Cheukting/mathqa huggingface dataset:
Question (physics): a tank is filled in 10 hours by 3 pipes a , b and c . the pipe c is twice as fast as b and b is twice as fast as a . how much time will pipe a alone take to fill the tank ?
Options: a ) 70 hours , b ) 30 hours , c ) 35 hours , d ) 50 hours , e ) 60 hours
Rationale: 1 / a + 1 / b + 1 / c = 1 / 10 ( a , b and c 1 hour work ) given . . 1 / b = 2 / a and 1 / c = 2 / b = 4 / a hence 1 / a + 2 / a + 4 / a = 1 / 10 on solving . . . . we get 1 / a = 1 / 70 ( work done by a in 1 hour ) therefore time taken by a is 70 hours to finish the whole work answer : a
Answer: a
Question (gain): in a certain production lot , 40 percent of the toys are red and the remaining toys are green . half of toys are small and half are large . if 10 percent of the toys are red and small , and 40 toys are green and large . how many of the toys are red and large ?
Options: a ) 40 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: 40 % toys are red . 50 % toys are small - 50 % are large red and small - 10 % red and large must be 30 % ( since there are total 40 % red toys ) but 50 % toys are large . if 30 % are red and large , the rest 20 % large toys must be green . so large and green toys are 20 % . these 20 % large and green toys are actually 40 so total number of toys must be 200 . since red and large toys are 30 % , they must be 60 . answer : b
Answer: b
Question (general): if 4 ( p ' s capital ) = 6 ( q ' s capital ) = 10 ( r ' s capital ) , then out of the total profit of rs 4030 , r will receive
Options: a ) 600 , b ) 780 , c ) 800 , d ) 900 , e ) none of these
Rationale: "explanation : let p ' s capital = p , q ' s capital = q and r ' s capital = r then 4 p = 6 q = 10 r = > 2 p = 3 q = 5 r = > q = 2 p / 3 r = 2 p / 5 p : q : r = p : 2 p / 3 : 2 p / 5 = 15 : 10 : 6 r ' s share = 4030 * ( 6 / 31 ) = 130 * 6 = 780 . answer : option b"
Answer: b
Question (physics): a train 150 m long is running with a speed of 68 kmph . in what time will it pass a man who is running at 8 kmph in the same direction in which the train is going ?
Options: a ) 5 seconds , b ) 6 seconds , c ) 9 seconds , d ) 8 seconds , e ) 7 seconds
Rationale: "relative speed of train and man = 60 kmph or 300 / 18 m / s time taken by the train to pass the man : length of the train / relative speed 150 / 300 / 18 = 9 seconds . answer : c"
Answer: c
Question (general): mark and ann together were allocated n boxes of cookies to sell for a club project . mark sold 11 boxes less than n and ann sold 2 boxes less than n . if mark and ann have each sold at least one box of cookies , but together they have sold less than n boxes , what is the value of n ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: if n = 12 mark sold 1 box and ann sold 10 boxes total 11 < 12 answer : c
Answer: c
Question (general): in a forest 10 rabbits were caught , tagged with electronic markers , then released . a month later , 10 rabbits were captured in the same forest . of these 10 rabbits , it was found that 2 had been tagged with the electronic markers . if the percentage of tagged rabbits in the second sample approximates the percentage of tagged rabbits in the forest , and if no rabbits had either left or entered the forest over the preceding month , what is the approximate number of rabbits in the forest ?
Options: a ) 150 , b ) 70 , c ) 50 , d ) 1500 , e ) 500
Rationale: given that 10 rabbits were caught and tagged in the first sample , and 10 were caught in the second sample of which 2 had tags , then 2 / 10 approximates the fraction of the population of tagged rabbits in the forest . proportion : a / x = c / d a = rabbits tagged first sample c / d = the fraction of the population of tagged rabbits in the forest x = the population of rabbits in the forest proportion : 10 / x = 1 / 5 x = ( 1 ) ( 10 ) ( 5 ) = 50 . there are approximately 50 rabbits in the forest . answer is c
Answer: c
Question (gain): a man ' s speed with the current is 18 km / hr and the speed of the current is 2.5 km / hr . the man ' s speed against the current is ?
Options: a ) 10 , b ) 18 , c ) 50 , d ) 30 , e ) 40
Rationale: "man ' s speed with the current = 18 km / hr = > speed of the man + speed of the current = 18 km / hr speed of the current is 2.5 km / hr hence , speed of the man = 18 - 2.5 = 20.5 km / hr man ' s speed against the current = speed of the man - speed of the current = 20.5 - 2.5 = 18 km / hr answer is b ."
