Cheukting/mathqa huggingface dataset:
Question (physics): a car started running at a speed of 30 km / hr and the speed of the car was increased by 2 km / hr at the end of every hour . find the total distance covered by the car in the first 9 hours of the journey .
Options: a ) 342 km , b ) 352 km , c ) 642 km , d ) 742 km , e ) 382 km
Rationale: "the total distance covered by the car in the first 10 hours = 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 = sum of 10 terms in ap whose first term is 30 and last term is 46 = 9 / 2 [ 30 + 46 ] = 342 km . answer : a"
Answer: a
Question (general): the sum of two numbers is 72 , and one of them is 12 more than the other . what are the two numbers ?
Options: a ) 36 - 48 , b ) 50 - 34 , c ) 60 - 24 , d ) 30 - 42 , e ) 21 - 63
Rationale: "in this problem , we are asked to find two numbers . therefore , we must let x be one of them . let x , then , be the first number . we are told that the other number is 12 more , x + 12 . the problem states that their sum is 72 : word problem = 72 the line over x + 12 is a grouping symbol called a vinculum . it saves us writing parentheses . we have : 2 x = 72 â ˆ ’ 12 = 60 . x = 60 / 2 = 30 . this is the first number . therefore the other number is x + 12 = 30 + 12 = 42 . the sum of 30 + 42 is 72 . d"
Answer: d
Question (physics): bob wants to run a mile in the same time as his sister . if bob ’ s time for a mile is currently 10 minutes 20 seconds and his sister ’ s time is currently 9 minutes 36 seconds , by what percent does bob need to improve his time in order run a mile in the same time as his sister ?
Options: a ) 3 % , b ) 5 % , c ) 7 % , d ) 10 % , e ) 12 %
Rationale: "bob ' s time = 620 secs . his sis ' time = 576 secs . percent increase needed = ( 620 - 576 / 620 ) * 100 = 44 / 640 * 100 = 7 % . ans ( c ) ."
Answer: c
Question (general): which digits should come in place of * and $ if the number 62684 * $ is divisible by both 8 and 5 ?
Options: a ) 8,5 , b ) 4,0 , c ) 1,4 , d ) 0,8 , e ) 8,0
Rationale: "since the given number is divisible by 5 , so 0 or 5 must come in place of $ . but , a number ending with 5 is never divisible by 8 . so , 0 will replace $ . now , the number formed by the last three digits is 4 * 0 , which becomes divisible by 8 , if * is replaced by 4 . hence , digits in place of * and $ are 4 and 0 respectively . answer b 4,0"
Answer: b
Question (general): an amount of money is to be divided between p , q and r in the ratio of 3 : 7 : 12 . if the difference between the shares of p and q is rs . 3200 , what will be the difference between q and r ' s share ?
Options: a ) 2788 , b ) 4000 , c ) 7282 , d ) 2782 , e ) 2729
Rationale: "4 - - - 3200 5 - - - ? = > 4000 answer : b"
Answer: b
Question (physics): a man can row downstream at 24 kmph and upstream at 10 kmph . find the speed of the man in still water and the speed of stream respectively ?
Options: a ) 2 , 7 , b ) 7 , 4 , c ) 8 , 7 , d ) 4 , 7 , e ) 17 , 7
Rationale: "let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 24 - - - ( 1 ) and x - y = 10 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 34 = > x = 17 , y = 7 answer : e"
Answer: e
Question (gain): john purchased a grinder and a mobile for rs . 15000 & rs . 8000 respectively . he sold the grinder at a loss of 4 % and the mobile phone at a profit of 15 % . overall how much he make a profit .
