Cheukting/mathqa huggingface dataset:
Question (gain): a glass was filled with 15 ounces of water , and 0.05 ounce of the water evaporated each day during a 15 - day period . what percent of the original amount of water evaporated during this period ?
Options: a ) 0.005 % , b ) 0.05 % , c ) 0.5 % , d ) 5 % , e ) 25 %
Rationale: "in 15 days 15 * 0.05 = 0.75 ounces of water evaporated , which is 0.75 / 15 â ˆ — 100 = 5 of the original amount of water . answer : d ."
Answer: d
Question (physics): a can do a piece of work in 15 days . a does the work for 5 days only and leaves the job . b does the remaining work in 10 days . in how many days b alone can do the work ?
Options: a ) 5 days , b ) 15 days , c ) 12 days , d ) 9 days , e ) 10 days
Rationale: "explanation : a ’ s 5 day work = 5 * 1 / 15 = 1 / 3 remaining work = 1 - 1 / 3 = 2 / 3 b completes 2 / 3 work in 6 days b alone can do in x days 2 / 3 * x = 10 x = 15 days answer : option b"
Answer: b
Question (general): in a hostel there were 100 students . to accommodate 25 more students the average is decreased by rupees 10 . but total expenditure increased by rs . 500 . find the total expenditure of the hostel now ?
Options: a ) 7500 , b ) 5000 , c ) 5400 , d ) 7000 , e ) 8500
Rationale: let average is x 100 x + 500 = 125 ( x – 10 ) x = 70 100 * 70 + 500 = 7500 answer : a
Answer: a
Question (geometry): the area of a square is 4356 sq cm . find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square .
Options: a ) 5 : 28 , b ) 5 : 19 , c ) 7 : 12 , d ) 5 : 13 , e ) 7 : 22
Rationale: "let the length and the breadth of the rectangle be l cm and b cm respectively . let the side of the square be a cm . a 2 = 4356 a = 66 l = 2 a and b = a - 24 b : l = a - 24 : 2 a = 42 : 132 = 7 : 22 answer : e"
Answer: e
Question (general): pat , kate , and mark charged a total of 144 hours to a certain project . if pat charged twice as much time to the project as kate and 1 / 3 as much time as mark , how many more hours did mark charge to the project than kate ?
Options: a ) 18 , b ) 80 , c ) 72 , d ) 90 , e ) 108
Rationale: "80 all u do is do 2 : 1 : 6 = > 2 x + x + 6 x = 144 = > x = 16 32 : 16 : 96 96 - 16 = 80 answer b"
Answer: b
Question (gain): at the end of the first quarter , the share price of a certain mutual fund was 30 percent higher than it was at the beginning of the year . at the end of the second quarter , the share price was 50 percent higher than it was at the beginning of the year . what was the percent increase in the share price from the end of the first quarter to the end of the second quarter ?
Options: a ) 15.3 % , b ) 25 % , c ) 30 % , d ) 33 % , e ) 40 %
Rationale: "another method is to use the formula for 2 successive percentage changes : total = a + b + ab / 100 50 = 30 + b + 30 b / 100 b = 15.3 answer ( a )"
Answer: a
Question (general): in the graduating class of a certain college , 48 percent of the students are male and 52 percent are female . in this class 50 percent of the male and 20 percent of the female students are 25 years old or older . if one student in the class is randomly selected , approximately what is the probability that he or she will be less than 25 years old ?
Options: a ) a ) 0.9 , b ) b ) 0.6 , c ) c ) 0.45 , d ) d ) 0.3 , e ) e ) 0.25
Rationale: percent of students who are 25 years old or older is 0.5 * 48 + 0.2 * 52 = ~ 34 , so percent of people who are less than 25 years old is 100 - 3 = 66 . answer : b .
