Cheukting/mathqa huggingface dataset:
Question (general): what is the units digit of ( 22 ^ 4 ) ( 16 ^ 3 ) ( 41 ^ 8 ) ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "the units digit of 22 ^ 4 is the units digit of 2 ^ 4 which is 6 . the units digit of 16 ^ 3 is the units digit of 6 ^ 3 which is 6 . the units digit of 41 ^ 8 is the units digit of 1 ^ 8 which is 1 . the units digit of 6 * 6 * 1 is 6 . the answer is e ."
Answer: e
Question (other): in a factory , each day the expected number of accidents is related to the number of overtime hour by linear equation . suppose that on one day there were 1000 overtime hours logged and 8 accidents reported and on another day there were 400 overtime hours logged and 5 accidents . what is the expected number of accidents when no overtime hours are logged ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: explanation : let , the number of over time hours be x and expected number of accidents be y . we will use the equation y = mx + c , where m and c are constant . now , according to the question , if x = 1000 , then y = 8 i . e 8 = 1000 x + c - - - - ( i ) and , if x = 400 , then y = 5 i . e 5 = 400 x + c . - - - - ( ii ) on solving these equations , we get m = 1 / 200 and c = 3 . hence , in case , no overtime is there i . e x = 0 , then the number of expected accident will be 3 . answer : b
Answer: b
Question (general): last week vartan spent 20 percent of his wages on recreation . this week , his wages are 20 percent less than last week ʼ s wages and he spent 40 percent of his wages on recreation . the amount he spends on recreation this week is what percent of the amount he spent on recreation last week ?
Options: a ) 150 % , b ) 170 % , c ) 175 % , d ) 160 % , e ) 180 %
Rationale: "say vartan ' s wages last week were $ 100 , so he spent 0.20 * 100 = $ 20 on recreation ; this week ' s wages is 0.8 * 100 = $ 80 , so he spends 0.4 * 80 = $ 32 on recreation ; 32 / 20 = 1.6 , hence the amount he spends on recreation this week is 160 % of the amount he spent on recreation last week : 20 * 1.6 = 32 answer : d"
Answer: d
Question (general): 4 , 12 , 48 , 240 , ( . . . )
Options: a ) 1440 , b ) 10080 , c ) 6200 , d ) 10020 , e ) 12500
Rationale: "explanation : go on multiplying the given numbers by 3 , 4 , 5 , 6 , answer : option a"
Answer: a
Question (gain): rs 3200 is divided into two parts such that one part is put out at 3 % and the other at 5 % . if the annual interest earned from both the investments be rs 144 , find the first part .
Options: a ) s 400 , b ) s 200 , c ) s 800 , d ) s 500 , e ) s 100
Rationale: "explanation : average rate = ( 144 / 3200 ) * 100 = 4.5 ratio = 5 : 15 so , first part = ( 5 / 20 ) * 3200 = rs 800 . answer : c"
Answer: c
Question (general): if you add all the numbers on your mobile phone except 8 and 2 , what is the answer ?
Options: a ) 55 , b ) 25 , c ) 85 , d ) 45 , e ) 35
Rationale: "we have to add 0 , 1,3 , 4,5 , 6,7 & 9 to find the answer . therefore 0 + 1 + 3 + 4 + 5 + 6 + 7 + 9 = 35 answer is e"
Answer: e
Question (physics): a pipe takes a hours to fill the tank . but because of a leakage it took 6 times of its original time . find the time taken by the leakage to empty the tank
Options: a ) 50 min , b ) 60 min , c ) 72 min , d ) 80 min , e ) 70 min
Rationale: "pipe a can do a work 60 min . lets leakage time is x ; then 1 / 60 - 1 / x = 1 / 360 x = 72 min answer : c"
Answer: c
Question (general): evaluate : 40 - 10 ÷ 2 × 2 =
Options: a ) 20 , b ) 25 , c ) 10 , d ) 16 , e ) 30
Rationale: "according to order of operations , 10 ÷ 2 × 2 ( division and multiplication ) is done first from left to right 10 ÷ 2 × 2 = 5 × 2 = 10 hence 40 - 10 ÷ 2 × 2 = 40 - 10 = 30 correct answer e ) 30"
Answer: e
Question (other): the number of stamps that kaye and alberto had were in the ration of 5 : 3 respectively . after kaye gave alberto 10 of her stamps , the ration of the number of kaye had to the number of alberto had was 6 : 4 . as a result of the gift , kaye had how many more stamps than alberto ?
