2 = 10201 10000 - - - - 201 100 - - - - ? = > 2.01 % answer : d
Answer: d
Problem: in gabriel ' s sheep herd , every sheep has either fleas or lice or both . half of the sheep have lice , and 84 sheep have both pests . if 94 sheep have lice , how many sheep have only fleas ?
Options: a ) 10 , b ) 20 , c ) 84 , d ) 94 , e ) 178
Rationale: n ( lice ) = n ( only lice ) + n ( both lice and fleas ) n ( both lice and fleas ) = 84 n ( lice ) = 94 n ( only lice ) = 94 - 84 = 10 since , it is also said that exactly half the sheep have lice , it can be inferred that half the number of sheep is 94 . therefore , the total number of sheep having only fleas is 10 ans : ( option a )
Answer: a
Problem: tanks a and b are each in the shape of a right circular cylinder . the interior of tank a has a height of 7 meters and a circumference of 8 meters , and the interior of tank b has a height of 8 meters and a circumference of 10 meters . the capacity of tank a is what percent of the capacity of tank b ?
Options: a ) 56 % , b ) 80 % , c ) 100 % , d ) 120 % , e ) 125 %
Rationale: "for a , r = 8 / 2 pi . its capacity = ( 4 pi ) ^ 2 * 7 = 112 pi for b , r = 10 / pi . its capacity = ( 5 pi ) ^ 2 * 8 = 200 pi a / b = 112 pi / 200 pi = 0.56 a"
Answer: a
Problem: the speed of a subway train is represented by the equation z = s ^ 2 + 2 s for all situations where 0 ≤ s ≤ 7 , where z is the rate of speed in kilometers per hour and s is the time in seconds from the moment the train starts moving . in kilometers per hour , how much faster is the subway train moving after 6 seconds than it was moving after 3 seconds ?
Options: a ) 4 , b ) 9 , c ) 15 , d ) 48 , e ) 33
Rationale: given : z = s ^ 2 + 2 s for 0 ≤ s ≤ 7 z ( 3 ) = 3 ^ 2 + 2 * 3 = 15 z ( 6 ) = 6 ^ 2 + 2 * 6 = 48 therefore z ( 7 ) - z ( 3 ) = 48 - 15 = 33 km / hr option e
Answer: e
Problem: notebooks are sold in packages of 4 or 7 only . if wilson bought 69 notebooks exactly , what could be the number of large packs wilson bought ?
Options: a ) 3 , b ) 4 , c ) 7 , d ) 8 , e ) 9
Rationale: let number of packs of four = f let number of packs of seven = s 4 f + 7 s = 69 now , we need to test for values of s . since sum 69 is odd and 4 f will always be even , e ca n ' t be even . now , we can test for values e = 3 , 7 and 9 4 * 5 + 7 * 7 = 20 + 49 = 69 answer c
Answer: c
Problem: a person lent a certain sum of money at 4 % per annum at simple interest and in 8 years the interest amounted to rs . 340 less than the sum lent . what was the sum lent ?
Options: a ) 228 , b ) 278 , c ) 289 , d ) 500 , e ) 821
Rationale: "p - 340 = ( p * 4 * 8 ) / 100 p = 500 answer : d"
Answer: d
Problem: a total of 40 percent of the geese included in a certain migration study were male . if some of the geese migrated during the study and 20 percent of the migrating geese were male , what was the ratio of the migration rate for the male geese to the migration rate for the female geese ? [ migration rate for geese of a certain sex = ( number of geese of that sex migrating ) / ( total number of geese of that sex ) ]
Options: a ) 15 / 40 , b ) 7 / 12 , c ) 2 / 3 , d ) 7 / 8 , e ) 8 / 7
Rationale: "let ' take the number of geese to be 100 . male = 40 . female = 60 . now the second part of the q , let ' s take the number migrated to be 20 . so we have 20 geese that migrated and out of that 20 % are male i . e 20 / 100 * 20 = 4 geese ( males ) and now we know out of the total 20 geese , 4 are male , then 16 have to be female . now the ratio part , male geese ratios = 4 / 40 = 1 / 10 . - a female geese ratios = 16 / 60 = 4 / 15 - b cross multiply equations a and b and you get = 15 / 40 . ans a"
Answer: a
Problem: a contractor isengaged for 30 days on the condition that he receives rs . 25 for eachday he works & fined rs . 7.50 for each day is absent . he gets rs . 425 in all . for how many days was heabsent ?
Options: a ) 8 , b ) 10 , c ) 15 , d ) 17 , e ) 21
Rationale: 30 * 25 = 750 425 - - - - - - - - - - - 325 25 + 7.50 = 32.5 325 / 32.5 = b
Answer: b
Problem: a garrison of 2000 men has provisions for 54 days . at the end of 15 days , a reinforcement arrives , and it is now found that the provisions will last only for 30 days more . what is the reinforcement ?
