Cheukting/mathqa huggingface dataset:
Question (other): there 3 kinds of books in the library physics , chemistry and biology . ratio of physics to chemistry is 3 to 2 ; ratio of chemistry to biology is 4 to 3 , and the total of the books is more than 3000 . which one of following can be the total w of the book ?
Options: a ) 3003 , b ) 3027 , c ) 3024 , d ) 3021 , e ) 3018
Rationale: "first , you have to find the common ratio for all 3 books . you have : p : c : b 3 : 2 - - > multiply by 2 ( gives you row 3 ) 4 : 6 6 : 4 : 3 hence : p : c : b : t ( total ) w 6 : 4 : 3 : 13 - - - - > this means , the total number must be a multiple of 13 . answer a is correct since 299 is divisible by 13 , hence is 2990 and so is 3003 ( 2990 + 13 ) ."
Answer: a
Question (physics): the diameter of the driving wheel of a bus in 140 cm . how many revolutions per minute must the wheel make in order to keep a speed of 33 kmph ?
Options: a ) 210 , b ) 220 , c ) 125 , d ) 240 , e ) 250
Rationale: "distance covered in 1 min = ( 33 * 1000 ) / 60 = 550 m circumference of the wheel = ( 2 * ( 22 / 7 ) * . 70 ) = 4.4 m no of revolution per min = 550 / 4.4 = 125 answer : c"
Answer: c
Question (physics): the population of a bacteria colony doubles every day . if it was started 8 days ago with 2 bacteria and each bacteria lives for 12 days , how large is the colony today ?
Options: a ) 512 , b ) 768 , c ) 1024 , d ) 2048 , e ) 4096
Rationale: "8 days ago - 2 7 days ago - 4 6 days ago - 8 5 days ago - 16 4 days ago - 32 3 days ago - 64 2 days ago - 128 yesterday - 256 today - 512 ans : a"
Answer: a
Question (general): how many quarters are equal to 7 dollars ?
Options: a ) 1 , b ) 28 , c ) 12 , d ) 9 , e ) 7
Rationale: "7 * 4 = 28 quarters answer : b"
Answer: b
Question (gain): what is 0.1 percent of 12,356 ?
Options: a ) 0.12356 , b ) 1.2356 , c ) 12.356 , d ) 0.012356 , e ) 0.0012356
Rationale: since , percent = 1 / 100 , what = something ( s ) , and is : = . we can write the question as s = 0.1 ( 1 / 100 ) 12,356 . the answer is 12.356 . hence , the correct answer is c .
Answer: c
Question (general): the difference between the value of a number increased by 25 % and the value of the original number decreased by 30 % is 22 . what is the original number ?
Options: a ) 40 , b ) 50 , c ) 65 , d ) 70 , e ) 90
Rationale: "let the original # be x then 1.25 x − 0.7 x = 22 - - > x = 40 answer : a ."
Answer: a
Question (general): if a - b = 3 and a ^ 2 + b ^ 2 = 33 , find the value of ab .
Options: a ) 12 , b ) 15 , c ) 10 , d ) 18 , e ) 13
Rationale: "2 ab = ( a ^ 2 + b ^ 2 ) - ( a - b ) ^ 2 = 33 - 9 = 24 ab = 12 . answer is a ."
Answer: a
Question (general): 1 : 3 = 1 2 / 3 : x . the value of x is ?
Options: a ) 1 , b ) 6 , c ) 7 , d ) 5 , e ) 8
Rationale: x * 1 = 3 * 5 / 3 x = 5 answer : d
Answer: d
Question (general): how many figures are required to number the pages the pages of a book containing 709 pages ?
