Cheukting/mathqa huggingface dataset:
Question (geometry): how many boxes do you need if you have to pack 240 pairs ornamental bangles into boxes that each hold 2 dozens of bangles ?
Options: a ) 40 , b ) 35 , c ) 20 , d ) 25 , e ) 30
Rationale: "c 20 240 pairs of bangles = 480 bangles = 40 dozens . 40 ÷ 2 = 20 boxes ."
Answer: c
Question (gain): in an election , candidate a got 85 % of the total valid votes . if 15 % of the total votes were declared invalid and the total numbers of votes is 560000 , find the number of valid vote polled in favor of candidate ?
Options: a ) 355600 , b ) 355800 , c ) 404600 , d ) 356800 , e ) 357000
Rationale: "total number of invalid votes = 15 % of 560000 = 15 / 100 × 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 – 84000 = 476000 percentage of votes polled in favour of candidate a = 85 % therefore , the number of valid votes polled in favour of candidate a = 85 % of 476000 = 85 / 100 × 476000 = 40460000 / 100 = 404600 c )"
Answer: c
Question (general): jerry bought a bottle of perfume for a gift for his wife . the perfume cost $ 92 before tax . if the total price including tax was $ 98.90 , find the tax rate
Options: a ) 7.5 % , b ) 5 % , c ) 12 % , d ) 8 % , e ) 10 %
Rationale: total price including tax is $ 98.90 perfume cost before tax is = 92 ie 92 * 7.5 % + 98.90 answer is 7.5 %
Answer: a
Question (other): tea worth rs . 126 per kg and rs . 135 per kg are mixed with a third variety of tea in the ratio 1 : 1 : 2 . if the mixture is worth rs . 153 per kg , what is the price of the third variety per kg ?
Options: a ) 175.5 , b ) 182.5 , c ) 170.0 , d ) 180.0 , e ) 190.0
Rationale: "tea worth rs . 126 ratio 1 : 1 average price = ( 126 + 135 ) / 2 = 130.5 mean price = ( x - 153 ) : 22.50 = > x - 153 = 22.50 x = 175.5 answer a"
Answer: a
Question (physics): the average speed of a car decreased by 3 miles per hour every successive 8 - minutes interval . if the car traveled 3.6 miles in the seventh 8 - minute interval , what was the average speed of the car , in miles per hour , in the first 8 minute interval ?
Options: a ) 33 , b ) 36 , c ) 39 , d ) 42 , e ) 45
Rationale: "( 3.6 miles / 8 minutes ) * 60 minutes / hour = 27 mph let x be the original speed . x - 6 ( 3 ) = 27 x = 45 mph the answer is e ."
Answer: e
Question (general): a 7 - digit number comprises of only 2 ' s and 3 ' s . how many of these are multiples of 12 ?
Options: a ) 11 , b ) 12 , c ) 10 , d ) 22 , e ) 44
Rationale: detailed solution number should be a multiple of 3 and 4 . so , the sum of the digits should be a multiple of 3 . we can either have all seven digits as 3 , or have three 2 ' s and four 3 ' s , or six 2 ' s and a 3 . ( the number of 2 ' s should be a multiple of 3 ) . for the number to be a multiple of 4 , the last 2 digits should be 32 . now , let us combine these two . all seven 3 ' s - no possibility . three 2 ' s and four 3 ' s - the first 5 digits should have two 2 ' s and three 3 ' s in some order . no of possibilities = 5 ! 3 ! 2 ! = 10 six 2 ' s and one 3 - the first 5 digits should all be 2 ' s . so , there is only one number 2222232 . so , there are a total of 10 + 1 = 11 solutions . correct answer : a .
Answer: a
Question (gain): mr . karan borrowed a certain amount at 6 % per annum simple interest for 9 years . after 9 years , he returned rs . 8110 / - . find out the amount that he borrowed .
