Cheukting/mathqa huggingface dataset:
Question (general): tough and tricky questions : word problems . a salesman ' s income consists of commission and base salary . his weekly income totals over the past 5 weeks have been $ 406 , $ 413 , $ 420 , $ 436 and $ 395 . what must his average ( arithmetic mean ) income over the next two weeks be to decrease his average weekly income to $ 400 over the 7 - week period ?
Options: a ) $ 350 , b ) $ 400 , c ) $ 365 , d ) $ 385 , e ) $ 375
Rationale: official solution : ( c ) first , we need to add up the wages over the past 5 weeks : $ 406 + $ 413 + $ 420 + $ 436 + $ 395 = $ 2070 . to average $ 400 over 7 weeks , the salesman would need to earn : $ 400 × 7 = $ 2800 . subtract $ 2070 from $ 2800 to determine how much he would need to earn , in total , over the next 2 weeks to average $ 400 for the 7 weeks : $ 2800 – $ 2070 = $ 730 . dividing $ 730 by 2 will give us the amount he needs to earn on average over the next 2 weeks : $ 730 / 2 = $ 365 . the correct answer is choice ( c ) .
Answer: c
Question (physics): a man walks at a rate of 10 mph . after every ten miles , he rests for 6 minutes . how much time does he take to walk 40 miles ?
Options: a ) 258 , b ) 318 , c ) 322 , d ) 324 , e ) 330
Rationale: "to cover 40 miles the man needs ( time ) = ( distance ) / ( rate ) = 40 / 10 = 4 hours = 240 minutes . he will also rest 3 times ( after 10 , 20 , and 30 miles ) , so total resting time = 3 * 6 = 18 minutes . total time = 240 + 18 = 258 minutes . answer : a ."
Answer: a
Question (probability): a bag contains 3 red , 6 yellow and 8 green balls . 3 balls are drawn randomly . what is the probability that the balls drawn contain balls of different colours ?
Options: a ) 2 / 7 , b ) 3 / 5 , c ) 3 / 11 , d ) 18 / 85 , e ) 7 / 16
Rationale: "total number of balls = 3 + 6 + 8 = 17 n ( s ) = 17 c 3 = 680 n ( e ) = 3 c 1 * 6 c 1 * 8 c 1 = 144 probability = 144 / 680 = 18 / 85 answer is d"
Answer: d
Question (physics): while working alone at their constant rates , computer x can process 240 files in 12 hours , and computer y can process 240 files in 4 hours . if all files processed by these computers are the same size , how many hours would it take the two computers , working at the same time at their respective constant rates , to process a total of 240 files ?
Options: a ) 2 , b ) 2.4 , c ) 2.7 , d ) 3 , e ) 3.5
Rationale: "both computers together process files at a rate of 240 / 12 + 240 / 4 = 20 + 60 = 80 files per hour . the time required to process 240 files is 240 / 80 = 3 hours the answer is d ."
Answer: d
Question (general): let s be the set of all positive integers that , when divided by 8 , have a remainder of 5 . what is the 72 th number in this set ?
Options: a ) 573 , b ) 608 , c ) 613 , d ) 616 , e ) 621
Rationale: the set s = { 5 , 13 , 21 , 29 , . . . . . . . . . . . . . . . . . . . . . } 1 st number = 8 * 0 + 5 = 5 2 nd number = 8 * 1 + 5 = 13 3 rd number = 8 * 2 + 5 = 21 72 th number = 8 * ( 72 - 1 ) + 5 = 573 answer = a
Answer: a
Question (general): how many positive integers will divide evenly into 190 ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 12 , e ) 16
Rationale: the question is asking how many factors 190 has . 190 = 2 * 5 * 19 the number of factors is 2 ^ 3 = 8 the answer is c .
Answer: c
Question (general): solution x is 10 percent alcohol by volume , and solution y is 30 percent alcohol by volume . how many milliliters of solution y must be added to 50 milliliters of solution x to create a solution that is 25 percent alcohol by volume ?
