Cheukting/mathqa huggingface dataset:
Question (physics): joe drives 240 miles at 60 miles per hour , and then he drives the next 120 miles at 40 miles per hour . what is his average speed for the entire trip in miles per hour ?
Options: a ) 42 , b ) 51 , c ) 50 , d ) 54 , e ) 56
Rationale: "t 1 = 240 / 60 = 4 hours t 2 = 120 / 40 = 3 hours t = t 1 + t 2 = 7 hours avg speed = total distance / t = 360 / 7 = 51 mph = b"
Answer: b
Question (general): what is the sum of the multiples of 4 between 38 and 127 inclusive ?
Options: a ) 1804 , b ) 1816 , c ) 1824 , d ) 1828 , e ) 1832
Rationale: "the fastest way in an ap is to find the average and multiply with total integers . . between 38 and 127 , the smallest multiple of 4 is 40 and largest = 124 . . average = ( 40 + 124 ) / 2 = 164 / 2 = 82 . . total numbers = ( 124 - 40 ) / 4 + 1 = = 84 / 4 + 1 = 27 + 1 = 22 . . sum = 82 * 22 = 1804 ans a"
Answer: a
Question (general): a certain car traveled twice as many miles from town a to town b as it did from town b to town c . from town a to town b , the car averaged 10 miles per gallon , and from town b to town c , the car averaged 18 miles per gallon . what is the average miles per gallon that the car achieved on its trip from town a through town b to town c ?
Options: a ) 13 , b ) 13.5 , c ) 14 , d ) 14.5 , e ) 15
Rationale: "ans is d given d _ ab = 2 * d _ bc let d _ ab = d and d _ bc = x so d = 2 x for average miles per gallon = ( d + x ) / ( ( d / 10 ) + ( x / 18 ) ) = 14.5 ( formula avg speed = total distance / total time )"
Answer: d
Question (physics): a train 110 m long is running with a speed of 30 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 ) 7 sec , b ) 6 sec , c ) 8 sec , d ) 11 sec , e ) 2 sec
Rationale: "speed of train relative to man = 30 + 6 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . time taken to pass the men = 110 / 10 = 11 sec . answer : d"
Answer: d
Question (general): there are 50 boys in a class . their average weight is 45 kg . when one boy leaves the class , the average reduces by 100 g . find the weight of the boy who left the class .
Options: a ) 40.9 kg , b ) 42.9 kg , c ) 49.9 kg , d ) 39.9 kg , e ) none of these
Rationale: here one boy is excluded and final average of the group decreases . ∴ change in average is ( – ) ve = – 0.1 kg . using the formula sum of the quantities excluded = ( changein no . ofquantities × origina laverage ) + ( changeinaverage × final no . ofquantities ) ⇒ weight of the boy who left = ( 1 × 45 ) – ( – 0.1 × 49 ) = 49.9 kg answer c
Answer: c
Question (physics): two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 20 kmph and 21 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ?
Options: a ) 288 , b ) 492 , c ) 877 , d ) 278 , e ) 178
Rationale: "1 h - - - - - 5 ? - - - - - - 60 12 h rs = 20 + 21 = 41 t = 12 d = 41 * 12 = 492 answer : b"
Answer: b
Question (general): how many positive integers less than 240 are multiple of 4 but not multiples of 6 ?
Options: a ) 40 , b ) 31 , c ) 42 , d ) 53 , e ) 64
Rationale: from here , it might be easier to go up in bounds of 60 , so we know that 61 - 120 gives 10 more numbers . 121 - 180 and 181 - 240 as well . this brings us up to 240 with 40 numbers . a cursory glance at the answer choices should confirm that it must be 42 , as all the other choices are very far away . answer choice a is correct here .
Answer: a
Question (general): if w / x = 1 / 3 and w / y = 4 / 15 , then ( x + y ) / y =
Options: a ) 4 / 5 , b ) 6 / 5 , c ) 7 / 5 , d ) 8 / 5 , e ) 9 / 5
Rationale: "w / x = 1 / 3 = > x = 3 w and w / y = 4 / 15 = > y = 15 / 4 w ( x + y ) / y = ( 3 w + 15 / 4 w ) / ( 15 / 4 w ) = ( 27 / 4 w ) / ( 15 / 4 w ) = 9 / 5 correct option : e"
Answer: e
Question (gain): tickets to a certain concert sell for $ 20 each . the first 10 people to show up at the ticket booth received a 40 % discount , and the next 20 received a 15 % discount . if 52 people bought tickets to the concert , what was the total revenue from ticket sales ?
