Cheukting/mathqa huggingface dataset:
Question (physics): a can do a piece of work in 20 days and b alone can do it in 10 days . b works at it for 5 days and then leaves . a alone can finish the remaining work in
Options: a ) 10 days , b ) 6 days , c ) 7.5 days , d ) 8.5 days , e ) 9 days
Rationale: "explanation : b ' s 5 days work = 1 / 10 ∗ 5 = 1 / 2 remaining work = 1 − 1 / 2 = 1 / 2 a can finish work = 20 ∗ 1 / 2 = 10 days option a"
Answer: a
Question (probability): what is the probability that the sum of two dice will yield a 6 , and then when both are thrown again , their sum will again yield a 6 ? assume that each die has 5 sides with faces numbered 1 to 5 .
Options: a ) 1 / 144 , b ) 1 / 25 , c ) 1 / 12 , d ) 1 / 6 , e ) 1 / 3
Rationale: solution - rolling dices is an independent event . the combinations to get 6 are ( 1,5 ) , ( 5,1 ) , ( 2,4 ) , ( 4,2 ) , ( 3,3 ) and total combinations of both dices is 25 . the probability of getting 6 in first attempt is 5 / 25 = 1 / 5 . probability of getting 6 again in second attempt = ( 1 / 5 ) * ( 1 / 5 ) = 1 / 25 . ans b
Answer: b
Question (general): the average of runs of a cricket player of 10 innings was 34 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?
Options: a ) 78 , b ) 79 , c ) 85 , d ) 87 , e ) 89
Rationale: "explanation : average = total runs / no . of innings = 34 so , total = average x no . of innings = 34 x 10 = 340 . now increase in avg = 4 runs . so , new avg = 34 + 4 = 38 runs total runs = new avg x new no . of innings = 38 x 11 = 418 runs made in the 11 th inning = 418 - 340 = 78 answer : a"
Answer: a
Question (physics): a truck covers a distance of 288 km at a certain speed in 8 hours . how much time would a car take at an average speed which is 18 kmph more than that of the speed of the truck to cover a distance which is 90 km more than that travelled by the truck ?
Options: a ) 6 hours , b ) 5 hours , c ) 7 hours , d ) 8 hours , e ) none
Rationale: "explanation : speed of the truck = distance / time = 288 / 8 = 36 kmph now , speed of car = ( speed of truck + 18 ) kmph = ( 36 + 18 ) = 54 kmph distance travelled by car = 288 + 90 = 378 km time taken by car = distance / speed = 378 / 54 = 7 hours . answer – c"
Answer: c
Question (general): a , b and c play a cricket match . the ratio of the runs scored by them in the match is a : b = 2 : 3 and b : c = 2 : 5 . if the total runs scored by all of them are 75 , the runs scored by b are ? a . 15 b . 18
Options: a ) 22 , b ) 18 , c ) 99 , d ) 77 , e ) 24
Rationale: a : b = 2 : 3 b : c = 2 : 5 a : b : c = 4 : 6 : 15 6 / 25 * 75 = 18 answer : b
Answer: b
Question (other): if 65 percent of a class answered the first question on a certain test correctly , 50 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ?
Options: a ) 25 % , b ) 30 % , c ) 35 % , d ) 40 % , e ) 45 %
Rationale: "65 % answered the first question correctly and 20 % answered neither correctly . then 15 % missed the first question but answered the second question correctly . then the percent who answered both correctly is 50 % - 15 % = 35 % . the answer is c ."
Answer: c
Question (gain): john and ingrid pay 30 % and 40 % tax annually , respectively . if john makes $ 56000 and ingrid makes $ 73000 , what is their combined tax rate ?
Options: a ) 32 % , b ) 34.4 % , c ) 35 % , d ) 35.6 % , e ) 36.4 %
Rationale: "( 1 ) when 30 and 40 has equal weight or weight = 1 / 2 , the answer would be 35 . ( 2 ) when 40 has larger weight than 30 , the answer would be in between 35 and 40 . unfortunately , we have 2 answer choices d and e that fit that condition so we need to narrow down our range . ( 3 ) get 73000 / 129000 = 73 / 129 is a little above 1 / 2 . thus , our answer is just a little above 35 . answer : d"
Answer: d
Question (general): the average ( arithmetic mean ) of 20 , 40 , and 60 is 6 more than the average of 10 , 70 , and what number ?