Options: a ) 150 , b ) 500 / 3 , c ) 400 , d ) 480 , e ) 600
Rationale: "we know that x is 10 % , y is 30 % and w . avg = 25 % . what does this mean with respect to w . avg technique ? w . avg is 1 portion away from y and 3 portion away from x so for every 1 portion of x we will have to add 3 portions of y . if x = 50 then y = 150 answer : a"
Answer: a
Question (general): in a certain quiz that consists of 10 questions , each question after the first is worth 4 points more than the preceding question . if the 10 questions on the quiz are worth a total of 400 points , how many points is the third question worth ?
Options: a ) 14 , b ) 18 , c ) 22 , d ) 26 , e ) 30
Rationale: "x x + 4 x + 8 x + 12 x + 16 x + 20 x + 24 x + 28 x + 32 x + 36 10 x + 180 = 400 10 x = 220 x = 22 3 rd question = x + 8 = 22 + 8 = 30 answer e"
Answer: e
Question (general): a pharmaceutical company received $ 5 million in royalties on the first $ 40 million in sales of and then $ 9 million in royalties on the next $ 210 million in sales . by approximately what percentage did the ratio of royalties to sales decrease from the first $ 40 million in sales to the next $ 210 million in sales ?
Options: a ) 8 % , b ) 15 % , c ) 45 % , d ) 52 % , e ) 66 %
Rationale: "( 9 / 210 ) / ( 5 / 40 ) = 12 / 35 = 34 % it means that 9 / 210 represents only 34 % . therefore a decrease of 66 % . answer e"
Answer: e
Question (physics): jane makes toy bears . when she works with an assistant , she makes 80 percent more bears per week and works 20 percent fewer hours each week . having an assistant increases jane ’ s output of toy bears per hour by what percent ?
Options: a ) 20 % , b ) 80 % , c ) 100 % , d ) 180 % , e ) 200 %
Rationale: "we can use fractional equivalents here to solve the problem 80 % = 4 / 5 ; this means that in 1 st case if she prepares 5 bears , in 2 nd case she prepares 9 bears 10 % = 1 / 10 ; this means that in 1 st case if she needs 10 hours , in 2 nd case she needs 9 hours now we come to productivity based on above fractional values the productivity in 1 st case is 0.5 bears / hour and in the 2 nd case it is 1 bear / hour hence the productivity is double with the assistant i . e . the increase in productivity is 180 % d"
Answer: d
Question (physics): the diameter of a garden roller is 1.4 m and it is 3 m long . how much area will it cover in 5 revolutions ? ( use ï € = 22 â  „ 7 )
Options: a ) 60 m 2 , b ) 64 m 2 , c ) 68 m 2 , d ) 66 m 2 , e ) none of these
Rationale: "required area covered in 5 revolutions = 5 ã — 2 ï € rh = 5 ã — 2 ã — 22 â  „ 7 ã — 0.7 ã — 3 = 66 m 2 answer d"
Answer: d
Question (gain): what will be the fraction of 8 %
Options: a ) 1 / 20 , b ) 1 / 50 , c ) 1 / 75 , d ) 2 / 25 , e ) none of these
Rationale: "explanation : 8 * 1 / 100 = 2 / 25 . option d"
Answer: d
Question (general): shipment - - - no . of defective chips / shipment - - - total chips in shipment s 1 - - - - - - - - - - - - - - - - - - - - - - 2 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 5000 s 2 - - - - - - - - - - - - - - - - - - - - - - 4 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 12000 s 3 - - - - - - - - - - - - - - - - - - - - - - 2 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 15000 s 4 - - - - - - - - - - - - - - - - - - - - - - 4 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 16000 a computer chip manufacturer expects the ratio of the number of defective chips to the total number of chips in all future shipments to equal the corresponding ratio for shipments s 1 , s 2 , s 3 , and s 4 combined , as shown in the table above . what ’ s the expected number of defective chips in a shipment of 60000 chips ?
