Cheukting/mathqa huggingface dataset:
Question (general): with a slope of 4 , with a straight line in the xy - plane which has a point with x - coordinate of the point 14 and y - coordinate 19 , find the y - intercept .
Options: a ) - 19 , b ) 18 , c ) - 37 , d ) 50 , e ) 37
Rationale: eq of line = y = mx + c m = 4 x = 14 y = 19 c = y - mx substitute given : c = 19 - ( 4 ) ( 14 ) c = - 37 correct option is c
Answer: c
Question (general): elena ’ s bread recipe calls for 3 ounces of butter for each 4 cups of flour used . she needs to make 4 times the original recipe . if 12 ounces of butter is used , then how many cups of flour are needed ?
Options: a ) 1 , b ) 4 , c ) 9 , d ) 13 , e ) 16
Rationale: "number of cups flour needed for 3 ounces of butter = 4 number of cups flour needed for 1 ounce of butter = 4 / 3 number of cups flour needed for 12 ounces of butter = 4 / 3 * 12 = 16 answer e"
Answer: e
Question (physics): excluding stoppages , the speed of a bus is 52 kmph and including stoppages , it is 45 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 7 min , b ) 6 min , c ) 9 min , d ) 8 min , e ) 11 min
Rationale: "due to stoppages , it covers 7 km less . time taken to cover 7 km = ( 7 / 52 ) x 60 = 8 min answer : d"
Answer: d
Question (general): what is the smallest positive integer x , such that √ 392 x is an integer ?
Options: a ) 2 , b ) 4 , c ) 7 , d ) 8 , e ) 14
Rationale: "for a perfect square , the powers of prime factors should be even . 392 can be broken up as 2 ^ 3 * 7 ^ 2 . you just need 2 to be multiplied to this number so that the number finally becomes 2 ^ 4 * 7 ^ 2 which is a perfect square . therefore x = 2 . answer : a"
Answer: a
Question (gain): the cost of an article is decreased by 10 % . if the original cost is $ 60 , find the decrease cost .
Options: a ) 33 , b ) 12 , c ) 68 , d ) 36 , e ) 54
Rationale: "original cost = $ 60 decrease in it = 10 % of $ 60 = 10 / 100 ã — 60 = 600 / 100 = $ 6 therefore , decrease cost = $ 60 - $ 6 = $ 54 answer : e"
Answer: e
Question (probability): if 4 people are selected from a group of 5 married couples , what is the probability that none of them would be married to each other ?
Options: a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 8 / 21
Rationale: "if we are to select 4 people from 5 couples without any restriction , how many ways can we make the selection ? 10 ! / 4 ! 6 ! = 210 if we are to select 4 people from 5 couples with restriction that no married couple can both make it to the group , only a representative ? 5 ! / 4 ! 1 ! = 5 but we know that to select a person from each couple , take 2 possibilities 5 * 2 * 2 * 2 * 2 = 80 probability = desired / all possibilities = 80 / 210 = 8 / 21 answer : e"
Answer: e
Question (physics): a leak in the bottom of a tank can empty the full tank in 6 hours . an inlet pipe fills water at the rate of 2.5 liters per minute . when the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours . the capacity of the tank is ?
Options: a ) 5729 , b ) 5760 , c ) 2889 , d ) 3600 , e ) 2799
Rationale: "1 / x - 1 / 6 = - 1 / 8 x = 24 hrs 24 * 60 * 2.5 = 3600 . answer : d"
Answer: d
Question (general): the average marks of 10 students in a class is 100 . but a student mark is wrongly noted as 50 instead of 10 then find the correct average marks ?
Options: a ) a ) 78 , b ) b ) 82 , c ) c ) 96 , d ) d ) 91 , e ) e ) 85
Rationale: "correct avg marks = 100 + ( 10 - 50 ) / 10 avg = 100 - 4 = 96 answer is c"
Answer: c
Question (gain): find the simple interest on $ 2500 for 3 years at 10 % per annum ?