Options: a ) s . 90 , b ) s . 620 , c ) s . 600 , d ) s . 650 , e ) s . 690
Rationale: "let the sp of the refrigerator and the mobile phone be rs . r and rs . m respectively . r = 15000 ( 1 - 4 / 100 ) = 15000 - 600 m = 8000 ( 1 + 15 / 100 ) = 8000 + 120 total sp - total cp = r + m - ( 15000 + 8000 ) = - 600 + 1200 = rs . 600 as this is positive , an overall profit of rs . 600 was made . c"
Answer: c
Question (physics): in a kilometer race , a beats b by 50 meters or 20 seconds . what time does a take to complete the race ?
Options: a ) 380 sec , b ) 190 sec , c ) 726 sec , d ) 127 sec , e ) 128 sec
Rationale: "time taken by b run 1000 meters = ( 1000 * 20 ) / 50 = 400 sec . time taken by a = 400 - 20 = 380 sec . answer : a"
Answer: a
Question (general): what is the least value of x . so that 24 x 57 is divisible by 3 .
Options: a ) 2 , b ) 0 , c ) 1 , d ) 3 , e ) 4
Rationale: "explanation : the sum of the digits of the number is divisible by 3 , then the number is divisible by 3 . 2 + 4 + x + 5 + 7 = 18 + x least value of x may be 0 therefore 18 + 0 = 18 is divisible by 3 . answer : option b"
Answer: b
Question (physics): if i walk at 5 km / h , i miss the bus by 12 minutes . if i walk at 6 km / h , i reach 15 minutes before the arrival of the bus . how far i walk to reach the bus stand ?
Options: a ) 11.0 km , b ) 13.8 km , c ) 11.5 km , d ) 12.5 km , e ) 13.5 km
Rationale: "d = product of speed difference of time / difference of speed d = 5 x 6 / 60 [ 12 â ˆ ’ ( â ˆ ’ 15 ) / 6 - 5 ] [ here , â € “ ve sign indicates before the schedule time ] â ‡ ’ d = 13.5 km answer e"
Answer: e
Question (geometry): a rectangular tank needs to be coated with insulation . the tank has dimensions of 4 feet , 5 feet , and 3 feet . each square foot of insulation costs $ 20 . how much will it cost to cover the surface of the tank with insulation ?
Options: a ) $ 1220 , b ) $ 1330 , c ) $ 1550 , d ) $ 1770 , e ) $ 1880
Rationale: "the total surface area is 2 ( 3 * 4 + 4 * 5 + 3 * 5 ) = 94 square feet the total cost is 94 * $ 20 = $ 1880 the answer is e ."
Answer: e
Question (gain): a sum of money deposited at c . i . amounts to rs . 3650 in 2 years and to rs . 4015 in 3 years . find the rate percent ?
Options: a ) 10 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 30 %
Rationale: "explanation : 3650 - - - - - - - - 365 100 - - - - - - - - ? ( 10 % ) answer : option a"
Answer: a
Question (general): if 5 - 5 / x = 4 + 4 / x , then x =
Options: a ) 1 , b ) 9 , c ) - 1 , d ) 5 / 4 , e ) - 4 / 5
Rationale: "we ' re given the equation 5 - 5 / x = 4 + 4 / x . we ' re asked for the value of x . the common - denominator of these 4 numbers is x , so we need to multiply both sides of the equation by x , giving us . . . 5 x - 5 x / x = 4 x + 4 x / x we can then eliminate that denominator , which gives us . . . . 5 x - 5 = 4 x + 4 9 = x b"
Answer: b
Question (geometry): the sum of the squares of two numbers is 3341 and the diference of their squares is 891 . the numbers are :
Options: a ) 35 and 46 , b ) 35 and 49 , c ) 35 and 42 , d ) 35 and 41 , e ) 35 and 48
Rationale: explanation : let the numbers be x and y . then , adding ( i ) and ( ii ) , we get : subtracting ( ii ) from ( i ) , we get : so , the numbers are 35 and 46 answer : a
Answer: a
Question (physics): two trains are moving in opposite direction @ 60 kmph and 90 kmph . their lengths are 1.10 km and 0.9 km respectively . the time taken by the slower train to cross the faster train in seconds is
Options: a ) 36 , b ) 45 , c ) 48 , d ) 49 , e ) 50
Rationale: r . s = ( 60 + 90 ) kmph = > ( 150 * 5 / 18 ) m / sec = > ( 125 / 3 ) m / sec distance covered = ( 1.10 + 0.9 ) km = ( 2 * 1000 ) = 2000 m . required time = ( 2000 * 3 / 125 ) = 48 sec . answer : c
Answer: c
Question (gain): a sum amounts to rs . 8820 in 2 years at the rate of 5 % p . a . if interest was compounded yearly then what was the principal ?
