regisss/math_qa huggingface dataset:
Problem: how many seconds will a 400 metre long train take to cross a man running with a speed of 6 km / hr in the direction of the moving train if the speed of the train is 46 km / hr ?
Options: a ) 25 , b ) 30 , c ) 40 , d ) 45 , e ) 36
Rationale: "explanation : speed of train relatively to man = ( 46 - 6 ) km / hr = 40 km / hr = ( 40 x 5 / 18 ) m / sec = 11.11 m / sec time taken to pass the man = ( 400 / 11.11 ) sec = 36 sec . answer : e"
Answer: e
Problem: if x + y = 24 , x - y = 40 , for integers of x and y , x = ?
Options: a ) 20 , b ) 23 , c ) 25 , d ) 32 , e ) 42
Rationale: "x + y = 24 x - y = 40 2 x = 64 x = 32 answer is d"
Answer: d
Problem: a car traveling at a certain constant speed takes 12 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 75 kilometers per hour . at what speed , in kilometers per hour , is the car traveling ?
Options: a ) 60 , b ) 72 , c ) 72.5 , d ) 73 , e ) 73.5
Rationale: "many approaches are possible , one of them : let the distance be 1 kilometer . time to cover this distance at 75 kilometers per hour is 1 / 75 hours = 3,600 / 75 seconds = 48 seconds ; time to cover this distance at regular speed is 48 + 12 = 60 seconds = 60 / 3,600 hours = 1 / 60 hours ; so , we get that to cover 1 kilometer 1 / 60 hours is needed - - > regular speed 60 kilometers per hour ( rate is a reciprocal of time or rate = distance / time ) . answer : a"
Answer: a
Problem: if 222 = 6 333 = 12 444 = 20 then , 555 = ? ?
Options: a ) 30 , b ) 35 , c ) 40 , d ) 45 , e ) 50
Rationale: 222 = 2 * 2 + 2 = 6 333 = 3 * 3 + 3 = 12 444 = 4 * 4 + 4 = 20 555 = 5 * 5 + 5 = 30 answer : a
Answer: a
Problem: if n = 6 ^ 11 – 6 , what is the units digit of n ?
Options: a ) 0 , b ) 1 , c ) 4 , d ) 6 , e ) 8
Rationale: always divide the power ( incase 11 ) by 4 and use the remainder as the new power . the question now becomes 6 ^ 3 - 6 . now 6 ^ 3 has last digit 6 . , we subtract 6 from 6 = 0 is the answer . option a
Answer: a
Problem: a certain industrial loom weaves 0.128 meters of cloth every second . approximately how many seconds will it take for the loom to weave 25 meters of cloth ?
Options: a ) 205 , b ) 200 , c ) 180 , d ) 195 , e ) 175
Rationale: "explanation : let the required number of seconds be x more cloth , more time , ( direct proportion ) hence we can write as ( cloth ) 0.128 : 25 : : 1 : x ⇒ 0.128 x = 25 ⇒ x = 25 / 0.128 = 25000 / 128 = 3125 / 16 ≈ 195 answer : option d"
Answer: d
Problem: a man goes from a to b at a speed of 14 kmph and comes back to a at a speed of 10 kmph . find his average speed for the entire journey ?
Options: a ) 11.6 kmph , b ) 12.9 kmph , c ) 12.8 kmph , d ) 11.9 kmph , e ) 12.6 kmph
Rationale: "distance from a and b be ' d ' average speed = total distance / total time average speed = ( 2 d ) / [ ( d / 14 ) + ( d / 10 ] = ( 2 d ) / [ 12 d / 70 ) = > 11.6 kmph . answer : a"
Answer: a
Problem: p software has coding line 5 % more than n , n software has coding line 4 / 20 more than m . m software has 80 lines of coding . find p lines .
Options: a ) 101 , b ) 107 , c ) 108 , d ) 109 , e ) 110
Rationale: "m s / w has 80 line of code n s / w has = 80 + 80 * 4 / 20 = 96 line of code p s / w 5 % more n ' code 96 + 4.8 = 100.8 or 101 line of code answer : a"
Answer: a
Problem: if f ( x ) = 5 - 2 x , then f - 1 ( - 3 ) = ?
Options: a ) 1 , b ) 8 , c ) 6 , d ) 4 , e ) 3
Rationale: find f - 1 ( x ) and then find f - 1 ( - 3 ) y = 5 - 2 x , given x = 5 - 2 y , interchange x and y 2 y = 5 - x , y = log 2 ( 5 - x ) , solve for y f - 1 ( x ) = log 2 ( 5 - x ) , inverse function f - 1 ( - 3 ) = log 2 ( 5 + 3 ) = log 2 ( 23 ) = 3 correct answer e
Answer: e
Problem: the weight of every type a widget is the same , the weight of every type b widget is the same , and the weight of every type c widget is the same . if the weight of 7 type a widgets is equal to the weight of 2 type b widgets , and the weight of 4 type b widgets is equal to the weight of 7 type c widgets . what is the ratio of the total weight of 1 type a widget and 1 type b widget , to the total weight of 1 type b widget and 1 type c widget ?
Options: a ) 3 : 5 , b ) 5 : 7 , c ) 7 : 9 , d ) 9 : 11 , e ) 11 : 13
Rationale: "4 b = 7 c and so b = 7 c / 4 7 a = 2 b and so a = 2 b / 7 = c / 2 a + b = c / 2 + 7 c / 4 = 9 c / 4 b + c = 7 c / 4 + c = 11 c / 4 the ratio of a + b : b + c = 9 : 11 the answer is d ."
Answer: d
Problem: ( 500 + 200 ) × 4 × ( 3 + 2 ) = ?
Options: a ) 2902 , b ) 14000 , c ) 8402 , d ) 16800 , e ) none of these
Rationale: "( 500 + 200 ) × 4 × ( 3 + 2 ) = ? or , ? = 700 × 4 × 5 = 14000 answer b"
Answer: b
Problem: how many seconds will a 700 meter long train moving with a speed of 63 km / hr take to cross a man walking with a speed of 3 km / hr in the direction of the train ?
Options: a ) 48 , b ) 36 , c ) 42 , d ) 11 , e ) 18
Rationale: "explanation : here distance d = 700 mts speed s = 63 - 3 = 60 kmph = 60 x 5 / 18 m / s time t = = 42 sec . answer : c"
Answer: c
Problem: joan and karl each bought a telescopes and the sum of their purchases was $ 400 . if twice of what joan paid was $ 74 more than what karl paid , what did joan pay for her telescope ?
Options: a ) $ 150 , b ) $ 152 , c ) $ 154 , d ) $ 156 , e ) $ 158
Rationale: j + k = 400 so k = 400 - j 2 j = k + 74 2 j = ( 400 - j ) + 74 3 j = 474 j = 158 the answer is e .
Answer: e
Problem: how many odd prime numbers are there less than 150 ?