Options: a ) $ 250 , b ) $ 300 , c ) $ 750 , d ) $ 600 , e ) $ 1000
Rationale: "si = ptr / 100 = 2500 * 3 * 10 / 100 = $ 750 answer is c"
Answer: c
Question (physics): due to construction , the speed limit along an 10 - mile section of highway is reduced from 55 miles per hour to 40 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) a ) 6.24 , b ) b ) 4.1 , c ) c ) 10 , d ) d ) 15 , e ) e ) 24
Rationale: "old time in minutes to cross 10 miles stretch = 10 * 60 / 55 = 10 * 12 / 11 = 10.9 new time in minutes to cross 10 miles stretch = 10 * 60 / 40 = 10 * 3 / 2 = 15 time difference = 4.1 ans : b"
Answer: b
Question (physics): p and q can complete a work in 40 days and 24 days respectively . p alone started the work and q joined him after 16 days till the completion of the work . how long did the work last ?
Options: a ) 5 days , b ) 10 days , c ) 14 days , d ) 22 days , e ) 25 days
Rationale: "explanation : work done by p in 1 day = 1 / 40 work done by q in 1 day = 1 / 24 work done by p in 16 days = 16 ã — ( 1 / 40 ) = 2 / 5 remaining work = 1 â € “ 2 / 5 = 3 / 5 work done by p and q in 1 day = 1 / 40 + 1 / 24 = 1 / 15 number of days p and q take to complete the remaining work = ( 3 / 5 ) / ( 1 / 15 ) = 9 total days = 16 + 9 = 25 answer : option e"
Answer: e
Question (gain): in an election between the two candidates , the candidates who gets 70 % of votes polled is winned by 360 vote ’ s majority . what is the total number of votes polled ?
Options: a ) 750 , b ) 700 , c ) 900 , d ) 850 , e ) none of these
Rationale: "explanation : note : majority ( 40 % ) = difference in votes polled to win ( 70 % ) & defeated candidates ( 30 % ) 40 % = 70 % - 30 % 40 % - - - - - > 360 ( 40 * 9 = 360 ) 100 % - - - - - > 900 ( 100 * 9 = 900 ) answer : option c"
Answer: c
Question (general): if the price of petrol increases by 25 , by how much must a user cut down his consumption so that his expenditure on petrol remains constant ?
Options: a ) 25 % , b ) 20 % , c ) 16.67 % , d ) 33.33 % , e ) none of these
Rationale: "explanation : let us assume before increase the petrol will be rs . 100 . after increase it will be rs ( 100 + 25 ) i . e 125 . now , his consumption should be reduced to : - = 125 − 100125 ∗ 100 . hence , the consumption should be reduced to 20 % . answer : b"
Answer: b
Question (gain): an association of mathematics teachers has 1,260 members . only 640 of these members cast votes in the election for president of the association . what percent of the total membership voted for the winning candidate if the winning candidate received 60 percent of the votes cast ?
Options: a ) 30.47 % , b ) 58 % , c ) 42 % , d ) 34 % , e ) 25 %
Rationale: "total number of members = 1260 number of members that cast votes = 640 since , winning candidate received 60 percent of the votes cast number of votes for winning candidate = ( 60 / 100 ) * 640 = 384 percent of total membership that voted for winning candidate = ( 384 / 1260 ) * 100 = 30.47 % answer a"
Answer: a
Question (general): there are 10 players in a chess group , and each player plays each of the others once . given that each game is played by two players , how many total games will be played ?
Options: a ) 10 , b ) 30 , c ) 45 , d ) 60 , e ) 90
Rationale: "10 players are there . two players play one game with one another . so 10 c 2 = 10 * 9 / 2 = 45 so option c is correct"
Answer: c
Question (gain): by selling 24 pencils for a rupee a man loses 20 % . how many for a rupee should he sell in order to gain 20 % ?