Options: a ) rs . 4,900 , b ) rs . 5,000 , c ) rs . 5,100 , d ) rs . 5266 , e ) none of these
Rationale: "explanation : let us assume mr . karan borrowed amount is rs . a . ( the principal ) by formula of simple interest , s . i . = prt / 100 where p = the principal , r = rate of interest as a % , t = time in years s . i . = ( p * 6 * 9 ) / 100 = 54 p / 100 amount = principal + s . i . 8110 = p + ( 54 p / 100 ) 8110 = ( 100 p + 54 p ) / 100 8110 = 154 p / 100 p = ( 8110 * 100 ) / 154 = rs . 5266.233 answer d"
Answer: d
Question (gain): a technician makes a round - trip to and from a certain service center by the same route . if the technician completes the drive to the center and then completes 10 percent of the drive from the center , what percent of the round - trip has the technician completed ?
Options: a ) 5 % , b ) 10 % , c ) 25 % , d ) 40 % , e ) 55 %
Rationale: "assuming that the technician makes a round - trip of 40 miles ( each way is 20 miles ) , then the technician would have completed 20 miles + 2 miles ( 10 % of the remaining 20 miles ) . therefore , the total is 22 miles . 22 miles / 40 miles is 55 % of the entire trip . answer : e"
Answer: e
Question (gain): the banker â € ™ s discount of a certain sum of money is rs . 60 and the true discount on the same sum for the same time is rs . 54 . the sum due is
Options: a ) 210 , b ) 280 , c ) 360 , d ) 720 , e ) none
Rationale: "sol . sum = b . d . * t . d . / b . d . - t . d . = rs . [ 60 * 54 / 60 - 54 ] = rs . [ 72 * 60 / 6 ] = rs . 720 answer d"
Answer: d
Question (physics): a certain number of workers can do a work in 25 days . if there were 10 workers more it could be finished in 10 days less . how many workers are there ?
Options: a ) 15 , b ) 30 , c ) 28 , d ) 24 , e ) 32
Rationale: number of workers = 10 * ( 25 - 10 ) / 10 = 15 answer is a
Answer: a
Question (general): a big container is 30 % full with water . if 9 liters of water is added , the container becomes 3 / 4 full . what is the capacity of the big container ?
Options: a ) 20 liters , b ) 40 liters , c ) 45 liters , d ) 54 liters , e ) 60 liters
Rationale: "a big container is 30 % full with water and after 9 liters of water is added , the container becomes 75 % full . hence these 9 liters account for 45 % of the container , which means that the capacity of it is 9 / 0.45 = 20 liters . or : if the capacity of the container is x liters then : 0.3 x + 9 = 0.75 x - - > x = 20 liters . answer : a ."
Answer: a
Question (gain): a man cheats while buying as well as while selling . while buying he takes 11 % more than what he pays for and while selling he gives 20 % less than what he claims to . find the profit percent , if he sells at 9.09 % below the cost price of the claimed weight .
Options: a ) 19.81 % , b ) 20 % , c ) 37.5 % , d ) 25 % , e ) 42.86 %
Rationale: there is a one step calculation method too . it requires more thought but is faster . the man takes 11 % more than what he pays for . so if he claims to take 100 pounds , he pays $ 100 but he actually takes 111 pounds for which he will take from the customer $ 111 . hence , in effect , there is a 11 % mark up . while selling , he sells 30 % less . this means , he claims to sell 100 pounds and gets $ 100 but actually sells only 70 pounds and should have got only $ 70 for it . so this is again a mark up of $ 30 on $ 70 . but he also sells at 9.09 % less i . e . gives a discount of 1 / 11 . ( 1 + m 1 % ) ( 1 + m 2 % ) ( 1 - d % ) = ( 1 + p % ) 11 / 10 * 10 / 7 * 10 / 11 = ( 1 + p % ) profit % = 42.86 % e
Answer: e
Question (physics): a train traveled the first d miles of its journey it an average speed of 60 miles per hour , the next d miles of its journey at an average speed of y miles per hour , and the final d miles of its journey at an average speed of 160 miles per hour . if the train ’ s average speed over the total distance was 90 miles per hour , what is the value of y ?
