Cheukting/mathqa huggingface dataset:
Question (other): there are two positive numbers in the ratio 5 : 8 . if the larger number exceeds the smaller by 27 , then find the smaller number ?
Options: a ) 25 , b ) 66 , c ) 45 , d ) 88 , e ) 44
Rationale: "let the two positive numbers be 5 x and 8 x respectively . 8 x - 5 x = 27 3 x = 27 = > x = 9 = > smaller number = 5 x = 45 . answer : c"
Answer: c
Question (gain): a worker is paid a regular rate of rs . 20 for completing a survey . the worker completes 100 surveys per week . for any survey involving the use of her cellphone , she is paid at a rate of that is 10 % higher than her regular rate . if she completed 70 surveys involving the use of her cellphone , how much did she get that week ?
Options: a ) 2140 , b ) 1140 , c ) 550 , d ) 650 , e ) 750
Rationale: amount earned using her cell phone = 70 * 22 = 1540 earned for remaining surveys = 30 * 20 = 600 total earning = 2140 answer : a
Answer: a
Question (general): if x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year , the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $ 38 . if $ 2,000 is the total amount invested , how much is invested at 8 percent ?
Options: a ) $ 700 , b ) $ 800 , c ) $ 900 , d ) $ 1100 , e ) $ 1200
Rationale: "0.1 x = 0.08 ( 2000 - x ) + 38 0.18 x = 198 x = 1100 then the amount invested at 8 % is $ 2000 - $ 1100 = $ 900 the answer is c ."
Answer: c
Question (general): if taxi fares were $ 2.00 for the first 1 / 5 mile and $ 0.40 for each 1 / 5 mile there after , then the taxi fare for a 4 - mile ride was
Options: a ) $ 4.60 , b ) $ 9.80 , c ) $ 19.60 , d ) $ 9.60 , e ) $ 29.60
Rationale: "in 4 miles , initial 1 / 5 mile charge is $ 2 rest of the distance = 4 - ( 1 / 5 ) = 19 / 5 rest of the distance charge = 19 ( 0.4 ) = $ 7.6 ( as the charge is 0.4 for every 1 / 5 mile ) = > total charge for 4 miles = 2 + 7.6 = 9.6 answer is d"
Answer: d
Question (physics): the time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream . if the speed of the boat in still water is 42 kmph , find the speed of the stream ?
Options: a ) 16 kmph , b ) 18 kmph , c ) 14 kmph , d ) 79 kmph , e ) 27 kmph
Rationale: "the ratio of the times taken is 2 : 1 . the ratio of the speed of the boat in still water to the speed of the stream = ( 2 + 1 ) / ( 2 - 1 ) = 3 / 1 = 3 : 1 speed of the stream = 42 / 3 = 14 kmph . answer : c"
Answer: c
Question (gain): by selling an article at rs . 300 , a profit of 25 % is made . find its cost price ?
Options: a ) s . 486 , b ) s . 455 , c ) s . 240 , d ) s . 480 , e ) s . 489
Rationale: "sp = 300 cp = ( sp ) * [ 100 / ( 100 + p ) ] = 300 * [ 100 / ( 100 + 25 ) ] = 300 * [ 100 / 125 ] = rs . 240 answer : c"
Answer: c
Question (gain): what will be the compound interest on rs . 25000 a ō er 3 years at the rate of 12 % per annum
Options: a ) rs 10123.20 , b ) rs 10123.30 , c ) rs 10123.40 , d ) rs 10123.50 , e ) none of these
Rationale: "explanation : ( 25000 × ( 1 + 12100 ) 3 ) = > 25000 × 2825 × 2825 × 2825 = > 35123.20 so compound interest will be 35123.20 - 25000 = rs 10123.20 answer : a"
Answer: a
Question (general): a batsman scores 26 runs and increases his average from 14 to 15 . find the runs to be made if he wants top increasing the average to 19 in the same match ?