Options: a ) 80 , b ) 85 , c ) 65 , d ) 55 , e ) 50
Rationale: "c k 1 = 5 x a 1 = 3 x k 2 = 5 x - 10 a 2 = 3 x + 10 k 2 / a 2 = 6 / 4 ( 5 x - 10 ) / ( 3 x + 10 ) = 6 / 4 4 * ( 5 x - 10 ) = 6 * ( 3 x + 10 ) 20 x - 40 = 18 x + 60 2 x = 100 x = 50 k 2 = 5 * 50 - 10 = 240 a 2 = 3 * 50 + 10 = 160 k 2 - a 2 = 80 answer : a"
Answer: a
Question (physics): the speed at which a man can row a boat in still water is 18 kmph . if he rows downstream , where the speed of current is 6 kmph , what time will he take to cover 100 metres ?
Options: a ) 6.67 seconds , b ) 18 seconds , c ) 26 seconds , d ) 14.99 seconds , e ) 6 seconds
Rationale: "speed of the boat downstream = 18 + 6 = 24 kmph = 24 * 5 / 18 = 6.67 m / s hence time taken to cover 100 m = 100 / 6.67 = 14.99 seconds . answer : d"
Answer: d
Question (physics): two cyclist start from the same places in opposite directions . one is going towards north at 10 kmph and the other is going towards south 25 kmph . what time will they take to be 50 km apart ?
Options: a ) 1.42 hr , b ) 2.22 hrs , c ) 3.24 hrs , d ) 5 hrs , e ) 6.02 hrs
Rationale: "to be ( 10 + 25 ) km apart , they take 1 hour to be 50 km apart , they take 1 / 35 * 50 = 1.42 hrs answer is a"
Answer: a
Question (gain): jerome anticipated that the webweb . com stock price would fall and sold all his webweb . com stocks for $ 5 per stock . he paid $ 10,000 tax on the revenue . a week later , jerome became convinced that the webweb . com stock price would rise , and he used the money that he had gotten from selling the webweb . com stocks to purchase them again , this time at $ 6 per stock . if jerome ended up having 5000 webweb . com stocks fewer than the number he had before selling them , how many webweb . com stocks did he have originally ?
Options: a ) 10,000 , b ) 11,600 , c ) 12,000 , d ) 15,000 , e ) 16,400
Rationale: "let the number of shares be x . 5 * x - 10000 ( money paid in taxes ) = 6 ( x - 5000 ) solving for x , we get the shares as 15000 . ans : ( option d )"
Answer: d
Question (other): the ratio of pens to pencils is 5 to 6 . there are 8 more pencils than pens . how many pencils are there ?
Options: a ) 30 , b ) 32 , c ) 48 , d ) 55 , e ) 64
Rationale: "let x equal the number of pens , and y the number of pencils . then , x = 5 / 6 y . we also know that x = y - 8 . and so , we can substitute : y - 8 = 5 / 6 y so to isolate y , we get : 1 / 6 y = 8 and therefore : y = 48 answer : c"
Answer: c
Question (other): if 0.4 of a number is equal to 0.06 of another number , the ratio of the numbers i
Options: a ) 2 : 3 , b ) 3 : 4 , c ) 3 : 20 , d ) 20 : 3 , e ) none
Rationale: "sol . 0.4 a = 0.06 b ⇔ a / b = 0.06 / 0.40 = 6 / 40 = 3 / 20 . ∴ a : b = 3 : 20 . answer c"
Answer: c
Question (physics): a 260 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds . what is the length of the other train ?