Options: a ) $ 600 , b ) $ 740 , c ) $ 850 , d ) $ 900 , e ) $ 1,140
Rationale: "price of 1 ticket = 20 $ revenue generated from sales of first 10 tickets = 10 * ( 60 / 100 * 20 ) = 10 * 12 = 120 revenue generated from sales of next 20 tickets = 20 * ( 85 / 100 * 20 ) = 20 * 17 = 340 revenue generated from sales of last 22 tickets = 20 * 22 = 440 revenue generated from sales of 52 tickets = 120 + 340 + 440 = 900 $ answer d"
Answer: d
Question (general): a bowl of nuts is prepared for a party . brand p mixed nuts are 20 % almonds and brand q ' s deluxe nuts are 25 % almonds . if a bowl contains a total of 64 ounces of nuts , representing a mixture of both brands , and 14 ounces of the mixture are almonds , how many ounces of brand q ' s deluxe mixed nuts are used ?
Options: a ) 14 , b ) 20 , c ) 32 , d ) 44 , e ) 48
Rationale: "lets say x ounces of p is mixed with q . = > 64 - x ounces of q is present in the mixture ( as the total = 64 ounces ) given total almond weight = 14 ounces ( 20 x / 100 ) + ( 25 / 100 ) ( 64 - x ) = 14 = > x = 40 = > 64 - 40 = 14 ounces of q is present in the mixture . answer is a ."
Answer: a
Question (physics): a policeman noticed a criminal from a distance of 265 km . the criminal starts running and the policeman chases him . the criminal and the policeman run at the rate of 8 km and 9 km per hour respectively . what is the distance between them after 3 minutes ?
Options: a ) 100 m , b ) 120 m , c ) 130 m , d ) 150 m , e ) none of these
Rationale: "explanation : solution : relative speed = ( 9 - 8 ) = 1 km / hr . distance covered in 3 minutes = ( 1 * 3 / 60 ) km = 1 / 20 km = 50 m . . ' . distance between the criminal and policeman = ( 265 - 50 ) m = 215 m . answer : e"
Answer: e
Question (general): a university cafeteria offers 6 flavors of pizza - pork , gobi - manjurian , pepperoni , chicken , hawaiian and vegetarian . if a customer has an option ( but not the obligation ) to add extra cheese , mushrooms or both to any kind of pizza , how many different pizza varieties are available ?
Options: a ) 4 , b ) 8 , c ) 12 , d ) 36 , e ) 32
Rationale: 6 flavours * 6 choices = 6 c 1 * 6 c 1 = 6 * 6 = 36 = d
Answer: d
Question (general): the sum of three consecutive multiples of 3 is 117 . what is the largest number ?
Options: a ) 45 , b ) 48 , c ) 51 , d ) 42 , e ) 54
Rationale: "let the numbers be 3 x , 3 x + 3 and 3 x + 6 . then , 3 x + ( 3 x + 3 ) + ( 3 x + 6 ) = 117 9 x = 108 x = 12 largest number = 3 x + 6 = 42 answer : d"
Answer: d
Question (other): in a zoo , the ratio of the number of cheetahs to the number 4 then what is the increase in the number of pandas ?
Options: a ) 2 , b ) 12 , c ) 5 , d ) 10 , e ) 15
Rationale: one short cut to solve the problem is c : p = 1 : 3 c increased to 5 = > 1 : 3 = 5 : x = > x = 15 = > p increased by 12 b is the answer
Answer: b
Question (physics): a train 250 m long running at 72 kmph crosses a platform in 50 sec . what is the length of the platform ?
Options: a ) 150 m , b ) 200 m , c ) 250 m , d ) 750 m , e ) 300 m
Rationale: "d = 72 * 5 / 18 = 50 = 1000 â € “ 250 = 750 m answer : d"
Answer: d
Question (general): how many multiples of 3 are there between 5 and 59 , 5 and 59 inclusive ?