Options: a ) 15 , b ) 25 , c ) 35 , d ) 22 , e ) 55
Rationale: "a 1 = 120 / 3 = 40 a 2 = a 1 - 6 = 34 sum of second list = 34 * 3 = 102 therefore the number = 102 - 80 = 22 answer : d"
Answer: d
Question (general): if 150 ! / 10 ^ n is an integer , what is the largest possible value of n ?
Options: a ) 38 , b ) 47 , c ) 32 , d ) 36 , e ) 37
Rationale: the question actually asks the highest power of 10 which divides 150 ! ( for a number to be an integer - without any remainder all the trailing zeroe ' s must be divided by the denominator ) 10 = 2 x 5 150 factorial will have 37 as - 150 / 5 = 30 30 / 5 = 6 6 / 5 = 1 so answer will be ( e ) 37
Answer: e
Question (general): the average height of 20 students in a class was calculated as 175 cm . it has later found that the height of one of the students in the class was incorrectly written as 151 cm whereas the actual height was 131 cm . what was the actual average height of the students in the class ?
Options: a ) 174 cm , b ) 173 cm , c ) 172 cm , d ) 171 cm , e ) 170 cm
Rationale: "the total height was 20 cm too much . the average height should be reduced by 20 cm / 20 = 1 cm the answer is a ."
Answer: a
Question (physics): a certain number of workers can do a work in 85 days . if there were 10 workers more it could be finished in 10 days less . how many workers are there ?
Options: a ) 75 , b ) 30 , c ) 28 , d ) 24 , e ) 32
Rationale: "number of workers = 10 * ( 85 - 10 ) / 10 = 75 answer is a"
Answer: a
Question (general): in cliff ’ s impressive rock collection , there are half as many igneous rocks as sedimentary rocks . of the igneous rocks , 4 / 5 are shiny and the rest are matte , while 1 / 5 of the sedimentary rocks are shiny . if there are 40 shiny igneous rocks , how many total rocks does cliff have ?
Options: a ) 30 , b ) 150 , c ) 60 , d ) 90 , e ) 135
Rationale: "we can start with the known quantity and then go on to find the others . shiny igneous ricks are 40 . these are ( 4 / 5 ) of total igneous rocks . ( 4 / 5 ) * total igneous rocks = 40 total igneous rocks = 40 * ( 5 / 4 ) = 50 total sedimentary rocks = 2 * total igneous rocks = 2 * 50 = 100 total number of rocks = 50 + 100 = 150 answer ( b )"
Answer: b
Question (gain): car z travels 48 miles per gallon of gasoline when driven at a constant rate of 45 miles per hour , but travels 20 percent fewer miles per gallon of gasoline when driven at a constant rate of 60 miles per hour . how many miles does car z travel on 10 gallons of gasoline when driven at a constant rate of 60 miles per hour ?
Options: a ) 320 , b ) 384 , c ) 400 , d ) 408.3 , e ) 440
Rationale: "the question stem asks us for the distance possible with 10 gallons of fuel at a constant speed of 60 miles per hour . we therefore first calculate the fuel efficiency at that speed . the stem tells us that at 45 miles / hour , the car will run 48 miles / gallon and at 60 miles / hour , that distance decreases by 20 % . we can therefore conclude that the car will travel 38.4 miles / gallon at a constant speed of 60 miles / gallon . with 10 gallons of fuel , the car can therefore travel 38.4 miles / gallon * 10 gallons = 384 miles . answer b ."
Answer: b
Question (general): mr yadav spends 60 % of his monthly salary on consumable items and 50 % of the remaining on clothes and transport . he saves the remaining amount . if his savings at the end of the year were 24000 , how much amount per month would he have spent on clothes and transport ?