Options: a ) 24 , b ) 34 , c ) 44 , d ) 54 , e ) 64
Rationale: "odd prime number less than 150 : 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , 43 , 47 , 53 , 59 , 61 , 67 , 71 , 73 , 79 , 83 , 89 , 97 , 101 , 103 , 107 , 109 , 113 , 127 , 131 , 137 , 139 , 149 there is 34 the odd prime number answer is b"
Answer: b
Problem: a can do a piece of work in 8 days . he works at it for 4 days and then b finishes it in 6 days . in how many days can a and b together finish the work ?
Options: a ) 4.1 days , b ) 4.8 days , c ) 3.8 days , d ) 2.8 days , e ) 4.5 days
Rationale: 4 / 8 + 6 / x = 1 = > x = 12 1 / 8 + 1 / 12 = 5 / 24 = > 4.8 days answer : b
Answer: b
Problem: a boat moves upstream at the rate of 1 km in 20 minutes and down stream 1 km in 12 minutes . then the speed of the current is :
Options: a ) 1 kmph , b ) 2 kmph , c ) 3 kmph , d ) 2.5 kmph , e ) 3.5 kmph
Rationale: rate upstream = ( 1 / 20 * 60 ) = 3 kmph rate dowm stream = 1 / 12 * 60 = 5 kmph rate of the current = ½ ( 5 - 3 ) = 1 kmph answer : a
Answer: a
Problem: a parking garage rents parking spaces for $ 10 per week or $ 40 per month . how much does a person save in a year by renting by the month rather than by the week ?
Options: a ) $ 40 , b ) $ 160 , c ) $ 220 , d ) $ 240 , e ) $ 260
Rationale: "10 $ per week ! an year has 52 weeks . annual charges per year = 52 * 10 = 520 $ 30 $ per month ! an year has 12 months . annual charges per year = 12 * 40 = 480 $ 520 - 480 = 40 ans a"
Answer: a
Problem: what sum of money will produce rs . 70 as simple interest in 4 years at 4 1 / 2 percent ?
Options: a ) 263 , b ) 500 , c ) 388.9 , d ) 368 , e ) 339
Rationale: "70 = ( p * 4 * 9 / 2 ) / 100 p = 388.9 answer : c"
Answer: c
Problem: in a dairy farm , 34 cows eat 34 bags of husk in 34 days . in how many days one cow will eat one bag of husk ?
Options: a ) 34 days , b ) 40 days , c ) 46 days , d ) 50 days , e ) none of these
Rationale: "explanation : less cows , more days ( indirect proportion ) less bags , less days ( direct proportion ) [ cows 1 34 bags 34 1 ] : : 34 : x = > x ∗ 34 ∗ 1 = 34 ∗ 1 ∗ 34 = > x = 34 option a"
Answer: a
Problem: if the sides of a triangle are 28 cm , 24 cm and 15 cm , what is its area ?
Options: a ) 180 cm 2 , b ) 112 cm 2 , c ) 776 cm 2 , d ) 666 cm 2 , e ) 886 cm 2
Rationale: "the triangle with sides 28 cm , 24 cm and 15 cm is right angled , where the hypotenuse is 28 cm . area of the triangle = 1 / 2 * 24 * 15 = 180 cm 2 answer : a"
Answer: a
Problem: if y is the smallest positive integer such that 3,150 multiplied by y is the square of an integer , then y must be
Options: a ) 2 , b ) 5 , c ) 6 , d ) 7 , e ) 14
Rationale: "3150 * y = a ^ 2 3 * 1050 * y = a ^ 2 3 * 5 * 210 * y = a ^ 2 3 * 5 * 7 * 3 * 2 * 5 * y = a ^ 2 2 * 3 ^ 2 * 5 ^ 2 * 7 * y = a ^ 2 concept : the factors of squared integer should occur in pair . so , the only numbers left are 2 * 7 hence 14 ; answer : e"
Answer: e
Problem: 10 play kabadi , 20 play kho kho only , 5 play both gmaes . then how many in total ?
Options: a ) 30 , b ) 35 , c ) 38 , d ) 40 , e ) 45
Rationale: "10 play kabadi = > n ( a ) = 10 , 5 play both gmaes . = > n ( anb ) = 5 20 play kho kho only , = > n ( b ) = n ( b only ) + n ( anb ) = 20 + 5 = 25 total = > n ( aub ) = n ( a ) + n ( b ) - n ( anb ) = 10 + 25 - 5 = 30 answer : a"
Answer: a
Problem: if each participant of a chess tournament plays exactly one game with each of the remaining participants , then 210 games will be played during the tournament . what is the number of participants ?
Options: a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: "let n be the number of participants . the number of games is nc 2 = n * ( n - 1 ) / 2 = 210 n * ( n - 1 ) = 420 = 21 * 20 ( trial and error ) the answer is d ."
Answer: d
Problem: the length of a rectangular floor is more than its breadth by 500 % . if rs . 324 is required to paint the floor at the rate of rs . 6 per sq m , then what would be the length of the floor ?
Options: a ) 24.6 m . , b ) 23.4 m . , c ) 22.5 m . , d ) 23.8 m . , e ) 25.5 m .
Rationale: "let the length and the breadth of the floor be l m and b m respectively . l = b + 500 % of b = l + 5 b = 6 b area of the floor = 324 / 6 = 54 sq m l b = 54 i . e . , l * l / 6 = 108 l 2 = 648 = > l = 25.5 m . answer : e"
Answer: e
Problem: sandy is younger than molly by 14 years . if the ratio of their ages is 7 : 9 , how old is sandy ?
Options: a ) 42 , b ) 49 , c ) 56 , d ) 63 , e ) 70
Rationale: "let sandy ' s age be 7 x and let molly ' s age be 9 x . 9 x - 7 x = 14 x = 7 sandy is 49 years old . the answer is b ."
Answer: b
Problem: find the product of the localvalue and absolutevalue of 1 in 20168 ?
Options: a ) 100 , b ) 110 , c ) 151 , d ) 120 , e ) 140
Rationale: "local value of 1 = 1 x 100 = 100 place value of 1 = 1 there fore = 1 x 100 = 100 a"
Answer: a
Problem: if a ( a - 6 ) = 7 and b ( b - 6 ) = 7 , where a ≠ b , then a + b =
Options: a ) − 48 , b ) − 2 , c ) 6 , d ) 9 , e ) 48
Rationale: "i . e . if a = - 1 then b = 7 or if a = 7 then b = - 1 but in each case a + b = - 1 + 7 = 6 answer : option c"
Answer: c
Problem: a train 605 meters long is running with a speed of 60 kmph . in what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ?
Options: a ) 51 , b ) 64 , c ) 11 , d ) 22 , e ) 33
Rationale: "speed of train relative to man = ( 60 + 6 ) km / hr = 66 km / hr [ 66 * 5 / 18 ] m / sec = [ 55 / 3 ] m / sec . time taken to pass the man = [ 605 * 3 / 55 ] sec = 33 sec answer : e"
Answer: e
Problem: the average of 13 numbers is 60 . average of the first 6 of them is 57 and that of the last 8 is 61 . find the 8 th number ?