Options: a ) 2020 , b ) 2019 , c ) 1019 , d ) 2029 , e ) 2039
Rationale: "1 to 9 = 9 * 1 = 9 10 to 99 = 90 * 2 = 180 100 to 709 = 610 * 3 = 1830 - - - - - - - - - - - 2019 answer : b"
Answer: b
Question (geometry): a cone of height 9 cm with diameter of its base 18 cm is carved out from a wooden solid sphere of radius 9 cm . the percentage of the wood wasted is :
Options: a ) 45 %
b ) 56 %
c ) 67 %
d ) 75 %
e ) none of these
Rationale: explanation : we will first subtract the cone volume from wood volume to get the wood wasted . then we can calculate its percentage . sphere volume = 4 / 3 π r 3 cone volume = 1 / 3 π r 2 h volume of wood wasted = ( 4 / 3 π ∗ 9 ∗ 9 ∗ 9 ) − ( 1 / 3 π ∗ 9 ∗ 9 ∗ 9 ) = π ∗ 9 ∗ 9 ∗ 9 cm 3 required percentage = π ∗ 9 ∗ 9 ∗ 9 / 4 / 3 π ∗ 9 ∗ 9 ∗ 9 ∗ 100 % = 3 / 4 ∗ 100 % = 75 % option d
Answer: d
Question (gain): of the votes cast on a certain proposal , 66 more were in favor of the proposal than were against it . if the number of votes against the proposal was 40 percent of the total vote , what was the total number of votes cast ? ( each vote cast was either in favor of the proposal or against it . )
Options: a ) 290 , b ) 310 , c ) 330 , d ) 350 , e ) 370
Rationale: "let x be the total number of votes cast . 0.6 x = 0.4 x + 66 0.2 x = 66 x = 330 the answer is c ."
Answer: c
Question (physics): a can finish a work in 72 days , b in 9 days and c in 2 days , b and c start the work but are forced to leave after 3 days . the remaining work was done by a in ?
Options: a ) 30 days , b ) 12 days , c ) 6 days , d ) 7 days , e ) 8 days
Rationale: "b + c 1 day work = 1 / 9 + 1 / 12 = 7 / 36 work done by b and c in 3 days = 7 / 36 * 3 = 7 / 12 remaining work = 1 - 7 / 12 = 5 / 12 1 / 24 work is done by a in 1 day 5 / 12 work is done by a in 72 * 5 / 12 = 30 days answer is a"
Answer: a
Question (general): the average earning of amechanic for the first 4 days of a week is rs . 25 and for the last 4 days is rs . 22 . if heearns rs . 20 on the fourth day , his average earning forthe whole week is ?
Options: a ) s . 10 , b ) s . 24 , c ) s . 30 , d ) s . 40 , e ) s . 50
Rationale: total earning for the week = sum of earning of first four days + sum of earning of last four days - earning of 4 th day = 4 x 25 + 4 x 22 - 20 = rs . 168 â ˆ ´ average earning = 168 / 7 = rs . 24 b
Answer: b
Question (gain): a sum of money deposited at c . i . amounts to rs . 2420 in 2 years and to rs . 3025 in 3 years . find the rate percent ?
Options: a ) 11 , b ) 10 , c ) 28 , d ) 25 , e ) 82
Rationale: "explanation : 2420 - - - 605 100 - - - ? = > 25 % answer : option d"
Answer: d
Question (physics): 9 men working 8 hours per day dig 30 m deep . how many extra men should be put to dig to a depth of 50 m working 6 hours per day ?
Options: a ) 33 , b ) 66 , c ) 88 , d ) 11 , e ) 281
Rationale: "( 9 * 8 ) / 30 = ( x * 6 ) / 50 = > x = 20 20 – 9 = 11 answer : d"
Answer: d
Question (physics): a building contractor employs 20 male , 15 female and 5 child workers . to a male worker he pays rs . 25 per day , to a female worker rs . 20 per day and a child worker rs . 8 per day . the average wage per day paid by the contractor is ?
Options: a ) 19 , b ) 21 , c ) 23 , d ) 25 , e ) 27
Rationale: explanation : 20 15 5 25 20 8 500 + 300 + 40 = 840 / 40 = 21 b
Answer: b
Question (general): what is the remainder when 3 ^ 33 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "the units digit of powers of 3 follow a repeating cycle of four : { 3 , 9 , 7 , 1 } 33 has the form 4 k + 1 , so the units digit of 3 ^ 33 is 3 . the remainder when dividing by 5 is 3 . the answer is d ."