Options: a ) 2000 , b ) 8076 , c ) 9691.2 , d ) 4845.6 , e ) none of these
Rationale: "∵ amount , he have spent in 1 month on clothes transport = amount spent on saving per month ∵ amount , spent on clothes and transport = 24000 ⁄ 12 = 2000 answer a"
Answer: a
Question (other): in the class of 50 students , 30 speak tamil and 40 speak telugu . what is the lowest possible number of students who speak both the languages ?
Options: a ) a ) 8 , b ) b ) 10 , c ) c ) 20 , d ) d ) 30 , e ) e ) 32
Rationale: let the student who speaks tamil - x let the student who speaks telugu - y as ( xuy ) - ( xny ) = total 30 + 40 - ( xny ) = 50 = 20 c )
Answer: c
Question (physics): two trains start simultaneously from opposite ends of a 175 - km route and travel toward each other on parallel tracks . train x , traveling at a constant rate , completes the 175 - km trip in 4 hours . train y , travelling at a constant rate , completes the 175 - km trip in 3 hours . how many kilometers had train x traveled when it met train y ?
Options: a ) 66 , b ) 69 , c ) 72 , d ) 75 , e ) 78
Rationale: if the two trains cover a total distance d , then train x travels ( 3 / 7 ) * d while train y travels ( 4 / 7 ) * d . if the trains travel 175 km to the meeting point , then train x travels ( 3 / 7 ) * 175 = 75 km . the answer is d .
Answer: d
Question (general): the sum of two numbers is 16 . the difference is 4 . what are the two numbers ? let x be the first number . ley y be the second number x + y = 16 x - y = 4
Options: a ) 10 and 6 , b ) 10 and 5 , c ) 10 and 4 , d ) 10 and 3 , e ) 10 and 2
Rationale: solution let x be the first number . ley y be the second number x + y = 16 x - y = 4 solve the system of equations by elimination adding the left sides and the right sides gives : x + x + y + - y = 16 + 4 2 x = 20 x = 10 since x + y = 16 , 10 + y = 16 10 + y = 16 10 - 10 + y = 16 - 10 y = 6 the numbers are 10 and 6 answer a
Answer: a
Question (general): if 6 x = 8 y = 10 z , then what is a possible sum of positive integers x , y , and z ?
Options: a ) 52 , b ) 58 , c ) 84 , d ) 94 , e ) 168
Rationale: "6 x = 8 y = 10 z 3 x = 4 y = 5 z 3 ( 4 * 5 ) = 4 ( 3 * 5 ) = 5 ( 3 * 4 ) addition = 20 + 15 + 12 = 47 answer would be multiple of 47 which is 94 answer : d"
Answer: d
Question (gain): what is the rate percent when the simple interest on rs . 2000 amount to rs . 320 in 4 years ?
Options: a ) 4.5 % , b ) 4.25 % , c ) 4 % , d ) 4.3 % , e ) 4.1 %
Rationale: "interest for 1 year = 320 / 4 = 80 interest on rs 2000 p / a = 80 interest rate = 80 / 2000 * 100 = 4 % answer : c"
Answer: c
Question (other): a ratio between two numbers is 4 : 5 and their l . c . m . is 200 . the first number is
Options: a ) 60 , b ) 40 , c ) 20 , d ) 15 , e ) none
Rationale: "sol . let the required numbers be 4 x and 5 x . then , their l . c . m . is 20 x . ∴ 20 x = 200 ⇔ x = 10 . hence , the first number is 40 . answer b"
Answer: b
Question (general): 10 camels cost as much as 24 horses , 16 horses cost as much as 4 oxen and 6 oxen as much as 4 elephants . if the cost of 10 elephants is rs . 170000 , find the cost of a camel ?