Options: a ) 46 , b ) 48 , c ) 50 , d ) 52 , e ) 54
Rationale: "sum of all the 13 numbers = 13 * 60 = 780 sum of the first 6 of them = 6 * 57 = 342 sum of the last 8 of them = 8 * 61 = 488 so , the 8 th number = 342 + 488 - 780 = 50 . answer : c"
Answer: c
Problem: is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 22 , then how old is b ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 22 5 x = 20 = > x = 4 hence , b ' s age = 2 x = 8 years . answer : b"
Answer: b
Problem: in a fuel station the service costs $ 2.20 per vehicle and every liter of fuel costs $ 0.70 . assuming that you fill up 3 mini - vans and 2 trucks , what will be the total cost , if a mini - van ' s tank is 65 liters and a truck ' s tank is 120 % bigger and they are all empty ?
Options: a ) $ 341.50 , b ) $ 344.60 , c ) $ 347.70 , d ) $ 350.80 , e ) $ 353.90
Rationale: "the service cost of 3 vans and 2 trucks is 5 * 2.20 $ 11.00 the fuel in 3 vans is 3 * 65 = 195 liters the fuel in 2 trucks is 2 * 65 * 2.2 = 286 liters the total fuel ( vans + trucks ) = 481 liters the total fuel cost is 481 * 0.7 = $ 336.70 the total cost is $ 336.70 + $ 11.00 = $ 347.70 the answer is c ."
Answer: c
Problem: four bells commence tolling together and toll at intervals of 2 , 3 , 4 and 5 seconds respectively . in 10 minutes , how many times do they toll together ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "lcm of 2 , 3 , 4 , and 5 is 60 . so , after each 60 seconds , they would toll together . hence , in 10 minutes , they would toll 10 * 60 seconds / 60 seconds = 10 times but then the question says they commence tolling together . so , they basically also toll at thebeginning ( 0 second ) . so , total tolls together = 10 + 1 = 11 answer : b"
Answer: b
Problem: an article is bought for rs . 600 and sold for rs . 550 , find the loss percent ?
Options: a ) 8.33 % , b ) 16 7 / 3 % , c ) 16 2 / 8 % , d ) 16 2 / 3 % , e ) 76 2 / 3 %
Rationale: "600 - - - - 50 100 - - - - ? = > 8.33 % answer : a"
Answer: a
Problem: it takes printer a 4 more minutes more than printer b to print 40 pages . working together , the two printers can print 50 pages in 6 minutes . how long will it take printer a to print 120 pages ?
Options: a ) 12 , b ) 18 , c ) 20 , d ) 24 , e ) 36
Rationale: "if it takes 4 more minutes for a to print 40 pages than it takes b , it takes 5 more minutes for a to print 50 pages than it takes b . thus if b is the number of minutes than b takes to print 50 pages , we can write : 1 / b + 1 / ( b + 5 ) = 1 / 6 ( since in 1 minute , they print 1 / 6 th of the 50 page job ) 6 ( 2 b + 5 ) = b ( b + 5 ) b ^ 2 - 7 b - 30 = 0 ( b - 10 ) ( b + 3 ) = 0 b = 10 thus it takes a 15 minutes to print 50 pages and 15 * 120 / 50 = 36 minutes to print 120 pages ( answer e )"
Answer: e
Problem: john want to buy a $ 100 trouser at the store , but he think it ’ s too expensive . finally , it goes on sale for $ 30 . what is the percent decrease ?
Options: a ) 20 % , b ) 30 % , c ) 40 % , d ) 70 % , e ) 80 %
Rationale: "the is always the difference between our starting and ending points . in this case , it ’ s 100 – 30 = 70 . the “ original ” is our starting point ; in this case , it ’ s 100 . ( 70 / 100 ) * 100 = ( 0.7 ) * 100 = 70 % . d"
Answer: d
Problem: for the symbol , m ” n = n ^ 2 − m for all values of m and n . what is the value of 5 ” 3 ?
Options: a ) 5 , b ) 3 , c ) 2 , d ) 4 , e ) 0
Rationale: "5 ” 3 = 9 - 5 = 4 answer : d"
Answer: d
Problem: if a car went the first third of the distance at 80 kmh , the second third at 24 kmh , and the last third at 44 kmh , what was the average speed of the car for the entire trip ?
Options: a ) 39 kmh , b ) 40 kmh , c ) 42 kmh , d ) 44 kmh , e ) 50 kmh
Rationale: "assume d / 3 = 2640 ( this number is convenient because it is divisible by 80 , 24 and 44 ) so : 2640 = 80 * t 1 = 33 hrs 2640 = 24 * t 2 = 110 hrs 2640 = 44 * t 3 = 60 hrs t = t 1 + t 2 + t 3 = 203 hrs d = rt ( 2640 * 3 ) = r * 203 r = 39 answer : a"
Answer: a
Problem: there are 408 boys and 312 girls in a school which are to be divided into equal sections of either boys or girls alone . find the total number of sections thus formed .
Options: a ) 31 , b ) 32 , c ) 35 , d ) 30 , e ) 45
Rationale: "explanation : hcf ( 408 , 312 ) = 24 the number of boys or girls that can be placed in a section = 24 . thus the total number of sections is given by 408 / 24 + 312 / 24 = 17 + 13 = 30 answer : d"
Answer: d
Problem: in 20 years , a will be twice as old as b was 20 years ago . if a is now 10 years older than b , the present age of b is ?
Options: a ) 35 yrs , b ) 40 yrs , c ) 50 yrs , d ) 60 yrs , e ) 70 yrs
Rationale: "let b ' s present age = x years then a ' s present age = x + 10 years x + 10 + 20 = 2 ( x - 20 ) x + 30 = 2 x - 40 x = 70 years answer is e"
Answer: e
Problem: a boat running downstream covers a distance of 44 km in 8 hours while for covering the same distance upstream , it takes 10 hours . what is the speed of the boat in still water ?
Options: a ) 5 kmph , b ) 4.95 kmph , c ) 6 kmph , d ) 7 kmph , e ) 8 kmph
Rationale: "explanation : speed downstream = 44 / 8 = 5.5 kmph speed upstream = 44 / 10 = 4.4 kmph speed of the boat in still water = ( 5.5 + 4.4 ) / 2 = 4.95 kmph answer : option b"
Answer: b
Problem: if a 10 percent deposit that has been paid toward the purchase of a certain product is $ 105 , how much more remains to be paid ?
Options: a ) $ 945 , b ) $ 965 , c ) $ 1025 , d ) $ 1050 , e ) $ 1105
Rationale: "90 % remains to be paid so the remaining amount is 9 * 105 = $ 945 . the answer is a ."
Answer: a
Problem: the volume v 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 , 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: calculate the dividend from caleb ' s stock , if caleb he invested rs . 2500 at 79 to obtain an income of rs . 200 .
