Cheukting/mathqa huggingface dataset:
Question (general): a merchant has selected two items to be placed on sale , one of which currently sells for 35 percent less than the other . if he wishes to raise the price of the cheaper item so that the two items are equally priced , by what percentage must he raise the price of the less expensive item ?
Options: a ) 30 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 70 %
Rationale: "expensive item = $ 100 ; cheap item = $ 65 ; we must increase $ 65 to $ 100 , so by $ 35 , which is approximately 50 % increase : ( 100 - 65 ) / 65 = ~ 0.53 . answer : c ."
Answer: c
Question (physics): the population of a bacteria colony doubles every day . if it was started 11 days ago with 2 bacteria and each bacteria lives for 12 days , how large is the colony today ?
Options: a ) 512 , b ) 768 , c ) 1024 , d ) 2048 , e ) 4096
Rationale: "2 ^ 11 ( 2 ) = 2 ^ 12 = 4096 the answer is e ."
Answer: e
Question (general): the unit digit in the product 7858 * 1086 * 4582 * 9783 is ?
Options: a ) 0 , b ) 1 , c ) 8 , d ) 3 , e ) 4
Rationale: "unit digit in the given product = unit digit in 8 * 6 * 2 * 3 = 8 answer is c"
Answer: c
Question (physics): a train speeds past a pole in 20 seconds and passes through a tunnel 500 m long in 40 seconds . its length is :
Options: a ) 200 m , b ) 400 m , c ) 500 m , d ) 700 m , e ) none of the above
Rationale: sol . let the length of the train be x metres and its speed be y m / sec . then , x / y = 20 ⇒ y = x / 20 ∴ ( x + 500 ) / 40 = x / 20 ⇔ x = 500 m . answer c
Answer: c
Question (gain): yesterday ' s closing prices of 1,980 different stocks listed on a certain stock exchange were all different from today ' s closing prices . the number of stocks that closed at a higher price today than yesterday was 20 percent greater than the number that closed at a lower price . how many of the stocks closed at a higher price today than yesterday ?
Options: a ) 484 , b ) 1080 , c ) 1,100 , d ) 1,320 , e ) 1,694
Rationale: lets consider the below - the number of stocks that closed at a higher price = h the number of stocks that closed at a lower price = l we understand from first statement - > h + l = 1980 - - - - ( 1 ) we understand from second statement - > h = ( 120 / 100 ) l = > h = 1.2 l - - - - ( 2 ) solve eq ( 1 ) ( 2 ) to get h = 1080 . b is my answer .
Answer: b
Question (general): 20 - 8 percent of the programmers in a startup company weigh 200 pounds or more . 20 - 5 percent of the programmers that are under 200 pounds in that same company weigh 100 pounds or less . what percent of the programmers in the startup company weigh between 100 and 200 pounds ?
Options: a ) 15 % , b ) 20 % , c ) 25 % , d ) 54 % , e ) 75 %
Rationale: initially 72 % and 28 % split 80 % is further divided as 25 % and 75 % q is asking about that 75 % let total be ' 100 ' then that 75 % is ( 3 / 4 ) ∗ 72 so , the required % is [ ( 3 / 4 ) ∗ 72 / 100 ] ∗ 100 = 54 % answer : d
Answer: d
Question (physics): the racing magic takes 90 seconds to circle the racing track once . the charging bull makes 40 rounds of the track in an hour . if they left the starting point together , how many minutes will it take for them to meet at the starting point for the second time ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: "time taken by racing magic to make one circle = 90 seconds time taken bycharging bullto make one circle = 60 mins / 40 = 1.5 mins = 90 seconds lcm of 90 and 90 seconds = 90 seconds time taken for them to meet at the starting point for the second time = 2 * 90 sec = 180 seconds = 3 mins answer a"
Answer: a
Question (gain): a lent rs . 5000 to b for 2 years and rs . 3000 to c for 4 years on simple interest at the same rate of interest and received rs . 3300 in all from both of them as interest . the rate of interest per annum is ?