Options: a ) 12 , b ) 18 , c ) 25 , d ) 74 , e ) 88
Rationale: number of runs scored more to increase the ratio by 1 is 26 - 14 = 12 to raise the average by one ( from 14 to 15 ) , he scored 12 more than the existing average . therefore , to raise the average by five ( from 14 to 19 ) , he should score 12 x 5 = 60 more than the existing average . thus he should score 14 + 60 = 74 . answer d
Answer: d
Question (physics): a and b can do a piece of work in 30 days and 30 days respectively . they work together for 10 days and b leaves . in how many days the whole work is completed ?
Options: a ) 30 days , b ) 35 days , c ) 40 days , d ) 45 days , e ) 50 days
Rationale: "explanation : ( a + b ) ’ s 10 days work = 10 [ 1 / 30 + 1 / 30 ] = 10 [ 1 + 1 / 30 ] = 2 / 3 a complete remaining work in 2 / 3 * 30 = 20 total work = 10 + 20 = 30 days answer : option a"
Answer: a
Question (general): a total of 520 players participated in a single tennis knock out tournament . what is the total number of matches played in the tournament ? ( knockout means if a player loses , he is out of the tournament ) . no match ends in a tie .
Options: a ) 511 , b ) 519 , c ) 256 , d ) 255 , e ) 1023
Rationale: there are 520 players , only 1 person wins , 519 players lose . in order to lose , you must have lost a game . 519 games . ans - b
Answer: b
Question (general): solving a linear equation with several occurrences of the variable , solve for w . simplify answer as much as possible . ( 7 w + 6 ) / 6 + ( 9 w + 8 ) / 2 = 22
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: ( 7 w + 6 ) / 6 + ( 9 w + 8 ) / 2 = 22 or , [ 7 w + 6 + 3 ( 9 w + 8 ) ] / 6 = 22 or , 7 w + 6 + 27 w + 24 = 132 or , 34 w + 30 = 132 or , 34 w = 132 - 30 or , 34 w = 102 or , w = 102 / 34 therefore , w = 3 answer : c
Answer: c
Question (general): given f ( x ) = 3 x – 5 , for what value of x does 2 * [ f ( x ) ] – 7 = f ( 3 x – 6 )
Options: a ) 0 , b ) 2 , c ) 6 , d ) 7 , e ) 13
Rationale: "answer = b = 2 f ( x ) = 3 x – 5 2 * [ f ( x ) ] – 7 = f ( 3 x – 6 ) 2 ( 3 x - 5 ) - 7 = 3 ( 3 x - 6 ) - 5 6 x - 17 = 9 x - 23 x = 2"
Answer: b
Question (physics): two good train each 750 m long , are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one .
Options: a ) 12 sec , b ) 24 sec , c ) 48 sec , d ) 72 sec , e ) none
Rationale: "sol . relative speed = ( 45 + 30 ) km / hr = ( 75 x 5 / 18 ) m / sec = ( 125 / 6 ) m / sec . distance covered = ( 750 + 750 ) m = 1500 m . required time = ( 1500 x 6 / 125 ) sec = 72 sec . answer d"
Answer: d
Question (geometry): the ratio of the length and the width of a rectangle is 4 : 3 and the area of the rectangle is 4800 sq cm . what is the ratio of the width and the area of the rectangle ?
Options: a ) 1 : 72
b ) 1 : 76
c ) 1 : 80
d ) 1 : 84
e ) 1 : 88
Rationale: let the length and the width be 4 x and 3 x respectively . area = ( 4 x ) ( 3 x ) = 4800 12 x ^ 2 = 4800 x ^ 2 = 400 x = 20 the ratio of the width and the area is 3 x : 12 x ^ 2 = 1 : 4 x = 1 : 80 the answer is c .
Answer: c
Question (physics): a work which could be finished in 7 days was finished 3 days earlier after 10 more men joined . the number of men employed was ?