Answer: d
Question (general): find ( 7 x + 2 y ) / ( x - 2 y ) if x / 2 y = 3 / 2 ?
Options: a ) 23 , b ) 25 , c ) 26 , d ) 27 , e ) 29
Rationale: "x / 2 y = 3 / 2 = > x = 6 y / 2 = 3 y = > ( 7 x + 2 y ) / ( x - 2 y ) = ( ( 7 * ( 3 y ) ) + 2 y ) / ( 3 y - 2 y ) = > 23 y / y = 23 answer : a"
Answer: a
Question (physics): john left home and drove at the rate of 45 mph for 2 hours . he stopped for lunch then drove for another 3 hours at the rate of 45 mph to reach his destination . how many miles did john drive ?
Options: a ) 235 miles . , b ) 245 miles . , c ) 225 miles . , d ) 265 miles . , e ) 275 miles .
Rationale: "the total distance d traveled by john is given by d = 45 * 2 + 3 * 45 = 225 miles . answer c"
Answer: c
Question (gain): a statue is being carved by a sculptor . the original piece of marble weighed 190 kg . in the first week 25 percent is cut away . in the second week 15 percent of the remainder is cut away . in the third week the statue is completed when 10 percent of the remainder is cut away . what is the weight of the final statue ?
Options: a ) 105 kg , b ) 103 kg , c ) 109 kg , d ) 125 kg , e ) 117 kg
Rationale: "c 109 kg 190 ã — 0.75 ã — 0.85 ã — 0.9 = 109 kg ."
Answer: c
Question (general): the population of a town increased from 1 , 75,000 to 2 , 97,500 in a decade . the average percent increase of population per year is
Options: a ) 4.37 % , b ) 5 % , c ) 6 % , d ) 8.75 % , e ) 7 %
Rationale: solution increase in 10 years = ( 297500 - 175000 ) = 122500 increase % = ( 122500 / 175000 ã — 100 ) % = 70 % . required average = ( 70 / 10 ) % = 7 % . answer e
Answer: e
Question (general): in an exam , gibi scored 59 percent , jigi scored 55 percent , mike scored 99 percent and lizzy 67 percent . the maximum score awarded in the exam is 700 . find the average mark scored by all the 4 students ?
Options: a ) 471 , b ) 490 , c ) 480 , d ) 453 , e ) 456
Rationale: average mark scored by all the three boys = [ 59 / 100 ( 700 ) + 55 / 100 ( 700 ) + 99 / 100 ( 700 ) + 67 / 100 ( 700 ) ] / 4 ( 413 + 385 + 693 + 469 ) / 4 = 490 answer : b
Answer: b
Question (general): in how many no . between 10 and 50 exactly two of the digits is 5 ?
Options: a ) 47 , b ) 65 , c ) 1 , d ) 35 , e ) 65
Rationale: "it ' s simple can be solved by elimination of answer choices . option b and d are too large , not possible . even ae are large to have correct choice . ans : c"
Answer: c
Question (physics): john and david work at a hospital with 8 other workers . for an internal review , 2 of the 8 workers will be randomly chosen to be interviewed . what is the probability that john and david will both be chosen ?
Options: a ) 1 / 30 , b ) 1 / 25 , c ) 1 / 20 , d ) 1 / 28 , e ) 1 / 30
Rationale: probability that john and david will both be chosen out of 8 workers = ( 2 / 8 ) * ( 1 / 7 ) = 1 / 28 answer d
Answer: d
Question (gain): by selling 8 pens for a rupee a woman loses 25 % . how many for a rupee should he sell in order to gain 25 % ?