Answer: b
Question (general): a grocer has a sale of rs . 5420 , rs . 5660 , rs . 6200 , rs . 6350 and rs . 6500 for 5 consecutive months . find the sale he should have in the sixth month , so that he gets an average sale of rs . 6200 ?
Options: a ) rs . 7070 , b ) rs . 5991 , c ) rs . 6020 , d ) rs . 6850 , e ) none of these
Rationale: "explanation : total sale for 5 months = rs . ( 5420 + 5660 + 6200 + 6350 + 6500 ) = rs . 30,130 therefore , required sale = rs . [ ( 6200 * 6 ) – 30,130 ] = rs . ( 37200 – 30,130 ) = rs . 7070 answer a"
Answer: a
Question (general): the population of a bacteria culture doubles every 2 minutes . approximately how many minutes will it take for the population to grow from 1,000 to 1 , 000,000 bacteria
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 20
Rationale: "the question basically asks how many minutes it takes for a population to increase by factor 1000 ( 1 , 000,000 / 1,000 = 1000 ) . now you know that every two minutes the population doubles , i . e . is multiplied by 2 . so the equation becomes : 2 ^ x > = 1000 , where x represents the number of times the population doubles . a lot of people remember that 2 ^ 10 = 1,024 . i . e . the population has to double 10 times . since it takes the population 2 minutes to double once it takes 10 * 2 minutes = 20 minutes to double nine times . thus , solution e = 20 is correct ."
Answer: e
Question (gain): the present worth of rs . 1183 due in 2 years at 4 % per annum compound interest is
Options: a ) rs . 150.50 , b ) rs . 154.75 , c ) rs . 156.25 , d ) rs . 1093.75 , e ) none
Rationale: "solution present worth = rs . [ 1183 / ( 1 + 4 / 100 ) ² ] = rs . ( 1183 x 25 / 26 x 25 / 26 ) = rs . 1093.75 answer d"
Answer: d
Question (gain): the c . p of 20 pens is equal to the s . p of 12 pens . find his gain % or loss % ?
Options: a ) 10 % , b ) 20 % , c ) 30 % , d ) 40 % , e ) 50 %
Rationale: "20 cp = 12 sp 20 - - - 8 cpgain 100 - - - ? = > 40 % answer : d"
Answer: d
Question (general): how many kg of pure salt must be added to 100 kg of 10 % solution of salt and water to increase it to a 15 % solution ?
Options: a ) a ) 5.8 , b ) b ) 1.3 , c ) c ) 9.6 , d ) d ) 12.5 , e ) e ) 7.9
Rationale: amount salt in 100 kg solution = 10 * 100 / 100 = 10 kg let x kg of pure salt be added then ( 10 + x ) / ( 100 + x ) = 15 / 100 200 + 20 x = 300 + 3 x 17 x = 100 x = 5.8 answer is a
Answer: a
Question (general): how many multiples of 4 are there between 16 and 112 , inclusive ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: "the multiples of 4 are from 4 * 4 up to 4 * 28 . 28 - 4 + 1 = 25 . the answer is e ."
Answer: e
Question (general): jill has 35 gallons of water stored in quart , half - gallon , and one gallon jars . she has equal numbers of each size jar holding the liquid . what is the total number of water filled jars ?
Options: a ) 3 , b ) 60 , c ) 9 , d ) 12 , e ) 14
Rationale: let the number of each size of jar = wthen 1 / 4 w + 1 / 2 w + w = 35 1 3 / 4 w = 35 w = 20 the total number of jars = 3 w = 60 answer : b
Answer: b
Question (gain): a cycle is bought for rs . 850 and sold for rs . 1080 , find the gain percent ?
Options: a ) 22 , b ) 27 , c ) 99 , d ) 88 , e ) 11
Rationale: 850 - - - - 180 100 - - - - ? = > 27 % answer : b
Answer: b
Question (general): the number of singles that a baseball player hit increased 5 percent from her first season to her second season , and the number of doubles that she hit in the same time period decreased by 2 percent . if the total number of singles and doubles that she hit increased 2 percent from her first season to her second season , what is the ratio of the number of singles she hit in her first season to the number of doubles she hit in her first season ?