Options: a ) 230 m , b ) 240 m , c ) 260 m , d ) 320 m , e ) 330 m
Rationale: "relative speed = ( 120 + 80 ) km / hr = ( 200 x ( 5 / 18 ) ) m / sec = ( 500 / 9 ) m / sec . let the length of the other train be x metres . then , ( x + 260 ) / 9 = 500 / 9 x + 260 = 500 x = 240 . b"
Answer: b
Question (physics): a boatman can row 96 km downstream in 8 hr . if the speed of the current is 4 km / hr , then find in what time he will be able to cover 8 km upstream ?
Options: a ) 3 hrs , b ) 7 hrs , c ) 9 hrs , d ) 2 hrs , e ) 6 hrs
Rationale: explanation : speed in downstream = 96 / 8 = 12 kmph speed of current = 4 km / hr speed of the boatman in still water = 12 â € “ 4 = 8 kmph speed in upstream = 8 â € “ 4 = 4 kmph time taken to cover 8 km upstream = 8 / 4 = 2 hours . answer : d
Answer: d
Question (general): choose the number pair / group which is different from others ?
Options: a ) 8 : 39 , b ) 8 : 38 , c ) 8 : 33 , d ) 8 : 32 , e ) 8 : 31
Rationale: explanation : in all other pairs , 2 nd number = ( 1 st number × 3 ) + 1 . answer : c ) 8 : 33
Answer: c
Question (general): the ratio of two numbers is 2 : 3 and the sum of their cubes is 945 . the difference of number is ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: 2 x 3 x 8 x cube + 27 x cube = 945 35 x cube = 945 x cube = 27 = > x = 3 . answer : a
Answer: a
Question (gain): a and b started a business in partnership investing rs . 20,000 and rs . 15,000 respectively . after 6 months , c joined them with rs . 20,000 . whatwill be b ' s share in total profit of rs . 21,000 earned at the end of 2 years from the startingof the business ?
Options: a ) s . 5,000 , b ) s . 5,500 , c ) s . 5,700 , d ) s . 6,300 , e ) s . 7,500
Rationale: "a : b : c = ( 20,000 x 24 ) : ( 15,000 x 24 ) : ( 20,000 x 18 ) = 4 : 3 : 3 . b ' s share = rs . 21000 x 3 / 10 = rs . 6,300 . d"
Answer: d
Question (general): the mean of 1 ^ 22 ^ 23 ^ 24 ^ 25 ^ 26 ^ 27 ^ 2 is ?
Options: a ) 15 , b ) 18 , c ) 20 , d ) 25 , e ) 30
Rationale: 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + - - - - - + n ^ 2 = n ( n + 1 ) ( 2 n + 1 ) / 6 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + - - - - - + 7 ^ 2 = 7 * 8 * 156 = 140 required average is = 140 / 7 = 20 answer is c
Answer: c
Question (general): if 25 % of x is 20 less than 15 % of 1500 , then x is ?
Options: a ) 872 , b ) 820 , c ) 837 , d ) 840 , e ) 83
Rationale: "25 % of x = x / 4 ; 15 % of 1500 = 15 / 100 * 1500 = 225 given that , x / 4 = 225 - 20 = > x / 4 = 205 = > x = 820 . answer : b"
Answer: b
Question (physics): circular gears p and q start rotating at the same time at constant speeds . gear p makes 10 revolutions per minute and gear q makes 40 revolutions per minute . how many seconds after the gears start rotating will gear q have made exactly 15 more revolutions than gear p ?
Options: a ) 12 , b ) 15 , c ) 20 , d ) 24 , e ) 30
Rationale: gear q makes 30 more revolutions each 60 seconds . the time to make 15 = 30 / 2 more revolutions is 60 / 2 = 30 seconds . the answer is e .
Answer: e
Question (general): ( 8956231 x 465 ) = ?
Options: a ) 4584638125 , b ) 4164647415 , c ) 4584638135 , d ) 4584638140 , e ) 4584638145
Rationale: 8956231 x 465 = 4164647415 ans b
Answer: b
Question (gain): population is 25000 . population increases by 10 % every year , then the population after 3 years is ?