Options: a ) 6.32 , b ) 5.32 , c ) 7.32 , d ) 2.32 , e ) 1.32
Rationale: by investing rs . 2500 , income = rs . 200 by investing rs . 79 , income = 200 ã — 79 / 2500 = 6.32 ie , dividend = 6.32 % answer is a .
Answer: a
Problem: in the biology lab of ` ` jefferson ' ' high school there are 5.4 * 10 ^ 6 germs , equally divided among 10,800 petri dishes . how many germs live happily in a single dish ?
Options: a ) 100 , b ) 200 , c ) 500 , d ) 1000 , e ) 5000
Rationale: 5.4 * 10 ^ 6 / 10800 = = > 54 * 10 ^ 3 / 108 = = > 54000 / 108 = 500 answer : c
Answer: c
Problem: a part - time employee whose hourly wage was decreased by 20 percent decided to increase the number of hours worked per week so that the employee ' s total income did not change . by what percent r should the number of hours worked be increased ?
Options: a ) 12.5 % , b ) 20 % , c ) 25 % , d ) 50 % , e ) 100 %
Rationale: "correct answer : c solution : c . we can set up equations for income before and after the wage reduction . initially , the employee earns w wage and works h hours per week . after the reduction , the employee earns . 8 w wage and works x hours . by setting these equations equal to each other , we can determine the increase in hours worked : wh = . 8 wx ( divide both sides by . 8 w ) 1.25 h = x we know that the new number of hours worked r will be 25 % greater than the original number . the answer is c ."
Answer: c
Problem: at what rate percent per annum will a sum of money double in 16 years .
Options: a ) 2.45 % , b ) 5.62 % , c ) 5.35 % , d ) 6.9 % , e ) 6.25 %
Rationale: "let principal = p then s . i . = p t = 16 yrs rate = ( 100 * p ) / ( p * 16 ) = 25 / 4 = 6.25 % p . a . answer is e"
Answer: e
Problem: a grocery shop has a sale of rs . 6535 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6500 ?
Options: a ) 4857 , b ) 4184 , c ) 4012 , d ) 4891 , e ) 5291
Rationale: "let the sale in the sixth month = x then ( 6535 + 6927 + 6855 + 7230 + 6562 + x ) / 6 = 6500 = > 6535 + 6927 + 6855 + 7230 + 6562 + x = 6 × 6500 = > 34109 + x = 39000 = > x = 39000 − 34109 = 4891 answer : d"
Answer: d
Problem: how many times will the digit 7 be written when listing the integers from 1 to 1000 ?
Options: a ) 110 , b ) 111 , c ) 271 , d ) 300 , e ) 304
Rationale: another approach : in the range 0 - 100 : 7 as units digit - 10 times ( 7 , 17 , 27 , . . . , 97 ) ; 7 as tens digit - 10 time ( 71 , 72 , 73 , . . . , 79 ) ; so in first one hundred numbers 7 is written 10 + 10 = 20 times . in 10 hundreds 7 as units or tens digit will be written 10 * 20 = 200 times . plus 100 times when 7 is written as hundreds digit ( 700 , 701 , 702 , . . . , 799 ) . total 200 + 100 = 300 . answer : d .
Answer: d
Problem: carol and jordan draw rectangles of equal area . if carol ' s rectangle measures 8 inches by 15 inches and jordan ' s rectangle is 4 inches long , how wide is jordan ' s rectangle , in inches ?
Options: a ) 24 , b ) 26 , c ) 28 , d ) 30 , e ) 32
Rationale: "area of first rectangle is 8 * 15 = 120 hence area of second would be 4 x = 120 x x = 30 answer is d"
Answer: d
Problem: the average salary of a person for the months of january , february , march and april is rs . 8000 and that for the months february , march , april and may is rs . 8450 . if his salary for the month of may is rs . 6500 , find his salary for the month of january ?
Options: a ) 2177 , b ) 2876 , c ) 4700 , d ) 2981 , e ) 2711
Rationale: "sum of the salaries of the person for the months of january , february , march and april = 4 * 8000 = 32000 - - - - ( 1 ) sum of the salaries of the person for the months of february , march , april and may = 4 * 8450 = 33800 - - - - ( 2 ) ( 2 ) - ( 1 ) i . e . may - jan = 1800 salary of may is rs . 6500 salary of january = rs . 4700 . answer : c"
Answer: c
Problem: a student was asked to find 4 / 5 of a number . but the student divided the number by 4 / 5 , thus the student got 45 more than the correct answer . find the number .
Options: a ) 60 , b ) 80 , c ) 100 , d ) 120 , e ) 140
Rationale: "let the number be x . ( 5 / 4 ) * x = ( 4 / 5 ) * x + 45 25 x = 16 x + 900 9 x = 900 x = 100 the answer is c ."
Answer: c
Problem: a quiz has one mcq question with a , b and c as options . and two questions with true / false answers . what is the probability of giving all 3 answers correct ?
Options: a ) 1 / 12 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 2 , e ) 1 / 6
Rationale: probability of getting mcq answer correct = 1 / 3 probability of getting one true / false answer correct = 1 / 2 probability of getting all 3 answers correct = 1 / 3 * 1 / 2 * 1 / 2 = 1 / 12 answer : a
Answer: a
Problem: what is the sum of natural numbers between 90 and 100
Options: a ) 1045 , b ) 4860 , c ) 5000 , d ) 5500 , e ) 5550
Rationale: "a = first number l = last number sn = n / 2 [ a + l ] between 90 and 100 numbers = 11 = > 100 - 90 = 10 + 1 = 11 sn = 11 / 2 ã — 190 = 11 ã — 95 = 1045 answer : a"
Answer: a
Problem: in a garden , there are 10 rows and 12 columns of mango trees . the distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden . what is the length of the garden ?
Options: a ) 30 m , b ) 28 m , c ) 26 m , d ) 24 m , e ) 22 m
Rationale: "explanation : between the 12 mango trees , there are 11 gaps and each gap has 2 meter length also , 1 meter is left from all sides of the boundary of the garden . hence , length of the garden = ( 11 × 2 ) + 1 + 1 = 24 meter answer : d"
Answer: d
Problem: in the manufacture of a certain product , 9 percent of the units produced are defective and 4 percent of the defective units are shipped for sale . what percent of the units produced are defective units that are shipped for sale ?
Options: a ) 0.125 % , b ) 0.36 % , c ) 0.8 % , d ) 1.25 % , e ) 2.0 %
Rationale: percent of defective produced = 9 % percent of the defective units that are shipped for sale = 4 % percent of units produced are defective units that are shipped for sale = ( 4 / 100 ) * ( 9 / 100 ) * 100 % = ( 36 / 10000 ) * 100 % = ( 36 / 100 ) % = . 36 % answer b
Answer: b
Problem: 70 students are required to paint a picture . 52 use green color and some children use red , 38 students use both the colors . how many students use red color ?
Options: a ) 53 , b ) 54 , c ) 55 , d ) 56 , e ) 57
Rationale: 70 = red + green - both red = 70 - green + both = 70 - 52 + 38 = 56 answer : d
Answer: d
Problem: the cost price of a radio is rs . 1500 and it was sold for rs . 1245 , find the loss % ?