Options: a ) 16 , b ) 22 , c ) 18 , d ) 11 , e ) 9
Rationale: "3 multiples are . . . 6,9 , 12,15 , 18,21 , 24,27 , 30,33 , 36,39 , 42,45 , 48,51 , 54,57 , . . . , the answer is = 18 answer is c"
Answer: c
Question (general): in a mixture of 45 litres the ratio of milk to water is 4 : 1 . additional 12 litres of water is added to the mixture . find the ratio of milk to water in the resulting mixture .
Options: a ) 12 / 7 , 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 + 12 ) = 36 / 21 = 12 / 7 . answer : a ."
Answer: a
Question (general): in 1979 approximately 1 / 3 of the 32.3 million airline passengers traveling to or from the united states used kennedy airport . if the number of such passengers that used miami airport was 1 / 2 the number that used kennedy airport and 4 times the number that used logan airport , approximately how many millions of these passengers used logan airport that year ?
Options: a ) 18.6 , b ) 9.3 , c ) 6.2 , d ) 1.33 , e ) 1.6
Rationale: "number of passengers using kennedy airport = 32 / 3 = ~ 10.67 passengers using miami airport = 10.67 / 2 = ~ 5.34 passengers using logan airport = 5.34 / 4 = ~ 1.33 so d"
Answer: d
Question (general): what is the greater of the two numbers whose product is 2496 , given that the sum of the two numbers exceeds their difference by 64 ?
Options: a ) a ) 96 , b ) b ) 108 , c ) c ) 110 , d ) d ) 78 , e ) of these
Rationale: "let the greater and the smaller number be g and s respectively . gs = 2496 g + s exceeds g - s by 64 i . e . , g + s - ( g - s ) = 64 i . e . , 2 s = 64 = > s = 32 . g = 2496 / s = 78 . answer : d"
Answer: d
Question (general): rs . 6490 is divided so that 4 times the first share , six times the 2 nd share and twice the third share amount to the same . what is the value of the first share ?
Options: a ) s 6490 , b ) s 1880 , c ) s 1660 , d ) s 1550 , e ) s 1770
Rationale: "a + b + c = 6490 4 a = 6 b = 2 c = x a : b : c = 1 / 4 : 1 / 6 : 1 / 2 = 3 : 2 : 6 3 / 11 * 6490 = rs 1770 answer : e"
Answer: e
Question (general): of the goose eggs laid at a certain pond , 2 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year . if 125 geese survived the first year and if no more than one goose hatched from each egg , how many goose eggs were laid at the pond ?
Options: a ) 280 , b ) 400 , c ) 540 , d ) 625 , e ) 840
Rationale: of the goose eggs laid at a certain pond , 2 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month : 2 / 3 * 3 / 4 = 1 / 2 survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year : ( 1 - 3 / 5 ) * 1 / 2 = 1 / 5 survived the first year . 120 geese survived the first year : 1 / 5 * ( total ) = 125 - - > ( total ) = 625 . answer : d .
Answer: d
Question (general): the average salary per month of 55 employees in a company is rs 8500 . if the managers salary is added , the average salary increases to rs 8800 , what is the salary of the manager ?
Options: a ) 10000 , b ) 12000 , c ) 23000 , d ) 25300 , e ) 45000
Rationale: explanation : salary of the manager = ( 56 * 8800 - 55 * 8500 ) = 25300 answer : d
Answer: d
Question (physics): there are 24 students in a seventh grade class . they decided to plant birches and roses at the school ' s backyard . while each girl planted 3 roses , every three boys planted 1 birch . by the end of the day they planted 2424 plants . how many birches were planted ?
