Cheukting/mathqa huggingface dataset:
Question (physics): 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
Question (general): 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
Question (general): 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
Question (physics): 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
Question (physics): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (general): ( 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
Question (physics): 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
Question (general): 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
Question (general): 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
Question (physics): 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
Question (physics): 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
Question (general): 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
Question (gain): 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
Question (physics): 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
Question (geometry): 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
Question (geometry): 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
Question (general): 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
Question (general): 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
Question (gain): 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
Question (other): 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
Question (general): 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
Question (general): 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
Question (physics): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (physics): 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
Question (gain): 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
Question (physics): 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
Question (general): 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
Question (general): 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
Question (physics): 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
Question (general): 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
Question (general): 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
Question (physics): 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
Question (general): 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
Question (geometry): 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
Question (gain): 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
Question (general): 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
Question (general): 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
Question (gain): 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
Question (general): 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
Question (general): 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
Question (geometry): 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
Question (general): 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
Question (general): 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
Question (probability): 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
Question (general): 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
Question (physics): 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
Question (gain): 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
Question (other): 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