Options: a ) 4 : 3 , b ) 9 : 11 , c ) 3 : 1 , d ) 2 : 1 , e ) 11 : 3
Rationale: "soln : - 1.05 s + 0.98 d = 1.02 [ s + d ] 0.03 s = 0.04 d s / d = 4 / 3 answer : a"
Answer: a
Question (physics): a person is traveling at 25 km / hr and reached his destiny in 5 hr find the distance ?
Options: a ) 100 km , b ) 95 km , c ) 135 km , d ) 80 km , e ) 125 km
Rationale: speed = 25 km / hr time = 5 hr distance = 25 * 5 = 125 km answer is e
Answer: e
Question (general): in a theater , the first row has 14 seats and each row has 3 more seats than previous row . if the last row has 50 seats , what is the total number of seats in the theater ?
Options: a ) 404 , b ) 408 , c ) 412 , d ) 416 , e ) 420
Rationale: the number of seats in the theater is 14 + ( 14 + 3 ) + . . . + ( 14 + 36 ) = 13 ( 14 ) + 3 ( 1 + 2 + . . . + 12 ) = 13 ( 14 ) + 3 ( 12 ) ( 13 ) / 2 = 13 ( 14 + 18 ) = 13 ( 32 ) = 416 the answer is d .
Answer: d
Question (physics): a train 200 m long takes 6 sec to cross a man walking at 5 kmph in a direction opposite to that of the train . find the speed of the train ?
Options: a ) 85 kmph , b ) 115 kmph , c ) 105 kmph , d ) 95 kmph , e ) 125 kmph
Rationale: "let the speed of the train be x kmph speed of the train relative to man = x + 5 = ( x + 5 ) * 5 / 18 m / sec 200 / [ ( x + 5 ) * 5 / 18 ] = 6 30 ( x + 5 ) = 3600 x = 115 kmph answer is b"
Answer: b
Question (general): 8 ^ 100 is divisible by 17 then find the remainder ?
Options: a ) 8 , b ) 10 , c ) 16 , d ) 17 , e ) 18
Rationale: "this is an extremely difficult problem to solve with out fermat ' s little theorem . by applying fermat ' s little theorem , we know that 816 when divided by 17 , the remainder is 1 . so divide 100 by 16 and find the remainder . remainder = 4 therefore , 100 = ( 16 × 6 ) + 4 now this problem can be written as 810017 = 816 × 6 + 417 = ( 816 ) 6 × 8417 now this problem simply boils down to ( 1 ) 6 × 8417 = 8417 84 = 82 × 82 , we need to find the remainder when 64 × 64 is divisible by 17 . or 13 × 13 = 169 . when 169 is divided by 17 , remainder is 16 . c"
Answer: c
Question (general): a student scored an average of 80 marks in 3 subjects : physics , chemistry and mathematics . if the average marks in physics and mathematics is 90 and that in physics and chemistry is 70 , what are the marks in physics ?
Options: a ) 21 , b ) 27 , c ) 26 , d ) 80 , e ) 28
Rationale: "given m + p + c = 80 * 3 = 240 - - - ( 1 ) m + p = 90 * 2 = 180 - - - ( 2 ) p + c = 70 * 2 = 140 - - - ( 3 ) where m , p and c are marks obtained by the student in mathematics , physics and chemistry . p = ( 2 ) + ( 3 ) - ( 1 ) = 180 + 140 - 240 = 80 . answer : d"
Answer: d
Question (general): in an election , candidate douglas won 54 percent of the total vote in counties x and y . he won 62 percent of the vote in county x . if the ratio of people who voted in county x to county y is 2 : 1 , what percent of the vote did candidate douglas win in county y ?