Options: a ) rs . 9800 , b ) rs . 3800 , c ) rs . 9800 , d ) rs . 6800 , e ) rs . 6880
Rationale: "cost of the camel = p 10 camels = 24 horses 16 horses = 4 oxen 6 oxen = 4 elephants 10 elephants = rs . 170000 p = rs . [ ( 24 * 4 * 4 * 170000 ) / ( 10 * 16 * 6 * 10 ) ] p = rs . ( 65280000 / 9600 ) = > p = rs . 6800 answer : d"
Answer: d
Question (gain): a sum of money at simple interest amounts to rs . 835 in 3 years and to rs . 854 in 4 years . the sum is :
Options: a ) 647 , b ) 698 , c ) 778 , d ) 847 , e ) 976
Rationale: "s . i . for 1 year = rs . ( 854 - 835 ) = rs . 19 . s . i . for 3 years = rs . ( 19 x 3 ) = rs . 57 . principal = rs . ( 835 - 57 ) = rs . 778 . answer : c"
Answer: c
Question (general): when the positive integer k is divided by the positive integer n , the remainder is 11 . if k / n = 81.1 , what is the value of n ?
Options: a ) 9 , b ) 20 , c ) 55 , d ) 70 , e ) 81
Rationale: "here ' s an approach that ' s based on number properties and a bit ofbrute forcemath : we ' re told that k and n are both integers . since k / n = 81.2 , we can say that k = 81.2 ( n ) n has tomultiply outthe . 2 so that k becomes an integer . with the answers that we have to work with , n has to be a multiple of 5 . eliminate a and e . with the remaining answers , we can test the answers and find the one that fits the rest of the info ( k / n = 81.2 and k / n has a remainder of 11 ) answer b : if n = 20 , then k = 1624 ; 1624 / 20 has a remainder of 4 not a match answer c : if n = 55 , then k = 4466 ; 4466 / 55 has a remainder of 11 match . final answer : e"
Answer: e
Question (general): if a person walks at 10 km / hr instead of 8 km / hr , he would have walked 14 km more . the actual distance traveled by him is ?
Options: a ) 50 , b ) 40 , c ) 56 , d ) 16 , e ) 20
Rationale: "let the actual distance traveled be x km . then , x / 8 = ( x + 14 ) / 10 2 x - 112 = > x = 56 km . answer : c"
Answer: c
Question (general): if twice of a number divided by 3 d gives 20 as the remainder , and 5 times of the same number gives 32 as the remainder . what will be the value of d ?
Options: a ) 11 , b ) 12 , c ) 15 , d ) 14 , e ) 18
Rationale: remainder in second case is , 32 . so , 3 d > = 33 . so , minimum value of d should 11 . if number = 28 . double of number = 56 and take d = 12 so 56 / 36 remainder = 20 . now 5 times of number = 140 . so 140 / 36 remainder = 32 . that is , 3 d = 36 satisfy the conditions . so d = 12 . answer : b
Answer: b
Question (general): 17 : 71 : : 18 : ?
Options: a ) 80 , b ) 25 , c ) 36 , d ) 81 , e ) 56
Rationale: "ans 81 reverse of 18 answer : d"
Answer: d
Question (general): 3 people candidates contested an election and they received 1136 , 7636 and 11628 votes respectively . what is the percentage of the total votes did the winning candidate get ?
Options: a ) 40 % , b ) 45 % , c ) 57 % , d ) 58 % , e ) 60 %
Rationale: tot no of votes = ( 1136 + 7636 + 11628 ) = 20400 req = > ( 11628 / 20400 * 100 ) = > 57 % answer c
Answer: c
Question (general): in the faculty of reverse - engineering , 500 second year students study numeric methods , 300 second year students study automatic control of airborne vehicles and 300 second year students study them both . how many students are there in the faculty if the second year students are approximately 50 % of the total ?
Options: a ) 1100 , b ) 1200 , c ) 1150 , d ) 1000 , e ) 1050
Rationale: "total number of students studying both are 500 + 300 - 300 = 500 ( subtracting the 300 since they were included in the both the other numbers already ) . so 50 % of total is 500 , so 100 % is 1000 answer is d"
Answer: d
Question (physics): two pipes a and b can separately fill a tank in 8 and 10 minutes respectively . a third pipe c can drain off 15 liters of water per minute . if all the pipes are opened , the tank can be filled in 10 minutes . what is the capacity of the tank ?