Options: a ) 22 , b ) 20 , c ) 60 , d ) 71 , e ) 11
Rationale: "x - - - - - - - 7 ( x + 10 ) - - - - 6 x * 7 = ( x + 10 ) 6 x = 60 \ answer : c"
Answer: c
Question (general): if ( 6 ) ( x ^ 2 ) has 3 different prime factors , at most how many different prime factors does x have ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: x can have at most 3 prime factors , namely the prime factors 2 and 3 , plus one other . if x had more than this number of prime factors , then ( 6 ) ( x ^ 2 ) would have more than 3 prime factors . the answer is c .
Answer: c
Question (gain): an item is being sold for $ 10 each . however , if a customer will “ buy at least 3 ” they have a promo discount of 30 % . also , if a customer will “ buy at least 10 ” items they will deduct an additional 8 % to their “ buy at least 3 ” promo price . if sam buys 10 pcs of that item how much should he pay ?
Options: a ) $ 92.00 , b ) $ 88.00 , c ) $ 87.04 , d ) $ 80.96 , e ) $ 65.00
Rationale: "without any discount sam should pay 10 * 10 = $ 100 . now , the overall discount would be slightly less than 38 % , thus he must pay slightly more than $ 62 . answer : e ."
Answer: e
Question (physics): a car gets 20 kilometers per gallon of gasoline . how many gallons of gasoline would the car need to travel 190 kilometers ?
Options: a ) 3.5 gallons , b ) 9.5 gallons , c ) 8.7 gallons , d ) 4.5 gallons , e ) 9.2 gallons
Rationale: each 40 kilometers , 1 gallon is needed . we need to know how many 40 kilometers are there in 180 kilometers ? 180 ã · 40 = 9.5 ã — 1 gallon = 9.5 gallons correct answer is b ) 9.5 gallons
Answer: b
Question (gain): what will be the compound interest on a sum of rs . 35,000 after 3 years at the rate of 12 % p . a . ?
Options: a ) s : 10123.19 , b ) s : 14172.48 , c ) s : 10123.20 , d ) s : 10123.28 , e ) s : 10123.12
Rationale: "amount = [ 35000 * ( 1 + 12 / 100 ) 3 ] = 35000 * 28 / 25 * 28 / 25 * 28 / 25 = rs . 49172.48 c . i . = ( 49172.48 - 35000 ) = rs : 14172.48 answer : b"
Answer: b
Question (general): from below option 48 is divisible by which one ?
Options: a ) a ) 3 , b ) b ) 5 , c ) c ) 9 , d ) d ) 7 , e ) e ) 11
Rationale: "48 / 3 = 16 a"
Answer: a
Question (gain): the list price of an article is rs . 66 . a customer pays rs . 56.16 for it . he was given two successive discounts , one of them being 10 % . the other discount is ?
Options: a ) 3.45 % , b ) 4.45 % , c ) 5.45 % , d ) 6.45 % , e ) 7.45 %
Rationale: "66 * ( 90 / 100 ) * ( ( 100 - x ) / 100 ) = 56.16 x = 5.45 % answer : c"
Answer: c
Question (gain): a trader marked the selling price of an article at 60 % above the cost price . at the time of selling , he allows certain discount and suffers a loss of 1 % . he allowed a discount of :
Options: a ) 10 % , b ) 10.5 % , c ) 6.8 % , d ) 12.5 % , e ) none
Rationale: "sol . let c . p . = rs . 100 . then , marked price = rs . 160 , s . p . = rs . 99 . ∴ discount % = [ 11 / 160 * 100 ] % = 6.8 % answer c"
Answer: c
Question (general): a number when divided by 243 gives a remainder 26 , what remainder will be obtained by dividing the same number 14 ?
Options: a ) 7 , b ) 6 , c ) 9 , d ) 2 , e ) 3
Rationale: "explanation : 243 + 26 = 269 / 14 = 3 ( remainder ) answer : e"
Answer: e
Question (general): a person saved $ 10 in buying an item on sale . if he spent $ 200 for the item , approximately how much percent he saved in the transaction ?