Options: a ) 16 % , b ) 12 % , c ) 74 % , d ) 10 % , e ) 15 %
Rationale: "let the rate be r % p . a . then , ( 5000 * r * 2 ) / 100 + ( 3000 * r * 4 ) / 100 = 3300 100 r + 120 r = 3300 r = 15 % answer : e"
Answer: e
Question (gain): in the first 10 overs of a cricket game , the run rate was only 3.2 . what should be the run rate in the remaining 40 overs to reach the target of 282 runs ?
Options: a ) 6.25 , b ) 7.25 , c ) 7.75 , d ) 7.35 , e ) 8.25
Rationale: "runs scored in the first 10 overs = 10 × 3.2 = 32 total runs = 282 remaining runs to be scored = 282 - 32 = 250 remaining overs = 40 run rate needed = 25040 = 6.25 answer : a"
Answer: a
Question (general): what is the unit ’ s digit of 7 ^ 6
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "7 ^ 1 = 7 7 ^ 2 = 49 7 ^ 3 = 343 7 ^ 4 = 1 ( last digit ) 7 ^ 5 = 7 ( last digit ) and the cycle repeats after every 4 powers therefore , last digit of 7 ^ 6 = 9 answer e"
Answer: e
Question (physics): a can finish a work in 4 days and b can do same work in half the time taken by a . then working together , what part of same work they can finish in a day ?
Options: a ) 1 / 4 , b ) 1 / 6 , c ) 1 / 7 , d ) 3 / 4 , e ) none of these
Rationale: explanation : please note in this question , we need to answer part of work for a day rather than complete work . it was worth mentioning here because many do mistake at this point in hurry to solve the question so lets solve now , a ' s 1 day work = 1 / 4 b ' s 1 day work = 1 / 2 [ because b take half the time than a ] ( a + b ) ' s one day work = ( 1 / 4 + 1 / 2 ) = 3 / 4 so in one day 3 / 4 work will be done answer : d
Answer: d
Question (physics): two pipes a and b can separately fill a tank in 16 and 10 minutes respectively . a third pipe c can drain off 60 liters of water per minute . if all the pipes are opened , the tank can be filled in 10 minutes . what is the capacity of the tank ?
Options: a ) 590 liters , b ) 960 liters , c ) 740 liters , d ) 560 liters , e ) 580 liters
Rationale: "1 / 16 + 1 / 10 - 1 / x = 1 / 10 x = 12 16 * 60 = 960 answer : b"
Answer: b
Question (physics): a train speeds past a pole in 15 sec and a platform 110 m long in 25 sec , its length is ?
Options: a ) 100 , b ) 150 , c ) 160 , d ) 165 , e ) 180
Rationale: "let the length of the train be x m and its speed be y m / sec . then , x / y = 15 = > y = x / 15 ( x + 110 ) / 25 = x / 15 = > x = 165 m . answer : option d"
Answer: d
Question (general): if ( t - 8 ) is a factor of t ^ 2 - kt - 47 , then k =
Options: a ) 16 , b ) 12 , c ) 2 , d ) 6 , e ) 14
Rationale: "t ^ 2 - kt - 48 = ( t - 8 ) ( t + m ) where m is any positive integer . if 48 / 8 = 6 , then we know as a matter of fact that : m = + 6 and thus k = 8 - 6 = 6 t ^ 2 - kt - m = ( t - a ) ( t + m ) where a > m t ^ 2 + kt - m = ( t - a ) ( t + m ) where a < m t ^ 2 - kt + m = ( t - a ) ( t - m ) t ^ 2 + kt + m = ( t + a ) ( t + m ) d"
Answer: d
Question (gain): during a special promotion , a certain filling station is offering a 10 percent discount on gas purchased after the first 10 gallons . if kim purchased 15 gallons of gas , and isabella purchased 25 gallons of gas , then isabella ‟ s total per - gallon discount is what percent of kim ‟ s total per - gallon discount ?
Options: a ) 80 % , b ) 100 % , c ) 116.7 % , d ) 120 % , e ) 180 %
Rationale: "kim purchased 15 gallons of gas . she paid for 10 + 0.9 * 5 = 14.5 gallons , so the overall discount she got was 0.5 / 15 = 3.33 % . isabella purchased 25 gallons of gas . she paid for 10 + 0.9 * 15 = 23.5 gallons , so the overall discount she got was 1.5 / 25 = 6 % . 6 is 6 / 3.33 * 100 = 180 % of 3.33 . answer : e ."