Options: a ) 68 , b ) 84 , c ) 90 , d ) 110 , e ) 135
Rationale: "average speed = total distance traveled / total time taken 3 d / d / 60 + d / y + d / 160 = 90 solving for d and y , 15 y = 11 y + 480 4 y = 440 y = 110 answer d"
Answer: d
Question (general): a number is doubled and 15 is added . if resultant is trebled , it becomes 75 . what is that number
Options: a ) 8 , b ) 10 , c ) 5 , d ) 14 , e ) 7
Rationale: "explanation : = > 3 ( 2 x + 15 ) = 75 = > 2 x + 15 = 25 = > x = 5 option c"
Answer: c
Question (general): divide rs . 2800 among a , b and c so that a receives 3 / 4 as much as b and c together and b receives 1 / 4 as a and c together . a ' s share is ?
Options: a ) 1300 , b ) 1200 , c ) 1375 , d ) 1400 , e ) 8400
Rationale: "a + b + c = 2800 a = 3 / 4 ( b + c ) ; b = 1 / 4 ( a + c ) a / ( b + c ) = 3 / 4 a = 1 / 7 * 8400 = > 1200 answer : b"
Answer: b
Question (general): if 1 + 2 + 3 + . . . + n = n ( n + 1 ) , then 3 ( 1 + 3 + 5 + . . . . + 69 ) = ?
Options: a ) 3675 , b ) 3575 , c ) 3475 , d ) 3375 , e ) 3275
Rationale: explanation : to solve this use the formula of ap , sn = ( n / 2 ) ( a + l ) . . . . . . . . . . . . . . . . ( 1 ) to find n , use = > tn = a + ( n - 1 ) d = > 69 = 1 + ( n - 1 ) 2 = > n = 35 use value of n in ( 1 ) then , sn = ( 35 / 2 ) ( 1 + 69 ) = 1225 ans : - 3 ( sn ) = 3675 answer : a
Answer: a
Question (general): if the average ( arithmetic mean ) of 8 consecutive odd integers is 414 , then the least of these integers is
Options: a ) a ) 407 , b ) b ) 518 , c ) c ) 519 , d ) d ) 521 , e ) e ) 525
Rationale: a very helpful rule to know in arithmetic is the rule that in evenly spaced sets , average = median . because the average will equal the median in these sets , then we quickly know that the median of this set of consecutive odd integer numbers is 414 . there are 8 numbers in the set , and in a set with an even number of terms the median is just the average of the two most median terms ( here the 4 th and 5 th numbers in the set ) . this means that numbers 4 and 5 in this set are 413 and 415 . because we know that number 4 is 413 , we know that the smallest number is 3 odd numbers below this , which means that it is 3 * 2 = 6 below this ( every odd number is every other number ) . therefore 413 - 6 = 407 , answer choice a
Answer: a
Question (other): a shipment of 250 smartphones contains 84 that are defective . if a customer buys two smartphones at random from the shipment , what is the approximate probability that both phones are defective ? a . b . c . d . e .
Options: a ) 1 / 250 , b ) 1 / 84 , c ) 1 / 11 , d ) 1 / 9 , e ) 1 / 3
Rationale: probability of choosing one defective phone from a lot of 250 which ontains 84 defective phones is = ( 84 / 250 ) probability of choosing one defective phone from a lot of 249 ( we already picked one ) which ontains 83 ( we already picked one ) defective phones is = ( 83 / 249 ) combined probability of series of events = product of the probabilities = ( 84 / 250 ) * ( 83 / 249 ) 84 / 250 is close to ( 1 / 3 ) and ( 83 / 249 ) = ( 1 / 3 ) so answer is ( 1 / 3 ) * ( 1 / 3 ) = ( 1 / 9 ) answer : d
Answer: d
Question (general): what is the positive difference between the sum of the squares of the first 7 positive integers and the sum of the prime numbers between the first square and fourth square ?
Options: a ) 11 , b ) 52 , c ) 83 , d ) 94 , e ) 99
Rationale: "forget conventional ways of solving math questions . in ps , ivy approach is the easiest and quickest way to find the answer . the sum of the squares of the first 4 positive integers = 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + . . . + 7 ^ 2 = 140 the sum of the prime numbers between the first square ( = 1 ) and fourth square ( = 16 ) = 2 + 3 + 5 + 7 + 11 + 13 = 41 . so the difference between 41 and 140 is 99 . so the answer is ( e ) ."