Options: a ) 8 , b ) 9 , c ) 16 , d ) 6 , e ) 4
Rationale: "80 % - - - 24 120 % - - - ? 80 / 120 * 24 = 16 answer : c"
Answer: c
Question (gain): ramesh purchased a refrigerator for rs . 13500 after getting a discount of 20 % on the labelled price . he spent rs . 125 on transport and rs . 250 on installation . at what price should it be sold so that the profit earned would be 10 % if no discount was offered ?
Options: a ) 34778 , b ) 26888 , c ) 2899 , d ) 18975 , e ) 12778
Rationale: "price at which the tv set is bought = rs . 13,500 discount offered = 20 % marked price = 13500 * 100 / 80 = rs . 16875 the total amount spent on transport and installation = 125 + 250 = rs . 375 \ total price of tv set = 15625 + 375 = rs . 16000 the price at which the tv should be sold to get a profit of 10 % if no discount was offered = 17250 * 110 / 100 = rs . 18975 answer : d"
Answer: d
Question (physics): suresh can complete a job in 15 hours . ashutosh alone can complete the same job in 15 hours . suresh works for 9 hours and then the remaining job is completed by ashutosh . how many hours will it take ashutosh to complete the remaining job alone ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 12 , e ) none of these
Rationale: "the part of job that suresh completes in 9 hours = 9 â  „ 15 = 3 â  „ 5 remaining job = 1 - 3 â  „ 5 = 2 â  „ 5 remaining job can be done by ashutosh in 2 â  „ 5 ã — 15 = 6 hours answer c"
Answer: c
Question (physics): water is leaking out from a cylinder container at the rate of 0.31 m ^ 3 per minute . after 10 minutes , the water level decreases 4 meters . what is value of the radius ?
Options: a ) 0.5 , b ) 1.0 , c ) 1.5 , d ) 2.0 , e ) 2.5
Rationale: "10 * 0.31 = 3.1 m ^ 3 = pi * r ^ 2 * h r ^ 2 = 3.1 / ( pi * 4 ) which is about 1 / 4 r = 1 / 2 the answer is a ."
Answer: a
Question (other): in a family 4 people eat only vegetarian , 3 people eat only non veg . , 2 people eat both veg and non veg . . how many people are in the family ?
Options: a ) 4 , b ) 3 , c ) 10 , d ) 2 , e ) 9
Rationale: "total number of people in family = veg + non veg + ( both veg and non veg ) total = 4 + 3 + 2 = 9 answer is e"
Answer: e
Question (other): how many of the positive factors of 36 are not factors of 72
Options: a ) 0 , b ) 3 , c ) 4 , d ) 5 , e ) 1
Rationale: "factors of 36 - 1 , 2,3 , 4,6 , 9,12 , 18,36 , factors of 72 - 1,2 , 3,4 , 6,8 , 9,12 , 18,24 , 36,72 , comparing both , we have no factors of 36 which are not factors of 72 - 0 answer ( a )"
Answer: a
Question (physics): trapezoid jklm in the x - y plane has coordinates j = ( – 2 , – 1 ) , k = ( – 2 , 1 ) , l = ( 6 , 7 ) , and m = ( 6 , – 1 ) . what is its perimeter ?
Options: a ) 34 , b ) 36 , c ) 31 , d ) 40 , e ) ( f ) 42
Rationale: "jk = 2 lm = 11 kl = using distance formula 10 jm = using distance formula 8 sum of all is 31 c"
Answer: c
Question (physics): noelle walks from point a to point b at an average speed of 4 kilometers per hour . at what speed , in kilometers per hour , must noelle walk from point b to point a so that her average speed for the entire trip is 6 kilometers per hour ?
