Cheukting/mathqa huggingface dataset:
Question (gain): a sum was put at simple interest at a certain rate for 10 years . had it been put at 5 % higher rate , it would have fetched rs . 200 more . what was the sum ?
Options: a ) s . 550 , b ) s . 1000 , c ) s . 600 , d ) s . 200 , e ) s . 400
Rationale: "at 5 % more rate , the increase in s . i for 10 years = rs . 200 ( given ) so , at 5 % more rate , the increase in si for 1 year = 200 / 10 = rs . 20 / - i . e . rs . 20 is 5 % of the invested sum so , 1 % of the invested sum = 20 / 5 therefore , the invested sum = 20 × 100 / 5 = rs . 400 answer : e"
Answer: e
Question (general): the sum of a certain number and its reciprocal is equal to 29 . what is the absolute value of the difference of this number and its reciprocal ?
Options: a ) 22 , b ) 12 , c ) 03 , d ) 04 , e ) 21
Rationale: x + 1 / x = 2.9 x - 1 / x = y add two equations 2 x = 2.9 + y so when 2.9 and correct answer choice are added , the final digit should be even so eliminate a , b and d substitute y = 0.3 x = 1.6 1.6 + 1 / 1.6 is not equal to 2.9 substitute y = 2.1 so x = 2.5 2.5 + 1 / 2.5 = 2.9 answer : e
Answer: e
Question (general): what is the total number of positive integers that are less than 500 and that have no positive factor in common with 500 other than 1 ?
Options: a ) 50 , b ) 100 , c ) 200 , d ) 300 , e ) 400
Rationale: since 500 = 2 ^ 2 * 5 ^ 3 then a number can not have 2 and / or 5 as a factor . the odd numbers do not have 2 as a factor and there are 250 odd numbers from 1 to 500 . we then need to eliminate the 50 numbers that end with 5 , that is 5 , 15 , 25 , . . . , 495 . there are a total of 250 - 50 = 200 such numbers between 1 and 500 . the answer is c .
Answer: c
Question (physics): a cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 8 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
Options: a ) 7.5 , b ) 7.4 , c ) 7.9 , d ) 7.2 , e ) 8.0
Rationale: "net part filled in 1 hour = ( 1 / 4 - 1 / 9 ) = 1 / 8 the cistern will be filled in 8 / 1 hrs i . e . , 8 hrs . answer : e"
Answer: e
Question (general): in a simultaneous throw of pair of dice . find the probability of getting the total more than 7 .
Options: a ) 5 / 19 , b ) 5 / 12 , c ) 5 / 28 , d ) 5 / 10 , e ) 5 / 11
Rationale: "explanation : here n ( s ) = ( 6 x 6 ) = 36 let e = event of getting a total more than 7 = { ( 2,6 ) , ( 3,5 ) , ( 3,6 ) , ( 4,4 ) , ( 4,5 ) , ( 4,6 ) , ( 5,3 ) , ( 5,4 ) , ( 5,5 ) , ( 5,6 ) , ( 6,2 ) , ( 6,3 ) , ( 6,4 ) , ( 6,5 ) , ( 6,6 ) } therefore , p ( e ) = n ( e ) / n ( s ) = 15 / 36 = 5 / 12 . answer : b ) 5 / 12"
Answer: b
Question (general): krishan and nandan jointly started a business . krishan invested 6 times as nandan did and invested his money for double time as compared to nandan . nandan earned rs . 6000 . if the gain is proportional to the money invested and the time for which the money is invested then the total gain was ?