Options: a ) 26630 , b ) 33275 , c ) 36625 , d ) 26625 , e ) 26825
Rationale: population after 1 st year = 25000 * 10 / 100 = 2500 = = = > 25000 + 2000 = 27500 population after 2 nd year = 27500 * 10 / 100 = 2750 = = = > 27500 + 2750 = 30250 population after 3 rd year = 30250 * 10 / 100 = 3025 = = = > 30250 + 3025 = 33275 answer : b
Answer: b
Question (general): a number , x is chosen at random from the set of positive integers less than 10 . what is the probability that ( 8 / x ) > x ?
Options: a ) 1 / 5 , b ) 2 / 8 , c ) 1 / 3 , d ) 2 / 3 , e ) 7 / 9
Rationale: number x has to be chosen from numbers 1 - 9 ( 8 / x ) > x = > 8 > x ^ 2 = > x ^ 2 - 8 < 0 x can have 2 values only 1 , 2 therefore , probability = 2 / 8 answer b
Answer: b
Question (general): x varies inversely as square of y . given that y = 3 for x = 1 . the value of x for y = 2 will be equal to :
Options: a ) 3 , b ) 6 , c ) 1 / 9 , d ) 1 / 3 , e ) 9 / 4
Rationale: "explanation : solution : given x = k / y ^ 2 , where k is constant . now , y = 3 and x = 1 gives k = 9 . . ' . x = 9 / y ^ 2 = > x = 9 / 2 ^ 2 = 9 / 4 answer : e"
Answer: e
Question (physics): it takes 1.5 hours for tim to mow the lawn . linda can mow the same lawn in 2 hours . how long will it take john and linda , work together , to mow the lawn ?
Options: a ) 51.1 minutes , b ) 51.3 minutes , c ) 51.5 minutes , d ) 51.7 minutes , e ) 51.9 minutes
Rationale: we first calculate the rate of work of john and linda john : 1 / 1.5 and linda 1 / 2 let t be the time for john and linda to mow the lawn . the work done by john alone is given by t * ( 1 / 1.5 ) the work done by linda alone is given by t * ( 1 / 2 ) when the two work together , their work will be added . hence t * ( 1 / 1.5 ) + t * ( 1 / 2 ) = 1 multiply all terms by 6 6 ( t * ( 1 / 1.5 ) + t * ( 1 / 2 ) ) = 6 and simplify 4 t + 3 t = 6 solve for t t = 6 / 7 hours = 51.5 minutes . answer c
Answer: c
Question (general): you collect pens . suppose you start out with 5 . mike gives you another 20 pens . since her father makes pens , cindy decides to double your pens . since you ' re nice , you give sharon 19 pens . how many pens do you have at the end ?
Options: a ) 39 , b ) 40 , c ) 31 , d ) 42 , e ) 43
Rationale: "solution start with 5 pens . mike gives you 20 pens : 5 + 20 = 25 pens . cindy doubles the number of pens you have : 25 ã — 2 = 50 pens . sharon takes 19 pens from you : 50 - 19 = 31 pens . so you have 31 at the end . correct answer : c"
Answer: c
Question (gain): the majority owner of a business received 25 % of the profit , with each of 4 partners receiving 25 % of the remaining profit . if the majority owner and two of the owners combined to receive $ 50,000 , how much profit did the business make ?
Options: a ) $ 80,000 , b ) $ 100,000 , c ) $ 120,000 , d ) $ 150,000 , e ) $ 200,000
Rationale: let p be the total profit . p / 4 + 1 / 2 * ( 3 p / 4 ) = p / 4 + 3 p / 8 = 5 p / 8 = 50000 p = $ 80,000 the answer is a .
Answer: a
Question (other): in a group of 28 junior high school students , 7 take french , 10 take spanish , and 2 take both languages . the students taking both french and spanish are not counted with the 7 taking french or the 10 taking spanish . how many students are not taking either french or spanish ?