Options: a ) 2 , b ) 14 , c ) 3 , d ) 5 , e ) 6
Rationale: "d 75 % - - - 8 125 % - - - ? 75 / 125 * 8 = 5"
Answer: d
Question (general): 3.20 can be expressed in terms of percentage as
Options: a ) 3.20 % , b ) 30.2 % , c ) 320.00 % , d ) 0.320 % , e ) none of these
Rationale: explanation : while calculation in terms of percentage we need to multiply by 100 , so 3.20 * 100 = 320 answer : option c
Answer: c
Question (general): a person was asked to subtract 25 % of a number from the original but he subtracted 25 from the number . his answer was 25 more than correct one . what was the original number ?
Options: a ) 288 , b ) 266 , c ) 288 , d ) 200 , e ) 111
Rationale: 25 + 25 = 50 25 % - - - - - - 50 100 % - - - - - ? = > 200 answer : d
Answer: d
Question (general): if x : y is 1 : 5 and y : z is 5 : 7 then x : z is equal to
Options: a ) 1 : 6 , b ) 1 : 5 , c ) 1 : 4 , d ) 1 : 7 , e ) 1 : 3
Rationale: the two ratios given are having the same number 5 for y in both the ratios . hence - x : y = 1 : 5 y : z = 5 : 7 = > x : z = 1 : 7 answer d
Answer: d
Question (other): divide $ 1000 among a , b in the ratio 1 : 3 . how many $ that a get ?
Options: a ) $ 50 , b ) $ 500 , c ) $ 150 , d ) $ 250 , e ) $ 600
Rationale: "sum of ratio terms = 1 + 3 = 4 a = 1000 * 1 / 4 = $ 250 answer is d"
Answer: d
Question (physics): maxwell leaves his home and walks toward brad ' s house at the same time that brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 72 kilometers , maxwell ' s walking speed is 6 km / h , and brad ' s running speed is 12 km / h . what is the distance traveled by maxwell when they meet in the middle ?
Options: a ) 14 , b ) 24 , c ) 16 , d ) 18 , e ) 20
Rationale: "consider max starts from point a and brad starts from point b and move towards each other . assume they shall meet at point o after time ' t ' . the question asks us to find oa . from the question stem we can make out : - distance oa = 50 km - distance ob = > 6 xt = 72 - 12 xt ( i . e distance = speed x time ) = > 18 t = 72 hence t = 4 oa = 6 x 4 = 24 km answer : b"
Answer: b
Question (general): carolyn bought 17 gumballs , lew bought 12 gumballs , and carey bought x gumballs . the average ( arithmetic mean ) number of gumballs the 3 bought is between 19 and 25 , inclusive . what is the difference between the greatest number and the smallest number of gumballs carey could have bought ?
Options: a ) 18 , b ) 20 , c ) 22 , d ) 24 , e ) 26
Rationale: smallest gumballs = ( 19 - 17 ) + ( 19 - 12 ) + 19 = 28 largest gumballs = ( 25 - 17 ) + ( 25 - 12 ) + 25 = 46 difference = 46 - 28 = 18 a
Answer: a
Question (physics): a train 250 m long passed a pole in 10 sec . how long will it take to pass a platform 1250 m long ?
Options: a ) 60 sec , b ) 90 sec , c ) 120 sec , d ) 150 sec , e ) 180 sec
Rationale: speed = 250 / 10 = 25 m / sec . required time = ( 250 + 1250 ) / 25 = 60 sec answer : a
Answer: a
Question (gain): one ball will drop from a certain height . the height it will reach after rebounding from the floor is 50 percent of the previous height . the total travel is 225 cm when it touches the floor on third time . what is the value of the original height ?
Options: a ) 80 cm , b ) 90 cm , c ) 100 cm , d ) 120 cm , e ) 130 cm
Rationale: "when ball comes down , then i have indicated the distance covered in green when ball goes up , then i have indicated the distance covered in red distance travelled uptil the ball touches the floor 3 rd time : h + 0.5 h + 0.5 h + 0.5 * 0.5 h + 0.5 * 0.5 h h + 2 * 0.5 * h + 2 * 0.25 * h = h ( 1 + 2 * 0.5 + 2 * 0.25 ) = h ( 1 + 1 + 0.5 ) = 225 2.5 h = 225 h = 90 . b is the answer ."