Options: a ) s . 4000 , b ) s . 5000 , c ) s . 4500 , d ) s . 4800 , e ) s . 8000
Rationale: "ci = 8820 , r = 5 , n = 2 ci = p [ 1 + r / 100 ] ^ 2 = p [ 1 + 5 / 100 ] ^ 2 8820 = p [ 21 / 20 ] ^ 2 8820 [ 20 / 21 ] ^ 2 8000 answer : e"
Answer: e
Question (general): a gardener wants to plant trees in his garden in rows in such away that the number of trees in each row to be the same . if there are 24 rows the number of trees in each row is 42 if there are 12 more rows find the number of trees in each row ?
Options: a ) 21 , b ) 28 , c ) 34 , d ) 32 , e ) 76
Rationale: required number of trees = 24 / 36 * 42 = 28 . answer : b
Answer: b
Question (physics): a contractor undertook to do a piece of work in 10 days . he employed certain number of laboures but 5 of them were absent from the very first day and the rest could finish the work in only 13 days . find the number of men originally employed ?
Options: a ) 21.6 , b ) 23.6 , c ) 22.6 , d ) 21.8 , e ) 21.3
Rationale: "let the number of men originally employed be x . 10 x = 13 ( x â € “ 5 ) or x = 21.6 answer a"
Answer: a
Question (probability): a string of 25 light bulbs is wired in such a way that if any individual light bulb fails , the entire string fails . if for each individual light bulb the probability of failing during time period t is 0.06 , what is the probability that the string of light bulbs will fail during the time period t ?
Options: a ) 0.06 , b ) ( 0.06 ) ^ 25 , c ) 1 - ( 0.06 ) ^ 25 , d ) 1 - ( 0.94 ) ^ 25 , e ) ( 0.94 ) ^ 25
Rationale: "the string of light bulbs will fail if at least one light bulb fails . so , let ' s find the probability of the opposite event and subtract that value from 1 . the opposite event is when none of the 25 light bulbs fails , since the probability of each light bulb not to fail is 1 - 0.06 = 0.94 the probability that none of the 25 light bulbs fails is 0.94 ^ 25 . hence , the probability that at least one light bulb fails is 1 - 0.94 ^ 25 . answer : d . now , you should have spotted that your reasoning was not right because of one simple thing , consider the case when we have 100 light bulbs instead of 25 , then according to your logic the probability that the string of light bulbs will fail would be 100 * 0.06 = 6 , which is not possible since the probability of an event can not be more than 1 ( 100 % ) ."
Answer: d
Question (general): in a race where 16 cars are running , the chance that car x will win is 1 / 4 , that y will win is 1 / 12 and that z will win is 1 / 7 . assuming that a dead heat is impossible , find the chance that one of them will win .
Options: a ) 1 / 140 , b ) 10 / 21 , c ) 27 / 410 , d ) 11 / 21 , e ) 57 / 120
Rationale: "required probability = p ( x ) + p ( y ) + p ( z ) ( all the events are mutually exclusive ) . = 1 / 4 + 1 / 12 + 1 / 7 = 10 / 21 answer : b"
Answer: b
Question (physics): a certain machine produces 650 units of product p per hour . working continuously at this constant rate , this machine will produce how many units of product p in 7 days ?