Options: a ) 1800 men , b ) 3900 men , c ) 600 men , d ) 3800 men , e ) 900 men
Rationale: "2000 - - - - 54 2000 - - - - 39 x - - - - - 20 x * 30 = 2000 * 39 x = 2600 2000 - - - - - - - 600 answer : c"
Answer: c
Problem: the ages of two person differ by 20 years . if 4 years ago , the elder one be 5 times as old as the younger one , their present ages ( in years ) are respectively
Options: a ) 30 , 10 , b ) 25 , 5 , c ) 29 , 9 , d ) 50 , 30 , e ) 20,10
Rationale: "let their ages be x and ( x + 20 ) years . then , 5 ( x - 4 ) = ( x + 20 - 4 ) = > 4 x = 36 = > x = 9 their present ages are 29 years and 9 year . answer : c"
Answer: c
Problem: 28 machines can do a work in 10 days . how many machines are needed to complete the work in 40 days ?
Options: a ) 10 , b ) 6 , c ) 4 , d ) 7 , e ) 5
Rationale: "required number of machines = 28 * 10 / 40 = 7 answer is d"
Answer: d
Problem: sandy buys an old scooter for $ 800 and spends $ 200 on its repairs . if sandy sells the scooter for $ 1400 , what is the gain percent ?
Options: a ) 20 % , b ) 30 % , c ) 40 % , d ) 50 % , e ) 60 %
Rationale: "selling price / total cost = 1400 / 1000 = 1.4 the gain percent is 40 % . the answer is c ."
Answer: c
Problem: a jogger running at 9 kmph alongside a railway track in 240 meters ahead of the engine of a 120 metres long train running at 45 kmph in the same direction . in how much time will the train pass the jogger ?
Options: a ) 18 seconds , b ) 26 seconds , c ) 36 seconds , d ) 16 seconds , e ) 46 seconds
Rationale: total distance ( d ) = 240 + 120 = 360 meter relative speed ( s ) = 45 - 9 = 36 kmph = 36 * 5 / 18 = 10 mps d = s * t 360 = 10 * t t = 36 seconds answer : c
Answer: c
Problem: a woman complete a journey in 15 hours . she travels first half of the journey at the rate of 21 km / hr and second half at the rate of 24 km / hr . find the total journey in km .
Options: a ) 336 km . , b ) 216 km . , c ) 314 km . , d ) 224 km . , e ) 544 km .
Rationale: "0.5 x / 21 + 0.5 x / 24 = 15 - - > x / 21 + x / 24 = 30 - - > x = 336 km . a"
Answer: a
Problem: how many 3 - digit integers exist such that all their digits are odd ?
Options: a ) 80 , b ) 100 , c ) 120 , d ) 125 , e ) 135
Rationale: so last digit can be filled in 5 ways - 1 , 3,5 , 7,9 there are 5 possibilities . the answer is 5 ∗ 5 ∗ 5 = 125 the correct answer is d
Answer: d
Problem: matt gets a $ 1,300 commission on a big sale . this commission alone raises his average commission by $ 150 . if matt ' s new average commission is $ 400 , how many sales has matt made ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "let , average commission = x no . of items sold = y total commission = xy new commission = xy + 1300 new average = ( xy + 1300 ) / ( y + 1 ) = 150 + x i . e . ( xy + 1300 ) = ( y + 1 ) * ( 150 + x ) i . e . ( xy + 1300 ) = ( xy + x + 150 y + 150 ) i . e . ( 1150 ) = ( x + 150 y ) new commission = 400 = 150 + x i . e . x = 250 i . e . y = 6 new sales = y + 1 = 7 answer : option d"
Answer: d
Problem: a train speeds past a pole in 15 seconds and a platform 100 meter long in 25 seconds . what is length of the train ?
Options: a ) 140 meter , b ) 145 meter , c ) 150 meter , d ) 155 meter , e ) 160 meter
Rationale: "explanation : let the length of the train is x meter and speed of the train is y meter / second then x / y = 15 [ because distance / speed = time ] = > y = 15 / x x + 100 / 25 = x / 15 x = 150 meters so length of the train is 150 meters answer is c"
Answer: c
Problem: 25 % of 30 % of 45 % is equal to ?
Options: a ) 0.03375 , b ) 0.03372 , c ) 0.0337 , d ) 0.03377 , e ) 0.03376
Rationale: "( 25 / 100 ) * ( 30 / 100 ) * ( 45 / 100 ) 1 / 4 * 3 / 10 * 9 / 20 27 / 800 = 0.03375 answer : a"
Answer: a
Problem: a student reached his school late by 20 mins by travelling at a speed of 9 kmph . if he had travelled at a speed of 12 kmph , he would have reached his school 20 mins early . what is the distance between house and school ?