Options: a ) 25 % , b ) 28 % , c ) 32 % , d ) 38 % , e ) 40 %
Rationale: "given voters in ratio 2 : 1 let x has 200 votersy has 100 voters for x 62 % voted means 62 * 200 = 124 votes combined for xy has 300 voters and voted 54 % so total votes = 162 balance votes = 162 - 124 = 38 as y has 100 voters so 38 votes means 38 % of votes required ans d"
Answer: d
Question (physics): the radius of a wheel is 14.6 cm . what is the distance covered by the wheel in making 100 resolutions ?
Options: a ) 754 m , b ) 704 m , c ) 90.524 m , d ) 706 m , e ) 91.688 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 100 resolutions . = 100 * 2 * 22 / 7 * 14.6 = 9168.8 cm = 91.688 m answer : e"
Answer: e
Question (general): harold and millicent are getting married and need to combine their already - full libraries . if harold , who has 1 / 2 as many books as millicent , brings 1 / 3 of his books to their new home , then millicent will have enough room to bring 1 / 2 of her books to their new home . what fraction of millicent ' s old library capacity is the new home ' s library capacity
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 4 / 5 , e ) 5 / 6
Rationale: because we see h willbring 1 / 3 of his booksto the new home - - > try to pick a number that isdivisible by 3 . before : assume h = 30 books h = 1 / 2 m - - > m = 60 books after : h ' = 1 / 3 h = 10 books m ' = 1 / 2 m = 30 books total = 40 books m ' = 40 = 5 / 6 * 60 ratio : 5 / 6 ans : e
Answer: e
Question (general): on dividing a number by 8 , we get 8 as quotient and 0 as remainder . on dividing the same number by 5 , what will be the remainder ?
Options: a ) 10 , b ) 4 , c ) 8 , d ) 6 , e ) 5
Rationale: "number = 8 * 8 + 0 = 64 5 ) 64 ( 12 60 - - - - - - - - 4 required number = 4 . answer : b"
Answer: b
Question (general): what are the last two digits of ( 301 * 402 * 503 * 604 * 646 * 547 * 448 * 348 ) ^ 2
Options: a ) 86 , b ) 76 , c ) 56 , d ) 36 , e ) 16
Rationale: "( ( 301 * 402 * 503 * 604 * 646 ) * ( 547 * 448 * 348 ) ) ^ 2 if you observe above digits , last digit are : 1,2 , 3,4 , 6,7 , 8,8 ; 5 is missing ; so i have rearranged them so that multiplication will be easy for me as initial 4 digits have last two digits as 01 , 02,03 , 04,46 and final three as 47 * 48 * 48 . solving for only last two digits and multiplying them we get : ( ( 06 * 04 * 46 ) ( 56 * 48 ) ) ^ 2 = ( 44 * 88 ) ^ 2 = 72 ^ 2 = 84 hence answer is a"
Answer: a
Question (other): the number of sailors on a ship is 82 % more than the number of officers . the ratio of sailors to officers would be
Options: a ) 33 : 25 , b ) 47 : 20 , c ) 47 : 25 , d ) 22 : 25 , e ) 91 : 50
Rationale: "sailor = 1.82 * officer sailor / officer = 1.82 / 1 = 182 / 100 = 91 / 50 answer will be e"
Answer: e
Question (general): let f ( x , y ) be defined as the remainder when ( x – y ) ! is divided by x . if x = 50 , what is the maximum value of y for which f ( x , y ) = 0 ?
Options: a ) 35 , b ) 36 , c ) 40 , d ) 42 , e ) 45
Rationale: the question is finding y such that ( 50 - y ) ! is a multiple of 50 . that means we need to have 2 * 5 ^ 2 in ( 50 - y ) ! 10 ! is the smallest factorial number with 2 * 5 ^ 2 as a factor . 50 - y = 10 y = 40 the answer is c .