Options: a ) 7,000 , b ) 24,000 , c ) 40,000 , d ) 109,200 , e ) 168,000
Rationale: "since 7 days consist of 24 * 7 hours the total hours of a week is 168 hours . since every hour the machine produces 650 units of product p the total product during 168 hours is 650 * 168 = 109,200 correct option : d"
Answer: d
Question (gain): a 20 % stock yielding 10 % is quoted at :
Options: a ) 83.33 , b ) 110 , c ) 200 , d ) 120 , e ) 160
Rationale: "solution to earn rs . 10 , money invested = rs . 100 . to earn rs . 20 , money invested = rs . ( 100 / 10 x 20 ) = rs . 200 . â ˆ ´ market value of rs . 100 stock = rs . 200 answer c"
Answer: c
Question (general): a cricket player whose bowling average was 24.50 runs per wicket , takes 5 wicket for 52 runs in a match . due to this his average decreases by 0.50 . what will be the number of wickets taken by him till the last match ?
Options: a ) 64 , b ) 72 , c ) 141 , d ) 96 , e ) 108
Rationale: "average = total runs / total wickets total runs after last match = 24.50 w + 52 total wickets after last match = w + 5 ( 24.50 w + 52 ) / ( w + 5 ) = 24.5 - 0.50 = 24 w = 136 so total wickets aftr last match = w + 5 = 141 answer : c"
Answer: c
Question (physics): sides of a rectangular park are in the ratio 3 : 2 and its area is 3750 sq m , the cost of fencing it at 20 ps per meter is ?
Options: a ) s . 122 , b ) s . 129 , c ) s . 125 , d ) s . 95 , e ) s . 121
Rationale: "3 x * 2 x = 3750 = > x = 25 2 ( 75 + 20 ) = 190 m 190 * 1 / 2 = rs . 95 answer : d"
Answer: d
Question (other): a polling company found that , of 300 households surveyed , 120 spent at least $ 100 per month on both gasoline and electricity , 60 spent at least $ 100 per month on gasoline but not on electricity , and for every household that did not spend at least $ 100 per month on gasoline or electricity , 4 spent at least $ 100 per month on electricity but not on gasoline . how many of the 300 households did not spend at least $ 100 per month on either gasoline or electricity ?
Options: a ) 24 , b ) 30 , c ) 36 , d ) 90 , e ) 96
Rationale: 120 spend $ 100 on gas & electricity 60 spend $ 100 on gas but not on electricity for every one that spent < $ 100 on both there are 4 that spent $ 100 on electricity not gas let the ones that spent on neither be x the ones that spent on just electricity will be 4 x total households = those who spend > $ 100 on both + those who spend > $ 100 on just one + those who spend < $ 100 on both = 120 + 60 + 4 x + x 300 = 180 + 5 x implies x = 24 answer is ( a )
Answer: a
Question (general): the cash realised on selling a 14 % stock is rs . 107.25 , brokerage being 1 / 4 % is ?
Options: a ) 366 , b ) 107 , c ) 102 , d ) 192 , e ) 122
Rationale: "cash realised = rs . ( 107.25 - 0.25 ) = rs . 107 . answer : b"
Answer: b
Question (gain): a shopkeeper sold an article offering a discount of 5 % and earned a profit of 38.7 % . what would have been the percentage of profit earned if no discount had been offered ?
Options: a ) 28.5 , b ) 46 , c ) 30 , d ) data inadequate , e ) none of these
Rationale: "giving no discount to customer implies selling the product on printed price . suppose the cost price of the article is 100 . then printed price = 100 ã — ( 100 + 38.7 ) / ( 100 â ˆ ’ 5 ) = 146 hence , required % profit = 146 â € “ 100 = 46 % answer b"
Answer: b
Question (other): the price of rice is reduced by 2 % . how many kilograms of rice can now be bought for the money which was sufficient to buy 49 kg of rice earlier ?