Answer: e
Question (general): 517 x 517 + 483 x 483 = ?
Options: a ) 79698 , b ) 80578 , c ) 500578 , d ) 81268 , e ) none of them
Rationale: "= ( 517 ) ^ 2 + ( 483 ) ^ 2 = ( 500 + 17 ) ^ 2 + ( 500 - 17 ) ^ 2 = 2 [ ( 500 ) ^ 2 + ( 17 ) ^ 2 ] = 2 [ 250000 + 289 ] = 2 x 250289 = 500578 answer is c"
Answer: c
Question (geometry): on dividing a number by 5 , we get 3 as remainder . what will be the remainder when the square of this number is divided by 5 ?
Options: a ) 0
b ) 1
c ) 3
d ) 4
e ) 2
Rationale: let the number be x and on dividing x by 5 , we get k as quotient and 3 as remainder . x = 5 k + 3 x ^ 2 = ( 5 k + 3 ) ^ 2 = ( 25 k ^ 2 + 30 k + 9 ) = 5 ( 5 k ^ 2 + 6 k + 1 ) + 4 on dividing x ^ 2 by 5 , we get 4 as remainder . answer is d
Answer: d
Question (general): a certain car uses one gallon of gasoline every 38 miles when it travels on highway , and one gallon of gasoline every 20 miles when it travels in the city . when a car travels 4 miles on highway and 4 additional miles in the city , it uses what percent more gasoline than if it travels 8 miles on the highway ?
Options: a ) 15 % , b ) 20 % , c ) 22.5 % , d ) 45 % , e ) 50 %
Rationale: "4 miles on the highway = 4 / 38 gallons ; 4 miles in the city = 4 / 20 gallons ; total = 4 / 38 + 4 / 20 = 29 / 95 gallons . 8 miles on the highway = 8 / 38 gallons . the % change = ( 29 / 95 - 8 / 38 ) / ( 8 / 38 ) = 0.45 . answer : d ."
Answer: d
Question (other): divide $ 300 among a , b in the ratio 1 : 2 . how many $ that a get ?
Options: a ) $ 50 , b ) $ 500 , c ) $ 150 , d ) $ 250 , e ) $ 100
Rationale: "sum of ratio terms = 1 + 2 = 3 a = 300 * 1 / 3 = $ 100 answer is e"
Answer: e
Question (physics): a man can row upstream at 45 kmph and downstream at 55 kmph , and then find the speed of the man in still water ?
Options: a ) 32 kmph , b ) 34 kmph , c ) 30 kmph , d ) 50 kmph , e ) 65 kmph
Rationale: "us = 45 ds = 55 m = ( 45 + 55 ) / 2 = 50 answer : d"
Answer: d
Question (geometry): the surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 8 cm each . the radius of the sphere is
Options: a ) 3 cm
b ) 4 cm
c ) 6 cm
d ) 8 cm
e ) none
Rationale: solution 4 î r 2 = 2 î 4 x 8 â ‡ ’ r 2 = ( 4 x 8 / 2 ) â ‡ ’ 16 â ‡ ’ r = 4 cm . answer b
Answer: b
Question (general): the sum of the non - prime numbers between 30 and 40 , non - inclusive , is
Options: a ) 202 , b ) 217 , c ) 232 , d ) 247 , e ) 262
Rationale: "sum of consecutive integers from 31 to 39 , inclusive = = = = > ( a 1 + an ) / 2 * # of terms = ( 31 + 39 ) / 2 * 9 = 35 * 9 = 315 sum of non - prime numbers b / w 30 and 40 , non inclusive = = = > 315 - 68 ( i . e . , 31 + 37 , being the prime # s in the range ) = 247 answer : d"
Answer: d
Question (general): find the value of a / b + b / a , if a and b are the roots of the quadratic equation x 2 + 9 x + 4 = 0 ?