Options: a ) 590 liters , b ) 160 liters , c ) 740 liters , d ) 560 liters , e ) 120 liters
Rationale: "1 / 8 + 1 / 10 - 1 / x = 1 / 10 x = 8 8 * 15 = 120 answer : e"
Answer: e
Question (gain): what annual installment will discharge a debt of $ 1092 due in 3 years at 12 % simple interest ?
Options: a ) $ 210 , b ) $ 115 , c ) $ 295 , d ) $ 325 , e ) $ 415
Rationale: "let each installment be x [ x + ( x * 12 * 1 / 100 ) ] + [ x + ( x * 12 * 2 / 100 ) ] + x = 1092 28 x / 25 + 31 x / 25 + x = 1092 x = 325 answer is d"
Answer: d
Question (geometry): a spirit and water solution is sold in a market . the cost per liter of the solution is directly proportional to the part ( fraction ) of spirit ( by volume ) the solution has . a solution of 1 liter of spirit and 1 liter of water costs 40 cents . how many cents does a solution of 1 liter of spirit and 2 liters of water cost ?
Options: a ) 40 , b ) 33 , c ) 50 , d ) 51 , e ) 52
Rationale: "yes , ensure that you understand the relation thoroughly ! cost per liter = k * fraction of spirit 40 cents is the cost of 2 liters of solution ( 1 part water , 1 part spirit ) . so cost per liter is 20 cents . fraction of spirit is 1 / 2 . 20 = k * ( 1 / 2 ) k = 40 cost per liter = 40 * ( 1 / 3 ) ( 1 part spirit , 2 parts water ) cost for 3 liters = 40 * ( 1 / 3 ) * 3 = 40 cents a . 40 cents"
Answer: a
Question (physics): if 12 men or 20 women can do a piece of work in 54 days , then in how many days can 9 men and 12 women together do the work ?
Options: a ) 10 days , b ) 30 days , c ) 20 days , d ) 80 days , e ) 40 days
Rationale: "e 40 days given that 12 m = 20 w = > 3 m = 5 w 9 men + 12 women = 15 women + 12 women = 27 women 20 women can do the work in 54 days . so , 27 women can do it in ( 20 * 54 ) / 27 = 40 days ."
Answer: e
Question (general): set q consists of integers { 3 , - 8 , y , 19 , - 6 } and set b consists of integers { k , - 3 , 0 , 16 , - 5 , 9 } . number l represents the median of set q , number m represents mode of set b and number z = l ^ m . if y is an integer greater than 21 , for what value of k will z be a divisor of 26 ?
Options: a ) - 2 , b ) - 1 , c ) 0 , d ) 1 , e ) 2
Rationale: a = { 3 , - 8 , y , 19 , - 6 } b = { k , - 3 , 0,16 , - 5,9 } y > 21 so l = median of q = 3 m = mode of set b z = ( 3 ) ^ m if z is a divisor of 26 , ( 3 ) ^ m = 1 because 26 does not have 3 as a factor = > m = 0 hence k = 0 , as m is mode and 0 will be the most frequently occuring number in set b . answer - c
Answer: c
Question (general): gold is 19 times as heavy as water and copper is 9 times as heavy as water . in what ratio should these be mixed to get an alloy 13 times as heavy as water ?
Options: a ) 1 : 2 , b ) 2 : 3 , c ) 4 : 1 , d ) 5 : 2 , e ) 6 : 5
Rationale: "g = 19 w c = 9 w let 1 gm of gold mixed with x gm of copper to get 1 + x gm of the alloy 1 gm gold + x gm copper = x + 1 gm of alloy 19 w + 9 wx = x + 1 * 13 w 19 + 9 x = 13 ( x + 1 ) x = 3 / 2 ratio of gold with copper = 1 : 3 / 2 = 2 : 3 answer is b"
Answer: b
Question (general): x and y are both integers . if x / y = 59.60 , then what is the sum of all the possible two digit remainders of x / y ?