Options: a ) 6.75 , b ) 7 , c ) 8 , d ) 12 , e ) 14
Rationale: "let ' s suppose that speed while returning was xkm / h since the distance is same , we can apply the formula of avg speed avg speed = 2 s 1 s 2 / s 1 + s 2 6 = 2 * 4 * x / 4 + x x = 12 d is the answer"
Answer: d
Question (general): the sum of all two digit numbers divisible by 4 is
Options: a ) 1242 , b ) 1542 , c ) 1742 , d ) 1610 , e ) 1842
Rationale: "required numbers are 12 , 16,20 . . . . . 96 this is an a . p . in which a = 12 , d = 4 and l = 96 . let the number of terms in it be n . then t = 96 so a + ( n - 1 ) d = 96 . 12 + ( n - 1 ) * 6 = 96 , 12 + 4 n - 4 = 96 4 + 4 n = 96 4 n = 96 - 4 n = 92 / 4 then n = 23 . required sum = n / 2 ( a + l ) = 23 / 2 ( 12 + 96 ) = 1242 answer is a"
Answer: a
Question (gain): the profits of qrs company rose 35 % from march to april , then dropped 20 % from april to may , then rose 50 % from may to june . what was the percent increase for the whole quarter , from march to june ?
Options: a ) 15 % , b ) 32 % , c ) 40 % , d ) 62 % , e ) 80 %
Rationale: assume 100 in march , then 135 in april as 35 % increase , then 108 in may as 20 % decrease from april , and then 162 in june which is 150 % of 108 . so overall increase is from 100 to 162 is 62 % answer d
Answer: d
Question (geometry): find the area of a parallelogram with base 36 cm and height 24 cm ?
Options: a ) 760 , b ) 284 , c ) 288 , d ) 864 , e ) 820
Rationale: "area of a parallelogram = base * height = 36 * 24 = 864 cm 2 answer : d"
Answer: d
Question (gain): what quantity of water should taken out to concentrate 18 liters of 40 % acidic liquid to 60 % acidic liquid ?
Options: a ) 5 liters , b ) 10 liters , c ) 15 liters , d ) 8 liters , e ) 6 liters
Rationale: "required answer is = 18 ( 60 - 40 ) / 60 = 6 liters answer is e"
Answer: e
Question (general): if the arithmetic mean of p and q is 10 and the arithmetic mean of q and r is 26 , what is the value of r - p ?
Options: a ) 20 , b ) 10 , c ) 32 , d ) 40 , e ) 5
Rationale: "arithmetic mean expression for p and q : ( p + q ) / 2 = 10 ; p + q = 20 - - - - eq 1 arithmetic mean expression for q and r : ( q + r ) / 2 = 20 ; q + r = 52 - - - - eq 2 subtracting eq 1 from eq 2 we get : r - p = 32 hence , the correct answer is c"
Answer: c
Question (physics): a can do a work in 6 days . b can do the same work in 4 days . both a & b together will finish the work and they got $ 2000 from that work . find their shares ?
Options: a ) 600,400 , b ) 500,500 , c ) 300,700 , d ) 800,1200 , e ) 550,1450
Rationale: "ratio of their works a : b = 6 : 4 ratio of their wages a : b = 2 : 3 a ' s share = ( 2 / 5 ) 2000 = 800 b ' s share = ( 3 / 5 ) 2000 = 1200 correct option is d"
Answer: d
Question (probability): 3.00001 unbiased coins are tossed . what is the probability of getting 2 tails ?
Options: a ) 3 / 4 , b ) 1 / 4 , c ) 3 / 8 , d ) 7 / 8 , e ) 1 / 8
Rationale: "let , h - - > head , t - - > tail here s = { ttt , tth , tht , htt , thh , hth , hht , hhh } let e = event of getting 2 tails then e = { tth , tht , htt } p ( e ) = n ( e ) / n ( s ) = 3 / 8 answer is c"
Answer: c
Question (other): veena ranks 73 rd from the top in a class of 182 . what is her rank from the bottom if 35 students have failed the examination ?
Options: a ) 88 , b ) 108 , c ) 110 , d ) 75 , e ) 93
Rationale: "total student = 182 failed = 35 paasd student = 182 - 35 = 160 from bottom her rank is = 147 - 73 + 1 = 75 answer : d"
Answer: d
Question (general): the first doughnut is priced at $ 1 and then if you purchase additional doughnuts as dozens then the price is $ 6 / dozen . what is the total number of doughnuts purchased if you paid $ 20 ?