Options: a ) rs . 78000 , b ) rs . 48000 , c ) rs . 6000 , d ) rs . 82000 , e ) rs . 32000
Rationale: 6 : 1 2 : 1 - - - - - - 12 : 1 1 - - - - - 6000 13 - - - - - ? = > rs . 78,000 answer : a
Answer: a
Question (general): consider the word rotor . whichever way you read it , from left to right or from right to left , you get the same word . such a word is known as palindrome . find the maximum possible number of 5 - letter palindromes
Options: a ) 1700 , b ) 7570 , c ) 1576 , d ) 17576 , e ) 500
Rationale: the first letter from the right can be chosen in 26 ways because there are 26 alphabets . having chosen this , the second letter can be chosen in 26 ways . = > the first two letters can be chosen in 26 ã — 26 = 67626 ã — 26 = 676 ways having chosen the first two letters , the third letter can be chosen in 26 ways . = > all the three letters can be chosen in 676 ã — 26 = 17576676 ã — 26 = 17576 ways . it implies that the maximum possible number of five letter palindromes is 17576 because the fourth letter is the same as the second letter and the fifth letter is the same as the first letter . answer d
Answer: d
Question (gain): a glass was filled with 25 ounces of water , and 0.04 ounce of the water evaporated each day during a 10 - day period . what percent of the original amount of water evaporated during this period ?
Options: a ) 0.004 % , b ) 0.04 % , c ) 0.4 % , d ) 1.6 % , e ) 20 %
Rationale: "in 10 days 10 * 0.04 = 0.4 ounces of water evaporated , which is 0.4 / 25 â ˆ — 100 = 1.6 of the original amount of water . answer : d ."
Answer: d
Question (physics): if teena is driving at 55 miles per hour and is currently 7.5 miles behind joe , who is driving at 40 miles per hour in the same direction then in how many minutes will teena be 37.5 miles ahead of joe ?
Options: a ) 15 , b ) 60 , c ) 180 , d ) 90 , e ) 105
Rationale: "this type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30 - 40 seconds for a difficult one . teena covers 55 miles in 60 mins . joe covers 40 miles in 60 mins so teena gains 15 miles every 60 mins teena need to cover 7.5 + 37.5 miles . teena can cover 7.5 miles in 30 mins teena will cover 37.5 miles in 150 mins so answer 30 + 150 = 180 mins . ( answer c )"
Answer: c
Question (gain): vijay lent out an amount rs . 10000 into two parts , one at 8 % p . a . and the remaining at 10 % p . a . both on simple interest . at the end of the year he received rs . 850 as total interest . what was the amount he lent out at 8 % pa . a ?
Options: a ) rs . 15000 , b ) rs . 6000 , c ) rs . 25000 , d ) rs . 10000 , e ) rs . 18000
Rationale: let the amount lent out at 8 % p . a . be rs . a = > ( a * 8 ) / 100 + [ ( 10000 - a ) * 10 ] / 100 = 850 = > a = rs . 15000 . answer : a
Answer: a
Question (general): find k if 64 ÷ k = 4 .
Options: a ) 8 , b ) 16 , c ) 24 , d ) 36 , e ) 40
Rationale: "since 64 ÷ k = 4 and 64 ÷ 16 = 4 , then k = 16 correct answer b"
Answer: b
Question (geometry): what is the area of square field whose side of length 12 m ?
Options: a ) 225 sq m , b ) 144 sq m , c ) 586 sq m , d ) 287 sq m , e ) 296 sq m
Rationale: "12 * 12 = 144 sq m answer : b"
Answer: b
Question (general): the mean of 50 observations is 200 . but later he found that there is decrements of 9 from each observations . what is the the updated mean is ?
Options: a ) 165 , b ) 185 , c ) 190 , d ) 191 , e ) 199
Rationale: "191 answer is d"
Answer: d
Question (general): a couple spent $ 184.80 in total while dining out and paid this amount using a credit card . the $ 184.80 figure included a 20 percent tip which was paid on top of the price which already included a sales tax of 10 percent on top of the price of the food . what was the actual price of the food before tax and tip ?
Options: a ) $ 124 , b ) $ 132 , c ) $ 140 , d ) $ 148 , e ) $ 156
Rationale: "let the price of the meal be x . after a 10 % sales tax addition , the price is 1.1 * x after a 20 % tip on this amount , the total is 1.2 * 1.1 * x = 1.32 x 1.32 x = 184.80 x = 140 the correct answer is c ."