Answer: e
Question (gain): a man can row downstream at the rate of 16 km / hr and upstream at 6 km / hr . find man ' s rate in still water and the rate of current ?
Options: a ) 9,6 , b ) 11,5 , c ) 9,3 , d ) 6,6 , e ) none of these
Rationale: "explanation : rate of still water = 1 / 2 ( 16 + 6 ) = 11 km / hr rate of current = 1 / 2 ( 16 - 6 ) = 5 km / hr answer : option b"
Answer: b
Question (geometry): a rectangular lawn of dimensions 100 m * 60 m has two roads each 10 m wide running in the middle of the lawn , one parallel to the length and the other parallel to the breadth . what is the cost of traveling the two roads at rs . 3 per sq m ?
Options: a ) a ) 3820 , b ) b ) 930 , c ) c ) 9309 , d ) d ) 4500 , e ) e ) 8302
Rationale: "explanation : area = ( l + b – d ) d ( 100 + 60 – 10 ) 10 = > 1500 m 2 1500 * 3 = rs . 4500 answer : option d"
Answer: d
Question (physics): find avrg speed if a man travels at speed of 18 km / hr up and 24 km / hr dawn at an altitude of 300 m .
Options: a ) 25.8 , b ) 26.8 , c ) 27.8 , d ) 20.5 , e ) 21.8
Rationale: "avg speed = 2 * x * y / ( x + y ) = 2 * 18 * 24 / ( 18 + 24 ) = 20.5 answer : d"
Answer: d
Question (other): nitin ranks 27 th in a class of 89 students . what is rank from the last ?
Options: a ) 63 , b ) 65 , c ) 67 , d ) 87 , e ) 89
Rationale: "explanation : number students behind the nitin in rank = ( 89 - 27 ) = 62 nitin is 63 th from the last answer : a ) 63"
Answer: a
Question (other): set a consists of the integers from 3 to 12 , inclusive , while set b consists of the integers from 6 to 20 , inclusive . how many distinct integers do belong to the both sets at the same time ?
Options: a ) 5 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "a = { 3,4 , 5,6 , 7,8 , 9,10 , 11,12 } b = { 6 , 7,8 , 9,10 , 11,12 . . . } thus we see that there are 7 distinct integers that are common to both . b is the correct answer ."
Answer: b
Question (general): what is the units digit of the expression 14 ^ 7 − 20 ^ 4 ?
Options: a ) 8 , b ) 3 , c ) 4 , d ) 6 , e ) 0
Rationale: i think answer on this one should be a too . since we know that 14 ^ 7 > 20 ^ 4 , as will said one should always check if the number is positive .
Answer: a
Question (general): the telephone company wants to add an area code composed of 2 letters to every phone number . in order to do so , the company chose a special sign language containing 424 different signs . if the company used 422 of the signs fully and two remained unused , how many additional area codes can be created if the company uses all 424 signs ?
Options: a ) 246 , b ) 248 , c ) 1692 , d ) 15,128 , e ) 30,256
Rationale: "# of 2 - letter codes possible from 424 different signs = 424 * 424 . # of 2 - letter codes possible from 422 different signs = 422 * 422 . the difference = 424 ^ 2 - 422 ^ 2 = ( 424 - 422 ) ( 424 + 422 ) = 1692 . answer : c ."
Answer: c
Question (geometry): thin rectangular slab of potato was cut into two pieces for an osmosis lab . one piece is 50 mm greater than the other . if the original uncut slab is 600 mm , what is the length of the other piece of the potato after it is cut .
Options: a ) 550
b ) 275
c ) 50
d ) 300
e ) 250
Rationale: piece one as p 1 , and piece two as p 2 . p 2 + 50 = p 1 as eq . a p 1 + p 2 = 600 as eq . b substitute eq . a into eq . b , resulting in ( p 2 + 50 ) + p 2 = 600 mm . group like terms , p 2 + p 2 = 600 - 50 ( 2 * p 2 / 2 ) = 550 / 2 solves to p 2 = 275 . ansewr is b .