Answer: b
Question (physics): a man fell in a 30 meter deep well , in one day he climbs 4 meters up and slips 3 meters down . how many days would it take for him to come out of the well ?
Options: a ) 22 , b ) 46 , c ) 17 , d ) 27 , e ) 33
Rationale: d i will take 27 days to come out of that well for that man , he climbs 4 meter every day and slips 3 meter down that means he climbs 1 meter in total each day , so like this on 26 th day he would have climbed 26 meter and on 27 th day he will climb 4 meeter again so total 30 meter he will climb in 27 days .
Answer: d
Question (general): if a mixture is 2 ⁄ 7 alcohol by volume and 3 ⁄ 7 water by volume , what is the ratio of the volume of alcohol to the volume of water in this mixture ?
Options: a ) 3 , b ) 1 / 3 , c ) 2 / 3 , d ) 3 / 5 , e ) 4 / 5
Rationale: should be a sub - 600 level q . . volume = { 2 / 7 } / { 3 / 7 } = 2 / 3 c
Answer: c
Question (general): 20 percent of country y ' s yearly exports come from fruit exports . one - sixth of all fruit exports from country y are orange exports . if country y generates $ 4.25 million from its orange exports , how much money does it generate from its yearly total of exports ?
Options: a ) $ 21.25 m , b ) $ 25.5 m , c ) $ 106.25 m , d ) $ 127.5 m , e ) $ 153 m
Rationale: 2 / 10 * 1 / 6 * ( total ) = 4.25 1 / 30 * ( total ) = 4.25 ( total ) = 4.25 * 30 = 127.5 answer : d .
Answer: d
Question (general): what is the value of n if the sum of the consecutive odd intergers w from 1 to n equals 169 ?
Options: a ) 47 , b ) 25 , c ) 37 , d ) 33 , e ) 29
Rationale: "before you tackle this question you must first understand that the question is comprised of two key parts , 1 st is finding out how manytermsis in that sequence and 2 nd whatactual number valuethat term is . in an arithmetic progression , in this case consecutive odd integers 1 , 3 , 5 , . . . . , there are two set of rules . rule # 1 ( arithmetic sequence ) : xn = a + d ( n - 1 ) identifies what the actual # in the sequence would be . each number in the sequence has a term such as 1 ( is the first term ) , 3 ( is the second term ) and so on . so if i were to ask you to find out what the 10 th term is of that sequence you would use that formula to find that value . a = 1 ( first term ) d = 2 ( the common difference ) remember in the sequence 1 , 3 , 5 , 7 the common difference is always 2 * on a side note we use n - 1 because we do n ' t have d in the first term , therefore if we were solving for the first term we would get 0 as n - 1 and 0 times d would give us 0 , leaving only the first term . this works regardless what your first term is in any sequence . but remember the question askswhat is thevalueof n if the sum of the consecutive odd integers from 1 to n equals 169 ? which means we first need a consecutive sequence that sums up to 169 and than find what the value of the n is , in this case it would be the last number in that sequence . in order to find that we first need to knowhow many terms ( how many of the n there is ) in order to be able to plug n in this formula given we know what the sum is . for that to happen we need to use rule # 2 . rule # 2 ( summing an arithmetic series ) : 169 = n / 2 ( 2 a + ( n - 1 ) d ) . given the question gives us what the sum is ( 169 in this case ) we would simply use this formula to solve for n . once we solve for n ( 13 in this case ) we can simply plug n into the first formula ( rule 1 ) and find the value . it feels very confusing and difficult at first , but once you identify the steps all you need to do is plug and play . we have the sum ( 169 ) of a sequence , the number of terms in that sequence is ( unknown ) . rule # 2 tells us how many numbers there are in that sequence and rule # 1 gives us what that last term is ."