Answer: c
Question (general): for any integer k greater than 1 , the symbol k * denotes the product of all the fractions of the form 1 / t , where t is an integer between 1 and k , inclusive . what is the value of 5 * / 6 * ?
Options: a ) 5 , b ) 5 / 4 , c ) 4 / 5 , d ) 1 / 4 , e ) 1 / 5
Rationale: "when dealing with ' symbolism ' questions , it often helps to ' play with ' the symbol for a few moments before you attempt to answer the question that ' s asked . by understanding how the symbol ' works ' , you should be able to do the latter calculations faster . here , we ' re told that k * is the product of all the fractions of the form 1 / t , where t is an integer between 1 and k , inclusive . based on this definition . . . . if . . . . k = 2 k * = ( 1 / 1 ) ( 1 / 2 ) = 1 / 2 if . . . . k = 3 k * = ( 1 / 1 ) ( 1 / 2 ) ( 1 / 3 ) = 1 / 6 we ' re asked to find the value of 5 * / 4 * now that we know how the symbol ' works ' , solving this problem should n ' t be too difficult . you can actually choose to do the math in a couple of different ways . . . . 5 * = ( 1 / 1 ) ( 1 / 2 ) ( 1 / 3 ) ( 1 / 4 ) ( 1 / 5 ) do n ' t calculate this just yet though . . . . since we ' re dividing by 4 * , many of those fractions will ' cancel out . ' 4 * = ( 1 / 1 ) ( 1 / 2 ) ( 1 / 3 ) ( 1 / 4 ) we ' re looking for the value of : ( 1 / 1 ) ( 1 / 2 ) ( 1 / 3 ) ( 1 / 4 ) ( 1 / 5 ) / ( 1 / 1 ) ( 1 / 2 ) ( 1 / 3 ) ( 1 / 4 ) since the first four fraction in the numerator and denominator cancel out , we ' re left with just one fraction : 1 / 4 d"
Answer: d
Question (gain): running at the same rate , 8 identical machines can produce 560 paperclips a minute . at this rate , how many paperclips could 30 machines produce in 6 minutes ?
Options: a ) 1344 , b ) 3360 , c ) 8400 , d ) 12600 , e ) 67200
Rationale: "8 machines produce 560 in 1 min 8 machines produce 560 * 6 in 6 min 30 machine produce 560 * 6 * ( 30 / 8 ) in 6 minutes 560 * 6 * 30 / 8 = 12600 answer is d ."
Answer: d
Question (physics): abel can complete a work in 10 days , ben in 12 days and carla in 15 days . all of them began the work together , but abel had to leave after 2 days and ben 5 days before the completion of the work . how long did the work last ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 8 1 / 9 , e ) 10
Rationale: "abel in the 2 days that he worked completed 1 / 5 of the job = 4 / 5 remains then if ben had to leave 5 days before the completion , this means that carla had to work alone for these 5 days in which she completed 1 / 3 of the job . now together , ben and carla completed the job in ( 1 / 12 + 1 / 15 ) ( t ) = 7 / 15 3 / 20 ( t ) = 7 / 15 - - - > t = 3 1 / 9 therefore , these 3 1 / 9 days worked plus the 5 days that carla had to work by herself add to 8 1 / 9 days answer : d"
Answer: d
Question (physics): a man can do a piece of work in 5 days , but with the help of his son , he can do it in 3 days . in what time can the son do it alone ?
Options: a ) 13 / 2 , b ) 7 , c ) 15 / 2 , d ) 8 , e ) 9
Rationale: "son ' s 1 day ' s work = ( 1 / 3 ) - ( 1 / 5 ) = 2 / 5 the son alone can do the work in 15 / 2 days answer is c"
Answer: c
Question (physics): annika hikes at a constant rate of 10 minutes per kilometer . she has hiked 2.75 kilometers east from the start of a hiking trail when she realizes that she has to be back at the start of the trail in 45 minutes . if annika continues east , then turns around and retraces her path to reach the start of the trail in exactly 45 minutes , for how many kilometers total did she hike east ?