Options: a ) 17 , b ) 88 , c ) 14 , d ) 65 , e ) 89
Rationale: "a / b + b / a = ( a 2 + b 2 ) / ab = ( a 2 + b 2 + a + b ) / ab = [ ( a + b ) 2 - 2 ab ] / ab a + b = - 9 / 1 = - 9 ab = 4 / 1 = 4 hence a / b + b / a = [ ( - 9 ) 2 - 2 ( 4 ) ] / 4 = 73 / 4 = 18.25 . b )"
Answer: b
Question (general): 6 wires are by average 80 cm long each . if the average length of one third of the wires is 70 cm , what is the average of the other wires ?
Options: a ) 75 . , b ) 85 . , c ) 90 . , d ) 94 . , e ) 100 .
Rationale: edit : given ( x 1 + x 2 . . . + x 6 ) / 6 = 80 ( x 1 + x 2 . . . + x 6 ) = 480 - - > eq 1 . now given avg length of one third wires is 70 . that means out 6 / 3 = 2 wires . let the avg length of two wires be ( x 1 + x 2 ) / 2 = 70 . ( x 1 + x 2 ) = 140 . - - > eq 2 . now we are asked to find the average of the remaining i . e . ( x 3 + x 4 + x 5 + x 6 ) substitute eq 2 in eq 1 then we get 140 + x 3 + x 4 + x 5 + x 6 = 480 = > x 3 + x 4 + x 5 + x 6 = 340 now divide 340 by 4 we get 85 . = > ( x 3 + x 4 + x 5 + x 6 ) / 4 = 85 = avg length of remaining wires . imo correct option is b .
Answer: b
Question (general): when 15 is divided by integer u , the remainder is 4 . for how many values of u is this be true ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: when 15 is divided by u , the remainder is 4 i . e . 4 mangoes left over after grouping , so u must be greater than 4 . it also means that 11 is completely divisible by u . factors of 11 are 1 and 11 . out of these , u could be 11 . answer ( a )
Answer: a
Question (physics): a dog takes 4 leaps for every 5 leaps of a hare but 3 leaps of a dog are equal to 4 leaps of the hare . compare their speeds ?
Options: a ) 4 : 5 , b ) 16 : 15 , c ) 9 : 13 , d ) 5 : 15 , e ) 9 : 17
Rationale: "let the distance covered in 1 leap of the dog be x and that covered in 1 leap of the hare be y then 3 x = 4 y x = 4 / 3 y 4 x = 16 / 3 y ratio of speeds of dog and hare = ratio of distances covered by them in the same time = 4 x : 5 y = 16 / 3 y : 5 = 16 : 15 answer is b"
Answer: b
Question (physics): 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 7 seconds than it was moving after 4 seconds ?
Options: a ) 4 , b ) 9 , c ) 39 , d ) 48 , e ) 63
Rationale: "given : z = s ^ 2 + 2 s for 0 ≤ s ≤ 7 z ( 4 ) = 4 ^ 2 + 2 * 4 = 24 z ( 7 ) = 7 ^ 2 + 2 * 7 = 63 therefore z ( 7 ) - z ( 3 ) = 63 - 24 = 39 km / hr option c"
Answer: c
Question (general): if p # q denotes the least common multiple of p and q , then w = ( ( 12 # 16 ) # ( 18 # 24 ) ) = ?
Options: a ) 216 , b ) 180 , c ) 144 , d ) 108 , e ) 72
Rationale: "there are several ways to find the least common multiple of two numbers . in this case , the most efficient method is to use the greatest common factor : ( a * b ) / ( gcf ab ) = lcm ab the greatest common factor of 12 and 16 is 4 . so , 12 # 16 = 12 * 16 / 4 = 48 . the greatest common factor of 18 and 24 is 6 . so , 18 # 24 = 18 * 24 / 6 = 72 finally , the greatest common factor of 48 and 72 is 24 . so , w = ( ( 12 # 16 ) # ( 18 # 24 ) ) = 48 # 72 = ( 48 * 72 ) / 24 = 2 * 72 = 144 the correct answer is c ."