Options: a ) 14 , b ) 20 , c ) 22 , d ) 24 , e ) 15
Rationale: for a total of 51000 chips ( adding s 1 , s 2 , s 3 , s 4 ) total number of defective chips is 17 ( ( adding defective chips of s 1 , s 2 , s 3 , s 4 ) so ratio is 12 / 48000 or 1 every 4000 chips . keeping this ratio constant for 60000 chips number of defective chips will be ( 1 / 4000 ) * 60000 = 15 e
Answer: e
Question (general): 3 / 4 of 1 / 2 of 2 / 5 of 5020 = ?
Options: a ) 392 , b ) 229 , c ) 753 , d ) 493 , e ) 540
Rationale: "c 753 ? = 5020 * ( 2 / 5 ) * ( 1 / 2 ) * ( 3 / 4 ) = 753"
Answer: c
Question (physics): a train running at a speed of 36 kmph crosses an electric pole in 12 seconds . in how much time will it cross a 360 m long platform ?
Options: a ) 19 , b ) 27 , c ) 29 , d ) 48 , e ) 28
Rationale: "let the length of the train be x m . when a train crosses an electric pole , the distance covered is its own length . so , x = 12 * 36 * 5 / 18 m = 120 m . time taken to cross the platform = ( 120 + 360 ) / 36 * 5 / 18 = 48 min . answer : d"
Answer: d
Question (general): an auto assembly plant performs 6 functions with each frame that arrives : add axles , add wheels to the axles , install the windshield to the frame , install the instrument panel , install the steering wheel , and install the interior seating . once those 6 tasks are performed , each car goes to a separate building for finishing touches . if these tasks can be arranged along a linear assembly line in any order , except that the axles must be installed before the wheels can be added , how many t ways can the assembly line be arranged ?
Options: a ) 120 , b ) 240 , c ) 360 , d ) 480 , e ) 720
Rationale: c ) 360 short way : there are 6 c ! ways to do the six tasks . half will have wheels before axles and half will have axles before wheels . so we want t = 6 c ! / 2 - > 720 / 2 = 360
Answer: c
Question (other): three numbers are in the ratio 1 : 4 : 6 and their h . c . f is 9 . the numbers are :
Options: a ) 1 , 4,6 , b ) 12 , 24,36 , c ) 10 , 20 , 30 , d ) 12 , 24 , 36 , e ) 9 , 36,54 .
Rationale: "let the required numbers be x , 4 x and 6 x . then , their h . c . f = x . so , x = 9 . the numbers are 9 , 36,54 . answer : e"
Answer: e
Question (general): the average marks of a class of 30 students is 30 and that of another class of 50 students is 60 . find the average marks of all the students ?
Options: a ) 52.5 , b ) 52.9 , c ) 52.1 , d ) 48.75 , e ) 42.5
Rationale: "sum of the marks for the class of 30 students = 30 * 30 = 900 sum of the marks for the class of 50 students = 50 * 60 = 3000 sum of the marks for the class of 80 students = 900 + 3000 = 3900 average marks of all the students = 3900 / 80 = 48.75 answer : d"
Answer: d
Question (probability): an urn contains 5 red , 6 blue and 8 green balls . 3 balls are randomly selected from the urn , find the probability that the drawn ball are 2 blue and 1 red ?
Options: a ) 25 / 323 , b ) 21 / 969 , c ) 28 / 989 , d ) 74 / 879 , e ) 23 / 589
Rationale: "sample space = no . of ways 3 balls were drawn from urn = 19 c 3 = 969 no . ways 2 blue balls and 1 red were drawn from bag = 6 c 2 * 5 c 1 = 75 probability = 75 / 969 = 25 / 323 ans - a"
Answer: a
Question (general): john purchased 1300 large bottles at $ 1.89 per bottle and 750 small bottles at $ 1.38 per bottle . what was the approximate average price paid per bottle ?
Options: a ) $ 1.63 , b ) $ 1.64 , c ) $ 1.68 , d ) $ 1.70 , e ) $ 1.76
Rationale: "( 1300 * 1.89 + 750 * 1.38 ) / ( 1300 + 750 ) = ~ 1.70 option ( d )"
Answer: d
Question (physics): two consultants can type up a report in 12.5 hours and edit it in 7.5 hours . if mary needs 30 hours to type the report and jim needs 12 hours to edit it alone , how many hours q will it take if jim types the report and mary edits it immediately after he is done ?