Answer: c
Question (general): what is the greatest positive integer x such that 3 ^ x is a factor of 9 ^ 9 ?
Options: a ) 5 , b ) 9 , c ) 10 , d ) 18 , e ) 30
Rationale: "what is the greatest positive integer x such that 3 ^ x is a factor of 9 ^ 9 ? 9 ^ 9 = ( 3 ^ 2 ) ^ 9 = 3 ^ 18 d . 18"
Answer: d
Question (physics): the speed of a railway engine is 84 km per hour when no compartment is attached , and the reduction in speed is directly proportional to the square root of the number of compartments attached . if the speed of the train carried by this engine is 24 km per hour when 9 compartments are attached , the maximum number of compartments that can be carried by the engine is :
Options: a ) 19 , b ) 18 , c ) 16 , d ) 17 , e ) 14
Rationale: "the reduction in speed is directly proportional to the square root of the number of compartments attached doesreductionmean amount subtracted ? or percentage decrease ? there are at least two interpretations , and the wording does not provide a clear interpretation between them . evidently what the question intends is the subtraction interpretation . what is subtracted from the speed is directly proportional to the square root of the number of compartments attached . in other words , if s = speed , and n = number of compartments , then s = 84 - k * sqrt ( n ) wherekis a constant of the proportionality . in general , if a is directly proportional to b , we can write a = k * b and solve for k . if n = 9 , then s = 24 24 = 84 - k * sqrt ( 9 ) = 84 - 3 k k = 20 now , we need to know : what value of n makes s go to zero ? 0 = 84 - 20 * sqrt ( n ) 20 * sqrt ( n ) = 84 sqrt ( n ) = 4.2 n = 4.2 ^ 2 > 17 with 18 compartments , the train does not budge . therefore , it would budge if there were one fewer cars . thus , 17 is the maximum number of cars the engine can pull and still move . d"
Answer: d
Question (physics): a train covers a distance of 90 km in 20 min . if it takes 9 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 675 , b ) 680 , c ) 685 , d ) 690 , e ) 695
Rationale: "speed = ( 90 / 20 * 60 ) km / hr = ( 270 * 5 / 18 ) m / sec = 75 m / sec . length of the train = 75 * 9 = 675 m . answer : option a"
Answer: a
Question (physics): 3 men and 8 women complete a task in same time as 6 men and 2 women do . how much fraction of work will be finished in same time if 3 men and 2 women will do that task .
Options: a ) 4 / 7 , b ) 3 / 10 , c ) 3 / 18 , d ) 13 / 16 , e ) 4 / 11
Rationale: "3 m + 8 w = 6 m + 2 w 3 m = 6 w 1 m = 2 w therefore 3 m + 8 w = 14 w 3 m + 2 w = 8 w answer is 8 / 14 = 4 / 7 answer : a"
Answer: a
Question (general): a third of arun â € ™ s marks in mathematics exceed a half of his marks in english by 20 . if he got 360 marks in two subjects together how many marks did he got in english ?
Options: a ) 120,60 , b ) 240,120 , c ) 280,90 , d ) 220,140 , e ) none of them
Rationale: "let arun â € ™ s marks in mathematics and english be x and y then ( 1 / 3 ) x - ( 1 / 2 ) y = 20 2 x - 3 y = 120 â € ¦ â € ¦ > ( 1 ) x + y = 360 â € ¦ â € ¦ . > ( 2 ) solving ( 1 ) and ( 2 ) x = 240 and y = 120 answer is b ."
Answer: b
Question (general): in an ngo the daily average wages of 20 illiterate employees is decreased from rs . 25 to rs . 10 , thus the average salary of all the literate and illiterate employees is decreased rs . 10 per day . the no . of educated employees working in the ngo is ?
