Cheukting/mathqa huggingface dataset:
Question (general): the average ( arithmetic mean ) of the integers from 200 to 800 , inclusive , is how much greater than the average of the integers from 50 to 300 , inclusive ?
Options: a ) 450 , b ) 375 , c ) 400 , d ) 425 , 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 800 , inclusive = ( 200 + 800 ) / 2 = 500 average of numbers between 50 to 300 , inclusive = ( 50 + 300 ) / 2 = 175 difference = 500 - 175 = 425 answer is d"
Answer: d
Question (general): the sum of the first 50 positive even integers is 2550 . what is the sum r of even integers from 102 to 200 inclusive ?
Options: a ) 5100 , b ) 7550 , c ) 10100 , d ) 15500 , e ) 20100
Rationale: "my solution is : first 50 even integers : 2 4 6 8 < . . . > integers from 102 to 200 102 104 106 108 < . . . > we notice that each integer from the second set is 100 more than the respective integer in the first set . since we have 50 even integers from 102 to 200 , then : r = 2550 + ( 100 * 50 ) = 7550 . b"
Answer: b
Question (general): bipin is 6 times old as alok . bipin ' s age will be twice of chandan ' s age after 10 years . if chandan ' s 7 th birthday was celebrated 3 years ago , what is alok ' s present age ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: let the present ages of bipin , alok , chandan are b , a , c respectively given conditions are 1 ) b = 6 a 2 ) ( b + 10 ) = 2 * ( c + 10 ) 3 ) chandans present age = c = 10 years therefore b = 30 so a = 5 answer : d
Answer: d
Question (general): a big container is 30 % full with water . if 36 liters of water is added , the container becomes 3 / 4 full . what is the capacity of the big container ?
Options: a ) 36 liters , b ) 40 liters , c ) 45 liters , d ) 54 liters , e ) 80 liters
Rationale: "a big container is 30 % full with water and after 36 liters of water is added , the container becomes 75 % full . hence these 36 liters account for 45 % of the container , which means that the capacity of it is 36 / 0.45 = 80 liters . or : if the capacity of the container is x liters then : 0.3 x + 36 = 0.75 x - - > x = 80 liters . answer : e ."
Answer: e
Question (physics): find the cost of fencing around a circular field of diameter 42 m at the rate of rs . 5 a meter ?
Options: a ) 655.9 , b ) 659.75 , c ) 650.57 , d ) 655.9 , e ) 600.3
Rationale: "2 * 22 / 7 * 14 = 131.95 131.95 * 5 = rs . 659.75 answer : b"
Answer: b
Question (physics): length of a rectangular plot is 60 mtr more than its breadth . if the cost of fencing the plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ?
Options: a ) 46 m , b ) 60 m , c ) 58 m , d ) 78 m , e ) 80 m
Rationale: "let breadth = x metres . then , length = ( x + 60 ) metres . perimeter = 5300 / 26.5 m = 200 m . 2 [ ( x + 60 ) + x ] = 200 2 x + 60 = 100 2 x = 40 x = 20 . hence , length = x + 60 = 80 m e"
Answer: e
Question (gain): exactly 36 % of the numbers in set a are even multiples of 3 . if 40 % of the even integers in set a are not multiples of 3 , what percent of the numbers in set a are not even integers ?
Options: a ) 76 % , b ) 60 % , c ) 50 % , d ) 40 % , e ) 24 %
Rationale: everything is correct except the red part with a typo : it should be n = 0.6 a - - > even numbers are 60 % of a - - > 40 % of a are not even integers . answer : d .
Answer: d
Question (general): the number of timeshare condos available at sunset beach is 3 / 5 the number of timeshare condos available at playa del mar . if the total number of timeshare condos available at the two beaches combined is 320 , what is the difference between the number of condos available at sunset beach and the number of condos available at playa del mar ?
Options: a ) 80 , b ) 90 , c ) 120 , d ) 150 , e ) 240
Rationale: "let x be the number of timeshare condos available at playa del mar . then number of timeshare condos available at sunset beach = 3 / 5 x we know , x + 3 / 5 x = 320 hence , x = 200 . so , number of timeshare condos available at playa del mar = 200 the difference between the number of condos available at sunset beach and the number of condos available at playa del mar = x - 3 / 5 x = 2 / 5 x = 2 / 5 ( 200 ) = 80 the correct answer is a ."