Answer: b
Question (physics): train a leaves the station traveling at 30 miles per hour . two hours later train в leaves the same station traveling in the same direction at 45 miles per hour . how many miles from the station was train a overtaken by train b ?
Options: a ) 100 , b ) 120 , c ) 140 , d ) 160 , e ) 180
Rationale: "after two hours , train a is ahead by 60 miles . train b can catch up at a rate of 15 miles per hour . the time to catch up is 60 / 15 = 4 hours . in 4 hours , train a travels another 30 * 4 = 120 miles for a total of 180 miles . the answer is e ."
Answer: e
Question (general): if a is a positive integer , and if the units digit of a ^ 2 is 9 and the units digit of ( a + 1 ) ^ 2 is 4 , what is the units g digit of ( a + 2 ) ^ 2 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) c . 14
Rationale: "i also got a . by punching in numers : g . . . 7 ^ 2 = . . . 9 . . . 8 ^ 2 = . . . 4 . . . 9 ^ 2 = . . . 1 . a"
Answer: a
Question (gain): a distributor sells a product through an on - line store , which take a commission of 20 % of the price set by the distributor . the distributor obtains the product from a producer at the price of $ 15 per item . what is the price that the buyer observers on - line if the distributor wants to maintain a 30 % profit on the cost of the item ?
Options: a ) 18 , b ) 21.6 , c ) 22 , d ) 25.7 , e ) 27
Rationale: "producer price = $ 15 ; the distributor wants to maintain a 20 % profit on the cost of the item , thus he must get $ 15 * 1.2 = $ 18 after the store takes a commission of 30 % of the final price - - > ( final price ) * 0.7 = $ 18 - - > ( final price ) = $ 25.7 . answer : d ."
Answer: d
Question (physics): micheal and adam can do together a piece of work in 20 days . after they have worked together for 15 days micheal stops and adam completes the remaining work in 10 days . in how many days micheal complete the work separately .
Options: a ) 40 days , b ) 100 days , c ) 120 days , d ) 110 days , e ) 90 days
Rationale: "rate of both = 1 / 20 together they do = 1 / 20 * 15 = 3 / 4 left work = 1 - 3 / 4 = 1 / 4 adam completes 1 / 4 work in 10 day so he took 10 * 4 = 40 days to complete the left work alone . thus the rate of adam is 40 / 1 rate of micheal = 1 / 20 - 1 / 40 = 1 / 40 thus micheal takes 40 days to complete the whole work . ans . a ."
Answer: a
Question (physics): pipe a can fill a tank in 6 hours . due to a leak at the bottom , it takes 10 hours for the pipe a to fill the tank . in what time can the leak alone empty the full tank ?
Options: a ) 13 , b ) 17 , c ) 15 , d ) 19 , e ) 12
Rationale: "let the leak can empty the full tank in x hours 1 / 6 - 1 / x = 1 / 10 = > 1 / x = 1 / 6 - 1 / 10 = ( 5 - 3 ) / 30 = 2 / 30 = 1 / 15 = > x = 15 . answer : c"
Answer: c
Question (other): rs . 1581 is divided among a , b and c in the ratio 10 : 15 : 6 . what is the share of b ?
Options: a ) 306 , b ) 765 , c ) 700 , d ) 510 , e ) 520
Rationale: "10 + 15 + 6 = 31 1581 / 31 = 51 so b ' s share = 15 * 51 = 765 a ' s share = 10 * 51 = 510 c ' s share = 6 * 51 = 306 answer : a"
Answer: a
Question (general): employees of a certain company are each to receive a unique 10 - digit identification code consisting of the digits 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , and 9 such that no digit is used more than once in any given code . in valid codes , the second digit in the code is exactly twice the first digit . how many valid codes are there ?
Options: a ) 145,660 , b ) 149,720 , c ) 155,420 , d ) 161,280 , e ) 167,480
Rationale: "there are 8 ! ways to make codes starting with 12 . there are 8 ! ways to make codes starting with 24 . there are 8 ! ways to make codes starting with 36 . there are 8 ! ways to make codes starting with 48 . the number of codes is 4 * 8 ! = 161,280 . the answer is d ."
Answer: d
Question (other): how many terminating zeroes w does 200 ! have ?