Options: a ) 48 kg , b ) 49 kg , c ) 50 kg , d ) 51 kg , e ) none
Rationale: sol . let the original price be rs . 100 per kg . money required to buy 49 kg of rice = rs . ( 100 x 49 ) = rs . 4900 . new price = rs . 98 per kg . ∴ quantity of rice bought = [ 4900 / 98 ] kg = 50 kg . answer c
Answer: c
Question (general): set a contains all the even numbers between 10 and 50 inclusive . set b contains all the even numbers between 110 and 150 inclusive . what is the difference between the sum of elements of set b and the sum of the elements of set a ?
Options: a ) 2100 , b ) 2550 , c ) 5050 , d ) 6275 , e ) 11325
Rationale: "set a contains 10 , 12,14 , 16 . . . 50 set b contains 110 , 112 , 114 . . . 150 number of terms in each set = 21 difference between corresponding terms in set a and b = 100 difference between sum of set b and set a = 100 * 21 = 2100 answer a"
Answer: a
Question (other): what is the number of integers from 1 to 1000 ( inclusive ) that are divisible by neither 15 nor by 20 ?
Options: a ) 887 , b ) 678 , c ) 765 , d ) 345 , e ) 256
Rationale: "in 1000 consecutive numbers , number of multiples of 15 = 1000 / 15 = 66 ( ignore decimals ) in 1000 consecutive numbers , number of multiples of 20 = 1000 / 20 = 50 number of multiples of 15 * 20 i . e . 300 = 1000 / 300 = 3 number of integers from 1 to 1000 that are divisible by neither 15 nor by 20 = 1000 - ( 66 + 50 - 3 ) { using the concept of sets here ) = 887 answer is a"
Answer: a
Question (general): if x is an integer such that 5 < x < 21 , 7 < x < 18 , 13 > x > 2 , 12 > x > 9 , and x + 1 < 13 , then x is
Options: a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) 11
Rationale: 5 < x < 21 , 7 < x < 18 , 2 < x < 13 9 < x < 12 x < 13 from above : 10 < x < 12 - - > x = 11 . answer : e .
Answer: e
Question (general): the cost of registration at a professional association meeting was $ 50 per person ; a lunch for registrants only was available for an additional $ 22 per person . if the number of registrants who paid for lunch was 20 more than the number who did not , and if receipts for registration and lunch totaled $ 50,240 , how many people paid just for registration at the meeting ?
Options: a ) 700 , b ) 800 , c ) 1,300 , d ) 1,500 , e ) 400
Rationale: hope this might be useful to you . let the number of people who have opted only to register = x now since the registration cost is 50 $ per person , the total amount sums to = 50 x $ as per the information given in the question , the number of registrants who paid for lunch was 20 more than the number who did not . that means , total number of people who registered and paid for lunch = 20 + x . for the people who registered for lunch the cost is 50 $ ( for the event registration ) + 22 $ ( for lunch ) = 72 $ . total amount in this case sums to = 72 ( 20 + x ) = 1440 + 72 x now , total amount received was 50240 . thus , from the above data , 50 x + 1440 + 72 x = 50240 122 x = 50240 - 1440 122 x = 48800 x = 400 . hence the correct ans is e
Answer: e
Question (general): 23 , 29 , 31 , 37 , 41 , 43 , 47 , ( . . . )
Options: a ) 53 , b ) 47 , c ) 48 , d ) 59 , e ) 45
Rationale: "explanation : all are prime numbers in their order , starting from 23 hence , next number is 53 answer : a"
Answer: a
Question (general): the denominator of a fraction is 15 greater than the numerator . if the numerator and the denominator are increased by 3 , the resulting fraction is equal to 3 â  „ 4 . what is the value of the original fraction ?