Answer: a
Question (physics): find the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 15 cm
Options: a ) 178 cm 2 , b ) 179 cm 2 , c ) 285 cm 2 , d ) 167 cm 2 , e ) 197 cm 2
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 15 ) = 285 cm 2 answer : c"
Answer: c
Question (general): if the operation @ is defined for all a and b by the equation a @ b = ( a ^ 2 * b ) * 3 , then 2 @ ( 3 @ - 1 ) =
Options: a ) - 324 , b ) 223 , c ) 324 , d ) - 223 , e ) - 410
Rationale: "work within the parenthesis first so solve ( 3 @ - 1 ) first ( 3 @ - 1 ) = ( ( 3 ^ 2 ) * - 1 ) * 3 = ( 9 * - 1 ) * 3 = - 9 * 3 = - 27 now take - 3 plug back into equation and solve the rest 2 @ ( - 27 ) = ( ( 2 ^ 2 ) * - 3 ) * 3 = ( 4 * - 27 ) * 3 = - 324 so - 324 is the answer . . . . this question is merely testing order of operations remember pemdas option a"
Answer: a
Question (geometry): a rectangular photograph is surrounded by a border that is 1 inch wide on each side . the total area of the photograph and the border is m square inches . if the border had been 7 inches wide on each side , the total area would have been ( m + 264 ) square inches . what is the perimeter of the photograph , in inches ?
Options: a ) 8 , b ) 12 , c ) 16 , d ) 20 , e ) 24
Rationale: "let x and y be the width and length of the photograph . ( x + 2 ) ( y + 2 ) = m and so ( 1 ) xy + 2 x + 2 y + 4 = m ( x + 14 ) ( y + 14 ) = m and so ( 2 ) xy + 14 x + 14 y + 196 = m + 264 let ' s subtract equation ( 1 ) from equation ( 2 ) . 12 x + 12 y + 192 = 264 2 x + 2 y = 12 , which is the perimeter of the photograph . the answer is b ."
Answer: b
Question (general): a picnic attracts 240 persons . there are 60 more men than women , and 60 more adults than children . how many men are at this picnic ?
Options: a ) 240 , b ) 75 , c ) 110 , d ) 130 , e ) 85
Rationale: "adult + children = 240 let , children = y then , adult = y + 60 i . e . y + ( y + 60 ) = 240 i . e . y = 90 i . e . adult = 90 + 20 = 110 adults include only men and women i . e . men + women = 110 let women , w = x then men , m = x + 60 i . e . x + ( x + 60 ) = 2 x + 60 = 110 i . e . x = 25 i . e . men , m = 25 + 60 = 85 answer : option e"
Answer: e
Question (general): the price for a loaf of bread in april was $ 1.17 , in may the price was $ 1.30 , and in june the price was $ 1.05 . if 2 / 3 as much bread was sold in april as in may , and twice as much was sold in june as in april , what was the average price for a loaf of bread sold during the 3 - month period ?
Options: a ) $ 1.13 , b ) $ 1.14 , c ) $ 1.15 , d ) $ 1.16 , e ) $ 1.17
Rationale: let x be the number of loaves sold in may . then 2 x / 3 loaves were sold in april and 4 x / 3 loaves were sold in june . the average price was ( 2 x / 3 ) ( 117 ) + 130 x + ( 4 x / 3 ) ( 105 ) / ( 2 x / 3 + x + 4 x / 3 ) = ( 78 + 130 + 140 ) / ( 3 ) = 348 / 3 = $ 1.16 the answer is d .
Answer: d
Question (physics): a person travels equal distances with speeds of 9 km / hr , 10 km / hr and 11 km / hr and takes a total time of 47 minutes . the total distance is ?
Options: a ) 6 km , b ) 3 km , c ) 8 km , d ) 9 km , e ) 2 km
Rationale: "let the total distance be 3 x km . then , x / 9 + x / 10 + x / 11 = 47 / 60 29 x / 96 = 47 / 60 = > x = 2.59 total distance = 3 * 2.59 = 7.78 km . answer : c"
Answer: c
Question (geometry): if the sides of a triangle are 26 cm , 22 cm and 10 cm , what is its area ?