Options: a ) 30 , b ) 32 , c ) 34 , d ) 36 , e ) 38
Rationale: "$ 20 = 3 * $ 6 + $ 2 the number of doughnuts is 3 * 12 + 2 = 38 the answer is e ."
Answer: e
Question (gain): a bowl was half full of water . 4 cups of water were then added to the bowl , filling the bowl to 70 % of its capacity . how many cups of water are now in the bowl ?
Options: a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: lets say total volume of the container = v initial water content is half of total volume = v / 2 then 4 cups of water were added . current water content = ( v / 2 ) + 4 cups = ( 70 / 100 ) v = > v = 20 cups = > current water content is equivalent to = v / 2 + 4 cups = 20 / 2 + 4 = 14 cups ; answer : a
Answer: a
Question (other): two numbers are in the ratio of 5 : 7 . if 25 be subtracted from each , they are in the ratio of 35 : 59 . find the numbers ?
Options: a ) 60,88 , b ) 60,86 , c ) 60,82 , d ) 60,84 , e ) 60,83
Rationale: "( 5 x - 25 ) : ( 7 x - 25 ) = 35 : 59 x = 12 = > 60,84 answer : d"
Answer: d
Question (general): the number 189 is equal to the sum of the cubes of two integers . what is the product of those integers ?
Options: a ) 8 , b ) 15 , c ) 20 , d ) 27 , e ) 39
Rationale: "4 ^ 3 + 5 ^ 3 = 189 the number is 4 * 5 = 20 c"
Answer: c
Question (general): in the biology lab of ` ` jefferson ' ' high school there are 0.036 * 10 ^ 5 germs , equally divided among 36000 * 10 ^ ( - 3 ) petri dishes . how many germs live happily in a single dish ?
Options: a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) 500
Rationale: "0.037 * 10 ^ 5 can be written as 3600 74000 * 10 ^ ( - 3 ) can be written as 36 required = 3600 / 36 = 100 answer : a"
Answer: a
Question (physics): in 120 m race , a covers the distance in 36 seconds and b in 45 seconds . in this race a beats b by :
Options: a ) 24 m , b ) 25 m , c ) 22.5 m , d ) 9 m , e ) 12 m
Rationale: "distance covered by b in 9 sec . = 120 / 45 x 9 m = 24 m . a beats b by 24 metres . answer : option a"
Answer: a
Question (physics): how many seconds will a 450 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
Options: a ) 20 , b ) 27 , c ) 42 , d ) 32 , e ) 60
Rationale: "speed of train relative to man = 63 - 3 = 60 km / hr . = 60 * 5 / 18 = 50 / 3 m / sec . time taken to pass the man = 450 * 3 / 50 = 27 sec . answer : option b"
Answer: b
Question (gain): fox jeans regularly sell for $ 10 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 9 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discounts rates is 22 percent , what is the discount rate on pony jeans ?
Options: a ) 9 % , b ) 10 % , c ) 11 % , d ) 12 % , e ) 40 %
Rationale: "x discount on pony jeans , ( 0.22 - x ) discount on fox jeans . set the equation : 3 * 10 ( 0.22 - x ) + 2 * 18 x = 9 - - > x = 0.4 = 40 % answer : e ."
Answer: e
Question (physics): a taxi leaves point a 3 hours after a bus left the same spot . the bus is traveling 30 mph slower than the taxi . find the speed of the taxi , if it overtakes the bus in three hours .