Answer: b
Question (physics): a alone can complete a work in 16 days and b alone can do in 12 days . star ɵ ng with a , they work on alternate days . the total work will be completed in
Options: a ) 1314 , b ) 1312 , c ) 1334 , d ) 1344 , e ) none of these
Rationale: explana ɵ on : a ' s 1 day work = 1 / 16 b ' s 1 day work = 1 / 12 as they are working on alternate day ' s so their 2 days work = ( 1 / 16 ) + ( 1 / 12 ) = 7 / 48 [ here is a small technique , total work done will be 1 , right , then mul ɵ ply numerator ɵ ll denominator , as 7 * 6 = 42 , 7 * 7 = 49 , as 7 * 7 is more than 48 , so we will consider 7 * 6 , means 6 pairs ] work done in 6 pairs = 6 * ( 7 / 48 ) = 7 / 8 remaining work = 1 - 7 / 8 = 1 / 8 on 13 th day it will a turn , then remaining work = ( 1 / 8 ) - ( 1 / 16 ) = 1 / 16 on 14 th day it is b turn , 1 / 12 work done by b in 1 day 1 / 16 work will be done in ( 12 * 1 / 16 ) = 3 / 4 day so total days = 1334 answer : c
Answer: c
Question (physics): a cistern which could be filled in 6 hours takes one hour more to be filled owing to a leak in its bottom . if the cistern is full in what time will the leak empty it ?
Options: a ) 76 hrs , b ) 99 hrs , c ) 15 hrs , d ) 90 hrs , e ) 11 hrs
Rationale: "1 / 6 - 1 / x = 1 / 10 = > 15 hrs answer : c"
Answer: c
Question (general): george is 8 years more than christopher and ford is 2 years younger than christopher . the sum of their ages is 60 . find the ages of ford .
Options: a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: "christopher age = x george age , y = x + 8 - - - - - - - - - - > ( 1 ) ford age , z = x - 2 - - - - - - - - - - - - > ( 2 ) sum of their ages , x + y + z = 60 - - - - > ( 3 ) substitute z and y values in equation ( 3 ) therefore , x + ( x + 8 ) + ( x - 2 ) = 60 = > 3 x + 8 - 2 = 60 = > 3 x = 60 - 6 = > 3 x = 54 = > x = 54 / 3 x = 18 ( christopher ' s age ) substitute x value in equation 1 & 2 y = x + 8 y = 18 + 8 y = 26 ( george ' s age ) z = x - 2 z = 18 - 2 z = 16 ( ford ' s age ) answer : c"
Answer: c
Question (general): on sunday , bill ran 4 more miles than he ran on saturday . julia did not run on saturday , but she ran twice the number of miles on sunday that bill ran on sunday . if bill and julia ran a total of 28 miles on saturday and sunday , how many miles did bill run on sunday ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "let bill run x on saturday , so he will run x + 4 on sunday . . julia will run 2 * ( x + 4 ) on sunday . . totai = x + x + 4 + 2 x + 8 = 28 . . 4 x + 12 = 28 . . x = 4 . . ans = x + 4 = 4 + 4 = 8 aswer d"
Answer: d
Question (gain): bhanu spends 30 % of his income on petrol on scooter 14 % of the remaining on house rent and the balance on food . if he spends rs . 300 on petrol then what is the expenditure on house rent ?
Options: a ) 98 , b ) 140 , c ) 62 , d ) 797 , e ) 123
Rationale: "given 30 % ( income ) = 300 ⇒ ⇒ income = 1000 after having spent rs . 300 on petrol , he left with rs . 700 . his spending on house rent = 14 % ( 700 ) = rs . 98 answer : a"
Answer: a
Question (physics): a man covered a certain distance at some speed . if he had moved 3 kmph faster , he would have taken 40 minutes less . if he had moved 2 kmph slower , he would have taken 40 minutes more . what is the distance in km ?