Answer: c
Question (general): a car travels from point a to point b . the average speed of the car is 60 km / hr and it travels the first half of the trip at a speed of 75 km / hr . what is the speed of the car in the second half of the trip ?
Options: a ) 40 , b ) 45 , c ) 48 , d ) 50 , e ) 55
Rationale: let d be the distance and let v be the speed in the second half . the total time = t 1 + t 2 d / 60 = d / 150 + ( d / 2 ) / v d / 100 = d / 2 v and so v = 50 km / hr the answer is d .
Answer: d
Question (geometry): a rectangular table , kept against a wall has a three sides free and the wall along the fourth side . the side opposite the wall is twice the length of each of the other two free sides . if the area of the rectangular table is 128 square feet , what is the total length of the table free sides , in feet ?
Options: a ) 4
b ) 8
c ) 16
d ) 32
e ) 64
Rationale: two sides each = x the third = 2 x and the wall side is thus 2 x too x * 2 x = 2 x ^ 2 = 128 ie x ^ 2 = 64 ie x = 8 l = 16 w = 8 total lenght of table ' s free sides = 2 * 8 + 16 = 32 my answer is d
Answer: d
Question (physics): a boat having a length 8 m and breadth 3 m is floating on a lake . the boat sinks by 1 cm when a man gets on it . the mass of the man is :
Options: a ) 100 kg , b ) 120 kg , c ) 89 kg , d ) 80 kg , e ) 240 kg
Rationale: "volume of water displaced = ( 8 x 3 x 0.01 ) m 3 = 0.24 m 3 . mass of man = volume of water displaced x density of water = ( 0.24 x 1000 ) kg = 240 kg . answer : e"
Answer: e
Question (physics): excluding stoppages , the speed of a bus is 86 kmph and including stoppages , it is 76 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 7.5 min , b ) 16 min , c ) 20 min , d ) 7 min , e ) 40 min
Rationale: "d 7 min due to stoppages , it covers 10 km less . time taken to cover 10 km = ( 10 / 86 x 60 ) min = 7 min"
Answer: d
Question (geometry): the perimeter of a square is equal to the perimeter of a rectangle of length 15 cm and breadth 14 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places )
Options: a ) 22.78
b ) 23.54
c ) 24.5
d ) 25.55
e ) 23.51
Rationale: let the side of the square be a cm . perimeter of the rectangle = 2 ( 15 + 14 ) = 58 cm perimeter of the square = 58 cm i . e . 4 a = 58 a = 14.5 diameter of the semicircle = 14.5 cm circumference of the semicircle = 1 / 2 ( ∏ ) ( 14.5 ) = 1 / 2 ( 22 / 7 ) ( 14.5 ) = 22.78 cm to two decimal places answer : a
Answer: a
Question (other): the ratio of numbers is 3 : 4 and their h . c . f is 4 . their l . c . m is ?
Options: a ) 23 , b ) 77 , c ) 88 , d ) 48 , e ) 11
Rationale: "let the numbers be 3 x and 4 x . then their h . c . f = x . so , x = 4 . so , the numbers are 12 and 16 . l . c . m of 12 and 16 = 48 . answer : d"
Answer: d
Question (gain): john makes $ 60 a week from his job . he earns a raise and now makes $ 120 a week . what is the % increase ?
Options: a ) 16 % , b ) 100 % , c ) 17 % , d ) 17.61 % , e ) 17.56 %
Rationale: "increase = ( 60 / 60 ) * 100 = ( 6 / 6 ) * 100 = 100 % . b"
Answer: b
Question (physics): a taxi leaves point a 5 hours after a bus left the same spot . the bus is traveling 20 mph slower than the taxi . find the speed of the taxi , if it overtakes the bus in three hours .
Options: a ) 34 , b ) 32 , c ) 36 , d ) 38 , e ) 40
Rationale: "let the speed of bus be v - 20 , speed of taxi be v the bus travelled a total of 8 hrs and taxi a total of 3 hrs . hence 8 * ( v - 20 ) = 3 v 8 v - 160 = 3 v 5 v = 160 v = 32 mph b"
Answer: b
Question (physics): a can finish a work in 12 days and b can do the same work in 15 days . b worked for 10 days and left the job . in how many days , a alone can finish the remaining work ?