Options: a ) 3.625 , b ) 3.5 , c ) 4 , d ) 4.5 , e ) 5
Rationale: "set up two r x t = d cases . 1 . 1 / 10 km / min x t = 2.75 from which t = 27.5 mins . we know total journey time now is 45 + 27.5 = 72.5 the rate is the same ie 1 / 10 km / min . set up second r x t = d case . 1 / 10 km / min x 72.5 = 7.25 km now the total journey would be halved as distance would be same in each direction . 7.25 / 2 = 3.625 . a ."
Answer: a
Question (general): the average of 10 numbers is calculated as 20 . it is discovered later on that while calculating the average , one number namely 36 was wrongly read as 26 . the correct average is ?
Options: a ) 12 , b ) 26 , c ) 16 , d ) 97 , e ) 20
Rationale: "10 * 20 + 36 – 26 = 200 / 10 = 20 answer : e"
Answer: e
Question (physics): two trains 161 meters and 165 meters in length respectively are running in opposite directions , one at the rate of 80 km and the other at the rate of 65 kmph . in what time will they be completely clear of each other from the moment they meet ?
Options: a ) 6.18 , b ) 7.12 , c ) 7.1 , d ) 8.09 , e ) 8.11
Rationale: "t = ( 161 + 165 ) / ( 80 + 65 ) * 18 / 5 t = 8.09 answer : d"
Answer: d
Question (gain): there is 60 % increase in an amount in 6 years at s . i . what will be the c . i . of rs . 12,000 after 3 years at the same rate ?
Options: a ) rs . 3932 , b ) rs . 3972 , c ) rs . 3372 , d ) rs . 3942 , e ) rs . 3772
Rationale: "explanation : let p = rs . 100 . then , s . i . rs . 60 and t = 6 years . r = ( 100 * 60 ) / ( 100 * 6 ) = 10 % p . a . now , p = rs . 12000 , t = 3 years and r = 10 % p . a . c . i . = [ 12000 * { ( 1 + 10 / 100 ) 3 - 1 } ] = 12000 * 331 / 1000 = rs . 3972 answer : option c"
Answer: c
Question (general): in a mixed college 160 students are there in one class . out of this 160 students 1 / 2 students are girls . how many boys are there ?
Options: a ) a ) 40 , b ) b ) 60 , c ) c ) 80 , d ) d ) 120 , e ) e ) 140
Rationale: "total number of students : 160 total girls : 160 * 1 / 2 = 80 total boys : 160 - 80 = 80 answer is c"
Answer: c
Question (general): the average weight of 8 person ' s increases by 4.2 kg when a new person comes in place of one of them weighing 65 kg . what is the weight of the new person ?
Options: a ) 75 kg , b ) 50 kg , c ) 85 kg , d ) 80 kg , e ) 98.6 kg
Rationale: "explanation : total increase in weight = 8 ã — 4.2 = 33.6 if x is the weight of the new person , total increase in weight = x â ˆ ’ 65 = > 33.6 = x - 65 = > x = 33.6 + 65 = 98.6 answer : option e"
Answer: e
Question (physics): on sunday morning , pugsley and wednesday are trading pet spiders . if pugsley were to give wednesday two of his spiders , wednesday would then have 9 times as many spiders as pugsley does . but , if wednesday were to give pugsley 6 of her spiders , pugsley would now have 6 fewer spiders than wednesday had before they traded . how many pet spiders does pugsley have before the trading game commences ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 20
Rationale: if pugsley were to give wednesday two of his spiders , wednesday would then have nine times as many spiders as pugsley does : ( w + 2 ) = 9 ( p - 2 ) if wednesday were to give pugsley six of her spiders , pugsley would now have six fewer spiders than wednesday had before they traded : p + 6 = w - 6 solving gives p = 4 and w = 16 . answer : a .