Options: a ) 41.4 , b ) 34.1 , c ) 13.4 , d ) 12.4 , e ) 10.8
Rationale: break down the problem into two pieces : typing and editing . mary needs 30 hours to type the report - - > mary ' s typing rate = 1 / 30 ( rate reciprocal of time ) ( point 1 in theory below ) ; mary and jim can type up a report in 12.5 and - - > 1 / 30 + 1 / x = 1 / 12.5 = 2 / 25 ( where x is the time needed for jim to type the report alone ) ( point 23 in theory below ) - - > x = 150 / 7 ; jim needs 12 hours to edit the report - - > jim ' s editing rate = 1 / 12 ; mary and jim can edit a report in 7.5 and - - > 1 / y + 1 / 12 = 1 / 7.5 = 2 / 15 ( where y is the time needed for mary to edit the report alone ) - - > y = 20 ; how many q hours will it take if jim types the report and mary edits it immediately after he is done - - > x + y = 150 / 7 + 20 = ~ 41.4 answer : a .
Answer: a
Question (physics): two men a and b start from place x walking at 4 ½ kmph and 5 ¾ kmph respectively . how many km apart they are at the end of 3 ½ hours if they are walking in the same direction ?
Options: a ) 4 3 / 6 , b ) 4 3 / 9 , c ) 4 3 / 8 , d ) 4 3 / 4 , e ) 4 3 / 1
Rationale: "rs = 5 3 / 4 - 4 1 / 2 = 1 1 / 4 t = 3 1 / 2 h . d = 5 / 4 * 7 / 2 = 35 / 8 = 4 3 / 8 km answer : c"
Answer: c
Question (general): if 2 ^ 4 , 3 ^ 3 , and 12 ^ 3 are factors of the product of 1,452 and w , where w is a positive integer , what is the smallest possible value of w ?
Options: a ) 198 , b ) 288 , c ) 432 , d ) 396 , e ) 484
Rationale: i will go with c ( pending elements to match is 2 ^ 2 * 3 ^ 2 * 12 ^ 1 = 432
Answer: c
Question (general): for all positive integers m and v , the expression m θ v represents the remainder when m is divided by v . what is the value of ( ( 94 θ 33 ) θ 17 ) - ( 96 θ ( 33 θ 17 ) ) ?
Options: a ) - 10 , b ) - 2 , c ) 8 , d ) 13 , e ) 17
Rationale: "( ( 94 θ 33 ) θ 17 ) the remainder of 98 divided by 33 is 28 ; the remainder of 28 divided by 17 is 11 ; ( 96 θ ( 33 θ 17 ) ) the remainder of 33 divided by 17 is 16 ; the remainder of 96 divided by 16 is 0 . 11 - 0 = 11 . answer : d ."
Answer: d
Question (general): a sports equipment store sold ping pong rackets for a total of $ 735 . if the average ( arithmetic mean ) price of a pair of rackets is $ 9.8 , how many pairs were sold ?
Options: a ) 50 , b ) 100 , c ) 490 , d ) 500 , e ) 75
Rationale: "average price for a pair of rackets = $ 9.8 total cost = $ 9.8 * x = $ 735 x = 75 pairs were sold . answer : e"
Answer: e
Question (other): john distributes his pencil among his 4 friends rose , mary , ranjan , and rohit in the ratio 1 / 3 : 1 / 3 : 1 / 4 : 1 / 5 . what is the minimum no . of pencils that the person should have ?