Options: a ) 120 , b ) 110 , c ) 130 , d ) 140 , e ) 150
Rationale: "the triangle with sides 26 cm , 22 cm and 10 cm is right angled , where the hypotenuse is 26 cm . area of the triangle = 1 / 2 * 22 * 10 = 110 cm 2 answer : option b"
Answer: b
Question (general): the average mark of the students of a class in a particular exam is 72 . if 5 students whose average mark in that exam is 40 are excluded , the average mark of the remaining will be 92 . find the number of students who wrote the exam ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 16 , e ) 15
Rationale: "let the number of students who wrote the exam be x . total marks of students = 80 x . total marks of ( x - 5 ) students = 92 ( x - 5 ) 72 x - ( 5 * 40 ) = 92 ( x - 5 ) 260 = 20 x = > x = 13 answer : b"
Answer: b
Question (gain): suresh borrowed some money at the rate of 12 % p . a . for the first 3 years , 9 % p . a . for the next 5 years and 13 % p . a . for the period beyond 8 years . if the total interest paid by him at the end of 11 years is rs . 8160 , how much money did he borrow ?
Options: a ) s . 8500 , b ) s . 6000 , c ) s . 6800 , d ) s . 9000 , e ) s . 7000
Rationale: using the formula s . i = p * t * r / 100 ( x * 12 * 3 / 100 ) + ( x * 9 * 5 / 100 ) + ( x * 13 * 3 / 100 ) = 8160 x = 6800 i . e money borrowed is rs . 6800 answer : c
Answer: c
Question (other): in township k , 1 / 4 of the housing units are equiped with cable tv . if 1 / 10 of the housing units , including 1 / 3 of those that are equiped with cable tv , are equipped with videocassette recorders , what fraction of the housing units have neither cable tv nor videocassette recorders ?
Options: a ) 23 / 30 , b ) 11 / 15 , c ) 7 / 10 , d ) 1 / 6 , e ) 2 / 15
Rationale: "1 / 4 - - cable tv ( this includes some data from video cassette recorder ) 1 / 10 - - video cassette recorder including 1 / 3 ( equiped with cable tv ) i . e . 1 / 3 ( 1 / 4 ) = 1 / 12 therefore only video cassette recorder = 1 / 10 - 1 / 12 = 1 / 60 total = 1 / 4 + 1 / 60 + neither cable tv nor videocassette recorders 1 = 4 / 15 + neither cable tv nor videocassette recorders therefore neither cable tv nor videocassette recorders = 1 - 4 / 15 = 11 / 15 hence b ."
Answer: b
Question (other): if both 5 ^ 2 and 3 ^ 4 are factors of the number a * 4 ^ 3 * 6 ^ 2 * 13 ^ 11 , then what is the smallest possible value of a ?
Options: a ) 80 , b ) 120 , c ) 150 , d ) 225 , e ) 300
Rationale: "the number a must include at least 3 ^ 2 * 5 ^ 2 = 225 the answer is d ."
Answer: d
Question (physics): the ratio between the length and the breadth of a rectangular park is 3 : 2 . if a man cycling alongthe oundary of the park at the speed of 12 km / hr completes one round in 8 min , then the area of the park ( in sq . m ) is ?
Options: a ) 7889890 m , b ) 2334356 m , c ) 1536001 m , d ) 1232431 m , e ) 2435467 m
Rationale: "perimeter = distance covered in 8 min . = 12000 x 8 m = 1600 m . 60 let length = 3 x metres and breadth = 2 x metres . then , 2 ( 3 x + 2 x ) = 1600 or x = 160 . length = 480 m and breadth = 320 m . area = ( 480 x 320 ) m 2 = 153600 m c"
Answer: c
Question (general): what will be the result of 12 ^ 4 + 3 + 2 ^ 9 + 3 - 8 / 2 ?
Options: a ) 58 , b ) 14 , c ) 145 , d ) 69 , e ) 74
Rationale: "the multiplication ( e . g . 12 ^ 4 ) and division ( e . g . 8 / 2 ) is done first and then the sum ( e . g . 48 + 3 ) and subtraction ( e . g . 4 - 4 ) , and the answer is 69 , option d ."