Options: a ) 23 / 38 , b ) 29 / 44 , c ) 33 / 48 , d ) 38 / 53 , e ) 42 / 57
Rationale: "let the numerator be x . then the denominator is x + 15 . x + 3 / x + 18 = 3 / 4 . 4 x + 12 = 3 x + 54 . x = 42 . the original fraction is 42 / 57 . the answer is e ."
Answer: e
Question (gain): a and b started a business investing rs . 50,000 and rs 20,000 respectively . in what ratio the profit earned after 2 years be divided between a and b respectively ?
Options: a ) 5 : 2 , b ) 9 : 2 , c ) 18 : 20 , d ) 1 : 4 , e ) 18 : 4
Rationale: "a : b = 50000 : 20000 = 5 : 2 answer : a"
Answer: a
Question (general): a grocer has a sale of rs . 6345 , 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 ) rs . 3000 , b ) rs . 4991 , c ) rs . 5991 , d ) rs . 6001 , e ) none
Rationale: "sol . total sale for 5 months = rs . ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs . 34009 . ∴ required sale = rs . [ ( 6500 x 6 ) - 34009 ] = rs . ( 39000 - 34009 ) = rs . 4991 . answer b"
Answer: b
Question (general): at deluxe paint store , fuchsia paint is made by mixing 4 parts of red paint with 2 parts of blue paint . mauve paint is made by mixing 3 parts of red paint with 6 parts blue paint . how many liters of blue paint must be added to 24 liters of fuchsia to change it to mauve paint ?
Options: a ) 9 , b ) 12 , c ) 15 , d ) 16 , e ) 24
Rationale: "in 24 liters , red = 4 / 6 * 24 = 16 and blue = 8 so , 16 / ( 8 + x ) = 3 / 6 or , x = 24 ( answer e )"
Answer: e
Question (general): h . c . f of 136 , 144 and a third number is 8 and their l . c . m is 2 ^ 4 * 3 ^ 2 * 17 * 7 . the third number is :
Options: a ) 154 , b ) 248 , c ) 360 , d ) 424 , e ) 168
Rationale: 136 = 2 ^ 3 * 17 ; 144 = 2 ^ 4 * 3 ^ 2 h . c . f = 2 ^ 3 = 8 since h . c . f is the product of lowest powers of common factors , so the third number must have ( 2 ^ 3 ) as its factor . since l . c . m is the product of highest powers of common prime factors , so the third number must have 3 and 7 as its factors . third number = 2 ^ 3 * 3 * 7 = 168 answer : e
Answer: e
Question (gain): from the beginning to the end of 2007 , the price of a stock rose 20 percent . in 2008 , it dropped 25 percent . in 2009 , it rose 25 percent . what percent of the stock â € ™ s 2007 starting price was the price of the stock at the end of 2009 ?
Options: a ) 80 , b ) 90 , c ) 95 , d ) 100 , e ) 112.5
Rationale: "assume a value at the beginning of 2007 . as this is a % question , assume p = 100 . at the end of 2007 it becmae = 1.2 * 100 = 120 at the end of 2008 it decreased by 25 % = 120 * . 75 = 90 at the end of 2009 it increased by 25 % = 90 * 1.25 = 112.5 thus ratio = 112.5 / 100 = 1.125 ( in % terms = 12.5 % ) . thus e is the correct answer ."
Answer: e
Question (physics): express a speed of 70 kmph in meters per second ?