Options: a ) 45 , b ) 67 , c ) 70 , d ) 77 , e ) 98
Rationale: "rakesh : rahul : ranjan : rohit = 1 / 3 : 1 / 3 : 1 / 4 : 1 / 5 step 1 : at first we need to do is lcm of 3 , 3,4 and 5 is 60 . step 2 : then pencil are distributed in ratio among friends , rakesh = ( 1 / 3 x 60 ) = 20 . rahul = ( 1 / 3 x 60 ) = 20 . ranjan = ( 1 / 4 x 60 ) = 15 . rohit = ( 1 / 5 x 60 ) = 12 . step 3 : total number of pencils are ( 20 x + 20 x + 15 x + 12 x ) = 67 x . for minimum number of pencils x = 1 . the person should have atleast 67 pencils . b )"
Answer: b
Question (general): divide rs . 3250 among a , b and c so that a receives 1 / 5 as much as b and c together and b receives 2 / 3 as a and c together . b ' s share is ?
Options: a ) 6500 , b ) 3250 , c ) 1100 , d ) 1300 , e ) 1200
Rationale: "a + b + c = 3250 a = 1 / 5 ( b + c ) ; b = 2 / 3 ( a + c ) b / ( a + c ) = 2 / 3 b = 1 / 5 * 6500 = > 1300 answer : d"
Answer: d
Question (general): the mean of 50 observations is 200 . but later he found that there is decrements of 15 from each observations . what is the the updated mean is ?
Options: a ) 150 , b ) 185 , c ) 190 , d ) 210 , e ) 220
Rationale: "185 answer is b"
Answer: b
Question (physics): if the perimeter of a rectangular garden is 600 m , its length when its breadth is 150 m is ?
Options: a ) 150 m , b ) 899 m , c ) 200 m , d ) 166 m , e ) 187 m
Rationale: "2 ( l + 150 ) = 600 = > l = 150 m answer : a"
Answer: a
Question (physics): a train 110 m long is running with a speed of 60 km / hr . in what time will it pass a trolley that is running with a speed of 12 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 4.31 , b ) 6.75 , c ) 7.92 , d ) 5.5 , e ) 6.5
Rationale: speed of train relative to trolley = 60 + 12 = 72 km / hr . = 72 * 5 / 18 = 20 m / sec . time taken to pass the trolley = 110 * 1 / 20 = 5.5 sec . answer : d
Answer: d
Question (geometry): in a certain parallelogram the degree measure of one angle exceeds that of the other by 10 what is the degree measure of the smaller angle ?
Options: a ) 75 , b ) 80 , c ) 85 , d ) 90 , e ) 95
Rationale: "in a parallelogram opposite angles are equal and the angles at each side are supplementary to each other ( supplementary angles are two angles that add up to 180 ° ) . given : x + ( x + 10 ) = 180 - - > x = 85 . answer : c ."
Answer: c
Question (general): the average of 10 numbers was calculated as 18 . it is discovered later on that while calculating the average , one number , namely 66 , was incorrectly read as 26 . what is the correct average ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: "10 * 18 - 26 + 66 = 220 220 / 10 = 22 the answer is c ."
Answer: c
Question (general): each child has 5 crayons and 14 apples . if there are 10 children , how many crayons are there in total ?
Options: a ) 22 , b ) 65 , c ) 12 , d ) 36 , e ) 50
Rationale: 5 * 10 = 50 . answer is e .
Answer: e
Question (geometry): what is the area of square field whose side of length 7 m ?
Options: a ) 225 , b ) 662 , c ) 772 , d ) 882 , e ) 49
Rationale: "7 * 7 = 49 sq m answer : e"
Answer: e
Question (general): how many integers between 1 and 1050 are divisible by 10 , 25 , and 35 ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 3
Rationale: prime factorization of given numbers 10 = 2 * 5 25 = 5 ^ 2 35 = 5 * 7 lcm of the given numbers = 2 * 5 ^ 2 * 7 = 50 * 7 = 350 therefore , number of integers = 1050 / 350 = 3 answer : option e
Answer: e
Question (general): 78 , 64 , 48 , 30 10 , ( . . . )
Options: a ) - 12 number , b ) - 14 , c ) 2 , d ) 8 , e ) 6
Rationale: "explanation : 78 - 14 = 64 64 - 16 = 48 48 - 18 = 30 30 - 20 = 10 10 - 22 = - 12 answer : option a"
Answer: a
Question (gain): a cycle is bought for rs . 900 and sold for rs . 1440 , find the gain percent ?