Options: a ) 36 , b ) 38 , c ) 40 , d ) 42 , e ) 45
Rationale: explanation : speed = 2 v 1 v 2 / v 1 − v 2 = 2 × 3 × 23 − 2 = 12 km / h = hr distance = vt 1 ( 1 + v / v 1 ) = 12 × 40 / 60 ( 1 + 12 / 3 ) = 40 km answer is c
Answer: c
Question (general): if x * y = xy – 2 ( x + y ) for all integers x and y , then 2 * ( – 3 ) =
Options: a ) – 16 , b ) – 11 , c ) – 4 , d ) 4 , e ) 16
Rationale: "the quickest ( rather only ) way is to apply the given formula : 2 * ( - 3 ) = 2 * ( - 3 ) - 2 ( 2 + ( - 3 ) ) = - 6 + 2 = - 4 option ( c )"
Answer: c
Question (general): a man is 18 years older than his son . in eight years , his age will be twice the age of his son . the present age of this son is
Options: a ) 5 years , b ) 10 years , c ) 15 years , d ) 20 years , e ) 25 years
Rationale: "explanation : let ' s son age is x , then father age is x + 18 . = > 2 ( x + 8 ) = ( x + 18 + 8 ) = > 2 x + 16 = x + 26 = > x = 10 years answer : option b"
Answer: b
Question (general): operation # is defined as : a # b = 4 a ^ 2 + 4 b ^ 2 + 8 ab for all non - negative integers . what is the value of ( a + b ) + 5 , when a # b = 100 ?
Options: a ) 5 , b ) 8 , c ) 10 , d ) 13 , e ) 17
Rationale: "official solution : ( b ) we know that a # b = 100 and a # b = 4 a ² + 4 b ² + 8 ab . so 4 a ² + 4 b ² + 8 ab = 100 we can see that 4 a ² + 4 b ² + 8 ab is a well - known formula for ( 2 a + 2 b ) ² . therefore ( 2 a + 2 b ) ² = 100 . ( 2 a + 2 b ) is non - negative number , since both a and b are non - negative numbers . so we can conclude that 2 ( a + b ) = 10 . ( a + b ) + 5 = 10 / 2 + 5 = 10 . the correct answer is c ."
Answer: c
Question (general): a student got 72 % in math and 84 % in history . to get an overall average of 75 % , how much should the student get in the third subject ?
Options: a ) 65 % , b ) 67 % , c ) 69 % , d ) 71 % , e ) 73 %
Rationale: "72 + 84 + x = 3 * 75 x = 69 the answer is c ."
Answer: c
Question (general): if f ( x ) = ax ^ 2 – 6 x + ax + 1 , then f ( b ) – f ( - b ) will equal :
Options: a ) 0 , b ) - 12 b + 2 ab , c ) 2 ab ^ 4 – 8 b ^ 2 – 6 , d ) - 2 ab ^ 4 + 8 b ^ 2 + 6 , e ) 2 ab ^ 4 – 8 b ^ 2 + 2 ab – 6
Rationale: f ( x ) = ax ^ 2 – 6 x + ax + 1 f ( b ) = ab ^ 2 – 6 b + ab + 1 f ( - b ) = ab ^ 2 + 6 b - ab + 1 f ( b ) - f ( - b ) = ab ^ 2 – 6 b + ab + 1 - ab ^ 2 - 6 b + ab - 1 = - 12 b + 2 ab answer b
Answer: b
Question (physics): a 100 meter long train crosses a man standing on the platform in 5 sec . what is the speed of the train ?
Options: a ) 72 kmph , b ) 108 kmph , c ) 176 kmph , d ) 134 kmph , e ) 161 kmph
Rationale: "s = 100 / 5 * 18 / 5 = 72 kmph answer : a"
Answer: a
Question (general): what is the sum r of all 3 digit numbers that leave a remainder of ' 2 ' when divided by 3 ?
Options: a ) 897 , b ) 164850 , c ) 164749 , d ) 149700 , e ) 156720
Rationale: the series is = > 101 + . . . 998 number of terms = > 300 sum = > 300 / 2 * [ 101 + 998 ] hence sum r = > 164850 i . e . option b
Answer: b
Question (physics): find the cost of carpeting a room 13 m long and 9 m broad with a carpet 75 cm wide at the rate of rs . 12 per square metre .