Options: a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28
Rationale: distance = distance either student reaches school before time or after time 9 ( t + 20 / 60 ) = 12 ( t - 20 / 60 ) i . e 9 ( t + 1 / 3 ) = 12 ( t - 1 / 3 ) 9 ( 3 t + 1 ) = 12 ( 3 t - 1 ) t = 7 / 3 put t value in any of distance equation put t = 7 / 3 in 9 ( t + 1 / 3 ) we get 24 km answer : a
Answer: a
Problem: the volume of a rectangular swimming pool is 840 cubic meters and water is flowing into the swimming pool . if the surface level of the water is rising at the rate of 0.5 meters per minute , what is the rate w , in cubic meters per minutes , at which the water is flowing into the swimming pool ?
Options: a ) 0.125
b ) 0.25
c ) 0.5
d ) 0.75
e ) not enough information to determine the rate
Rationale: the correct answer is e . there are not enough info to answer the question . a 840 cubic meters rectangle is built from : height * length * width . from the question we know the volume of the pool and the filling rate . a pool can have a height of 10 * width 8.4 * length 10 and have a volume of 840 cubic meters , and it can have a height of 1 meter , width of 100 meters and length of 8.4 . in both cases the pool will fill up in a different rate = e
Answer: e
Problem: the sum of four consecutive even numbers is 292 . what would be the smallest number ?
Options: a ) 49 , b ) 68 , c ) 60 , d ) 57 , e ) 70
Rationale: "e 70 let the four consecutive even numbers be 2 ( x - 2 ) , 2 ( x - 1 ) , 2 x , 2 ( x + 1 ) their sum = 8 x - 4 = 292 = > x = 37 smallest number is : 2 ( x - 2 ) = 70 ."
Answer: e
Problem: a student is ranked 13 th from right and 8 th from left . how many are there ?
Options: a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: "13 th from right means = x + 12 8 th from left means = 7 + x total = 12 + 7 + 1 = 20 answer : c"
Answer: c
Problem: how many 4 - digit odd numbers do not use any digit more than once ?
Options: a ) 1728 , b ) 2160 , c ) 2240 , d ) 2268 , e ) 2520
Rationale: let a 4 - digit number be represented by abcd here a can have any value between 1 to 9 - so total 9 b can have any value between 0 to 9 , but not a - so total 9 c can have any value between 0 to 9 , but not a or b - so total 8 d can have any value between 0 to 9 , but not a , b or c - so total 7 no . of all possible 4 - digit nos ( without repeating any digit ) = 9 * 9 * 8 * 7 = 4536 half of these would be odd . therefor , no . of odd possible 4 - digit nos ( without repeating any digit ) = 4536 / 2 = 2268 answer should be d .
Answer: d
Problem: revenues were recorded for store a and store b over a period of 3 months . in the first month , store a ' s revenues were $ 12000 higher than store b ' s revenues . in the second month , store a ' s revenues were $ 8000 higher than store b ' s revenues . if store a ' s average ( arithmetic mean ) monthly revenue for the 3 months was $ 2000 greater than store b ' s average monthly revenue , then store b ' s revenue in the third month was how much greater than store a ' s revenue ?
Options: a ) $ 14,000 , b ) $ 15,000 , c ) $ 42,000 , d ) $ 46,000 , e ) $ 50,000
Rationale: answer : cit may be tempting to come up with a lot of variables , one each for each month ' s revenue for each company . however , focus on the differences . in the first month , the difference was + 12 in favor of a . ( note that we can drop the thousands since every number in the question is in terms of thousands . ) in the second , the difference was + 8 in favor of a . the average was + 2 in favor of a . with these numbers , use the average formula to find the third month ( t ) : ( 12 + 8 + t ) / 3 = 2 20 + t = 6 t = - 14 since positive numbers indicate a difference in favor of a , negative numbers are in favor of b . - 14 represents a $ 14,000 advantage in favor of store b . choice ( a ) is correct .
Answer: a
Problem: a is older than b by 5 years . 7 years hence , thrice a ' s age shall be equal to 4 times that of b . find their present ages .
Options: a ) 14 , 7 , b ) 10 , 5 , c ) 13 , 8 , d ) 12 , 8 , e ) 8 , 12
Rationale: explanation : let the present ages of a and b be ' a ' and ' b ' respectively . 3 ( a + 7 ) = 4 ( ( b + 7 ) - - - ( 1 ) = > 3 a - 4 b = 7 - - - - - - - ( 1 ) a - b = 5 - - - - - - - ( 2 ) solving ( 1 ) and ( 2 ) we get b = 8 substituting b = 8 in second equation , we get a = 13 . answer : c = > 2 a = 32 = > a = 16 . answer : c
Answer: c
Problem: three numbers are in the ratio 3 : 4 : 5 and their l . c . m is 2400 . their h . c . f is ?