Options: a ) 11 , b ) 82 , c ) 10 , d ) 28 , e ) 23
Rationale: "explanation : total employees = \ inline \ frac { ( 25 - 10 ) \ times 20 } { 10 } = 30 hence number of educated employees = 30 - 20 = 10 answer : c"
Answer: c
Question (gain): in the fifth grade at parkway elementary school there are 500 students . 350 students are boys and 250 students are playing soccer . 86 % of the students that play soccer are boys . how many girl student are in parkway that is not playing soccer ?
Options: a ) 69 . , b ) 73 . , c ) 81 . , d ) 91 . , e ) 115 .
Rationale: "total students = 500 boys = 350 , girls = 150 total playing soccer = 250 86 % of 250 = 215 are boys who play soccer . girls who play soccer = 35 . total girls who do not play soccer = 150 - 35 = 115 . correct option : e"
Answer: e
Question (general): for what value of x between − 8 and 8 , inclusive , is the value of x ^ 2 − 10 x + 16 the greatest ?
Options: a ) − 8 , b ) − 2 , c ) 0 , d ) 2 , e ) 8
Rationale: "we can see from the statement that two terms containing x , x ^ 2 will always be positive and - 10 x will be positive if x is - ive . . so the equation will have greatest value if x is - ive , and lower the value of x , greater is the equation . so - 8 will give the greatest value . . ans a"
Answer: a
Question (geometry): what positive number , when squared , is equal to the cube of the positive square root of 16 ?
Options: a ) 64 , b ) 32 , c ) 8 , d ) 4 , e ) 2
Rationale: "let the positive number be x x ^ 2 = ( ( 16 ) ^ ( 1 / 2 ) ) ^ 3 = > x ^ 2 = 4 ^ 3 = 64 = > x = 8 answer c"
Answer: c
Question (general): the difference of two numbers is 1515 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder . what is the smaller number ?
Options: a ) a ) 270 , b ) b ) 280 , c ) c ) 290 , d ) d ) 300 , e ) e ) 310
Rationale: "let the smaller number be x . then larger number = ( x + 1515 ) . x + 1515 = 6 x + 15 5 x = 1500 x = 300 smaller number = 300 . d )"
Answer: d
Question (gain): mr . john used to purchase certain number of mangoes for $ 360 since the price of mangoes is reduced by 10 % he got 12 more mangoes today . find the original price of 115 mangoes .
Options: a ) 360 , b ) 383 , c ) 400 , d ) 406 , e ) 412
Rationale: "mr . john used to purchase certain number of mangoes for $ 360 since the price of mangoes is reduced by 10 % he got 12 more mangoes today . find the original price of 120 mangoes . method 1 : let price per mango = x . let number of mangoes be n . then , nx = 360 . now price = 0.9 x ; number of mangoes = n + 12 . total amount = 0.9 x * ( n + 12 ) = 360 . nx = 0.9 nx + 10.8 x = > 0.1 nx = 10.8 x = > n = 108 = > x = 360 / 108 = 3.33 original price of 115 mangoes = 115 * 3.33 = 383 . answer b"
Answer: b
Question (general): if a randomly selected positive single digit multiple of 3 is multiplied by a randomly selected prime number less than 20 , what is the probability r that this product will be a multiple of 45 ?
Options: a ) 1 / 32 , b ) 1 / 28 , c ) 1 / 24 , d ) 1 / 16 , e ) 1 / 14
Rationale: "there are 3 single digit multiple of 3 , that is , 3 , 6,9 . there are 8 prime nos less than 20 - 2,3 , 5,7 , 11,13 , 17,19 total outcome - 8 * 3 = 24 favourable outcome = 1 ( 9 * 5 ) hence required probability r = 1 / 24 . answer c ."
Answer: c
Question (physics): a and b can do a work in 4 days , b and c in 5 days , c and a in 7 days . if a , b and c work together , they will complete the work in ?