Options: a ) 1824 , b ) 1854 , c ) 1872 , d ) 1888 , e ) 1999
Rationale: explanation : area of the carpet = area of the room = ( 13 × 9 ) m 2 = 117 m 2 . length of the carpet = ( area / width ) = 117 × ( 4 / 3 ) m = 156 m . therefore cost of carpeting = ( 156 × 12 ) = rs . 1872 answer : option c
Answer: c
Question (general): each week a restaurant serving mexican food uses the same volume of chili paste , which comes in either 25 - ounce cans or 15 - ounce cans of chili paste . if the restaurant must order 30 more of the smaller cans than the larger cans to fulfill its weekly needs , then how many larger cans are required to fulfill its weekly needs ?
Options: a ) 60 , b ) 70 , c ) 80 , d ) 100 , e ) 45
Rationale: let x be the number of 25 ounce cans . therefore ( x + 30 ) is the number of 15 ounce cans . total volume is same , therefore 25 x = 15 ( x + 30 ) 10 x = 450 x = 45 ans - e
Answer: e
Question (physics): a boat running downstream covers a distance of 22 km in 4 hours while for covering the same distance upstream , it takes 5 hours . what is the speed of the boat in still water ?
Options: a ) 2.75 , b ) 5.95 , c ) 7.95 , d ) 3.25 , e ) 4.95
Rationale: "speed downstream = 22 / 4 = 5.5 kmph speed upstream = 22 / 5 = 4.4 kmph speed of the boat in still water = ( 5.5 + 4.4 ) / 2 = 4.95 kmph answer : e"
Answer: e
Question (physics): express a speed of 54 kmph in meters per second ?
Options: a ) 10 mps , b ) 76 mps , c ) 15 mps , d ) 97 mps , e ) 16 mps
Rationale: "54 * 5 / 18 = 15 mps answer : c"
Answer: c
Question (gain): the cash difference between the selling prices of an article at a profit of 8 % and 6 % is rs 3 . the ratio of two selling prices is
Options: a ) 51 : 52 , b ) 52 : 53 , c ) 53 : 54 , d ) 54 : 53 , e ) none of these
Rationale: "explanation : let the cost price of article is rs . x required ratio = ( 108 % of x ) / ( 106 % of x ) = 108 / 106 = 54 / 53 = 54 : 53 . answer : d"
Answer: d
Question (general): the tax on a commodity is diminished by 16 % and its consumption increased by 15 % . the effect on revenue is ?
Options: a ) 2 % , b ) 3.8 % , c ) 3.4 % , d ) 3.6 % , e ) 1 %
Rationale: 100 * 100 = 10000 84 * 115 = 9660 - - - - - - - - - - - 10000 - - - - - - - - - - - 340 100 - - - - - - - - - - - ? = > 3.4 % decrease answer : c
Answer: c
Question (general): the maximum number of student amoung them 2010 pens and 1050 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :
Options: a ) 90 , b ) 60 , c ) 30 , d ) 1911 , e ) none of these
Rationale: "solution required number of student = h . c . f of 2010 and 1050 = 30 . answer c"
Answer: c
Question (general): two quarts containing 2 ⁄ 3 water and 1 ⁄ 3 formula are mixed with 3 quarts containing 3 ⁄ 8 water and 5 ⁄ 8 formula . approximately what percent of the combined 5 - quart mixture is water ?
Options: a ) 40 % , b ) 45 % , c ) 50 % , d ) 55 % , e ) 60 %
Rationale: since we are asking of water in the end , lets concentrate on water only . . a solution has 2 quarts with fraction of water = 2 / 3 , almost 67 % . . b solution has 3 quarts with fraction of water = 3 / 8 almost 37 % . . so the ratio a : b = 2 : 3 . . . the average will therefore be closer to b % and will be 2 / ( 2 + 3 ) of { 67 - 37 } away from b . . 2 / ( 2 + 3 ) of { 67 - 37 } = 2 / 5 * 30 = 12 . . so 37 + 12 = 49 nearly 50 % answer : c
Answer: c
Question (other): two numbers are in the ratio 3 : 4 . if their l . c . m . is 48 . what is sum of the numbers ?