Options: a ) 40 , b ) 99 , c ) 88 , d ) 44 , e ) 11
Rationale: "let the numbers be 3 x , 4 x and 5 x . then , their l . c . m = 60 x . so , 60 x = 2400 or x = 40 . the numbers are ( 3 * 40 ) , ( 4 * 40 ) and ( 5 * 40 ) . hence , required h . c . f = 40 . answer : a"
Answer: a
Problem: what is x if x + 2 y = 20 and y = 5 ?
Options: a ) a ) 10 , b ) b ) 8 , c ) c ) 6 , d ) d ) 4 , e ) e ) 2
Rationale: "x = 20 - 2 y x = 20 - 10 . x = 10 answer : a"
Answer: a
Problem: a certain experimental mathematics program was tried out in 2 classes in each of 34 elementary schools and involved 40 teachers . each of the classes had 1 teacher and each of the teachers taught at least 1 , but not more than 3 , of the classes . if the number of teachers who taught 3 classes is n , then the least and greatest possible values of n , respectively , are
Options: a ) 0 and 13 , b ) 0 and 14 , c ) 1 and 10 , d ) 1 and 9 , e ) 2 and 8
Rationale: one may notice that greatest possible values differ in each answer choice in contrast to the least values , which repeat . to find out the greatest value you should count the total classes ( 34 * 2 = 68 ) , then subtract the total # of teachers since we know from the question that each teacher taught at least one class ( 68 - 40 = 28 ) . thus we get a number of the available extra - classes for teachers , and all that we need is just to count how many teachers could take 2 more classes , which is 28 / 2 = 14 . so the greatest possible value of the # of teachers who had 3 classes is 14 . only answer b has this option .
Answer: b
Problem: nicky and cristina are running a race . since cristina is faster than nicky , she gives him a 48 meter head start . if cristina runs at a pace of 5 meters per second and nicky runs at a pace of only 3 meters per second , how many seconds will nicky have run before cristina catches up to him ?
Options: a ) 15 seconds , b ) 18 seconds , c ) 24 seconds , d ) 30 seconds , e ) 45 seconds
Rationale: "used pluging in method say t is the time for cristina to catch up with nicky , the equation will be as under : for nicky = n = 3 * t + 48 for cristina = c = 5 * t @ t = 24 , n = 120 c = 120 right answer ans : c"
Answer: c
Problem: a walks at 10 kmph and 6 hours after his start , b cycles after him at 20 kmph . how far from the start does b catch up with a ?
Options: a ) 100 km , b ) 150 km , c ) 50 km , d ) 120 km , e ) 200 km
Rationale: suppose after x km from the start b catches up with a . then , the difference in the time taken by a to cover x km and that taken by b to cover x km is 6 hours . x / 10 - x / 20 = 6 x = 120 km answer is d
Answer: d
Problem: how many words , with or without meaning , can be formed using all letters of the word sharp using each letter exactly once ?
Options: a ) 90 , b ) 100 , c ) 110 , d ) 120 , e ) 130
Rationale: "the word sharp has exactly 5 letters which are all different . therefore the number of words that can be formed = number of permutations of 5 letters taken all at a time . = p ( 5 , 5 ) = 5 ! = 5 x 4 x 3 x 2 × 1 = 120 answer : d"
Answer: d
Problem: mary works in a restaurant a maximum of 80 hours . for the first 20 hours , she is paid $ 8 per hour . for each overtime hour , she is paid at a rate which is 25 % higher than her regular rate . how much mary can earn in a week ?
Options: a ) 600 , b ) 720 , c ) 760 , d ) 620 , e ) 700
Rationale: "mary receives $ 8 ( 20 ) = $ 160 for the first 20 hours . for the 60 overtime hours , she receives $ 8 ( 0.25 ) + $ 8 = $ 10 per hour , that is $ 10 ( 60 ) = $ 600 . the total amount is $ 160 + $ 600 = $ 760 answer c 360 ."