Options: a ) 8 % , b ) 10 % , c ) 2 % , d ) 5 % , e ) 6 %
Rationale: "actual price = 200 + 10 = $ 210 saving = 10 / 210 * 100 = 100 / 21 = 5 % approximately answer is d"
Answer: d
Question (general): the average age of 36 students in a group is 14 years . when teacher ' s age is included to it , the average increases by one . find out the teacher ' s age in years ?
Options: a ) 50 , b ) 49 , c ) 53 , d ) 54 , e ) 51
Rationale: "average age of 36 students in a group is 14 sum of the ages of 36 students = 36 × 14 when teacher ' s age is included to it , the average increases by one = > average = 15 sum of the ages of 36 students and the teacher = 37 × 15 hence teachers age = 37 × 15 - 36 × 14 = 37 × 15 - 14 ( 37 - 1 ) = 37 × 15 - 37 × 14 + 14 = 37 ( 15 - 14 ) + 14 = 37 + 14 = 51 answer is e ."
Answer: e
Question (physics): the amounts of time that three secretaries worked on a special project are in the ratio of 1 to 2 to 5 . if they worked a combined total of 128 hours , how many hours did the secretary who worked the longest spend on the project ?
Options: a ) 90 , b ) 70 , c ) 56 , d ) 16 , e ) 14
Rationale: "8 x = 128 = > x = 16 therefore the secretary who worked the longest spent 16 x 5 = 90 hours on the project option ( a )"
Answer: a
Question (physics): a is 1.5 times as fast as b . a alone can do the work in 20 days . if a and b working together , in how many days will the work be completed ?
Options: a ) 23 , b ) 22 , c ) 12 , d ) 24 , e ) 25
Rationale: a can finish 1 work in 20 days b can finish 1 / 1.5 work in 20 days - since a is 1.5 faster than b this means b can finish 1 work in 20 * 1.5 days = 30 days now using the awesome gmat formula when two machines work together they can finish the job in = ab / ( a + b ) = 20 * 30 / ( 20 + 30 ) = 20 * 30 / 50 = 12 days so answer is c
Answer: c
Question (gain): if a speaks the truth 65 % of the times , b speaks the truth 60 % of the times . what is the probability that they tell the truth at the same time
Options: a ) 0.39 , b ) 0.48 , c ) 0.41 , d ) 0.482 , e ) 0.411
Rationale: "explanation : probability that a speaks truth is 65 / 100 = 0.65 probability that b speaks truth is 60 / 100 = 0.6 since both a and b are independent of each other so probability of a intersection b is p ( a ) × p ( b ) = 0.65 × 0.6 = 0.39 answer : a"
Answer: a
Question (physics): a not - so - good clockmaker has four clocks on display in the window . clock # 1 loses 35 minutes every hour . clock # 2 gains 15 minutes every hour relative to clock # 1 ( i . e . , as clock # 1 moves from 12 : 00 to 1 : 00 , clock # 2 moves from 12 : 00 to 1 : 15 ) . clock # 3 loses 20 minutes every hour relative to clock # 2 . finally , clock # 4 gains 20 minutes every hour relative to clock # 3 . if the clockmaker resets all four clocks to the correct time at 12 noon , what time will clock # 4 display after 6 actual hours ( when it is actually 6 : 00 pm that same day ) ?