Answer: a
Question (general): rates for having a manuscript typed at a certain typing service are $ 10 per page for the first time a page is typed and $ 5 per page each time a page is revised . if a certain manuscript has 100 pages , of which 30 were revised only once , 20 were revised twice , and the rest required no revisions , what was the total cost of having the manuscript typed ?
Options: a ) $ 1250 , b ) $ 1350 , c ) $ 1150 , d ) $ 1360 , e ) $ 1370
Rationale: "50 pages typed 1 x 30 pages typed 2 x ( original + one revision ) 20 pages typed 3 x ( original + two revisions ) 50 ( 10 ) + 30 ( 10 + 5 ) + 20 ( 10 + 5 + 5 ) = 500 + 450 + 400 = 1350 answer - b"
Answer: b
Question (gain): shekhar started a business investing rs . 25,000 in 1999 . in 2000 , he invested an additional amount of rs . 10,000 and rajeev joined him with an amount of rs . 35,000 . in 2001 , shekhar invested another additional amount of rs . 10,000 and jatin joined them with an amount of rs . 35,000 . what will be rajeev ’ s share in the profit of rs . 1 , 50,000 earned at the end of 3 years from the start of the business in 1999 ? .
Options: a ) rs . 10000 , b ) rs . 20000 , c ) rs . 30000 , d ) rs . 40000 , e ) rs . 50000
Rationale: shekhar : rajeev : jatin = ( 25000 x 12 + 35000 x 12 + 45000 x 12 ) : ( 35000 x 24 ) : ( 35000 x 12 ) = 1260000 : 840000 : 420000 = 3 : 2 : 1 . rajeev ’ s share = rs . ( 150000 × 2 / 6 ) = rs . 50000 answer e
Answer: e
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 $ 74 . if $ 2,000 is the total amount invested , how much is invested at 8 percent ?
Options: a ) $ 600 , b ) $ 700 , c ) $ 800 , d ) $ 900 , e ) $ 1000
Rationale: "0.1 x = 0.08 ( 2000 - x ) + 74 0.18 x = 234 x = 1300 then the amount invested at 8 % is $ 2000 - $ 1300 = $ 700 the answer is b ."
Answer: b
Question (general): at the opening of a trading day at a certain stock exchange , the price per share of stock k was $ 28 . if the price per share of stock k was $ 29 at the closing of the day , what was the percent increase in the price per share of stock k for that day ?
Options: a ) 3.57 % , b ) 5.9 % , c ) 11.1 % , d ) 12.5 % , e ) 23.6 %
Rationale: "opening = 28 closing = 29 rise in price = 1 so , percent increase = 1 / 28 * 100 = 3.57 answer : a"
Answer: a
Question (gain): the population of a town is 20000 . it increases annually at the rate of 20 % p . a . what will be its population after 2 years ?
Options: a ) 24440 , b ) 24800 , c ) 28400 , d ) 28800 , e ) 28600
Rationale: "explanation : formula : ( after = 100 denominator ago = 100 numerator ) 20000 * 120 / 100 * 120 / 100 = 120 * 120 * 2 = 28800 answer : option d"
Answer: d
Question (general): bookman purchased 55 copies of a new book released recently , 10 of which are hardback and sold for $ 20 each , and rest are paperback and sold for $ 10 each . if 14 copies were sold and the total value of the remaining books was 360 , how many paperback copies were sold ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 19 , e ) 16
Rationale: the bookman had 10 hardback ad 55 - 10 = 45 paperback copies ; 14 copies were sold , hence 55 - 14 = 41 copies were left . let # of paperback copies left be p then 10 p + 20 ( 41 - p ) = 560 - - > 10 p = 260 - - > p = 26 # of paperback copies sold is 45 - 26 = 19 answer : d
Answer: d
Question (general): in a company with 48 employees , some part - time and some full - time , exactly ( 1 / 3 ) of the part - time employees and ( 1 / 4 ) of the full - time employees take the subway to work . what is the greatest possible number r of employees who take the subway to work ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: "p / 3 + f / 4 = p / 3 + ( 48 - p ) / 4 = 12 + p / 2 p / 3 + f / 3 = ( p + f ) / 3 = 48 / 3 = 16 p / 4 + f / 4 = 12 p / 3 + f / 3 > p / 3 + f / 4 > p / 4 + f / 4 - - > 16 > 12 + p / 12 > 12 greatest possible r : 12 + p / 12 = 15 - - > p = 36 ( integer - - > good ) 15 or d is the answer"
Answer: d
Question (geometry): in an electric circuit , three resistors with resistances 2 ohms , 5 ohms and 6 ohms are connected in parallel . in this case , if r is the combined resistance of these three resistors , then the reciprocal of r is equal to the sum of the reciprocals resistors . what is r value ?