Options: a ) 4 , b ) 5 1 / 2 , c ) 6 , d ) 8 , e ) none of these
Rationale: "b ' s 10 day ' s work = ( 1 / 15 * 10 ) = 2 / 3 remaining work = ( 1 - 2 / 3 ) = 1 / 3 now , 1 / 18 work is done by a in 1 day 1 / 3 work is done by a in ( 12 * 1 / 3 ) = 4 days . correct option : a"
Answer: a
Question (physics): two trains are moving in opposite directions with speed of 90 km / hr and 90 km / hr respectively . their lengths are 1.10 km and 0.9 km respectively . the slower train cross the faster train in - - - seconds
Options: a ) 56 , b ) 40 , c ) 47 , d ) 26 , e ) 25
Rationale: "explanation : relative speed = 90 + 90 = 180 km / hr ( since both trains are moving in opposite directions ) total distance = 1.1 + . 9 = 2 km time = 2 / 180 hr = 1 / 90 hr = 3600 / 90 seconds = 40 seconds answer : option b"
Answer: b
Question (physics): a can do a piece of work in 40 days ; b can do the same in 20 days . a started alone but left the work after 10 days , then b worked at it for 10 days . c finished the remaining work in 10 days . c alone can do the whole work in ?
Options: a ) 24 days , b ) 65 days , c ) 86 days , d ) 40 days , e ) 17 days
Rationale: "10 / 40 + 10 / 20 + 10 / x = 1 x = 40 days answer : d"
Answer: d
Question (general): for any number s , s * is defined as the greatest positive even integer less than or equal to s . what is the value of 5.2 – 5.2 * ?
Options: a ) 0.2 , b ) 1.2 , c ) 1.8 , d ) 2.2 , e ) 4.0
Rationale: since s * is defined as the greatest positive even integer less than or equal to s , then 5.2 * = 4 ( the greatest positive even integer less than or equal to 5.2 is 4 ) . hence , 5.2 – 5.2 * = 5.2 - 4 = 1.2 answer : b .
Answer: b
Question (general): the present ages of a , b & c are in the ratio of 5 : 7 : 8 . 7 years ago , the sum oftheir ages was 59 . what is the present age of eldest one ?
Options: a ) 30 , b ) 31 , c ) 32 , d ) 35 , e ) 36
Rationale: let their present ages be 5 x , 7 x and 8 x . 7 years ago , sum of their ages was 59 . sum of their present ages = 59 + ( 3 x 7 ) = 80 sum of their present ages given is 5 x + 7 x + 8 x = 20 x 20 x = 80 = > x = 80 20 = 4 age of the eldest one = 8 x = 8 x 4 = 32 years . c
Answer: c
Question (gain): ? % of 360 = 129.6
Options: a ) 277 , b ) 36 , c ) 64 , d ) 72 , e ) none of these
Rationale: "? % of 360 = 129.6 or , ? = 129.6 × 100 / 360 = 36 answer b"
Answer: b
Question (general): if the average ( arithmetic mean ) of 16 consecutive odd integers is 414 , then the least of these integers is
Options: a ) a ) 399 , b ) b ) 418 , c ) c ) 519 , d ) d ) 521 , e ) e ) 525
Rationale: "a very helpful rule to know in arithmetic is the rule that in evenly spaced sets , average = median . because the average will equal the median in these sets , then we quickly know that the median of this set of consecutive odd integer numbers is 414 . there are 16 numbers in the set , and in a set with an even number of terms the median is just the average of the two most median terms ( here the 7 th and 8 th numbers in the set ) . this means that numbers 7 and 8 in this set are 413 and 415 . because we know that number 7 is 413 , we know that the smallest number is 7 odd numbers below this , which means that it is 7 * 2 = 14 below this ( every odd number is every other number ) . therefore 413 - 14 = 399 , answer choice a ."
Answer: a