Options: a ) 2 , b ) 5 , c ) 8 , d ) 6 , e ) 4
Rationale: "let x be the number of roses . then the number of birches is 24 − x , and the number of boys is 3 × ( 24 − x ) . if each girl planted 3 roses , there are x 3 girls in the class . we know that there are 24 students in the class . therefore x 3 + 3 ( 24 − x ) = 24 x + 9 ( 24 − x ) = 3 ⋅ 24 x + 216 − 9 x = 72 216 − 72 = 8 x 1448 = x 1 x = 18 so , students planted 18 roses and 24 - x = 24 - 18 = 6 birches . correct answer is d ) 6"
Answer: d
Question (other): how many of the positive factors of 10 , 16 and how many common factors are there in numbers ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "factors of 12 - 1 , 2 , 3 , 4 , 6 , and 12 factors of 16 - 1 , 2 , 4 , 8 and 16 comparing both , we have three common factors of 45,16 - 3 answer c"
Answer: c
Question (general): in a simultaneous throw of pair of dice . find the probability of getting the total more than 7
Options: a ) 5 / 7 , b ) 4 / 7 , c ) 5 / 12 , d ) 4 / 7 , e ) 1 / 6
Rationale: here n ( s ) = ( 6 * 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 ) } p ( e ) = n ( e ) / n ( s ) = 15 / 36 = 5 / 12 option c
Answer: c
Question (general): calculate the largest 6 digit number which is exactly divisible by 99 ?
Options: a ) 999991 , b ) 999965 , c ) 999912 , d ) 999936 , e ) 999930
Rationale: "largest 4 digit number is 999999 after doing 999999 ÷ 96 we get remainder 55 hence largest 4 digit number exactly divisible by 88 = 9999 - 55 = 9944 answer : d"
Answer: d
Question (general): a green grocer received a boxful of tomatoes and on opening the box found that several had gone bad . he then counted them up so that he could make a formal complaint and found that 68 were mouldy , which was 16 per cent of the total contents of the box . how many tomatoes were in the box ?
Options: a ) 336 , b ) 425 , c ) 275 , d ) 235 , e ) 689
Rationale: b 425 ( 68 ã · 16 ) ã — 100
Answer: b
Question (gain): the water level in a reservoir has been dropping at the rate of 12 inches per day . exactly 5 days ago , the water level was at w inches . what will be the water level exactly 4 days from now if the rate at which the level is dropping remains the same ?
Options: a ) w − 108 , b ) w − 56 , c ) w − 14 , d ) w + 14 , e ) w + 126
Rationale: drop = 12 inches / day 5 days ago = w , means now it ' s equal w - 60 and in 4 days = w - 60 - 48 = w - 108 answer a
Answer: a
Question (general): how many boxes do we need if we have to carry 250 apples into boxes that each hold 25 apples ?
Options: a ) a ) 9 , b ) b ) 5 , c ) c ) 7 , d ) d ) 10 , e ) e ) none of the above
Rationale: sol . apples 250 each carries 25 = 250 / 25 = 10 answer : d
Answer: d
Question (physics): how many seconds does sandy take to cover a distance of 600 meters , if sandy runs at a speed of 15 km / hr ?
Options: a ) 128 , b ) 136 , c ) 144 , d ) 152 , e ) 160
Rationale: "15 km / hr = 15000 m / 3600 s = ( 150 / 36 ) m / s = ( 25 / 6 ) m / s time = 600 / ( 25 / 6 ) = 144 seconds the answer is c ."
Answer: c
Question (other): if shares of two persons in profits are rs . 600 and rs . 300 then ratio of their capitals is
Options: a ) 3 : 4 , b ) 2 : 3 , c ) 4 : 3 , d ) 1 : 3 , e ) 2 : 1
Rationale: "total profit = 1000 ratio = 600 / 300 = 2 : 1 answer : e"
Answer: e
Question (general): the mean of 50 observations was 36 . it was found later that an observation 48 was wrongly taken as 23 . the corrected new mean is :
Options: a ) 36.5 , b ) 35 , c ) 34 , d ) 33 , e ) 32.5
Rationale: "correct sum = ( 36 * 50 + 48 - 23 ) = 1825 . correct mean = 1825 / 50 = 36.5 answer a"
Answer: a
Question (general): a school has received 60 % of the amount it needs for a new building by receiving a donation of $ 500 each from people already solicited . people already solicited represent 50 % of the people from whom the school will solicit donations . how much average contribution is requited from the remaining targeted people to complete the fund raising exercise ?