Options: a ) 17 % , b ) 16 % , c ) 19 % , d ) 78 % , e ) 28 %
Rationale: "1500 - - - - 255 100 - - - - ? = > 17 % answer : a"
Answer: a
Problem: a person buys an article at $ 500 . at what price should he sell the article so as to make a profit of 20 % ?
Options: a ) 560 , b ) 449 , c ) 600 , d ) 740 , e ) 460
Rationale: "c 600 cost price = $ 500 profit = 20 % of 500 = $ 100 selling price = cost price + profit = 500 + 100 = 600"
Answer: c
Problem: ramu bought an old car for rs . 36400 . he spent rs . 8000 on repairs and sold it for rs . 68400 . what is his profit percent ?
Options: a ) 16 % , b ) 17 % , c ) 18 % , d ) 54 % , e ) 13 %
Rationale: "total cp = rs . 36400 + rs . 8000 = rs . 44400 and sp = rs . 68400 profit ( % ) = ( 68400 - 44400 ) / 44400 * 100 = 54 % answer : d"
Answer: d
Problem: i bought two books ; for rs . 480 . i sold one at a loss of 15 % and other at a gain of 19 % and then i found each book was sold at the same price . find the cost of the book sold at a gain ?
Options: a ) a ) 657 , b ) b ) 200 , c ) c ) 438 , d ) d ) 290 , e ) e ) 427
Rationale: "x = price of a book sold at loss x * ( 85 / 100 ) = ( 480 - x ) 119 / 100 x = 280 price of book sold at gain = 480 - 280 = 200 answer : b"
Answer: b
Problem: a ladder 25 m long reaches a window of building 20 m above the ground . then the distance of the foot of the ladder from the building is ?
Options: a ) 35 m , b ) 45 m , c ) 30 m , d ) 15 m , e ) 25 m
Rationale: let it forms a right angled triangle and follow c ^ 2 = a ^ 2 + b ^ 2 then 25 ^ 2 = 20 ^ 2 + b ^ 2 b ^ 2 = 625 - 400 b = 15 answer : d
Answer: d
Problem: when positive integer n is divided by positive integer j , the remainder is 10 . if n / j = 134.08 , what is value of j ?
Options: a ) 125 , b ) 56 , c ) 78 , d ) 112 , e ) 175
Rationale: "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 134.08 here 134 is the quotient . given that remainder = 10 so , 134.08 = 134 + 10 / j so , j = 125 ans a"
Answer: a
Problem: when positive integer n is divided by positive integer j , the remainder is 18 . if n / j = 204.03 , what is value of j ?
Options: a ) 600 , b ) 200 , c ) 400 , d ) 800 , e ) 1000
Rationale: "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 204.03 here 204 is the quotient . given that remainder = 18 so , 204.03 = 204 + 18 / j so , j = 600 answer : a"
Answer: a
Problem: if 2 + 7 = 57 ; 3 + 6 = 63 ; 5 + 9 = 206 then 4 + 8 = ?
Options: a ) 125 , b ) 126 , c ) 127 , d ) 128 , e ) 129
Rationale: 2 ^ 3 + 7 ^ 2 = 57 3 ^ 3 + 6 ^ 2 = 63 5 ^ 3 + 9 ^ 2 = 206 and 4 ^ 3 + 8 ^ 2 = 128 answer : d
Answer: d
Problem: a tank is filled to one quarter of its capacity with a mixture consisting of water and sodium chloride . the proportion of sodium chloride in the tank is 30 % by volume and the capacity of the tank is 24 gallons . if the water evaporates from the tank at the rate of 0.4 gallons per hour , and the amount of sodium chloride stays the same , what will be the concentration of water in the mixture in 6 hours ?
Options: a ) 30 % , b ) 35 % , c ) 40 % , d ) 45 % , e ) 50 %
Rationale: "the number of gallons in the tank is ( 1 / 4 ) 24 = 6 gallons the amount of sodium chloride is 0.3 ( 6 ) = 1.8 gallons at the start , the amount of water is 0.7 ( 6 ) = 4.2 gallons after 6 hours , the amount of water is 4.2 - 0.4 ( 6 ) = 1.8 gallons the concentration of water is 1.8 / ( 1.8 + 1.8 ) = 1.8 / 3.6 = 50 % the answer is e ."
Answer: e
Problem: by selling 20 pencils for a rupee a man loses 35 % . how many for a rupee should he sell in order to gain 30 % ?
Options: a ) 8 , b ) 9 , c ) 6 , d ) 14 , e ) 10
Rationale: 65 % - - - 20 130 % - - - ? 65 / 130 * 20 = 10 answer : e
Answer: e
Problem: 1804 x 1804 = ?
Options: a ) a ) 3254416 , b ) b ) 3624216 , c ) c ) 3624316 , d ) d ) 3625116 , e ) e ) 3625216
Rationale: "1804 x 1804 = ( 1804 ) 2 = ( 1800 + 4 ) 2 = ( 1800 ) 2 + ( 4 ) 2 + ( 2 x 1800 x 4 ) = 3240000 + 16 + 14400 . = 3254416 . a )"
Answer: a
Problem: in order to obtain an income of rs . 500 from 30 % stock at rs . 90 , one must make an investment of
Options: a ) rs . 1550 , b ) rs . 1430 , c ) rs . 1450 , d ) rs . 1400 , e ) rs . 1500
Rationale: "explanation : market value = rs . 90 required income = rs . 500 . here face value is not given . take face value as rs . 100 if it is not given in the question to obtain rs . 30 ( ie , 30 % of the face value 100 ) , investment = rs . 90 to obtain rs . 15000 , investment = 90 / 30 ã — 500 = rs . 1500 answer : option e"
Answer: e
Problem: if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer q that must divide n is ?
Options: a ) 6 , b ) 12 , c ) 24 , d ) 36 , e ) 48
Rationale: "q : if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer q that must divide n is : a 6 , b 12 , c 24 , d 36 , e 48 n ^ 2 is divisible by 72 , but it must also be greater than 72 . if n is an integer , then n ^ 2 must be a perfect square . the factorization of 72 is ( 8 ) ( 9 ) , so if it is multiplied by 2 , it will be ( 2 ) ( 8 ) ( 9 ) = ( 16 ) ( 9 ) = 144 , a perfect square . so n ^ 2 must be at least 144 or a multiple of 144 , which means that n must be 12 or a multiple of 12 . b"
Answer: b
Problem: the value of ( 2.502 + 0.064 ) ^ 2 - ( 2.502 - 0.064 ) ^ 2 / 2.502 * 0.064
Options: a ) . 25 , b ) . 235 , c ) 4 , d ) 3 , e ) 2
Rationale: "( 2.502 + 0.064 ) 2 - ( 2.502 - 0.064 ) 2 / 2.502 * 0.064 = ( a + b ) 2 - ( a - b ) / ab = 4 ab / ab = 4 answer : c"
Answer: c
Problem: a , b and c have rs . 500 between them , a and c together have rs . 200 and b and c rs . 320 . how much does c have ?