Options: a ) 40 , b ) 48 , c ) 49 , d ) 55 , e ) 64
Rationale: you have 40 multiples of 5 , 8 of 25 and 1 of 125 . this will give 49 zeros . c
Answer: c
Question (physics): two trains 500 m and 750 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
Options: a ) 10.6 , b ) 45 , c ) 10.4 , d ) 10.8 , e ) 10.1
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 500 + 750 = 1250 m . required time = 1250 * 9 / 250 = 45 sec . answer : b"
Answer: b
Question (physics): a train 110 m long is running with a speed of 36 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 9 , e ) 5
Rationale: "speed of train relative to man = 36 + 6 = 42 km / hr . = 42 * 5 / 18 = 35 / 3 m / sec . time taken to pass the men = 110 * 3 / 35 = 9 sec . answer : d"
Answer: d
Question (general): if x + y = 3 and y / x = 2 then y = ?
Options: a ) 0 , b ) 1 / 2 , c ) 1 , d ) 3 / 2 , e ) 2
Rationale: "from the given data : y / ( 3 - y ) = 2 = > y = 6 - 2 y = > y = 2 answer : e"
Answer: e
Question (general): tough and tricky questions : remainders . 1 ^ 1 + 2 ^ 2 + 3 ^ 3 + . . . + 7 ^ 7 is divided by 7 . what is the remainder ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: a number is divisible by 5 , if its last digit is divisible by 5 let ' s look into the sum of last digits of each term of the given expression 1 ^ 1 = 1 2 ^ 2 = 4 3 ^ 3 = 7 4 ^ 4 = 6 5 ^ 5 = 5 6 ^ 6 = 6 7 ^ 7 = 3 adding all these numbers we get 32 which gives a remainder of 4 when divided by 7 . so answer must be 4 . bunuel , can you please confirm the answer of this question . yes , the oa is c . clicked the wrong button when posting . edited . thank you . e
Answer: e
Question (gain): a sells a bicycle to b and makes a profit of 50 % . b sells the same bicycle to c at a profit of 25 % . if the final s . p . of the bicycle was rs . 225 , find out the cost price of the bicycle for a .
Options: a ) 237 , b ) 126 , c ) 971 , d ) 611 , e ) 120
Rationale: "explanation : let cp be 100 a sells at 50 % profit so sp = 150 b sells at 25 % profit = 150 x ( 1 + 25 / 100 ) = 187.50 cp - - - sp 100 - - - 187.50 x - - - 225 cp = 225 x 100 / 187.50 = 120 answer : e"
Answer: e
Question (general): what is the units digit of ( 147 ^ 17 ) ^ 47 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: the units digit of the exponents of 7 repeat in a cycle of four , which is { 7,9 , 3,1 } . the number 17 has the form 4 n + 1 so the units digit is 7 inside the bracket . the exponent 47 has the form 4 n + 3 , so the units digit is 3 . the answer is b .
Answer: b
Question (general): how many times digit 5 is used while writing numbers from 100 to 1000 ?
Options: a ) 648 , b ) 300 , c ) 252 , d ) 225 , e ) 290
Rationale: "there are 100 numbers which begin with 600 next , in every 10 numbers such as 100 to 110 , 110 to 120 , 120 to 130 5 comes at least once . number of such intervals = end limit - first no . / interval . our range of numbers is 100 - 1000 1000 - 100 = 900 / 10 = 90 number of 10 s interval in this is 90 . so 90 ' 6 s ' so far we have calculated 190 . the total now comes to 280 . the nearest to which is 290 . hence e ."
Answer: e
Question (general): one - third of rahul ' s savings in national savings certificate is equal to one - half of his savings in public provident fund . if he has rs . 1 , 90,000 as total savings , how much has he saved in public provident fund ?
Options: a ) 80000 , b ) 60000 , c ) 50000 , d ) 76000 , e ) 90000
Rationale: "let savings in n . s . c and p . p . f . be rs . x and rs . ( 190000 - x ) respectively . then , = 1 / 3 x = 1 / 2 ( 190000 - x ) = x / 3 + x / 2 = 95000 = 5 x / 6 = 95000 = x = 95000 x 6 / 5 = 114000 savings in public provident fund = rs . ( 190000 - 114000 ) = rs . 76000 answer is d"
Answer: d
Question (general): average marks of a , b , c is 48 . when d joins average becomes 47 . e has 3 more marks than d . average marks of b , c , d , e is 48 . what is the marks of a ?