Options: a ) 560 , b ) 315 , c ) 672 , d ) 900 , e ) 1024
Rationale: "remainder = 0.60 - - > 60 / 100 - - > can be written as ( 60 / 4 ) / ( 100 / 4 ) = 15 / 25 so remainders can be 15 , 30 , 45 , 60 , . . . . . 90 . we need the sum of only 2 digit remainders - - > 15 + 30 + 45 + 60 + 75 + 90 = 315 answer : b"
Answer: b
Question (general): a and b started a business jointly a ' s investment was thrice the investment of b and the period of his investment was two times the period of investment of b . if b received rs . 4000 as profit , then their total profit is
Options: a ) 23477 , b ) 28000 , c ) 28877 , d ) 1987 , e ) 1771
Rationale: "explanation : suppose b invested rs . x for y months . then , a invested rs . 3 x for 2 y months . so , a : b = ( 3 x * 2 y ) : ( x * y ) = 6 xy : xy = 6 : 1 . b ' s profit : total profit = 1 : 7 . let the total profit be rs . x then , 1 / 7 = 4000 / x or x = 28000 . answer : b ) 28000"
Answer: b
Question (general): excluding stoppages , the average speed of a bus is 100 km / hr and including stoppages , the average speed of the bus is 40 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 15 min , b ) 18 min , c ) 16 min , d ) 20 min , e ) 36 min
Rationale: in 1 hr , the bus covers 100 km without stoppages and 40 km with stoppages . stoppage time = time take to travel ( 100 - 40 ) km i . e 60 km at 100 km / hr . stoppage time = 60 / 100 hrs = 36 min answer : e
Answer: e
Question (physics): tom traveled the entire 60 miles trip . if he did the first 15 miles of at a constant rate 24 miles per hour and the remaining trip of at a constant rate 45 miles per hour , what is the his average speed , in miles per hour ?
Options: a ) 35.62 mph , b ) 25.45 mph , c ) 34.52 mph , d ) 36.92 mph , e ) 36.29 mph
Rationale: avg speed = total distance / total time = ( d 1 + d 2 ) / ( t 1 + t 2 ) = ( 15 + 45 ) / ( ( 15 / 24 ) + ( 45 / 45 ) ) = 60 * 2 / 3 = 36.92 mph d
Answer: d
Question (general): a new home buyer pays 4 % annual interest on her first mortgage and 9 % annual interest on her second mortgage . if she borrowed a total of $ 325,000 , 80 % of which was in the first mortgage , what is her approximate monthly interest payment ?
Options: a ) $ 1,354 , b ) $ 1,733 , c ) $ 3,466 , d ) $ 13,333 , e ) $ 20,796
Rationale: "0.04 x + 0.09 y = 325000 [ 1 ] 0.04 x = 0.80 * 325000 = 260000 [ 2 ] 260000 + 0.09 y = 325000 - - > 0.09 y = 65000 [ 3 ] 260000 / 12 = 21666.67 [ 4 ] 65000 / 12 = 5416.667 [ 5 ] adding [ 4,5 ] we get : 27083.33 [ 6 ] dividing [ 6 ] / 2 to get an average we get 1.354 , ans a"
Answer: a
Question (general): 80 white and black tiles will be used to form a 10 x 10 square pattern . if there must be at least one black tile in every row and at least one white tile in every column , what is the maximum difference between the number of black and white tiles that can be used ?
Options: a ) 75 , b ) 80 , c ) 85 , d ) 90 , e ) 60
Rationale: "answer = e please refer diagram below 70 - 10 = 60"
Answer: e
Question (other): if w is the set of all the integers between 49 and 114 , inclusive , that are either multiples of 3 or multiples of 2 or multiples of both , then w contains how many numbers ?