Options: a ) 50 , b ) 78 , c ) 267 , d ) 20 , e ) 27
Rationale: a + b + c = 500 a + c = 200 b + c = 320 - - - - - - - - - - - - - - a + b + 2 c = 520 a + b + c = 500 - - - - - - - - - - - - - - - - c = 20 answer : d
Answer: d
Problem: what is 10 - 8 + 6 - 4 + . . . + ( - 18 ) ?
Options: a ) - 8 , b ) 10 , c ) 12 , d ) - 4 , e ) 16
Rationale: "the expression considers all even numbers between 10 and - 18 with alternate addition and subtraction of the numbers . the numbers to be used are : 10 , 8 , 6 , 4 , 2 , 0 , - 2 , - 4 , - 6 , - 8 , - 10 , - 12 , - 14 , - 16 , and - 18 . now , the first term is positive and the next term is subtracted . so , the required expression becomes , 10 - 8 + 6 - 4 + 2 - 0 + ( - 2 ) - ( - 4 ) + ( - 6 ) - ( - 8 ) + ( - 10 ) - ( - 12 ) + ( - 14 ) - ( - 16 ) + ( - 18 ) = 10 - 8 + 6 - 4 + 2 - 0 - 2 + 4 - 6 + 8 - 10 + 12 - 14 + 16 - 18 = 58 - 62 = - 4 hence the correct answer choice is d ."
Answer: d
Problem: car a runs at the speed of 70 km / hr & reaches its destination in 10 hr . car b runs at the speed of 35 km / h & reaches its destination in 10 h . what is the respective ratio of distances covered by car a & car b ?
Options: a ) 11 : 5 , b ) 11 : 8 , c ) 13 : 7 , d ) 15 : 7 , e ) 2 : 1
Rationale: "sol . distance travelled by car a = 70 × 10 = 700 km distance travelled by car b = 35 × 10 = 350 km ratio = 700 / 350 = 2 : 1 answer : e"
Answer: e
Problem: car x began traveling at an average speed of 35 miles per hour . after 72 minutes , car y began traveling at an average speed of 50 miles per hour . when both cars had traveled the same distance , both cars stopped . how many miles did car x travel from the time car y began traveling until both cars stopped ?
Options: a ) 105 , b ) 120 , c ) 140 , d ) 147 , e ) 98
Rationale: "car y began travelling after 72 minutes or 1.2 hours . let t be the time for which car y travelled before it stopped . both cars stop when they have travelled the same distance . so , 35 ( t + 1.2 ) = 50 t t = 2.8 distance travelled by car x from the time car y began traveling until both cars stopped is 35 x 2.8 = 98 miles answer : - e"
Answer: e
Problem: a and b together can do a work in 4 days . if a alone can do it in 14 days . in how many days can b alone do it ?
Options: a ) 10 , b ) 6 , c ) 77 , d ) 55 , e ) 21
Rationale: 1 / 4 – 1 / 12 = 1 / 6 = > 6 answer : b
Answer: b
Problem: sally has a gold credit card with a certain spending limit , and a platinum card with twice the spending limit of the gold card . currently , she has a balance on her gold card that is 1 / 3 of the spending limit on that card , and she has a balance on her platinum card that is 1 / 6 of the spending limit on that card . if sally transfers the entire balance on her gold card to her platinum card , what portion of her limit on the platinum card will remain unspent ?
Options: a ) 2 / 3 , b ) 29 / 60 , c ) 17 / 30 , d ) 19 / 30 , e ) 11 / 15
Rationale: "let s assume the platinum card spending limit = x gold card spending limit will be = x / 2 balance on gold card is = x / 2 * 1 / 3 = x / 6 platinum card unspent limit is = x - 1 / 6 x = 5 / 6 x so if gold card balance is transferred then the rest unspent will be 5 / 6 x - x / 6 = 2 / 3 x so the ans is a"
Answer: a
Problem: find the compound ratio of ( 2 : 3 ) , ( 6 : 11 ) and ( 11 : 2 ) is
Options: a ) 3 : 2 , b ) 2 : 1 , c ) 1 : 2 , d ) 4 : 5 , e ) 2 : 3
Rationale: "required ratio = 2 / 3 * 6 / 11 * 11 / 2 = 2 / 1 = 2 : 1 answer is b"
Answer: b
Problem: city a and city b are 140 miles apart . train c departs city a , heading towards city b , at 4 : 00 and travels at 40 miles per hour . train d departs city b , heading towards city a , at 5 : 30 and travels at 20 miles per hour . the trains travel on parallel tracks . at what time do the two trains meet ?
Options: a ) 5 : 00 , b ) 7 : 30 , c ) 6 : 00 , d ) 6 : 30 , e ) 7 : 00
Rationale: train c has traveled 20 mi in the half hour before train d has started its journey . 140 - 20 = 120 40 + 20 = 60 mph 120 mi / 60 mph = 2 hrs 5 : 30 pm + 2 hrs = 7 : 30 pm answer : b . 7 : 30
Answer: b
Problem: the perimeter of a triangle is 32 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle ?
Options: a ) 87 cm 2 , b ) 28 cm 2 , c ) 98 cm 2 , d ) 26 cm 2 , e ) 40 cm 2
Rationale: "area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 32 / 2 = 40 cm 2 answer : e"
Answer: e
Problem: you cook a pot of beef stew for you and your roommate . normally it lasts 7 days between the two of you . if 3 guests are now staying with you and your roommate , how many days will the beef stew now last if everyone eats it ?
Options: a ) 2.8 , b ) 1 , c ) 3.5 , d ) 14 , e ) 1.6
Rationale: first set up a ratio with all the relevant values and also the unknown variable : 2 * 7 = 5 * x now solve by multiplying 2 by 7 and then dividing that product by 5 : 2 * 7 = 14 14 / 5 = x x = 2.8 the value of x represents the amount of days a bot of beef stew will last for 5 total people . answer : a
Answer: a
Problem: a person can swim in still water at 12 km / h . if the speed of water 2 km / h , how many hours will the man take to swim back against the current for 10 km ?
Options: a ) 1 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "m = 12 s = 2 us = 12 - 2 = 10 d = 10 t = 10 / 10 = 1 answer : a"
Answer: a
Problem: a train running at the speed of 54 km / hr crosses a pole in 9 seconds . what is the length of the train ?