Options: a ) 43 , b ) 44 , c ) 45 , d ) 46 , e ) 47
Rationale: a + b + c = 144 a + b + c + d = 188 d = 44 e = 47 b + c + d + e = 192 b + c = 101 a = 43 answer : a
Answer: a
Question (gain): a sum of money at simple interest amounts to rs . 720 after 2 years and to rs . 1020 after a further period of 5 years . the sum is :
Options: a ) 400 , b ) 500 , c ) 600 , d ) 700 , e ) 800
Rationale: "si of 5 year = ( 1020 - 720 ) = 300 so , si of 1 year = 300 / 5 = 60 so , si of 2 year = 60 * 2 = 120 so , sum is = ( 720 - 120 ) = 600 answer : c"
Answer: c
Question (gain): 3 candidates in an election and received 3136 , 7636 and 11628 votes respectively . what % of the total votes did the winning candidate got in that election ?
Options: a ) 45 % , b ) 49 % , c ) 52 % , d ) 59 % , e ) 61 %
Rationale: "total number of votes polled = ( 3136 + 7636 + 11628 ) = 22400 so , required percentage = 11628 / 22400 * 100 = 52 % c"
Answer: c
Question (physics): two pipes p and q can fill a cistern in 12 and 15 minutes respectively . both are opened together , but at the end of 2 minutes the first is turned off . how many more minutes will it take for the cistern to fill after the first pipe is turned off ?
Options: a ) 8.5 , b ) 9.5 , c ) 10.5 , d ) 11.5 , e ) 12.5
Rationale: "let x be the total time it takes for the cistern to fill . 2 / 12 + x / 15 = 1 x / 15 = 5 / 6 x = 12.5 after the first pipe is turned off , it takes 10.5 more minutes to fill the cistern . the answer is c ."
Answer: c
Question (general): 864.942 - ? + 45.76 = 547.905
Options: a ) a ) 899.015 , b ) b ) 752.804 , c ) c ) 714.642 , d ) d ) 362.797 , e ) of these
Rationale: "explanation : 362.797 answer : option d"
Answer: d
Question (other): the l . c . m . of 2 numbers is 66 . the numbers are in the ratio 2 : 3 . find their sum ?
Options: a ) 36 , b ) 40 , c ) 48 , d ) 32 , e ) 55
Rationale: "let the numbers be 2 x and 3 x l . c . m . = 6 x 6 x = 66 x = 11 the numbers are = 22 and 33 required sum = 22 + 33 = 55 answer is e"
Answer: e
Question (other): a company conducted a survey about its two brands , a and b . x percent of respondents liked product a , ( x – 20 ) percent liked product b , 23 percent liked both products , and 23 percent liked neither product . what is the minimum number g of people surveyed by the company ?
Options: a ) 46 , b ) g = 80 , c ) g = 90 , d ) g = 100 , e ) 200
Rationale: "100 = x + x - 20 + 23 - 23 x = 60 , so , product a = 60 % , product b = 40 % , both = 23 % , neither = 23 % 23 % of the total no . of people should be an integer . so , a , bc are out . 60 % of d and 40 % of d are both integers . so , d satisfies all conditions . so , answer is d ."
Answer: d
Question (general): the product x of two prime numbers is between 17 and 55 . if one of the prime numbers is greater than 2 but less than 6 and the other is greater than 11 but less than 25 , then x =
Options: a ) 18 , b ) 29 , c ) 37 , d ) 44 , e ) 65
Rationale: "option bc can be ruled out as they themselves are prime numbers 18 = 2 * 9 = 3 * 6 > > ignore 44 = 2 * 22 = 4 * 11 > > ignore 65 = 5 * 13 > > answer answer = e"
Answer: e
Question (physics): a train traveling at 72 kmph crosses a platform in 33 seconds and a man standing on the platform in 18 seconds . what is the length of the platform in meters ?
Options: a ) 240 meters , b ) 360 meters , c ) 420 meters , d ) 300 meters , e ) can not be determined
Rationale: "speed of train = 72 * ( 5 / 18 ) = 20 m / s lets consider the man as a stationery point on the platform . crossing the point gives us the length of the train . lt = 20 * 18 = 360 m . crossing the platform gives us the length of trainlength of platform . l ( t + p ) = 20 * 33 = 660 m . so , length of platform = 660 - 360 = 300 m imo , answer d"
Answer: d
Question (general): lagaan is levied on the 60 percent of the cultivated land . the revenue department collected total rs . 3 , 84,000 through the lagaan from the village of mutter . mutter , a very rich farmer , paid only rs . 480 as lagaan . the percentage of total land of mutter over the total taxable land of the village is :
Options: a ) 0.20833 , b ) 0.14544 , c ) 0.25632 , d ) 0.35466 , e ) 0.63435
Rationale: "total land of sukhiya = \ inline \ frac { 480 x } { 0.6 } = 800 x \ therefore cultivated land of village = 384000 x \ therefore required percentage = \ inline \ frac { 800 x } { 384000 } \ times 100 = 0.20833 a"
Answer: a
Question (other): the weights of one liter vegetable ghee packet of two brands ‘ a ’ and ‘ b ’ are 800 gm and 850 gm respectively . if they are mixed in the ratio of 3 : 2 by volumes to form a mixture of 3 liters , what is the weight ( in kg ) of the mixture ?