Answer: c
Problem: if 2 x + y = 4 and x + 2 y = 5 , then ( x + y ) / 3 =
Options: a ) 1 , b ) 4 / 3 , c ) 17 / 5 , d ) 18 / 5 , e ) 4
Rationale: "we have two equations : 2 x + y = 4 x + 2 y = 5 notice that something nice happens when we add them . we get : 3 x + 3 y = 9 divide both sides by 3 to get : x + y = 3 so , ( x + y ) / 3 = 3 / 3 = 1 answer : a"
Answer: a
Problem: the least number which when increased by 6 each divisible by each one of 24 , 32 , 36 and 54 is :
Options: a ) 858 , b ) 859 , c ) 869 , d ) 4320 , e ) none of these
Rationale: "solution required number = ( l . c . m . of 24 , 32 , 36 , 54 ) - 5 = 864 - 6 = 858 . answer a"
Answer: a
Problem: find the mean proportional between 81 & 100 ?
Options: a ) a ) 59 , b ) b ) 61 , c ) c ) 63 , d ) d ) 65 , e ) e ) 90
Rationale: "formula = √ a × b a = 81 and b = 100 √ 81 × 100 = 9 × 10 = 90 e"
Answer: e
Problem: if the sum of the first n positive integers is s , what is the sum of the first n positive integers divisible by 5 , in terms of s ?
Options: a ) s / 2 , b ) s , c ) 2 s , d ) 2 s + 2 , e ) 5 s
Rationale: "answer is e given sum of 1 2 3 . . . . . n = s sum of 5 , 10 , 15 . . . . 5 n = 5 [ sum ( 1 2 3 . . . . n ) ] = 5 s"
Answer: e
Problem: a man can row upstream at 30 kmph and downstream at 60 kmph , and then find the speed of the man in still water ?
Options: a ) 27 , b ) 29 , c ) 30 , d ) 20 , e ) 45
Rationale: "us = 30 ds = 60 m = ( 30 + 60 ) / 2 = 45 answer : e"
Answer: e
Problem: if the average ( arithmetic mean ) of 2 a + 16 , 3 a - 8 is 94 , what is the value of a ?
Options: a ) 25 , b ) 30 , c ) 28 , d ) 36 , e ) 42
Rationale: "am of 2 a + 16 , 3 a - 8 = 2 a + 16 + 3 a - 8 / 2 = 5 a + 8 / 2 given that 5 a + 8 / 2 = 94 a = 36 answer is d"
Answer: d
Problem: a group of students was interviewed for that if it was asked whether or not they speak french and / or english . among those who speak french , 10 speak english well , while 40 of them do not speak english . if 75 % of students do not speak french , how many students were surveyed ?
Options: a ) 210 , b ) 225 , c ) 200 , d ) 250 , e ) 300
Rationale: "number of students who speak french are 40 + 10 = 50 of total students , the percentage of students who do not speak french was 75 % - - > percentage of who do is 25 % 50 - - - - - - - 25 % x - - - - - - - 100 % x = 50 * 100 / 25 = 200 = number of all students answer is c"
Answer: c
Problem: a train crosses a platform of 120 m in 15 sec , same train crosses another platform of length 250 m in 20 sec . then find the length of the train ?
Options: a ) a ) 150 m , b ) b ) 270 m , c ) c ) 180 m , d ) d ) 158 m , e ) e ) 350 m
Rationale: "length of the train be ‘ x ’ x + 120 / 15 = x + 250 / 20 4 x + 480 = 3 x + 750 x = 270 m answer : b"
Answer: b
Problem: two numbers are in the ratio 3 : 4 . if their l . c . m . is 36 . what is sum of the numbers ?
Options: a ) 21 , 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 36 = > 12 x = 36 = > x = 36 / 12 = 3 sum of the numbers = 3 x + 4 x = 7 x = 7 x 3 = 21 answer : option a"
Answer: a
Problem: in what time will a train 120 m long cross an electric pole , it its speed be 144 km / hr ?
Options: a ) 2.5 sec , b ) 3 sec , c ) 8.9 sec , d ) 6.9 sec , e ) 2.9 sec
Rationale: "speed = 144 * 5 / 18 = 40 m / sec time taken = 120 / 40 = 3 sec . answer : b"
Answer: b
Problem: evaluate : 1234562 - 12 * 3 * 2 = ?
Options: a ) 32435453 , b ) 1234554 , c ) 76768786 , d ) 97979797 , e ) 75868656
Rationale: "according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 1234562 - 12 * 3 * 2 = 1234562 - 8 = 1234554 correct answer b"
Answer: b
Problem: 33 1 / 3 % of 360 ?
Options: a ) 80 , b ) 90 , c ) 110 , d ) 120 , e ) 130
Rationale: "33 1 / 3 % = 1 / 3 1 / 3 × 360 = 120 d )"
Answer: d
Problem: what is the area of a square field whose sides have a length of 14 meters ?
Options: a ) 196 sq m , b ) 286 sq m , c ) 298 sq m , d ) 267 sq m , e ) 231 sq m
Rationale: "14 * 14 = 196 sq m the answer is a ."