Options: a ) 7 , b ) 6 , c ) 9 , d ) 4 , e ) 8
Rationale: "c 9 add 7 + 10 + 2 to get 19 then subtract 21 from the total students ⇒ 28 – 19 = 9 . answer is c"
Answer: c
Question (physics): a wheel rotates 10 times every minute and moves 20 cm during each rotation . how many ems does the wheel move in 1 hour ?
Options: a ) 20000 , b ) 14000 , c ) 23000 , d ) 120000 , e ) none of these
Rationale: explanation : number of wheel moves in 1 hour = 10 * 60 = 600 distance moved = 600 * 200 = 12000 answer : d
Answer: d
Question (general): the average ( arithmetic mean ) of the integers from 200 to 400 , inclusive , is how much greater than the average of the integers from 100 to 200 , inclusive ?
Options: a ) 150 , b ) 175 , c ) 200 , d ) 225 , e ) 300
Rationale: "for an ap the mean or average of series is average of first and last term . so , average of numbers between 200 to 400 , inclusive = ( 200 + 400 ) / 2 = 300 average of numbers between 100 to 200 , inclusive = ( 100 + 200 ) / 2 = 150 difference = 300 - 150 = 150 answer is a"
Answer: a
Question (general): the total circumference of two circles is 64 . if the first circle has a circumference that is exactly twice the circumference of the second circle , then what is the approximate sum of their two radii ?
Options: a ) 5.7 , b ) 6.0 , c ) 6.7 , d ) 10.2 , e ) 18.0
Rationale: let r = radius of smaller circle . let r = radius of larger circle therefore : 2 π r + 2 π r = 64 where 2 r = r thus : 2 π r + 4 π r = 64 6 π r = 64 r = approx 3.4 π r + 2 r π = 64 3 π r = 64 r = approx 6.8 r + r = approx 10.2 answer d
Answer: d
Question (physics): a car takes 6 hours to cover a distance of 469 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 48 kmph , b ) 50 kmph , c ) 52 kmph , d ) 56 kmph , e ) 60 kmph
Rationale: "time = 6 distence = 469 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 469 / 9 = 52 kmph c"
Answer: c
Question (physics): excluding stoppages , the speed of a bus is 62 kmph and including stoppages , it is 56 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 70 min , b ) 16 min , c ) 7 min , d ) 6 min , e ) 40 min
Rationale: "d 10 min due to stoppages , it covers 6 km less . time taken to cover 6 km = ( 6 / 62 x 60 ) min = 6 min"
Answer: d
Question (general): the greatest number that divides 3560 and 3450 leaving remainder 4 and 6 respectively is :
Options: a ) 23 , b ) 25 , c ) 26 , d ) 28 , e ) 30
Rationale: "explanation : 3560 - 4 = 3556 , 3450 - 6 = 3444 highest number that can divide 3556 and 3444 is hcf of numbers hcf of 3556 and 3444 = 28 answer : d"
Answer: d
Question (gain): if the cost price is 75 % of selling price then what is the profit percentage .
Options: a ) 30.33 , b ) 31.33 , c ) 32.33 , d ) 33.33 , e ) 34.33
Rationale: "selling price = rs 100 : then cost price = rs 75 : profit = rs 25 . profit = { ( 25 / 75 ) * 100 } % = 33.33 % answer is d ."
Answer: d
Question (gain): find the simple interest on $ 500 for 3 years at 10 % per annum ?
Options: a ) $ 250 , b ) $ 300 , c ) $ 500 , d ) $ 150 , e ) $ 100
Rationale: "si = ptr / 100 = 500 * 3 * 10 / 100 = $ 150 answer is d"
Answer: d
Question (general): what is the sum of all possible solutions to | x - 4 | ^ 2 + | x - 4 | = 12 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "denote | x - 4 | as y : y ^ 2 + y = 12 - - > y = - 4 or y = 3 . discard the first solution since y = | x - 4 | , so it ' s an absolute value and thus can not be negative . y = | x - 4 | = 3 - - > x = 7 or x = 0 . the sum = 7 . answer : e ."
Answer: e
Question (physics): a cistern is normally filled in 4 hrs , but takes 2 hrs longer to fill because of a leak on its bottom , if cistern is full , how much time citern would empty ?