Options: a ) 3.84 , b ) 1.75 , c ) 3.52 , d ) 2.46 , e ) none of these
Rationale: "here ' s how i did it . my notes from reading the problem were : 1 l a = 800 gm 1 l b = 850 gm we are mixing five parts ( 3 parts a plus 2 parts b , 5 parts total ) to get 3 l , so 5 x = 3 - - - > x = 3 / 5 . each part is 3 / 5 of a liter . so if we have 3 parts a , we have 800 * 3 * ( 3 / 5 ) = 1440 if we have 2 parts b , we have 850 * 2 * ( 3 / 5 ) = 1020 1440 + 1020 = 2460 solving for units gives us 2.46 so the answer is d"
Answer: d
Question (general): if 4 xz + yw = 10 and xw + yz = 20 , what is the value of the expression ( 2 x + y ) ( 2 z + w ) ?
Options: a ) 9 . , b ) 12 . , c ) 15 . , d ) 50 . , e ) 18 .
Rationale: "( 2 x + y ) * ( 2 z + w ) = 10 + 2 ( 20 ) = 50 answer : d"
Answer: d
Question (gain): $ 9,000 is deposited in a savings account that pays 14 % annual interest compounded semiannually . to the nearest dollar , how much is in the account at the end of the year ?
Options: a ) $ 11304.12 , b ) $ 12304.54 , c ) $ 11604.14 , d ) $ 10304.10 , e ) $ 9304.41
Rationale: this is the case of semi - annual compoundingso , multiply time period by 2 and divide rate by 2 so , new time = 2 periods and new rate = 14 / 2 = 7 % now , ca = 9000 ( 1 + 7 / 100 ) ^ 2 = $ 10304.10 hence answer is d
Answer: d
Question (physics): a certain bacteria colony doubles in size every day for 25 days , at which point it reaches the limit of its habitat and can no longer grow . if two bacteria colonies start growing simultaneously , how many days will it take them to reach the habitat ’ s limit ?
Options: a ) 6.33 , b ) 7.5 , c ) 10 , d ) 15 , e ) 24
Rationale: "if there is one bacteria colony , then it will reach the limit of its habitat in 25 days . if there are two bacteria colonies , then in order to reach the limit of habitat they would need to double one time less than in case with one colony . thus colonies need to double 24 times . answer : e . similar questions to practice : hope it helps ."
Answer: e
Question (general): two kinds of vodka are mixed in the ratio 1 : 2 and 2 : 1 and they are sold fetching the profit 10 % and 10 % respectively . if the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4 / 3 and 5 / 3 times respectively , then the mixture will fetch the profit of
Options: a ) 10 % , b ) 20 % , c ) 21 % , d ) 23 % , e ) can not be determined
Rationale: answer : a .
Answer: a
Question (physics): if daily wages of a man is 4 times to that of a woman , how many men should work for 25 days to earn rs . 14400 ? given that wages for 40 women for 30 days are rs . 21600 .
Options: a ) 12 , b ) 4 , c ) 6 , d ) 8 , e ) 20
Rationale: explanation : wages of 1 woman for 1 day = 21600 / 40 ã — 30 wages of 1 man for 1 day = 21600 ã — 4 / 40 ã — 30 wages of 1 man for 25 days = 21600 ã — 4 ã — 25 / 40 ã — 30 number of men = 14400 / ( 21600 ã — 4 ã — 25 / 40 ã — 30 ) = 144 / ( 216 ã — 100 / 40 ã — 30 ) = 8 answer : option d
Answer: d
Question (gain): jerry went to a shop and bought things worth rs . 20 , out of which 30 % went on sales tax on taxable purchases . if the tax rate was 6 % , then what was the cost of the tax free items ?