Answer: a
Problem: x can do a piece of work in 40 days . he works at it for 8 days and then y finished it in 32 days . how long will y take to complete the work ?
Options: a ) 10 , b ) 40 , c ) 15 , d ) 18 , e ) 20
Rationale: "work done by x in 8 days = 8 * 1 / 40 = 1 / 5 remaining work = 1 - 1 / 5 = 4 / 5 4 / 5 work is done by y in 32 days whole work will be done by y in 32 * 5 / 4 = 40 days answer is b"
Answer: b
Problem: a man traveled a total distance of 1800 km . he traveled one - third of the whole trip by plane and the distance traveled by train is three - fifth of the distance traveled by bus . if he traveled by train , plane and bus , then find the distance traveled by bus ?
Options: a ) 239 , b ) 247 , c ) 277 , d ) 270 , e ) 898
Rationale: "explanation : total distance traveled = 1800 km . distance traveled by plane = 600 km . distance traveled by bus = x distance traveled by train = 3 x / 5 = > x + 3 x / 5 + 600 = 1800 = > 8 x / 5 = 1200 = > x = 750 km . answer : d"
Answer: d
Problem: if k is a non - negative integer and 12 ^ k is a divisor of 856,736 then 3 ^ k - k ^ 3 =
Options: a ) 0 , b ) 1 , c ) 36 , d ) 120 , e ) 524
Rationale: "8 + 5 + 6 + 7 + 3 + 6 = 35 , so this number is not divisible by 3 and thus not divisible by 12 . therefore , k = 0 3 ^ k - k ^ 3 = 1 - 0 = 1 the answer is b ."
Answer: b
Problem: the length of a rectangular plot is 10 mtr more than its width . the cost of fencing the plot along its perimeter at the rate of rs . 6.5 mtr is rs . 1950 . the perimeter of the plot is ?
Options: a ) 126
b ) 156
c ) 190
d ) 300
e ) 260
Rationale: sol . let width = x , length = ( 10 + x ) perimeter = 2 ( x + ( 10 + x ) ) = 2 ( 2 x = 10 ) & 2 ( 2 x + 10 ) * 6.5 = 1950 x = 70 required perimeter = 2 ( 70 + 80 ) = 300 d
Answer: d
Problem: a can do a piece of work in 8 days . b can do it in 6 days . with the assistance of c they completed the work in 2 days . find in how many days can c alone do it ?
Options: a ) 8.7 days , b ) 2.0 days , c ) 6.6 days , d ) 7.7 days , e ) 4.8 days
Rationale: "c = 1 / 2 - 1 / 8 - 1 / 8 = 5 / 24 = > 4.8 days answer : e"
Answer: e
Problem: a car started running at a speed of 30 km / hr and the speed of the car was increased by 2 km / hr at the end of every hour . find the total distance covered by the car in the first 10 hours of the journey .
Options: a ) 342 km , b ) 390 km , c ) 642 km , d ) 742 km , e ) 382 km
Rationale: "the total distance covered by the car in the first 10 hours = 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 + 48 = sum of 10 terms in ap whose first term is 30 and last term is 48 = 10 / 2 [ 30 + 48 ] = 390 km . answer : b"
Answer: b
Problem: the maximum number of students among them 1230 pens and 920 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :
Options: a ) 91 , b ) 10 , c ) 1001 , d ) 1911 , e ) none of these
Rationale: "explanation : required number of students = h . c . f of 1230 and 920 = 10 . answer : b"
Answer: b
Problem: the length of a room is 7 m and width is 4.75 m . what is the cost of paying the floor by slabs at the rate of rs . 900 per sq . metre .
Options: a ) 25650 , b ) 25750 , c ) 26550 , d ) 26750 , e ) 29925
Rationale: "area = 7 × 4.75 sq . metre . cost for 1 sq . metre . = rs . 900 hence total cost = 7 × 4.75 × 900 = 7 × 4275 = rs . 29925 answer is e"
Answer: e
Problem: a train 110 m long is running with a speed of 27 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 7 sec , b ) 6 sec , c ) 8 sec , d ) 4 sec , e ) 12 sec
Rationale: "speed of train relative to man = 27 + 6 = 33 km / hr . = 33 * 5 / 18 = 9.1667 m / sec . time taken to pass the men = 110 / 9.1667 = 12 sec . answer : e"
Answer: e
Problem: a , b and c can do a piece of work in 24 days , 30 days and 60 days respectively . they began the work together but c left 4 days before the completion of the work . in how many days was the work completed ?