Options: a ) 39 % , b ) 20 % , c ) 23 % , d ) 74 % , e ) 60 %
Rationale: "900 - - - - 540 100 - - - - ? = > 60 % answer : e"
Answer: e
Question (physics): a and b can finish a work in 7 days and 8 days respectively . if both do work one day and leave one day . and a start the work then in how much days work will finish ?
Options: a ) 52 / 7 , b ) 8 , c ) 14 / 2 , d ) 6 , e ) 43 / 6
Rationale: ( a + b ) work in 2 days = [ 1 / 7 + 1 / 8 ] = 15 / 56 ( a + b ) work in 6 days = 45 / 56 now , the turn of a , work of a in 1 day = 1 / 7 . till now completed work = [ 45 / 56 + 1 / 7 ] = 53 / 56 , remaining work = [ 1 - 53 / 56 ] = 3 / 56 now , turn of b , 1 / 8 work b do in 1 day so , 3 / 56 part of work b do = [ 8 * 3 / 56 ] = 3 / 7 days total time taken = 6 + 1 + 3 / 7 = 52 / 7 days answer a
Answer: a
Question (physics): 5 pumps , working 9 hours a day , can empty a tank in 3 days . how many hours a day should 6 pumps work in order to empty the tank in 1 day ?
Options: a ) 20 hours , b ) 22.5 hours , c ) 23 hours , d ) 23.5 hours , e ) 24 hours
Rationale: "let the required hours needed be x more pumps , less hours ( indirect proportion ) more days , less hours ( indirect proportion ) hence we can write as ( pumps ) 5 : 6 } : : x : 9 ( days ) 3 : 1 = > 5 * 3 * 9 = 6 * 1 * x = > x = 45 / 2 = > 22.5 answer : b"
Answer: b
Question (general): if the average ( arithmetic mean ) of ( 2 a + 16 ) and ( 3 a - 8 ) is 79 , what is the value of a ?
Options: a ) 25 , b ) 30 , c ) 28 , d ) 36 , e ) 42
Rationale: "( ( 2 a + 16 ) + ( 3 a - 8 ) ) / 2 = ( 5 a + 8 ) / 2 = 79 a = 30 the answer is b ."
Answer: b
Question (general): we run a business that rents out canoes and kayaks . a canoe rental costs $ 12 per day , and a kayak rental costs $ 18 dollars per day . one day , our business rents out 3 canoes for every 2 kayaks and receives a total of $ 504 in revenue . how many more canoes than kayaks were rented out ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "let x be the number of canoes . then 2 x / 3 is the number of kayaks . 12 x + ( 2 x / 3 ) * 18 = 504 12 x + 12 x = 504 24 x = 504 x = 21 ( canoes ) 2 x / 3 = 14 ( kayaks ) there were 21 - 14 = 7 more canoes rented out . the answer is c ."
Answer: c
Question (general): the average of runs of a cricket player of 20 innings was 32 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?
Options: a ) 96 , b ) 106 , c ) 122 , d ) 116 , e ) 122
Rationale: "average = total runs / no . of innings = 32 so , total = average x no . of innings = 32 * 20 = 640 now increase in avg = 4 runs . so , new avg = 32 + 4 = 36 runs total runs = new avg x new no . of innings = 36 * 21 = 756 runs made in the 11 th inning = 756 - 640 = 116 answer : d"
Answer: d
Question (general): a cube with its sides numbered 1 through 6 is rolled twice , first landing on a and then landing on b . if any roll of the cube yields an equal chance of landing on any of the numbers 1 through 6 , what is the probability r that a + b is prime ?