Options: a ) 14 , b ) 14.7 , c ) 21.3 , d ) 21.5 , e ) 21.7
Rationale: total cost of the items he purchased = rs . 20 given that out of this rs . 20 , 30 % is given as tax = > total tax incurred = 30 % = rs . 30 / 100 let the cost of the tax free items = x given that tax rate = 6 % ∴ ( 20 − 30 / 100 − x ) 6 / 100 = 30 / 100 ⇒ 6 ( 20 − 0.3 − x ) = 30 ⇒ ( 20 − 0.3 − x ) = 5 ⇒ x = 20 − 0.3 − 5 = 14.7 b )
Answer: b
Question (general): 5005 - 5000 ÷ 10.00 = ?
Options: a ) 0.5 , b ) 50 , c ) 5000 , d ) 4505 , e ) none
Rationale: "answer given expression = 5005 - 5000 ÷ 10.00 = 5005 - 500 = 4505 correct option : d"
Answer: d
Question (physics): machine a takes 50 hours to complete a certain job and starts that job at 6 am . after four hour of working alone , machine a is joined by machine b and together they complete the job at 1 pm . how long would it have taken machine b to complete the job if it had worked alone for the entire job ?
Options: a ) 9 , b ) 88.88 , c ) 4.88 , d ) 2.88 , e ) 3.88
Rationale: "let us assume total job = 100 units a finishes 100 units in 50 hrs ( given ) hence a ( working rate ) = 2 units / hr now given that a works for 4 hr ( so 8 units done ) then a and b finish total work in 7 hours . hence a and b finish 92 units in 3 hours . of these 3 x 2 = 6 units were done by a . hence b did 86 units in 3 hours . hence b ( working rate ) = 86 / 3 units / hr hence b takes 100 x 3 / 86 = 3.88 hours to complete the job . answer e ."
Answer: e
Question (general): a random 10 - letter code is to be formed using the letters a , b , c , d , e , f , g , h , i and i ( only the “ i ” will be used twice ) . what is the probability that a code that has the two i ’ s adjacent to one another will be formed ?
Options: a ) 1 / 10 , b ) 1 / 8 , c ) 1 / 5 , d ) 1 / 4 , e ) 1 / 2
Rationale: total number of combinations possible = 10 ! / 2 ! 10 ! / 2 ! total favorable combinations = 9 ! 9 ! - we have considered the two is as one element . since we have two is , they can interchange their positions , without affecting the code . probability = 9 ! / ( 10 ! / 2 ! ) = 9 ! ∗ 2 ! / 10 ! = 1 / 59 ! / ( 10 ! / 2 ! ) = 9 ! ∗ 2 ! / 10 ! = 1 / 5 ans : c
Answer: c
Question (general): at the end of the day , february 14 th , a florist had 90 roses left in his shop , all of which were red , white or pink in color and either long or short - stemmed . a third of the roses were short - stemmed , 15 of which were white and 10 of which were pink . the percentage of pink roses that were short - stemmed equaled the percentage of red roses that were short - stemmed . if none of the long - stemmed roses were white , what percentage of the long - stemmed roses were red ?
Options: a ) 20 % , b ) 75 % , c ) 50 % , d ) 33.3 % , e ) 80 %
Rationale: r + w + p = 90 s + l = 90 1 / 3 * 90 = 30 short - stemmed white = 15 short - stemmed pink = 10 = > short - stemmed red = 5 10 / p = 5 / r = > r = p / 2 , p = 2 r so total long stemmed = 60 and long stemmed red + long stemmed pink = 60 so long stemmed red / long stemmed = ? total white = 15 ( as no long stemmed white ) = > r + 2 r + 15 = 90 = > 3 r = 75 and r = 25 long stemmed r = 25 - 5 = 20 so long stemmed red / r = 20 / 60 = 33.3 % answer - d
Answer: d
Question (general): the average salary / head of allthe workers in a workshop is rs . 1200 , if the average salary / head of 10 technician is rs . 1400 and the average salary / head of the rest is rs . 900 , the total no . of workers in the work - shop is ?
Options: a ) 18 , b ) 17 , c ) 15 , d ) 19 , e ) 21
Rationale: let the total number of workers be y . so sum of salary for all workers = sum of salary of 10 technician + sum of salary for other y - 10 workers . 10 x 1400 + 900 ( y - 10 ) = 1200 y ⇒ 14000 + 900 y - 9000 = 1200 y ⇒ 300 y = 5000 ∴ y = 17 so total number of workers = 17 b
Answer: b