Options: a ) 10 hours , b ) 20 hours , c ) 30 hours , d ) 40 hours , e ) 12 hours
Rationale: "if leakage / hour = 1 / x , then 1 / 4 - 1 / x = 1 / 6 , solving 1 / x = 1 / 12 so in 12 hours full cistern will be empty . answer : e"
Answer: e
Question (general): in a house a hall is 20 m long , 15 m wide and 5 m high . its interior has to be covered with mat . what will be the total expenditure if it costs rs . 30 per square m ?
Options: a ) s . 28500 , b ) s . 50000 , c ) s . 57000 , d ) s . 60000 , e ) s . 62000
Rationale: "length ( l ) = 20 m , breadth ( b ) = 15 m and height ( h ) = 5 m total area of the hall to be covered with mat = 2 ( lb + bh + hl ) = 2 ( 20 * 15 + 15 * 5 + 5 * 20 ) = 2 ( 300 + 75 + 100 ) = 2 * 475 = 950 sq . m total expenditure = 30 * 950 = rs . 28,500 a"
Answer: a
Question (general): an old man distributed all the gold coins he had to his two sons into two different numbers such that the difference between the squares of the two numbers is 16 times the difference between the two numbers . how many coins did the old man have ?
Options: a ) 24 , b ) 26 , c ) 30 , d ) 16 , e ) 40
Rationale: "let the number of coins one son got be x and the number of coins another got be y . total = x + y . x ^ 2 - y ^ 2 = 16 ( x - y ) - - > x + y = 16 . answer : d ."
Answer: d
Question (gain): a shopkeeper sells his goods at cost price but uses a faulty meter that weighs 960 grams . find the profit percent .
Options: a ) 4.166 , b ) 3.1 , c ) 2.1 , d ) 1.256 , e ) 3.759
Rationale: "explanation : ( 100 + g ) / ( 100 + x ) = true measure / faulty measure x = 0 true measure = 1000 faulty measure = 960 100 + g / 100 + 0 = 1000 / 960 100 + g = 100 / 96 * 100 g = 4.166 answer : a"
Answer: a
Question (general): the sum of the numbers is 220 . if the first number be twice the second and third number be one - third of the first , then the second number is :
Options: a ) 48 , b ) 54 , c ) 72 , d ) 60 , e ) 27
Rationale: "let the second number be x . then , first number = 2 x and third number = 2 x / 3 . 2 x + x + 2 x / 3 = 220 11 x / 3 = 220 x = 60 answer : d"
Answer: d
Question (gain): the profit earned by selling an article for 832 is equal to the loss incurred when the same article is sold for 448 . what should be the sale price of the article for making 50 per cent profit ?
Options: a ) 960 , b ) 1060 , c ) 1,200 , d ) 920 , e ) none of these
Rationale: "let the profit or loss be x and 832 – x = 448 + x or , x = 384 ⁄ 2 = 192 \ cost price of the article = 832 – x = 448 + x = 640 \ sp of the article = 640 × 150 ⁄ 100 = 960 answer a"
Answer: a
Question (general): for what value of â € œ k â €  will the equation ( 2 kx 2 + 6 kx + 2 ) = 0 have equal roots ?
Options: a ) 2 / 7 , b ) 4 / 9 , c ) 16 / 25 , d ) 7 / 1 , e ) 7 / 2
Rationale: "for a 2 nd degree equation ax 2 + bx _ c = 0 has equal roots the condition is b 2 - 4 ac = 0 in the given equation ( 6 k ) ^ 2 - 4 * 2 k * 2 = 0 by solving this equation we get k = 0 , k = 4 / 9 answer : b"
Answer: b
Question (gain): the cost price of a radio is rs . 1500 and it was sold for rs . 1305 , find the loss % ?