Options: a ) 10 days , b ) 11 days , c ) 13 days , d ) 21 days , e ) 31 days
Rationale: one day work of a , b and c = 1 / 24 + 1 / 30 + 1 / 60 = 11 / 120 work done by a and b together in the last 4 days = 4 * ( 1 / 24 + 1 / 30 ) = 3 / 10 remaining work = 7 / 10 the number of days required for this initial work = 7 days . the total number of days required = 4 + 7 = 11 days . answer : b
Answer: b
Problem: machine p and machine q are each used to manufacture 550 sprockets . it takes machine p 10 hours longer to produce 550 sprockets than machine q . machine q produces 10 % more sprockets per hour than machine a . how many sprockets per hour does machine a produce ?
Options: a ) 5 , b ) 15 , c ) 55 , d ) 95 , e ) 125
Rationale: "p makes x sprockets per hour . then q makes 1.1 x sprockets per hour . 550 / x = 550 / 1.1 x + 10 1.1 ( 550 ) = 550 + 11 x 11 x = 55 x = 5 the answer is a ."
Answer: a
Problem: what percent of a day is 7 hours ?
Options: a ) 29.2 % , b ) 12.5 % , c ) 13 % , d ) 11.3 % , e ) none of these
Rationale: explanation : solution : required percentage = ( 7 / 100 * 24 ) = 29.2 % answer : a
Answer: a
Problem: if 4 xz + yw = 5 and xw + yz = 10 , what is the value of the expression ( 2 x + y ) ( 2 z + w ) ?
Options: a ) 9 . , b ) 12 . , c ) 15 . , d ) 16 . , e ) 25
Rationale: "( 2 x + y ) * ( 2 z + w ) = 5 + 2 ( 10 ) = 25 answer : e"
Answer: e
Problem: rectangular tile each of size 70 cm by 30 cm must be laid horizontally on a rectangular floor of size 110 cm by 130 cm , such that the tiles do not overlap and they are placed with edges jutting against each other on all edges . a tile can be placed in any orientation so long as its edges are parallel to the edges of floor . no tile should overshoot any edge of the floor . the maximum number of tiles that can be accommodated on the floor is :
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "area of tile = 70 * 30 = 2100 area of floor = 130 * 110 = 14300 no of tiles = 14300 / 2100 = 6.8 so , the no of tile = 6 answer : b"
Answer: b
Problem: 1394 x 1394 = ?
Options: a ) a ) 1951609 , b ) b ) 1951601 , c ) c ) 1951602 , d ) d ) 1943236 , e ) e ) 1951604
Rationale: "1394 x 1394 = ( 1394 ) 2 = ( 1400 - 6 ) 2 = ( 1400 ) 2 + ( 6 ) 2 - ( 2 x 1400 x 6 ) = 1960000 + 36 - 16800 = 1960036 - 16800 = 1943236 . answer : d"
Answer: d
Problem: a circular ground whose diameter is 34 metres , has a 2 metre - broad garden around it . what is the area of the garden in square metres ?
Options: a ) 226.3
b ) 226.2
c ) 228.2
d ) 227
e ) 226
Rationale: req . area = ï € [ ( 19 ) 2 â € “ ( 17 ) 2 ] = 22 â  „ 7 ã — ( 36 ã — 2 ) [ since a 2 - b 2 = ( a + b ) ( a - b ) ] = ( 22 ã — 36 ã — 2 ) / 7 = 226.3 sq m answer a
Answer: a
Problem: 3889 + 12.808 - ? = 3854.002
Options: a ) a ) 47.095 , b ) b ) 47.752 , c ) c ) 47.806 , d ) d ) 47.95 , e ) of the above
Rationale: let 3889 + 12.808 - x = 3854.002 . then x = ( 3889 + 12.808 ) - 3854.002 = 3901.808 - 3854.002 = 47.806 . answer = c
Answer: c
Problem: a sum of money is sufficient to pay a ' s wages for 20 days and b ' s wages for 30 days . the same money is sufficient to pay the wages of both for ?
Options: a ) 12 days , b ) 15 days , c ) 20 days , d ) 18 days , e ) 22 days
Rationale: "let the total money be $ x a ' s 1 day work = $ x / 20 b ' s 1 day work = $ x / 30 a + b 1 day work = $ x / 12 money is sufficient to pay the wages of both for 12 days answer is a"
Answer: a
Problem: a river boat leaves silver town and travels upstream to gold town at an average speed of 6 kilometers per hour . it returns by the same route at an average speed of 8 kilometers per hour . what is the average speed for the round - trip in kilometers per hour ?