Answer: b
Question (gain): indu gave bindu rs . 7500 on compound interest for 2 years at 4 % per annum . how much loss would indu has suffered had she given it to bindu for 2 years at 4 % per annum simple interest ?
Options: a ) 5 , b ) 2 , c ) 9 , d ) 5 , e ) 12
Rationale: "7500 = d ( 100 / 4 ) 2 d = 12 answer : e"
Answer: e
Question (general): evaluate : 7899665 - 12 * 3 * 2 = ?
Options: a ) 2455835 , b ) 2789255 , c ) 6868575 , d ) 7899657 , e ) 1023666
Rationale: "according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 7899665 - 12 * 3 * 2 = 7899665 - 8 = 7899657 correct answer d"
Answer: d
Question (physics): a can do a half of certain work in 70 days and b one third of the same in 35 days . they together will do the whole work in ?
Options: a ) 1 / 65 , b ) 1 / 62 , c ) 1 / 63 , d ) 1 / 60 , e ) 1 / 61
Rationale: a = 140 days b = 105 days 1 / 140 + 1 / 105 = 7 / 420 = 1 / 60 = > 60 days answer : d
Answer: d
Question (general): if 9 / ( 1 + 4 / x ) = 1 , then x =
Options: a ) 3 , b ) 1 / 2 , c ) 1 / 3 , d ) - 1 / 3 , e ) - 3
Rationale: "the expression 9 / ( 1 + 4 / x ) = 1 should have been equal to something . if 9 / ( 1 + 4 / x ) = 1 = 1 = > 9 x / ( x + 4 ) = 1 = > 9 x = x + 4 = > 8 x = 4 = > x = 1 / 2 correct option : b"
Answer: b
Question (other): what is the prime factors ’ number of 12 ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "prime factors ’ number , as i assume , for a number x = a ^ n * b ^ m * c ^ o * d ^ p . . . is = n + m + o + p . . . so , 24 = 2 ^ 2 * 3 ^ 1 prime factors ’ number will be 2 + 1 = 3 . hence , answer is b ."
Answer: b
Question (general): in 2 bags , there are to be put together 5 red and 12 white balls , neither bag being empty . how must the balls be divided so as to give a person who draws 1 ball from either bag - the least chance of drawing a red ball ?
Options: a ) 1 / 32 , b ) 2 / 32 , c ) 3 / 32 , d ) 4 / 32 , e ) 5 / 32
Rationale: "least chance . p = 1 / 2 * 5 / 16 + 1 / 2 * 0 = 5 / 32 answer : e"
Answer: e
Question (general): what is the sum of the odd integers from 55 to 75 , inclusive ?
Options: a ) 495 , b ) 550 , c ) 555 , d ) 600 , e ) 715
Rationale: "the mean is 65 . sum = mean ( # of elements ) there are 11 odd numbers between 55 - 75 inclusive . 11 * 65 = 715 e"
Answer: e
Question (general): in the first m games of a team ' s season , the ratio of the team ' s wins to its losses was 1 : 2 . in the subsequent n games , the ratio of the team ´ s wins to losses was 2 : 3 . if m : n = 4 : 5 , what was the ratio of the team ' s wins to its losses for all m + n games ?
Options: a ) 7 : 18 , b ) 9 : 23 , c ) 10 : 17 , d ) 23 : 54 , e ) 31 : 77
Rationale: "m = 4 / 9 of total games n = 5 / 9 of total games wins = 1 / 3 * 4 / 9 + 2 / 5 * 5 / 9 = 4 / 27 + 6 / 27 = 10 / 27 losses = 1 - 10 / 27 = 17 / 27 the ratio of wins to losses is 10 : 17 . the answer is c ."
Answer: c
Question (general): for all even integers n , h ( n ) is defined to be the sum of the even integers between 2 and n , inclusive . what is the value of h ( 20 ) / h ( 10 ) ?