Options: a ) $ 200 , b ) $ 333.33 , c ) $ 100.25 , d ) $ 277.78 , e ) $ 377.00
Rationale: "let us suppose there are 100 people . 50 % of them donated $ 25000 ( 500 * 50 ) $ 25000 is 60 % of total amount . so total amount = 25000 * 100 / 60 remaining amount is 40 % of total amount . 40 % of total amount = 25000 * ( 100 / 60 ) * ( 40 / 100 ) = 50000 / 3 this amount has to be divided by 50 ( remaining people are 50 ) so per head amount is 50000 / 3 / 50 = 32000 / 180 = 333.33 ; answer : b"
Answer: b
Question (physics): a certain bacteria colony doubles in size every day for 19 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 ) 18 , e ) 19
Rationale: "if there is one bacteria colony , then it will reach the limit of its habitat in 20 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 18 times . answer : d . similar questions to practice : hope it helps ."
Answer: d
Question (geometry): the diameter of a circle is 4 / π . find the circumference of the circle .
Options: a ) 8
b ) 4 π
c ) 4
d ) 6
e ) 5
Rationale: circumference = 2 * pi * r = 2 * pi * 4 / pi = > 8 a
Answer: a
Question (general): simplify : 0.3 * 0.3 + 0.3 * 0.3
Options: a ) 0.52 , b ) 0.42 , c ) 0.18 , d ) 0.64 , e ) 0.46
Rationale: "given exp . = 0.3 * 0.3 + ( 0.3 * 0.3 ) = 0.09 + 0.09 = 0.18 answer is c ."
Answer: c
Question (general): how many prime numbers exist between 260 and 280 ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: straight a way lets exclude all the even numbers between 260 and 280 . so now the number starts from 261 to 279 ( only odd ) 261 is a divisible of 3 and next odd divisible by 3 will be 261 + 6 = 267 + 6 = 273 + 6 = 279 . also we can eliminate numbers ending with ' 5 ' so in odd , the excluded numbers are 261 , 265,267 , 273,279 , which leave us with 263,269 , 271,277 . checked the above listed four numbers are divisible by any numbers till 20 . answer : e
Answer: e
Question (physics): one robot builds a robot in 1 hour , another one builds a robot in 2 hours . the 2 robots work together and when a new robot is complete , it joins the others , working at a constant rate of one robot in 2 hours . how much time will it take until there are 8 robots altogether , if the robots build only one robot at a time ?
Options: a ) 70 min , b ) 94 min , c ) 110 min , d ) 131 1 / 7 min , e ) 146 1 / 7 min
Rationale: "first the 2 robots work at the rate of 1 + 1 / 2 = 3 / 2 so they complete one robot in 2 / 3 rd of an hour = 40 minutes - ( 1 ) now the 3 robots work together at the rate of 1 + 1 / 2 + 1 / 2 = 4 / 2 = 2 / 1 so they complete one robot in 1 / 2 an hour , i . e 30 minutes - ( 2 ) now the 4 robots work together at the rate of 1 + 1 / 2 + 1 / 2 + 1 / 2 = 5 / 2 so they complete one robot in 2 / 5 th of an hour - ( 3 ) now the 5 robots work together at the rate of 1 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 = 3 so they complete one robot in 1 / 3 th of an hour - ( 4 ) now the 6 robots work together at the rate of 1 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 = 7 / 2 so they complete one robot in 2 / 7 th of an hour - ( 5 ) now the 7 robots work together at the rate of 1 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 = 9 / 2 so they complete one robot in 2 / 9 th of an hour - ( 6 ) and now we have 8 robots so total = ( 1 ) + ( 2 ) + ( 3 ) + ( 4 ) + ( 5 ) + ( 6 ) = 146 1 / 7 minutes answer - e"
Answer: e
Question (general): { - 10 , - 6 , - 5 , - 4 , - 2.5 , - 1 , 0 , 2.5 , 4 , 6 , 7 , 10 } a number is to be selected at random from the set above . what is the probability that the number will be a solution to the equation ( x - 4 ) ( x + 9 ) ( 2 x + 5 ) = 0 ?
Options: a ) 1 / 12 , b ) 1 / 6 , c ) 1 / 4 , d ) 1 / 3 , e ) 1 / 2
Rationale: x = - 2.5 prob = 1 / 12 answer - a
Answer: a
Question (physics): a crow leaves its nest , and flies back and forth from its nest to a nearby ditch to gather worms . the distance between the nest and the ditch is 300 meters . in one and a half hours , the crow manages to bring worms to its nest 15 times . what is the speed of the crow in kilometers per hour ?