Options: a ) 0 , b ) 1 / 12 , c ) 5 / 12 , d ) 7 / 18 , e ) 4 / 9
Rationale: total # of outcomes is 6 * 6 = 36 ; favorable outcomes : a - b - - > prime 1 - 1 - - > 2 ; 1 - 2 - - > 3 ; 2 - 1 - - > 3 ; 1 - 4 - - > 5 ; 4 - 1 - - > 5 ; 2 - 3 - - > 5 ; 3 - 2 - - > 5 ; 1 - 6 - - > 7 ; 6 - 1 - - > 7 ; 2 - 5 - - > 7 ; 5 - 2 - - > 7 ; 3 - 4 - - > 7 ; 4 - 3 - - > 7 ; 6 - 5 - - > 11 ; 5 - 6 - - > 11 . total of 15 favorable outcomes r = 15 / 36 . answer : c .
Answer: c
Question (gain): a and b started a business in partnership investing rs . 20,000 and rs . 15,000 respectively . after 6 months , c joined them with rs . 20,000 . whatwill be b ' s share in total profit of rs . 22,000 earned at the end of 2 years from the startingof the business ?
Options: a ) s . 5,000 , b ) s . 5,500 , c ) s . 5,700 , d ) s . 6,600 , e ) s . 7,500
Rationale: "a : b : c = ( 20,000 x 24 ) : ( 15,000 x 24 ) : ( 20,000 x 18 ) = 4 : 3 : 3 . b ' s share = rs . 22000 x 3 / 10 = rs . 6,600 . d"
Answer: d
Question (general): find the value for x from below equation : x / 3 = - 6 ?
Options: a ) - 16 , b ) 11 , c ) - 12 , d ) - 18 , e ) 14
Rationale: "1 . multiply both sides by 3 : x * 3 / 3 = - 6 / 3 simplify both sides : x = - 18 d"
Answer: d
Question (physics): x can do a piece of work in 8 hours . y and z together can do it in 6 hours , while x and z together can do it in 4 hours . how long will y alone take to do it ?
Options: a ) 24 hours , b ) 20 hours , c ) 34 hours , d ) 12 hours , e ) 10 hours
Rationale: x ' s 1 hour work = 1 / 8 ( y + z ) ' s 1 hour work = 1 / 6 ( x + z ) ' s 1 hour work = 1 / 4 ( x + y + z ) ' s 1 hour work = ( 1 / 8 + 1 / 6 ) = 7 / 24 y ' s 1 hour ' s work = ( 7 / 24 - 1 / 4 ) = 1 / 24 y alone will take 24 hours to do the work . correct option is a
Answer: a
Question (gain): a , b and c invested rs . 6300 , rs . 4200 and rs . 10500 respectively , in a partnership business . find the share of a in profit of rs . 13000 after a year ?
Options: a ) 3630 , b ) 3900 , c ) 8828 , d ) 2387 , e ) 2813
Rationale: "6300 : 4200 : 10500 3 : 2 : 5 3 / 10 * 13000 = 3900 answer : b"
Answer: b
Question (physics): if two students starting from same point , walking in the opposite directions with 6 km / hr and 9 km / hr as average speeds respectively . then the distance between them after 4 hours is ?
Options: a ) 65 km , b ) 55 km , c ) 15 km , d ) 60 km , e ) 75 km
Rationale: explanation : total distance = distance traveled by person a + distance traveled by person b = ( 6 × 4 ) + ( 9 × 4 ) = 24 + 36 = 60 km answer : d
Answer: d
Question (general): dacid obtained 51 , 65 , 82 , 67 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 29 , b ) 38 , c ) 39 , d ) 70 , e ) 75
Rationale: "average = ( 51 + 65 + 82 + 67 + 85 ) / 5 = 70 answer : d"
Answer: d
Question (general): in a mixture of 45 litres the ratio of milk to water is 4 : 1 . additional 23 litres of water is added to the mixture . find the ratio of milk to water in the resulting mixture .
Options: a ) 9 / 8 , b ) 4 / 1 , c ) 2 / 3 , d ) 3 / 4 , e ) 3 / 2
Rationale: "given that milk / water = 4 x / x and 4 x + x = 45 - - > x = 9 . thus milk = 4 x = 36 liters and water = x = 9 liters . new ratio = 36 / ( 9 + 23 ) = 36 / 32 = 9 / 8 . answer : a ."
Answer: a