Options: a ) 3 days , b ) 5 days , c ) 7 days , d ) 1 days , e ) 2 dasy
Rationale: "a + b 1 day work = 1 / 4 b + c 1 day work = 1 / 5 c + a 1 day work = 1 / 7 adding we get 2 ( a + b + c ) = 1 / 4 + 1 / 5 + 1 / 7 = 83 / 140 a + b + c 1 day work = 83 / 280 a , b , c can finish the work in 280 / 83 days = 3 days approximately answer is a"
Answer: a
Question (probability): there are 9 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair . what is the number of pair that can be formed .
Options: a ) 62 , b ) 70 , c ) 72 , d ) 71 , e ) 76
Rationale: "first of all you should remember that there is a difference in left and right sock . now no . of way to select any of the sock = 9 and for second = 8 so total methods = 9 * 8 = 72 answer : c"
Answer: c
Question (probability): how many cubes of 3 cm edge can be cut out of a cube of 18 cm edge
Options: a ) 36 , b ) 232 , c ) 216 , d ) 455 , e ) 363
Rationale: "number of cubes = ( 18 x 18 x 18 ) / ( 3 x 3 x 3 ) = 216 answer : c"
Answer: c
Question (general): 600 x 223 + 600 x 77 = ?
Options: a ) 180000 , b ) 138800 , c ) 658560 , d ) 116740 , e ) none of them
Rationale: "= 600 x ( 223 + 77 ) ( by distributive law ) = 600 x 300 = 180000 answer is a"
Answer: a
Question (geometry): a volume of 10976 l water is in a container of sphere . how many hemisphere of volume 4 l each will be required to transfer all the water into the small hemispheres ?
Options: a ) 2812 , b ) 8231 , c ) 2734 , d ) 2744 , e ) 4254
Rationale: "a volume of 4 l can be kept in 1 hemisphere therefore , a volume of 10976 l can be kept in ( 10976 / 4 ) hemispheres ans . 2744 answer : d"
Answer: d
Question (general): at the end of the day , february 14 th , a florist had 150 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 , 20 of which were white and 15 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 ) 50 % , b ) 25 % , c ) 250 % , d ) 75 % , e ) 80 %
Rationale: "r + w + p = 150 s + l = 150 1 / 3 * 150 = 50 short - stemmed white = 20 short - stemmed pink = 15 = > short - stemmed red = 15 15 / p = 15 / r = > r = p so total long stemmed = 100 and long stemmed red + long stemmed pink = 100 so long stemmed red / long stemmed = ? total white = 20 ( as no long stemmed white ) = > r + r + 20 = 150 = > r = 130 and r = 65 long stemmed r = 65 - 15 = 50 so long stemmed red / r = 50 / 100 = 50 % answer - a"
Answer: a
Question (gain): a discount electronics store normally sells all merchandise at a discount of 10 percent to 30 percent off the suggested retail price . if , during a special sale , an additional 20 percent were to be deducted from the discount price , what would be the lowest possible price of an item costing $ 260 before any discount ?
Options: a ) $ 130.00 , b ) $ 145.60 , c ) $ 163.80 , d ) $ 182.00 , e ) $ 210.00
Rationale: "original price : 260 $ max first discount = - 30 % thus : 260 ∗ ( 1 − 30 / 100 ) = 182 second discount on the discounted price = - 20 % thus : 182 ∗ ( 1 − 20 / 100 ) = 145,6 answer b ."
Answer: b
Question (general): what is the lowest positive integer that is divisible by each of the integers 1 through 11 inclusive ?
Options: a ) 420 , b ) 840 , c ) 1260 , d ) 2520 , e ) 27,720
Rationale: "we have to find the lcm of 1 , 2 , 3 , 2 ^ 2 , 5 , 2 * 3 , 7 , 2 ^ 3 , 3 ^ 2 , 2 * 5 , and 11 . the lcm is 1 * 2 ^ 3 * 3 ^ 2 * 5 * 7 * 11 = 27,720 the answer is e ."
Answer: e