Options: a ) 5 : 00 , b ) 5 : 34 , c ) 5 : 42 , d ) 6 : 00 , e ) 6 : 24
Rationale: "c 1 loses 15 minutes every hour . so after 60 minutes have passed , c 1 displays that 60 - 15 = 45 minutes have passed . c 2 gains 15 minutes for every 60 minutes displayed on c 1 . thus , the time displayed on c 2 is 75 / 60 = 5 / 4 the time displayed on c 1 . so after 60 minutes have passed , c 2 displays the passing of ( 5 / 4 * 45 ) minutes . c 3 loses 20 minutes for every 60 minutes displayed on c 2 . thus , the time displayed on c 3 is 40 / 60 = 2 / 3 the time displayed on c 2 . so after 60 minutes have passed , c 3 displays the passing of ( 2 / 3 * 5 / 4 * 45 ) minutes . c 4 gains 20 minutes for every 60 minutes displayed on c 3 . thus , the time displayed on c 4 is 80 / 60 = 4 / 3 the time displayed on clock 3 . so after 60 minutes have passed , c 4 displays the passing of 4 / 3 * 2 / 3 * 5 / 4 * 45 = 50 minutes . c 4 loses 10 minutes every hour . in 6 hours , c 4 will lose 6 * 10 = 60 minutes = 1 hour . since the correct time after 6 hours will be 6 pm , c 4 will show a time of 6 - 1 = 6 : 24 pm . the correct answer is e ."
Answer: e
Question (general): if a = 1 , what is the value of – ( a ^ 2 + a ^ 3 + a ^ 4 + a ^ 5 ) ?
Options: a ) - 14 , b ) - 4 , c ) 0 , d ) 4 , e ) 14
Rationale: if a = 1 , then putting values in equation = - [ ( 1 ) ^ 2 + ( 1 ) ^ 3 + ( 1 ^ 4 ) + ( 1 ^ 5 ) ] = - [ 1 + 1 + 1 + 1 ] = - 4 answer = b = - 4
Answer: b
Question (gain): what profit percent is made by selling an article at a certain price , if by selling at 2 / 3 rd of that price , there would be a loss of 30 % ?
Options: a ) 20 % , b ) 29 % , c ) 70 % , d ) 27 % , e ) 5 %
Rationale: "sp 2 = 2 / 3 sp 1 cp = 100 sp 2 = 70 2 / 3 sp 1 = 70 sp 1 = 105 100 - - - 105 = > 5 % answer : e"
Answer: e
Question (general): an astronomer noted that a grouping of red giant stars had an average solar mass of 8 m each , and a grouping of white dwarf stars had an average solar mass of 1.5 m each . if the astronomer calculated the total solar mass of both groupings to be 49 m , what total number of red giant stars and white dwarf stars did the astronomer note ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: we can determine quickly that total number should range between 49 / 8 < = n < = 49 / 1.5 , so ans should be between 6 and 33 . now solving the expression 8 a + 1.5 b = 49 decreasing 49 in multiple of 8 and checking divisibility of that number by 1.5 . this way we get 2 red giants , 22 white dwarfs we get 49 , but 2 + 22 = 24 and 24 is not an option . next we get 5 red giants and 6 white dwarfs to get 49 , 5 * 8 + 6 * 1.5 = 49 hence total number is 5 + 6 = 11 ans b
Answer: b
Question (general): village a ’ s population is 300 greater than village b ' s population . if village b ’ s population were reduced by 600 people , then village a ’ s population would be 4 times as large as village b ' s population . what is village b ' s current population ?
Options: a ) 900 , b ) 1000 , c ) 1100 , d ) 1200 , e ) 1300
Rationale: a = b + 300 . a = 4 ( b - 600 ) . 4 ( b - 600 ) = b + 300 . 3 b = 2700 . b = 900 . the answer is a .
Answer: a
Question (general): the cost of 2 chairs and 3 tables is rs . 1500 . the cost of 3 chairs and 2 tables is rs . 1200 . the cost of each table is more than that of each chair by ?
Options: a ) 228 , b ) 287 , c ) 277 , d ) 188 , e ) 300
Rationale: "explanation : 2 c + 3 t = 1500 - - - ( 1 ) 3 c + 2 t = 1200 - - - ( 2 ) subtracting 2 nd from 1 st , we get - c + t = 300 = > t - c = 300 answer : e"
Answer: e
Question (gain): a sum amounts to rs . 4851 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 . 4400 , d ) s . 4800 , e ) s . 5800
Rationale: "ci = 4851 , r = 5 , n = 2 ci = p [ 1 + r / 100 ] ^ 2 = p [ 1 + 5 / 100 ] ^ 2 4851 = p [ 21 / 20 ] ^ 2 4851 [ 20 / 21 ] ^ 2 4400 answer : c"
Answer: c
Question (general): the average monthly salary of 10 employees in an organisation is rs . 1600 . if the manager ' s salary is added , then the average salary increases by rs . 100 . what is the manager ' s monthly salary ?