Options: a ) 135 , b ) 278 , c ) 255 , d ) 150 , e ) 287
Rationale: "speed = ( 54 * 5 / 18 ) m / sec = ( 15 ) m / sec length of the train = ( speed x time ) = ( 15 * 9 ) m = 135 m . answer : a"
Answer: a
Problem: the average weight of a , b and c is 45 kg . if the average weight of a and b be 40 kg and that of b and c be 44 kg , then the weight of b is :
Options: a ) 31 kg , b ) 32 kg , c ) 33 kg , d ) 34 kg , e ) none of these
Rationale: "explanation : let a , b , c represent their respective weights . then , we have : a + b + c = ( 45 x 3 ) = 135 … . ( i ) a + b = ( 40 x 2 ) = 80 … . ( ii ) b + c = ( 44 x 2 ) = 88 … . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 168 … . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 33 . b ’ s weight = 33 kg . answer : c"
Answer: c
Problem: the duplicate ratio of 3 : 4 is ?
Options: a ) 1 : 2 , b ) 1 : 4 , c ) 1 : 8 , d ) 9 : 16 , e ) 1 : 13
Rationale: "3 ^ 2 : 4 ^ 2 = 9 : 16 answer : d"
Answer: d
Problem: in the first 15 overs of a cricket game , the run rate was only 3.2 . what should be the run rate in the remaining 35 overs to reach the target of 275 runs ?
Options: a ) 5.55 , b ) 6.25 , c ) 6.75 , d ) 7.02 , e ) 6.48
Rationale: required run rate = 275 - ( 3.2 x 15 ) / 35 = 227 / 35 = 6.48 option e
Answer: e
Problem: a car salesman earns a base salary of $ 1000 per month plus a commission of $ 200 for each car he sells . if the car salesman earned $ 1800 in january , how many cars does he need to sell in february in order to double his january earnings ?
Options: a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17
Rationale: 1000 + 200 x = 3600 x = 13 cars . the answer is a .
Answer: a
Problem: the area of a sector of a circle of radius 4 cm formed by an arc of length 3.5 cm is ?
Options: a ) 7 , b ) 7.67 , c ) 8.75 , d ) 8.98 , e ) 8.28
Rationale: "( 4 * 3.5 ) / 2 = 7 answer : a"
Answer: a
Problem: working alone , a can complete a certain kind of job in 12 hours . a and d , working together at their respective rates , can complete one of these jobs in 4 hours . in how many hours can d , working alone , complete one of these jobs ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 6 , e ) 9
Rationale: "let total time taken by s to complete the job = s total time taken by a to complete the job = 12 work done by a in an hour 1 / a = 1 / 12 working together a and d can complete the job in 4 hours 1 / a + 1 / d = 1 / 4 = > 1 / d = 1 / 4 - 1 / 12 = 1 / 4 - 1 / 12 = 1 / 6 = > d = 6 hours answer d"
Answer: d
Problem: the perimeter of a triangle is 35 cm and the inradius of the triangle is 4.5 cm . what is the area of the triangle ?
Options: a ) 22 , b ) 75 , c ) 78 , d ) 54 , e ) 23
Rationale: "area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 4.5 * 35 / 2 = 78.75 cm 2 answer : c"
Answer: c
Problem: a ’ s speed is 22 / 19 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ?
Options: a ) 1 / 22 , b ) 1 / 19 , c ) 3 / 19 , d ) 2 / 19 , e ) 3 / 22
Rationale: "we have the ratio of a ’ s speed and b ’ s speed . this means , we know how much distance a covers compared with b in the same time . this is what the beginning of the race will look like : ( start ) a _________ b ______________________________ if a covers 22 meters , b covers 19 meters in that time . so if the race is 22 meters long , when a reaches the finish line , b would be 3 meters behind him . if we want the race to end in a dead heat , we want b to be at the finish line too at the same time . this means b should get a head start of 3 meters so that he doesn ’ t need to cover that . in that case , the time required by a ( to cover 22 meters ) would be the same as the time required by b ( to cover 19 meters ) to reach the finish line . so b should get a head start of 3 / 22 th of the race . answer ( e )"
Answer: e
Problem: the average weight of 8 girls increases by 3 kg when a new girl comes in place of one of them weighing 70 kg . what might be the weight of the new girl ?
Options: a ) 94 kg , b ) 95 kg , c ) 96 kg , d ) 97 kg , e ) 98 kg
Rationale: total weight increased = 8 x 3 kg = 24 kg . weight of new person = 70 + 24 kg = 94 kg answer : a
Answer: a
Problem: if t = 5 / 9 * ( k - 32 ) , and if t = 35 , then what is the value of k ?
Options: a ) 92 , b ) 95 , c ) 98 , d ) 101 , e ) 104
Rationale: "k - 32 = 9 t / 5 k = 9 t / 5 + 32 k = 9 ( 35 ) / 5 + 32 = 95 the answer is b ."
Answer: b
Problem: from an island , it is possible to reach the mainland by either ferry p or ferry q . ferry p travels for 3 hours at 6 kilometers per hour , while ferry q takes a route that is two times longer . if ferry p is slower than ferry q by 3 kilometers per hour , how many hours longer is the journey of ferry q compared with the journey of ferry p ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "the distance traveled by ferry p is 18 km . then the distance traveled by ferry q is 36 km . ferry q travels at a speed of 9 kph . the time of the journey for ferry q is 36 / 9 = 4 hours , which is 1 hour more than ferry p . the answer is a ."
Answer: a
Problem: 48.95 - 32.006 = ?
Options: a ) 16.089 , b ) 16.35 , c ) 16.89 , d ) 16.944 , e ) none of them
Rationale: "48.950 - 32.006 - - - - - - - - - 16.944 answer is d"
Answer: d
Problem: the effective annual rate of interest corresponding to a nominal rate of 8 % per annum payable half - yearly is ?
Options: a ) 6.06 % , b ) 8.16 % , c ) 6.08 % , d ) 6.09 % , e ) 6.19 %
Rationale: amount of rs . 100 for 1 year when compounded half - yearly = [ 100 * ( 1 + 4 / 100 ) 2 ] = rs . 108.16 effective rate = ( 108.16 - 100 ) = 8.16 % answer : b
Answer: b
Problem: a certain number of horses and an equal number of men are going somewhere . half of the owners are on their horses ' back while the remaining ones are walking along leading their horses . if the number of legs walking on the ground is 50 , how many horses are there ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "legs 10 * 4 = 40 now half on their horses so remaining on the walk so 5 men 5 men has 10 legs so , 10 + 40 = 50 legs walking answer : a"
Answer: a
Problem: 15.06 * 0.0000001 = ?
Options: a ) 15060000 , b ) 0.001506 , c ) 1.506 e - 06 , d ) 0.1506 , e ) none of these
Rationale: "explanation : clearly after decimal 9 digits should be there . option c"
Answer: c
Problem: if a car went the first third of the distance at 80 kmh , the second third at 24 kmh , and the last third at 60 kmh , what was the average speed of the car for the entire trip ?
Options: a ) 36 kmh , b ) 40 kmh , c ) 42 kmh , d ) 44 kmh , e ) 50 kmh
Rationale: "assume d / 3 = 240 ( this number is convenient because it is divisible by 80 , 24 and 60 ) so : 240 = 80 * t 1 = 3 hrs 240 = 24 * t 2 = 10 hrs 240 = 60 * t 3 = 4 hrs t = t 1 + t 2 + t 3 = 17 hrs d = rt ( 240 * 3 ) = r * 17 r = 42.35 answer : c"
Answer: c
Problem: in 1990 the budgets for projects q and v were $ 540000 and $ 780000 , respectively . in each of the next 10 years , the budget for q was increased by $ 30000 and the budget for v was decreased by $ 10000 . in which year was the budget for q equal to the budget for v ?