Options: a ) 6.8 , b ) 7.1 , c ) 7.2 , d ) 7.5 , e ) 8.0
Rationale: "pick a number which is lcm of 8 and 6 = 24 . upstream time = 24 / 6 = 4 hrs downstream time = 24 / 8 = 3 hrs total time = 7 hrs total distance = 48 average speed = 48 / 7 = 6.8 km / hr"
Answer: a
Problem: the sides of a square region , measured to the nearest centimeter , are 7 centimeters long . the least possible value of the actual area of the square region is
Options: a ) 42.25 sq cm
b ) 45.25 sq cm
c ) 43.25 sq cm
d ) 50.25 sq cm
e ) 52.25 sq cm
Rationale: though there might be some technicalities concerning the termnearest ( as 6.5 is equidistant from both 6 and 7 ) the answer still should be a : 6.5 ^ 2 = 42.25 . answer : a
Answer: a
Problem: a box contains 6 white , 5 red and 8 white marbles . 5 marbles are drawn from the box at random . what is the probability that both the marbles are of the same color ?
Options: a ) 19 / 11628 , b ) 36 / 11628 , c ) 613 / 11628 , d ) 6113 / 11628 , e ) 63 / 11628
Rationale: explanation : total marbles in a box = 6 black + 5 red + 8 green marbles = 19 marbles 5 marbles are drawn from 19 marbles at random . therefore , n ( s ) = 19 c 5 = 11628 ways let a be the event that 2 marbles drawn at random are of the same color . number of cases favorable to the event a is n ( a ) = 6 c 5 + 5 c 5 + 8 c 5 = 6 + 1 + 56 = 63 therefore , by definition of probability of event a , p ( a ) = n ( a ) / n ( s ) = 63 / 11628 answer : e
Answer: e
Problem: 105 * 2
Options: a ) 11025 , b ) 23889 , c ) 29088 , d ) 1999 , e ) 17710
Rationale: "here d = 5 . 100 + 2 × × 5 / 25 = 11025 answer : a"
Answer: a
Problem: what will be the reminder when ( 43 ^ 43 + 43 ) is divided by 44 ?
Options: a ) 32 , b ) 42 , c ) 83 , d ) 71 , e ) 92
Rationale: "( x ^ n + 1 ) will be divisible by ( x + 1 ) only when n is odd ; ( 43 ^ 43 + 1 ) will be divisible by ( 43 + 1 ) ; ( 43 ^ 43 + 1 ) + 42 when divided by 44 will give 42 as remainder . correct option : b"
Answer: b
Problem: maxwell leaves his home and walks toward brad ' s house at the same time that brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 40 kilometers , maxwell ' s walking speed is 4 km / h , and brad ' s running speed is 6 km / h , what is the distance traveled by brad ?
Options: a ) 16 , b ) 18 , c ) 20 , d ) 24 , e ) 30
Rationale: "time taken = total distance / relative speed total distance = 40 kms relative speed ( opposite side ) ( as they are moving towards each other speed would be added ) = 6 + 4 = 10 kms / hr time taken = 40 / 10 = 4 hrs distance traveled by brad = brad ' s speed * time taken = 6 * 4 = 24 kms . . . answer - d"
Answer: d
Problem: the total of 342 of 20 paise and 25 paise make a sum of rs . 71 . the no of 20 paise coins is
Options: a ) 238 , b ) 290 , c ) 278 , d ) 200 , e ) 288
Rationale: "explanation : let the number of 20 paise coins be x . then the no of 25 paise coins = ( 342 - x ) . 0.20 * ( x ) + 0.25 ( 342 - x ) = 71 = > x = 290 . . answer : b ) 290"
Answer: b
Problem: a retailer buys a radio for rs 225 . his overhead expenses are rs 15 . he sellis the radio for rs 350 . the profit percent of the retailer is
Options: a ) 10 % , b ) 45.8 % , c ) 25 % , d ) 52 % , e ) none of these
Rationale: "explanation : cost price = ( 225 + 15 ) = 240 sell price = 350 gain = ( 110 / 240 ) * 100 = 45.8 % . answer : b"
Answer: b
Problem: a man can row upstream at 35 kmph and downstream at 45 kmph , and then find the speed of the man in still water ?
Options: a ) 32 kmph , b ) 34 kmph , c ) 40 kmph , d ) 45 kmph , e ) 65 kmph
Rationale: "us = 35 ds = 45 m = ( 35 + 45 ) / 2 = 40 answer : c"
Answer: c
Problem: a 220 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds . what is the length of the other train ?
Options: a ) 230 m , b ) 240 m , c ) 250 m , d ) 260 m , e ) 280 m
Rationale: speed = ( 120 + 80 ) km / h ( because direction is opposite hence relative velocity is added ) = 500 / 9 m / s time = 9 sec let the lenght of second train is x total distance covered = 220 + x therefore , d = speed * time thus 220 + x = 500 / 9 * 9 x = 500 - 220 = 280 m answer : e
Answer: e