Options: a ) 28 , b ) 56 , c ) 76 , d ) 84 , e ) 85
Rationale: "explanation : let the numbers be 3 x and 4 x lcm of 3 x and 4 x = 12 x ( since lcm of 3 and 4 is 12 . hence lcm of 3 x and 4 x is 12 x ) given that lcm of 3 x and 4 x is 48 = > 12 x = 48 = > x = 48 / 12 = 4 sum of the numbers = 3 x + 4 x = 7 x = 7 x 4 = 28 answer : option a"
Answer: a
Question (general): a cricketer scored 134 runs which included 12 boundaries and 2 sixes . what percent of his total score did he make by running between the wickets .
Options: a ) 55.22 % , b ) 54.54 % , c ) 63 % , d ) 70 % , e ) none of these
Rationale: "explanation : number of runs made by running = 134 - ( 12 x 4 + 2 x 6 ) = 134 - ( 60 ) = 74 now , we need to calculate 72 is what percent of 134 . = > 74 / 134 * 100 = 55.22 % answer : a"
Answer: a
Question (physics): a worker makes a toy in every 2 h . if he works for 80 h , then how many toys will he make ?
Options: a ) 40 , b ) 54 , c ) 45 , d ) 39 , e ) none
Rationale: "answer let number of toys be n . more hours , more toys ( direct proportion ) 2 : 80 : : 1 : n ⇒ n = 80 / 2 = 40 toys correct option : a"
Answer: a
Question (physics): bhavan travelled for 20 hours . he covered the first half of the distance at 50 kmph and remaining half of the distance at 40 kmph . find the distance travelled by bhavan ?
Options: a ) 888.89 , b ) 788.89 , c ) 899.89 , d ) 688.89 , e ) 899.99
Rationale: let the distance travelled be x km . total time = ( x / 2 ) / 50 + ( x / 2 ) / 40 = 20 = > x / 100 + x / 80 = 20 = > ( 4 x + 5 x ) / 400 = 20 = > x = 888.89 km answer : a
Answer: a
Question (general): what is the tens digit of 7 ^ 957 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "7 ^ 1 = 7 7 ^ 2 = 49 7 ^ 3 = 343 7 ^ 4 = 2401 7 ^ 5 = 16807 7 ^ 6 = 117649 we should see this as pattern recognition . we have a cycle of 4 . ( we can multiply the last 2 digits only as we care about ten ' s digit ) 0 , 4 , 4 , 0 . 957 = 4 * 239 + 1 the ten ' s digit will be 0 . answer d"
Answer: d
Question (general): ? x 40 = 173 x 240
Options: a ) 545 , b ) 685 , c ) 1038 , d ) 495 , e ) 534
Rationale: "let y x 40 = 173 x 240 then y = ( 173 x 240 ) / 40 = 1038 answer : c"
Answer: c
Question (general): rose made a part payment of $ 300 toward buying a brand new car , which represents 5 % of the total cost of the car , how much remains to be paid ?
Options: a ) $ 5700 , b ) $ 5500 , c ) $ 5800 , d ) $ 5200 , e ) $ 5880
Rationale: explanation : let ' s start with what the total price of the car would be . if 5 % is equal to $ 300 then 100 % equals $ x . we just have to multiply $ 300 by 20 to get total amount = $ 6000 . out of this amount we then need to deduct the amount already paid which was $ 300 so we have $ 6000 - $ 300 = $ 5700 answer : option a
Answer: a
Question (physics): a pump can fill a tank with water in 2 hours . because of a leak , it took 2 x 1 / 3 hours to fill the tank . the leak can drain all the water of the tank in
Options: a ) 5 hours , b ) 7 hours , c ) 8 hours , d ) 14 hours , e ) 18 hours
Rationale: "work done by the leak in 1 hour = 1 / 2 - 3 / 7 = 1 / 14 . leak will empty the tank in 14 hrs . answer : d"
Answer: d
Question (geometry): in a rectangular coordinate system , what is the area of a rhombus whose vertices have the coordinates ( 0 , 3.5 ) , ( 12 , 0 ) , ( 0 , - 3.5 ) , ( - 12 , 0 ) ?
Options: a ) 84 , b ) 88 , c ) 112 , d ) 116 , e ) 120
Rationale: "area of rhombus = 1 / 2 * d 1 * d 2 length of 1 st diagonal = 12 + 12 = 24 length of 2 nd diagonal = 3.5 + 3.5 = 7 area = 1 / 2 * 24 * 7 = 84 a is the answer"
Answer: a