Options: a ) 10 mps , b ) 19.44 mps , c ) 97.44 mps , d ) 17.44 mps , e ) 18.44 mps
Rationale: "70 * 5 / 18 = 19.44 mps answer : b"
Answer: b
Question (general): if n = ( 33 ) ^ 43 + ( 43 ) ^ 32 what is the units digit of n ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: first of all , the units digit of ( 33 ) ^ 43 is the same as that of 3 ^ 43 and the units digit of ( 43 ) ^ 32 is the same as that of 3 ^ 32 . so , we need to find the units digit of 3 ^ 43 + 3 ^ 33 . next , the units digit of 3 in positive integer power repeats in blocks of four { 3 , 9 , 7 , 1 } : 3 ^ 1 = 3 ( the units digit is 3 ) 3 ^ 2 = 9 ( the units digit is 9 ) 3 ^ 3 = 27 ( the units digit is 7 ) 3 ^ 4 = 81 ( the units digit is 1 ) 3 ^ 5 = 243 ( the units digit is 3 again ! ) . . . thus : the units digit of 3 ^ 43 is the same as the units digit of 3 ^ 3 , so 7 ( 43 divided by the cyclicity of 4 gives the remainder of 3 ) . the units digit of 3 ^ 33 is the same as the units digit of 3 ^ 1 , so 3 ( 33 divided by the cyclicity of 4 gives the remainder of 1 ) . therefore the units digit of ( 33 ) ^ 43 + ( 43 ) ^ 32 is 7 + 5 = 2 . answer : b .
Answer: b
Question (gain): on a certain transatlantic crossing , 20 percent of a ship ’ s passengers held round - trip tickets and also took their cars abroad the ship . if 20 percent of the passengers with round - trip tickets did not take their cars abroad the ship , what percent of the ship ’ s passengers held round - trip tickets ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 40 %
Rationale: "let t be the total number of passengers . let x be the number of people with round trip tickets . 0.2 t had round trip tickets and took their cars . 0.8 x had round trip tickets and took their cars . 0.8 x = 0.2 t x = 0.25 t the answer is b ."
Answer: b
Question (physics): a train running at the speed of 126 km / hr crosses a pole in 9 seconds . find the length of the train .
Options: a ) 150 meter , b ) 286 meter , c ) 186 meter , d ) 315 meter , e ) 265 meter
Rationale: "speed = 126 * ( 5 / 18 ) m / sec = 35 m / sec length of train ( distance ) = speed * time ( 35 ) * 9 = 315 meter answer : d"
Answer: d
Question (general): what is the smallest number which when diminished by 20 , is divisible 15 , 30 , 45 and 60 ?
Options: a ) 200 , b ) 220 , c ) 240 , d ) 322 , e ) 342
Rationale: "required number = ( lcm of 15 , 30 , 45 and 60 ) + 20 = 180 + 20 = 200 option a"
Answer: a
Question (other): mrs . evans gave a test to her freshmen economics class , which has 25 students enrolled and 22 of them answered question 1 correctly . if 20 answered question 2 correctly and 3 did not take the test then how many answered both questions correctly ?
Options: a ) 30 , b ) 20 , c ) 23 , d ) 17 , e ) 19
Rationale: "total number of enrolled students = 25 number of students who did not take test = 3 hence , number of students who took test = 25 - 3 = 22 number of students who answered q 2 correctly = 20 , therefore , all students who took test answered q 2 correctly . so , number of students who answered q 1 correctly , also answered q 2 correctly = 20 . number of students who answered both q 1 & q 2 correctly = 20 . answer : b"
Answer: b
Question (other): in two alloys , copper and tin are related in the ratios of 4 : 1 and 1 : 3 . 10 kg of ist alloy , 16 kg of 2 nd alloy and some pure copper melted together . an alloy obtained in which the ratio of copper and tin was 3 : 2 . find the weight of the new alloy .
Options: a ) 34 kg , b ) 35 kg , c ) 36 kg , d ) 30 kg , e ) 32 kg
Rationale: suppose x kg of pure copper is melted with 10 kg of ist alloy and 16 kg of 2 nd alloy , then pure cooper in new alloy = 10 * 4 / 5 + 16 * 1 / 4 + x = 12 + x kg pure tin in new alloy = 10 * 1 / 5 + 16 * 3 / 4 = 14 kg as per given condition ( 12 + x ) / 14 = 3 / 2 24 + 2 x = 42 x = 9 kg total weight of new alloy = 10 + 16 + 9 = 35 kg answer : b
Answer: b