Options: a ) 1 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "the distance between the nest and the ditch is 300 meters . 15 times mean = a crow leaves its nest , and flies back ( going and coming back ) i . e . 2 times we get total 30 rounds . so the distance is 30 * 300 = 9000 . d = st 9000 / 1.5 = t , i think we can take 9000 meters as 9 km , then only we get t = 6 . ( 1000 meters = 1 km ) d )"
Answer: d
Question (physics): a and b are two multiples of 36 , and q is the set of consecutive integers between a and b , inclusive . if q contains 9 multiples of 9 , how many multiples of 4 are there in q ?
Options: a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: "now given that q is set the consecutive integers between a and b . and q contains 9 multiples of 9 let take a as 36 . then 36 45 54 63 72 81 90 99 108 . . . so b will 108 . now let ' s check the multiples of 4 among this set 108 - 36 / 4 + 1 = > 18 + 1 = > 19 ans option b ."
Answer: b
Question (general): find the value of ( 20 c 18 ) * ( 20 c 20 )
Options: a ) 400 , b ) 380 , c ) 360 , d ) 350 , e ) 330
Rationale: "20 c 20 = 1 ( 20 c 2 ) * ( 20 c 20 ) = 20 ! * 1 / 18 ! = 20 * 19 * 18 ! / 18 ! = 20 * 19 * 1 = 380 answer : b"
Answer: b
Question (gain): if 30 % of a class averages 95 % on a test , 50 % of the class averages 79 % on the test , and the remainder of the class averages 60 % on the test , what is the overall class average ? ( round final answer to the nearest percent ) .
Options: a ) 76 % , b ) 77 % , c ) 78 % , d ) 79 % , e ) 80 %
Rationale: "this question is a weighted average question with a series of dependent variables . the remaining portion of the class represents 100 % - 30 % - 50 % = 20 % of the class converting the portions of the class population to decimal weights , we find : class average = 0.30 x 95 + 0.50 x 79 + 0.20 x 60 = 80 the class average ( rounded ) is 80 % final answer e ) 80 %"
Answer: e
Question (general): two kinds of vodka are mixed in the ratio 2 : 6 and 6 : 3 and they are sold fetching the profit 10 % and 20 % 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 ) 20 % , b ) 40 % , c ) 18 % , d ) 23 % , e ) can not be determined
Rationale: "the profit on the first kind of vodka = x % ; the profit on the second kind of vodka = y % . when they are mixed in the ratio 1 : 2 ( total of 3 parts ) the average profit is 10 % : ( x + 2 y ) / 3 = 10 . when they are mixed in the ratio 2 : 1 ( total of 3 parts ) the average profit is 20 % : ( 2 x + y ) / 3 = 20 . solving gives : x = 30 % and y = 0 % . after the individual profit percent on them areincreased by 4 / 3 and 5 / 3 times respectively the profit becomes 40 % and 0 % , on the first and te second kinds of vodka , respectively . if they are mixed in equal ratio ( 1 : 1 ) , then the mixture will fetch the profit of ( 40 + 0 ) / 2 = 20 % . answer : a"
Answer: a
Question (physics): if the tens digit of positive integers m , y are 6 , how many values of the tens digit of 2 ( m + y ) can be there ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: if the tens digit of positive integers m , y are 6 , how many values of the tens digit of 2 ( m + y ) can be there ? a . 2 b . 3 c . 4 d . 5 e . 6 - > if m = y = 60 , 2 ( m + y ) = 240 is derived . if m = y = 69 , 2 ( m + y ) = 276 is derived , which makes 4,5 , 6,7 possible for the tens digit . therefore , the answer is c .
Answer: c
Question (general): the maximum number of students among them 848 pens and 630 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils ?
Options: a ) 10 , b ) 4 , c ) 2 , d ) 14 , e ) 16
Rationale: "number of pens = 848 number of pencils = 630 required number of students = h . c . f . of 848 and 630 = 2 answer is c"
Answer: c
Question (geometry): find the ratio of the curved surfaces of two cylinders of same heights if their radii are in the ratio 1 : 2 ?
Options: a ) 1 : 2
b ) 2 : 3
c ) 2 : 9
d ) 2 : 1
e ) 2 : 2
Rationale: 1 : 2 answer : a
Answer: a