Options: a ) 1992 , b ) 1993 , c ) 1994 , d ) 1995 , e ) 1996
Rationale: let the no of years it takes is x . 540 + 30 x = 780 - 10 x - - > 40 x = 240 and x = 6 . thus , it happens in 1996 . e .
Answer: e
Problem: a shopkeeper sells 500 metres of cloth for rs . 15000 at a loss of rs . 10 per metre . find his cost price for one metre of cloth ?
Options: a ) s . 40 , b ) s . 12 , c ) s . 96 , d ) s . 50 , e ) s . 13
Rationale: "sp per metre = 15000 / 500 = rs . 30 loss per metre = rs . 10 cp per metre = 30 + 10 = rs . 40 answer : a"
Answer: a
Problem: a larger cube has 216 cubic inch as a volume and in the cube there are 216 smaller cubes such that their volume is 1 cubic inch . what is the difference between the surface areas ’ sum of the 216 smaller cubes and the surface area of the larger cube , in square inch ?
Options: a ) 54 , b ) 64 , c ) 81 , d ) 1080 , e ) 120
Rationale: "volume of larger cube = 216 = 6 ^ 3 side of larger cube = 6 volume of smaller cube = 1 - - > side of smaller cube = 1 surface area of larger cube = 6 * 6 ^ 2 = 216 surface area of 27 smaller cubes = 216 * 6 * 1 = 1296 difference = 1296 - 216 = 1080 answer : d"
Answer: d
Problem: in a colony the municipality decided to number the houses and the shops . they want to number the shops with the numbers containing 3 between 1 - 100 . the houses are 10 - 20 floored and at the back of the houses 8 feet is left for fire exit . how many shops can be numbered ?
Options: a ) 19 , b ) 20 , c ) 21 , d ) 22 , e ) 23
Rationale: 3 numbers containing 3 - - - > 3 , 1323 , . . . = 10 numbers - - - - > 30 , 3132 . . . = 10 numbers total = 20 - 1 = 19 answer : a
Answer: a
Problem: a sporting goods store sold 64 frisbees in one week , some for $ 3 and the rest for $ 4 each . if receipts from frisbee sales for the week totaled $ 196 what is the fewest number of $ 4 frisbees that could have been sold ?
Options: a ) 24 , b ) 12 , c ) 8 , d ) 2 , e ) 4
Rationale: "in this question however , because we are told that exactly 64 frisbees have been sold and revenue was exactly $ 204 , there is only one possible solution for the number of $ 3 and $ 4 frisbees sold . to solve , we have 2 equations and 2 unknowns let x = number of $ 3 frisbees sold let y = number of $ 4 frisbees sold x + y = 64 3 x + 4 y = 196 x = 64 - y 3 ( 64 - y ) + 4 y = 196 192 - 3 y + 4 y = 196 y = 4 answer : e"
Answer: e
Problem: the average ( arithmetic man ) of 3 integers a , b , and c is exactly half the median . if a < b < c and a = 0 , what is the value of c / b ?
Options: a ) 2 , b ) 3 / 2 , c ) 4 , d ) 5 , e ) can not be determined from the information given .
Rationale: the average of three integers a , b , and c is exactly twice the median - - > ( a + b + c ) / 3 = 1 b / 2 - - > since a = 0 , then ( 0 + b + c ) / 3 = 1 b / 2 - - > c = 3 b / 2 - - > c / b = 3 / 2 . answer : b .
Answer: b
Problem: in a room with 10 people , 7 people have exactly 1 friend in the room and 6 people have exactly 2 friends in the room ( assuming that friendship is a mutual relationship , i . e . if jane is paul ' s friend , paul is jane ' s friend ) . if two individuals are selected from the room at random , what is the probability that those two individuals are not friends ?
Options: a ) 5 / 21 , b ) 3 / 7 , c ) 4 / 7 , d ) 5 / 7 , e ) 49 / 45
Rationale: "( 7 / 10 ) ( 8 / 9 ) + ( 6 / 10 ) ( 7 / 9 ) if you choose one of the 7 with one other friend , then you have a 8 / 9 chance of not picking their friend 2 nd . if you choose one of the 6 with 2 friends , you have a 7 / 9 chance of not picking one of their friends second . add them up . 56 / 90 + 42 / 90 98 / 90 = 49 / 45 e . 49 / 45"
Answer: e
Problem: dan ’ s car gets 32 miles per gallon . if gas costs $ 4 / gallon , then how many miles can dan ’ s car go on $ 46 of gas ?
Options: a ) 124 , b ) 256 , c ) 368 , d ) 424 , e ) 512
Rationale: "46 / 4 = 11.5 gallons 11.5 * 32 = 368 miles the answer is c ."
Answer: c
Problem: company s produces two kinds of stereos : basic and deluxe . of the stereos produced by company s last month , 2 / 3 were basic and the rest were deluxe . if it takes 6 / 5 as many hours to produce a deluxe stereo as it does to produce a basic stereo , then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos ?
Options: a ) 6 / 16 , b ) 14 / 31 , c ) 7 / 15 , d ) 17 / 35 , e ) 1 / 2
Rationale: "# of basic stereos was 2 / 3 of total and # of deluxe stereos was 1 / 3 of total , let ' s assume total = 15 , then basic = 10 and deluxe = 5 . now , if time needed to produce one deluxe stereo is 1 unit than time needed to produce one basic stereo would be 6 / 5 units . total time for basic would be 10 * 1 = 10 and total time for deluxe would be 5 * 6 / 5 = 6 - - > total time for both of them would be 10 + 6 = 16 - - > deluxe / total = 6 / 16 . answer : a ."
Answer: a
Problem: an object thrown directly upward is at a height of h feet after t seconds , where h = - 12 ( t - 3 ) ^ 2 + 120 . at what height , in feet , is the object 2 seconds after it reaches its maximum height ?
Options: a ) 48 , b ) 54 , c ) 60 , d ) 66 , e ) 72
Rationale: "we see that h will be a maximum h = 120 when t - 3 = 0 , that is when t = 3 . at t = 5 , h = - 12 * ( 5 - 3 ) ^ 2 + 120 = - 12 ( 4 ) + 120 = 72 the answer is e ."
Answer: e
Problem: if | x - 5 | = 23 what is the sum of all the values of x .
Options: a ) 46 , b ) 10 , c ) 56 , d ) - 46 , e ) 28
Rationale: "there will be two cases x - 5 = 23 and x - 5 = - 23 solve for x = > x = 23 + 5 = > x = 28 or x = - 23 + 5 = > x = - 18 the sum of both values will be 28 + - 18 = 10 answer is b"
Answer: b