Options: a ) 34 , b ) 44 , c ) 45 , d ) 55 , e ) 72
Rationale: "official solution : number of multiples of 3 step 1 . subtract the extreme multiples of 3 within the range ( the greatest is 114 , the smallest is 51 ) : 114 - 51 = 63 step 2 . divide by 3 : 63 / 3 = 21 step 3 . add 1 : 21 + 1 = 22 . so there are 22 multiples of 3 within the range : examples are 51 , 54 , 57 , 60 , etc . number of multiples of 2 step 1 . subtract the extreme multiples of 2 within the range ( the greatest is 114 , the smallest is 50 ) : 114 - 50 = 64 step 2 . divide by 2 : 64 / 2 = 32 step 3 . add 1 : 32 + 1 = 33 . so there are 33 multiples of 2 within the range : examples are 50 , 52 , 54 , 56 , 58 , 60 etc . add the 22 multiples of 3 and the 33 multiples of 2 : 22 + 33 = 55 . however , by adding the multiples of 2 and the multiples of 3 , we are effectively counting several numbers twice : for example , 54 and 60 are parts of both the lists above . so we ca n ' t just take 22 + 33 = 55 . find the number of multiples of 6 ( which are the double counted , as 6 is divisible by both 2 and 3 ) , and subtract it from 55 : step 1 . subtract the extreme multiples of 6 within the range ( the greatest is 72 , the smallest is 54 ) : 114 - 54 = 60 step 2 . divide by 6 : 60 / 6 = 10 step 3 . add 1 : 10 + 1 = 11 . so there are 11 multiples of 6 within the range : we counted 11 numbers twice . subtract the 11 multiples of 6 from the sum of the multiples of 2 and 3 : = 22 + 33 - 11 = 55 - 11 = 44 therefore , the final number of multiples of 2 , 3 or 6 is 44 . hence , this is the correct answer . ( b )"
Answer: b
Question (physics): four machines , each working at the same constant rate , together can complete a certain job in 12 days . how many additional machines , each working at the same constant rate , will be needed to complete the job in 8 days ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: "another solution which is faster is since each machine works at a constant rate . the time needs to bought down from 12 to 8 . so the new time is 2 / 3 of the original time . thus to achieve this we need the rate to be 3 / 2 of original . so 3 / 2 * 4 = 6 so we need 6 - 4 = 2 more machines . answer : a"
Answer: a
Question (gain): a shopkeeper sold 8 articles at the cost price of 10 articles . then find the profit % or lost %
Options: a ) 10 % , b ) 25 % , c ) 20 % , d ) 30 % , e ) 50 %
Rationale: "here 8 articles selling price = 10 articles cost price so the difference = 10 - 8 = 2 % of profit = 2 * 100 / 8 = 25 % correct option is b"
Answer: b
Question (geometry): what is the maximum number of pieces that a circular pizza can be cut into with 5 linear cuts ?
Options: a ) 10 , b ) 14 , c ) 15 , d ) 16 , e ) 17
Rationale: "1 cut makes 2 pieces a second cut can make 4 pieces a third cut can make 7 pieces by cutting through 3 of the pieces a fourth cut can make 11 pieces by cutting through 4 of the pieces a fifth cut can make 16 pieces by cutting through 5 of the pieces d"
Answer: d
Question (general): the general hospital is comprised of , 3 / 5 pediatricians , 1 / 4 surgeons , and the rest are gp doctors . if 1 / 4 of the surgeons are heart surgeons , and the hospital doubles the number of gp doctors , what proportion of the hospital are now heart surgeons ?
Options: a ) 2 / 5 , b ) 1 / 4 , c ) 1 / 2 , d ) 1 / 24 , e ) 1 / 25
Rationale: ped = 3 / 5 = 12 / 20 sur = 1 / 4 = 4 / 20 gp = 1 - ( 12 / 20 + 4 / 20 ) = 1 - 16 / 20 = 4 / 20 hsur = ( 1 / 4 ) ( 4 / 20 ) = 1 / 20 if gp doubled = > ( 2 ) ( 4 ) = 8 ; then , total = 12 + 4 + 8 = 24 , and 1 is hsur = > proportion = 1 / 24 . answer : d
Answer: d