Options: a ) 13 / 15 ohms
b ) 15 / 13 ohms
c ) 5 / 8 ohms
d ) 3 / 7 ohms
e ) 45 / 18 ohms
Rationale: the wording is a bit confusing , though basically we are told that 1 / r = 1 / 2 + 1 / 5 + 1 / 6 , from which it follows that r = 13 / 15 ohms option : a
Answer: a
Question (physics): if the weight of 13 meters long rod is 23.4 kg . what is the weight of 6 meters long rod ?
Options: a ) 7.2 kg . , b ) 10.8 kg . , c ) 12.4 kg . , d ) 18.0 kg , e ) none
Rationale: "answer ∵ weight of 13 m long rod = 23.4 kg ∴ weight of 1 m long rod = 23.4 / 13 kg ∴ weight of 6 m long rod = 23.4 x 6 / 13 = 10.8 kg option : b"
Answer: b
Question (gain): if the simple interest on a certain sum of money for 7 years is one – fifth of the sum , then the rate of interest per annum is
Options: a ) 4 % , b ) 2.50 % , c ) 6.20 % , d ) 5 % , e ) 2.85 %
Rationale: "explanation : let the principal ( p ) be x then , simple interest ( si ) = x / 5 time ( t ) = 7 years rate of interest per annum ( r ) = ( 100 × si ) / pt = ( 100 × ( x / 5 ) / ( x × 7 ) = 20 / 7 = 2.85 % answer : option e"
Answer: e
Question (geometry): in may , the grounds keeper at spring lake golf club built a circular green with an area of 64 π square feet . in august , he doubled the distance from the center of the green to the edge of the green . what is the total area of the renovated green ?
Options: a ) 100 pi , b ) 144 pi , c ) 196 pi , d ) 256 pi , e ) 78
Rationale: "area of circle 64 pi sq feet = pi r ^ 2 therefore r = 8 now green radi doubled i . e r = 16 area = 256 pi d"
Answer: d
Question (general): how many positive integers less than 60 are equal to the product of a positive multiple of 5 and an even number ?
Options: a ) 4 , b ) 5 , c ) 9 , d ) 10 , e ) 11
Rationale: "number of positive multiples of 5 less than 60 = 11 5 * 1 = 5 5 * 2 = 10 5 * 3 = 15 5 * 4 = 20 5 * 5 = 25 5 * 6 = 30 5 * 7 = 35 5 * 8 = 40 5 * 9 = 45 5 * 10 = 50 5 * 11 = 55 only 5 of the above are a product of a positive multiple of 5 and an even number - 10 , 20,30 , 40,50 answer b"
Answer: b
Question (general): alex has to take a quiz , which has 10 true false - type question each carry 1 mark . what is the probability that alex ' s can score more than 8 mark in the quiz . given that he decides to guess randomly on the quiz .
Options: a ) 12 / 1024 , b ) 11 / 1024 , c ) 11 / 256 , d ) 12 / 256 , e ) 14 / 256
Rationale: each question has 2 options ( true or false ) . total number of ways of answering all 10 questions = ( 2 ) 10 ( 2 ) 10 more than 8 correct means either 9 correct or all correct . number of ways such that 9 correct = 10 ! / 9 ! = 10 number of ways of all correct = 1 therefore , probability of more than 8 correct = 11 / ( 2 ) 1011 / ( 2 ) 10 = 11 / 1024 answer : b
Answer: b
Question (general): if x and y are the two digits of the number 653 xy such that this number is divisible by 80 , then x + y = ?