Options: a ) 13 % , b ) 16 % , c ) 17 % , d ) 78 % , e ) 28 %
Rationale: "1500 - - - - 195 100 - - - - ? = > 13 % answer : a"
Answer: a
Question (general): $ 366 is divided amongst a , b and c so that a may get 1 / 2 as much as b and c together , b may get 2 / 3 as much as a and c together , then the share of a is
Options: a ) $ 122 , b ) $ 150 , c ) $ 176 , d ) $ 200 , e ) $ 250
Rationale: "a : ( b + c ) = 1 : 2 a ' s share = 366 * 1 / 3 = $ 122 answer is a"
Answer: a
Question (physics): a constructor estimates that 5 people can repair mr rohan ' s house in 6 days . if he uses 6 people instead of 5 , how long will they take to complete the job ?
Options: a ) 2 , b ) 8 , c ) 1 , d ) 3 , e ) 5
Rationale: explanation : use formula for a work members ã — days = constant 5 ã — 6 = 6 ã — a a = 5 so answer is 3 days answer : e
Answer: e
Question (general): if 12 boys meet at a reunion and each boy shakes hands exactly once with each of the others , then what is the total number of handshakes
Options: a ) 41 , b ) 42 , c ) 43 , d ) 66 , e ) 45
Rationale: "n ( n - 1 ) / 2 = 12 * 11 / 2 = 66 answer : d"
Answer: d
Question (gain): if the cost price is 25 % of selling price . then what is the profit percent .
Options: a ) 150 % , b ) 200 % , c ) 300 % , d ) 350 % , e ) none of these
Rationale: "explanation : let the s . p = 100 then c . p . = 25 profit = 75 profit % = ( 75 / 25 ) * 100 = 300 % . answer : c"
Answer: c
Question (other): in a certain animal shelter , the ratio of the number of dogs to the number of cats is 15 to 7 . if 16 additional cats were to be taken in by the shelter , the ratio of the number of dogs to the number of cats would be 15 to 11 . how many dogs are in the shelter ?
Options: a ) 15 , b ) 25 , c ) 30 , d ) 45 , e ) 60
Rationale: "this ratio question can be solved in a couple of different ways . here ' s an algebraic approach . . . we ' re told that the ratio of the number of dogs to the number of cats is 15 : 7 . we ' re then told that 16 more cats are added to this group and the ratio becomes 15 : 11 . we ' re asked for the number of dogs . algebraically , since the number of dogs is a multiple of 15 and the number of cats is a multiple of 7 , we can write this initial relationship as . . . 15 x / 7 x when we add the 12 cats and factor in the ' ending ratio ' , we have an equation . . . . 15 x / ( 7 x + 16 ) = 15 / 11 here we have 1 variable and 1 equation , so we can solve for x . . . . ( 15 x ) ( 11 ) = ( 7 x + 16 ) ( 15 ) ( x ) ( 11 ) = ( 7 x + 16 ) ( 1 ) 11 x = 7 x + 16 4 x = 16 x = 4 with this x , we can figure out the initial number of dogs and cats . . . initial dogs = 15 x = 15 ( 4 ) = 60 final answer : e"
Answer: e
Question (geometry): in a rectangular coordinate system , what is the area of a quadrilateral whose vertices have the coordinates ( 4 , - 3 ) , ( 4 , 7 ) , ( 12 , 2 ) , ( 12 , - 7 ) ?
Options: a ) 64
b ) 68
c ) 72
d ) 76
e ) 80
Rationale: by graphing the points , we can see that this figure is a trapezoid . a trapezoid is any quadrilateral that has one set of parallel sides , and the formula for the area of a trapezoid is : area = ( 1 / 2 ) × ( base 1 + base 2 ) × ( height ) , where the bases are the parallel sides . we can now determine the area of the quadrilateral : area = 1 / 2 × ( 10 + 9 ) × 8 = 76 . the answer is d .
Answer: d
Question (physics): circular gears p and q start rotating at the same time at constant speeds . gear p makes 10 revolutions per minute and gear q makes 40 revolutions per minute . how many seconds after the gears start rotating will gear q have made exactly 5 more revolutions than gear p ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 15
Rationale: "gear q makes 30 more revolutions each 60 seconds . the time to make 5 = 30 / 6 more revolutions is 60 / 6 = 10 seconds . the answer is c ."
Answer: c