Options: a ) 1.8 , b ) 60 , c ) 6 , d ) 18 , e ) 3
Rationale: "concept : when terms are in arithmetic progression ( a . p . ) i . e . terms are equally spaced then mean = median = ( first + last ) / 2 and sum = mean * number of terms h ( 20 ) = [ ( 2 + 20 ) / 2 ] * 9 = 99 h ( 10 ) = ( 2 + 10 ) / 2 ] * 5 = 30 h ( 18 ) / h ( 10 ) = ( 99 ) / ( 30 ) ~ 3 answer : e"
Answer: e
Question (gain): a shopkeeper sold an article at $ 1170 and gained a 20 % profit . what was the cost price ?
Options: a ) $ 950 , b ) $ 975 , c ) $ 1000 , d ) $ 1025 , e ) $ 1050
Rationale: "let x be the cost price . 1.2 x = 1170 x = 1170 / 1.2 = 975 the answer is b ."
Answer: b
Question (general): how many positive integers less than 70 have a reminder 01 when divided by 3 ?
Options: a ) 13 , b ) 24 , c ) 35 , d ) 16 , e ) 17
Rationale: "1 also gives the remainder of 1 when divided by 3 . so , there are total of 24 numbers . answer : b ."
Answer: b
Question (general): an automobile parts supplier charges $ 25 per package of gaskets . when a customer orders more than 10 packages of gaskets , the supplier charges 4 / 5 the price for each package in excess of 10 . during a certain week , the supplier sold 60 packages of gaskets . if 15 percent of the gaskets went to company x , 15 percent to company y , and the rest to company z , what was the total amount , in dollars , that the parts supplier received in payment for the gaskets ?
Options: a ) 1340 , b ) 1445 , c ) 1375 , d ) 1415 , e ) 1455
Rationale: $ 25 per packet of gasket in case a customer orders less than 10 in case a customer orders > 10 price per gasket = 25 * 4 / 5 = 20 a certain week the supplier sold 60 gasket 1 . he sold 15 % of the gaskets to x = 9 gaskets = 25 * 9 = 225 2 . he sold 15 % of the gaskets to y = 9 gaskets = 25 * 9 = 225 3 . he sold remaining 70 % to z = 42 gaskets = 25 * 10 = 250 + 20 * 32 = 890 thus , total money earned 225 + 225 + 890 = 1340 answer is a
Answer: a
Question (gain): suresh started a business , investing rs . 18000 . after 3 months and 4 months respectively , rohan and sudhir joined him with capitals of 12000 and 9000 . at the end of the year the total profit was rs . 3982 . what is the difference between rohan ’ s and sudhir ’ s share in the profit ?
Options: a ) rs . 362 , b ) rs . 383 , c ) rs . 398 , d ) rs . 399 , e ) rs . 400
Rationale: "suresh : rohan : sudhir ratio of their investments = 18000 × 12 : 12000 × 9 : 9000 × 8 = 6 : 3 : 2 the difference between rohan ’ s and sudhir ’ s share = 1 share : . i . e . = rs . 3982 × 1 / 11 = rs . 362 . a )"
Answer: a
Question (general): how many words , with or without meaning , can be formed using all letters of the word orange using each letter exactly once ?
Options: a ) 700 , b ) 720 , c ) 740 , d ) 760 , e ) 780
Rationale: "the word orange has exactly 6 letters which are all different . therefore the number of words that can be formed = number of permutations of 6 letters taken all at a time . = p ( 6 , 6 ) = 6 ! = 6 × 5 x 4 x 3 x 2 × 1 = 720 answer : b"
Answer: b
Question (general): if p is the product of the integers from 1 to 32 , inclusive , what is the greatest integer k for which 3 ^ k is a factor of p ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "32 ! has 3 , 6 , 9 , . . . . 30 as factors , which are 10 multiples of 3 . we need to add 4 more to 10 because of 9 , 18 , and 27 . the answer is c ."
Answer: c