Options: a ) rs . 3601 , b ) rs . 3618 , c ) rs . 2700 , d ) rs . 3619 , e ) rs . 3610
Rationale: "manager ' s monthly salary = rs . ( 1700 * 11 - 1600 * 10 ) = rs . 2700 answer : c"
Answer: c
Question (gain): if a lends rs . 1200 to b at 10 % per annum and b lends the same sum to c at 18 % per annum then the gain of b in a period of 2 years is ?
Options: a ) 190 , b ) 188 , c ) 192 , d ) 145 , e ) 188
Rationale: "( 1200 * 8 * 2 ) / 100 = > 192 answer : c"
Answer: c
Question (general): if an integer n is to be chosen at random from the integers 1 to 96 , inclusive , what is the probability that n ( n + 1 ) ( n + 2 ) will be divisible by 6 ?
Options: a ) 2 / 3 , b ) 3 / 8 , c ) 1 / 2 , d ) 5 / 8 , e ) 3 / 4
Rationale: i get 5 / 8 as well 1 to 96 inclusive means we have 48 odd and 48 even integers e o e / 6 = integer , therefore we have 48 / 96 numbers divisible by 6 o e o / 6 = not integer we can not forget multiples of 6 from 1 to 96 we have 16 numbers that are multiple of 8 therefore , 48 / 96 + 16 / 96 = 64 / 96 = 2 / 3 answer : a
Answer: a
Question (general): how many integers from 0 to 50 inclusive have a remainder of 3 when divided by 5 ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "the numbers should be of the form 5 c + 3 . the minimum is 3 when c = 0 . the maximum is 48 when c = 9 . there are 10 such numbers . the answer is e ."
Answer: e
Question (general): 6 students wrote science exam . their average marks are 70 . 5 students got 65 , 75 , 55 , 72 and 69 marks respectively . therefore what is the marks of the sixth student ?
Options: a ) 84 , b ) 68 , c ) 85 , d ) 75 , e ) 42
Rationale: explanation total marks of 5 students = ( 65 + 75 + 55 + 72 + 69 ) = 336 required marks = [ ( 70 x 6 ) – 336 ] = ( 420 – 336 ) = 84 answer a
Answer: a
Question (physics): two trains of length 100 m and 200 m are 100 m apart . they start moving towards each other on parallel tracks , at speeds 54 kmph and 90 kmph . in how much time will the trains cross each other ?
Options: a ) 10 sec , b ) 11 sec , c ) 12 sec , d ) 60 / 7 sec , e ) 90 / 7 sec
Rationale: "a relative speed = ( 54 + 90 ) * 5 / 18 = 8 * 5 = 40 mps . the time required = d / s = ( 100 + 100 + 200 ) / 35 = 400 / 40 = 10 sec ."
Answer: a
Question (gain): a bowl was filled with 10 ounces of water , and 0.010 ounce of the water evaporated each day during a 50 - day period . what percent of the original amount of water evaporated during this period ?
Options: a ) 0.004 % , b ) 0.04 % , c ) 0.40 % , d ) 5 % , e ) 40 %
Rationale: "total amount of water evaporated each day during a 50 - day period = . 008 * 50 = . 010 * 100 / 2 = 1.0 / 2 = . 5 percent of the original amount of water evaporated during this period = ( . 5 / 10 ) * 100 % = 5 % answer d"
Answer: d
Question (other): what is the prime factors ’ number of 28 ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "prime factors ’ number , as i assume , for a number x = a ^ n * b ^ m * c ^ o * d ^ p . . . is = n + m + o + p . . . so , 28 = 2 ^ 2 * 7 ^ 1 prime factors ’ number will be 2 + 1 = 3 . hence , answer is b ."