Options: a ) 60 , b ) 72 , c ) 48 , d ) 36 , e ) 64
Rationale: let the speed of bus be v - 30 , speed of taxi be v the bus travelled a total of 6 hrs and taxi a total of 3 hrs . hence 6 * ( v - 30 ) = 3 v 6 v - 180 = 3 v 3 v = 180 v = 60 mph a
Answer: a
Question (physics): a single reservoir supplies the petrol to the whole city , while the reservoir is fed by a single pipeline filling the reservoir with the stream of uniform volume . when the reservoir is full and if 40,000 liters of petrol is used daily , the suply fails in 90 days . if 32,000 liters of petrol is used daily , it fails in 60 days . how much petrol can be used daily with out the supply ever failing ?
Options: a ) 64000 liters
b ) 56000 liters
c ) 78000 liters
d ) 60000 liters
e ) none of these
Rationale: explanation : let x liter be the per day filling and v litr be the capacity of the reservoir , then 90 x + v = 40000 × 90 - - - - - ( 1 ) 60 x + v = 32000 × 60 - - - - - - ( 2 ) solving eq . ( 1 ) and ( 2 ) , we get x = 56000 hence , 56000 liters per day can be used without the failure of supply . answer : b
Answer: b
Question (physics): a train 100 m long crosses a platform 250 m long in 7 sec ; find the speed of the train ?
Options: a ) 94 kmph , b ) 58 kmph , c ) 54 kmph , d ) 180 kmph , e ) 59 kmph
Rationale: "d = 100 + 250 = 350 t = 7 s = 350 / 7 * 18 / 5 = 180 kmph answer : d"
Answer: d
Question (general): what is the greatest positive integer x such that 6 ^ x is a factor of 216 ^ 10 ?
Options: a ) 5 , b ) 9 , c ) 10 , d ) 20 , e ) 30
Rationale: "216 ^ 10 = ( 6 ^ 3 ) ^ 10 = 6 ^ 30 answer : e"
Answer: e
Question (physics): the length of the bridge , which a train 100 metres long and travelling at 45 km / hr can cross in 30 seconds , is ?
Options: a ) 10 m , b ) 16 m , c ) 275 m , d ) 19 m , e ) 27 m
Rationale: "speed = [ 45 x 5 / 18 ] m / sec = [ 25 / 2 ] m / sec time = 30 sec let the length of bridge be x metres . then , ( 100 + x ) / 30 = 25 / 2 = > 2 ( 100 + x ) = 750 = > x = 275 m . answer : c"
Answer: c
Question (gain): simple interest on a certain sum at a certain annual rate of interest is 1 / 4 of the sum . if the numbers representing rate percent and time in years be equal , then the rate of interest is :
Options: a ) 4 % . , b ) 25 / 4 % . , c ) 5 % , d ) 6 % . , e ) 3 % .
Rationale: "explanation : let sum = x . then , s . i . = x / 4 let rate = r % and time = r years . [ x * r * r / 100 ] = x / 4 ? r ^ 2 = 100 / 4 = 25 r = 5 hence , rate of interest = 5 % . answer : c"
Answer: c
Question (gain): ravish has to secure 40 % marks to clear his board exam of class 10 th . he got 40 marks and failed by 40 marks . what is the maximum marks ?
Options: a ) 150 , b ) 135 , c ) 160 , d ) 200 , e ) 155
Rationale: d 200 to pass the exam ravish needs 40 + 40 = 80 marks . = > ( 80 / 40 ) * 100 = 200
Answer: d
Question (other): there are 172 lights which are functional and each is controlled by a separate on / off switch . two children a and b start playing with the switches . a starts by pressing every third switch till he reaches the end . b , thereafter , presses every fifth switch till he too reaches the end . if all switches were in off position at the beggining , how many lights are switched on by the end of this operation ?
Options: a ) 83 , b ) 85 , c ) 87 , d ) 79 , e ) 89
Rationale: "editing my solution : number of switches = 172 number of switches turned on by a : 3 , 6 , . . . 171 = 57 number of switches turned on by b : 5 , 10 , . . . . 170 = 34 few switches are turned on by a and later turned off by b : lcm ( 3,5 ) = 15 x = 15 , 30 , . . . . 90 = 6 . subtract the above 6 switches from both a and b as they are turned off . number of switches that are turned on = ( 57 - 6 ) + ( 34 - 6 ) = 79 answer : d"
Answer: d
Question (physics): car x began traveling at an average speed of 35 miles per hour . after 72 minutes , car y began traveling at an average speed of 41 miles per hour . when both cars had traveled the same distance , both cars stopped . how many miles did car x travel from the time car y began traveling until both cars stopped ?