Options: a ) 6 , b ) 4 , c ) 8 , d ) 8 , e ) none of these
Rationale: "80 = 2 x 5 x 8 since 653 xy is divisible by 2 and 5 both , so y = 0 . now , 653 x is divisible by 8 , so 13 x should be divisible by 8 . this happens when x = 6 . x + y = ( 6 + 0 ) = 6 . answer : a"
Answer: a
Question (general): if x and y are integers , what is the least positive number of 24 x + 9 y ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 6 , e ) 9
Rationale: "24 x + 9 y = 3 ( 8 x + 3 y ) which will be a minimum positive number when 8 x + 3 y = 1 . 8 ( - 1 ) + 3 ( 3 ) = 1 then 3 ( 8 x + 3 y ) can have a minimum positive value of 3 . the answer is b ."
Answer: b
Question (general): the average earning of a mechanic for the first - 4 days of a week is rs . 18 and for the last 4 days is rs . 22 . if he earns rs . 13 on the fourth day , his average earning for the whole week is ?
Options: a ) rs . 18.95 , b ) rs 16 , c ) rs . 21 , d ) rs . 25.71 , e ) none of these
Rationale: answer total earning for the week = sum of earning of first four days + sum of earning of last four days - earning of 4 th day = 4 x 18 + 4 x 22 - 13 = rs . 147 â ˆ ´ average earning = 147 / 7 = rs . 21 correct option : c
Answer: c
Question (physics): six bells commence tolling together and toll at intervals of 4 , 6 , 8 , 10 , 12 and 14 seconds respectively . in 70 minutes , how many times do they toll together ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "lcm of 4 , 6 , 8 10 , 12 and 14 is 840 . so , after each 840 seconds , they would toll together . hence , in 70 minutes , they would toll 70 * 60 seconds / 840 seconds = 5 times but then the question says they commence tolling together . so , they basically also toll at thebeginning ( 0 second ) . so , total tolls together = 5 + 1 = 6 answer : e"
Answer: e
Question (general): can you please walk me through how to best approach this problem ? thanks if # p # = ap ^ 3 + bp – 1 where a and b are constants , and # - 5 # = 10 , what is the value of # 5 # ?
Options: a ) 5 , b ) - 12 , c ) - 2 , d ) - 3 , e ) - 5
Rationale: # p # = ap ^ 3 + bp - 1 # - 5 # = 10 putting p = - 5 in above equation - 125 a - ( 5 b + 1 ) = 10 or # - 5 # = ( 125 a + 5 b + 1 ) = - 10 therefore 125 a + 5 b = - 11 . . . . . ( 1 now putting p = 5 # 5 # = 125 a + 5 b - 1 using equation 1 ( 125 a + 5 b = - 11 ) # 5 # = - 11 - 1 = - 12 hence b
Answer: b
Question (general): what is the unit digit in the product ( 3 ^ 68 x 6 ^ 59 x 7 ^ 71 ) ?
Options: a ) 1 , b ) 2 , c ) 4 , d ) 6 , e ) none of them
Rationale: "unit digit in 3 ^ 4 = 1 = > unit digit in ( 3 ^ 4 ) ^ 16 = 1 therefore , unit digit in 3 ^ 65 = unit digit in [ ( 3 ^ 4 ) ^ 16 x 3 ] = ( 1 x 3 ) = 3 unit digit in 6 ^ 59 = 6 unit digit in 7 ^ 4 = 1 = > unit digit in ( 7 ^ 4 ) ^ 17 is 1 unit digit in 7 ^ 71 = unit digit in [ ( 7 ^ 4 ) ^ 17 x 7 ^ 3 ] = ( ( 1 x 3 ) = 3 therefore , required digit = unit digit in ( 3 x 6 x 3 ) = 4 answer is c"
Answer: c