Answer: b
Question (general): the sum of 7 th and 23 rd term of a . p . is equal to the sum of 8 th , 15 th and 13 th term . find the term which is 0
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: t 7 + t 23 = t 8 + t 15 + t 13 = > a + 6 d + a + 22 d = a + 7 d + a + 14 d + a + 12 d = > a + 5 d = 0 = > t 6 = 0 i . e . 6 th term is zero . answer : a
Answer: a
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 30 more than the number who did not , and if receipts for registration and lunch totaled $ 75,360 , how many people paid just for registration at the meeting ?
Options: a ) 700 , b ) 800 , c ) 600 , d ) 1,500 , e ) 1,800
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 30 more than the number who did not . that means , total number of people who registered and paid for lunch = 30 + 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 ( 30 + x ) = 2160 + 72 x now , total amount received was 75360 . thus , from the above data , 50 x + 2160 + 72 x = 75360 122 x = 75360 - 2160 122 x = 73200 x = 600 . hence the correct ans is c"
Answer: c
Question (geometry): what is the perimeter of a rectangular field whose diagonal is 5 m and length is 4 m ?
Options: a ) 20 m , b ) 15 m , c ) 14 m , d ) 10 m , e ) 25 m
Rationale: "sol : breadth of the rectangular plot is = 5 ^ 2 - 4 ^ 2 = 3 m therefore , perimeter of the rectangular plot = 2 ( 4 + 3 ) = 14 m c ) 14 m"
Answer: c
Question (general): the least number which must be subtracted from 709 to make it exactly divisible by 9 is :
Options: a ) a ) 2 , b ) b ) 3 , c ) c ) 7 , d ) d ) 5 , e ) e ) 6
Rationale: "on dividing 709 by 9 , we get remainder = 7 therefore , required number to be subtracted = 7 answer : c"
Answer: c
Question (general): let c be defined as the sum of all prime numbers between 0 and 35 . what is c / 3
Options: a ) 155 , b ) 129 , c ) 64.3 , d ) 47 , e ) 43
Rationale: prime numbers between 0 and 30 - 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 33 sum , c = 193 c / 3 = 64.3 answer c
Answer: c
Question (physics): the speed of a boat in still water in 22 km / hr and the rate of current is 5 km / hr . the distance travelled downstream in 24 minutes is :
Options: a ) 10.6 , b ) 10.2 , c ) 10.8 , d ) 10.4 , e ) 10.0
Rationale: speed downstream = ( 22 + 5 ) = 27 kmph time = 24 minutes = 24 / 60 hour = 2 / 5 hour distance travelled = time × speed = 2 / 5 × 27 = 10.8 km answer is c .
Answer: c
Question (physics): a boat having a length 3 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 ) 90 kg , e ) 110 kg
Rationale: "volume of water displaced = ( 3 x 3 x 0.01 ) m 3 = 0.09 m 3 . mass of man = volume of water displaced x density of water = ( 0.09 x 1000 ) kg = 90 kg . answer : d"
Answer: d
Question (gain): by selling 12 pencils for a rupee a man loses 20 % . how many for a rupee should he sell in order to gain 20 % ?
Options: a ) 8 , b ) 76 , c ) 17 , d ) 7 , e ) 77
Rationale: "80 % - - - 12 120 % - - - ? 80 / 120 * 12 = 8 answer : a"
Answer: a
Question (physics): due to construction , the speed limit along an 10 - mile section of highway is reduced from 55 miles per hour to 35 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) 6.24 , b ) 8 , c ) 10 , d ) 15 , e ) 24
Rationale: "old time in minutes to cross 10 miles stretch = 10 * 60 / 55 = 10 * 12 / 11 = 10.9 new time in minutes to cross 10 miles stretch = 10 * 60 / 35 = 10 * 12 / 7 = 17.14 time difference = 6.24 ans : a"
Answer: a