Options: a ) 140 , b ) 175 , c ) 210 , d ) 245 , e ) 280
Rationale: "in 72 minutes , car x travels 42 miles . car y gains 6 miles each hour , so it takes 7 hours to catch car x . in 7 hours , car x travels 245 miles . the answer is d ."
Answer: d
Question (physics): a man swims downstream 36 km and upstream 48 km taking 6 hours each time , what is the speed of the man in still water ?
Options: a ) 5 , b ) 24 , c ) 7 , d ) 42 , e ) 6
Rationale: "36 - - - 6 ds = 6 ? - - - - 1 48 - - - - 6 us = 8 ? - - - - 1 m = ? m = ( 6 + 8 ) / 2 = 7 answer : c"
Answer: c
Question (other): a certain manufacturer of cake , muffin , and bread mixes has 100 buyers , of whom 50 purchases cake mix , 40 purchase muffin mix , and 17 purchase both cake mix and muffin mix . if a buyer is to be selected at random from the 100 buyers , what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix ?
Options: a ) 1 / 10 , b ) 3 / 10 , c ) 1 / 2 , d ) 27 / 100 , e ) 9 / 100
Rationale: c + m + b - cm - mb - cb - 2 cmb = 100 c - cake buyers , m - muffin and b - bread buyers . cm , mb , cb and cmb are intersecting regions . the question asks for people who have bought only bread mixes = b - cb - mb - 2 cmb has to be found out . 50 + 40 + b - cb - mb - 17 - 2 cmb = 100 b - cb - mb - 2 cmb = 27 hence the probability = 27 / 100 d
Answer: d
Question (general): the original price of a suit is $ 150 . the price increased 20 % , and after this increase , the store published a 20 % off coupon for a one - day sale . given that the consumers who used the coupon on sale day were getting 20 % off the increased price , how much did these consumers pay for the suit ?
Options: a ) $ 130 , b ) $ 136 , c ) $ 144 , d ) $ 150 , e ) $ 160
Rationale: "0.8 * ( 1.2 * 150 ) = $ 144 the answer is c ."
Answer: c
Question (physics): convert 350 inches into centimeter ?
Options: a ) 812 cm , b ) 820 cm , c ) 850 cm , d ) 889 cm , e ) 854 cm
Rationale: "1 inch = 2.54 cm 350 inches = 100 * 2.54 = 889 cm answer is d"
Answer: d
Question (gain): the length of a rectangular floor is more than its breadth by 200 % . if rs . 624 is required to paint the floor at the rate of rs . 4 per sq m , then what would be the length of the floor ?
Options: a ) 22.8 m . , b ) 21.6 m . , c ) 21.1 m . , d ) 20.6 m . , e ) 22.5 m .
Rationale: "let the length and the breadth of the floor be l m and b m respectively . l = b + 200 % of b = l + 2 b = 3 b area of the floor = 624 / 4 = 156 sq m l b = 156 i . e . , l * l / 3 = 156 l 2 = 468 = > l = 21.6 m . answer : b"
Answer: b
Question (physics): a is twice as fast as b . if b alone can do a piece of work in 10 days , in what time can a and b together complete the work ?
Options: a ) 10 / 3 , b ) 8 , c ) 9 , d ) 7 / 3 , e ) 12
Rationale: "a can do the work in 10 / 2 i . e . , 5 days . a and b ' s one day ' s work = 1 / 5 + 1 / 10 = ( 2 + 1 ) / 10 = 10 / 3 so a and b together can do the work in 10 / 3 days . answer : a"
Answer: a