Answer: d
Question (general): in a certain game of dice , the player ’ s score is determined as a sum of two throws of a single die . the player with the highest score wins the round . if more than one player has the highest score , the winnings of the round are divided equally among these players . if jim plays this game against 21 other players , what is the probability of the minimum score that will guarantee jim some monetary payoff ?
Options: a ) 41 / 50 , b ) 1 / 221 , c ) 1 / 216 , d ) 1 / 36 , e ) 1 / 42
Rationale: toguaranteethat jim will get some monetary payoff he must score the maximum score of 6 + 6 = 12 , because if he gets even one less than that so 11 , someone can get 12 and jim will get nothing . p ( 12 ) = 1 / 6 ^ 2 = 1 / 36 . answer : d
Answer: d
Question (general): how many times will the digit 6 be written when listing the integers from 1 to 1000 ?
Options: a ) 150 , b ) 280 , c ) 310 , d ) 420 , e ) 300
Rationale: "many approaches are possible . for example : consider numbers from 0 to 999 written as follows : 1 . 000 2 . 001 3 . 002 4 . 003 . . . . . . . . . 1000 . 999 we have 1000 numbers . we used 3 digits per number , hence used total of 3 * 1000 = 3000 digits . now , why should any digit have preferences over another ? we used each of 10 digits equal # of times , thus we used each digit ( including 6 ) 3000 / 10 = 300 times . answer : e ."
Answer: e
Question (general): an assembly line produces 20 cogs per hour until an initial order of 60 cogs is completed . the speed of the assembly line is then immediately increased so that it can produce 60 cogs per hour until another 60 cogs are produced . what is the overall average output , in cogs per hour , for the assembly line during this whole time ?
Options: a ) 25 , b ) 30 , c ) 35 , d ) 40 , e ) 45
Rationale: "the time to produce the first 60 cogs is 60 / 20 = 3 hours . the time to produce the next 60 cogs is 60 / 60 = 1 hour . the average output is 120 cogs / 4 hours = 30 cogs per hour . the answer is b ."
Answer: b
Question (gain): what is 120 % of 13 / 24 of 960 ?
Options: a ) 420 , b ) 484 , c ) 526 , d ) 578 , e ) 624
Rationale: "120 % * 13 / 24 * 360 = 1.2 * 13 * 40 = 624 the answer is e ."
Answer: e
Question (gain): 3 candidates in an election and received 1136 , 7636 and 11628 votes respectively . what % of the total votes did the winningcandidate got in that election ?
Options: a ) 45 % , b ) 56 % , c ) 57 % , d ) 70 % , e ) 72 %
Rationale: "total number of votes polled = ( 1136 + 7636 + 11628 ) = 20400 so , required percentage = 11628 / 20400 * 100 = 57 % c"
Answer: c
Question (general): the average of first 80 non - zero positive numbers is :
Options: a ) 22.25 , b ) 31.25 , c ) 35 , d ) 40.5 , e ) none of these
Rationale: "explanation : sum of first n natural numbers = n ( n + 1 ) / 2 so , average of first n natural numbers = n ( n + 1 ) / 2 n = ( n + 1 ) / 2 required average = ( 80 + 1 ) / 2 = 81 / 2 = 40.5 . answer : d"
Answer: d
Question (physics): yesterday it took robert 4 hours to drive from city a to city b . today it took robert 3.5 hours to drive back from city в to city a along the same route . if he had saved 15 minutes in both trips , the speed for the round trip would be 60 miles per hour . what is the distance between city a and city b ?
Options: a ) 90 , b ) 120 , c ) 150 , d ) 210 , e ) 300
Rationale: "2 d / 60 = 7 ( because time = 4 + 3.5 - 0.5 hrs ) = > d = 210 answer - d"
Answer: d
Question (gain): a shopkeeper loses 15 % , if an article is sold for rs . 153 . what should be the selling price of the article to gain 20 % ?
Options: a ) s . 147 , b ) s . 248 , c ) s . 244 , d ) s . 229 , e ) s . 216
Rationale: given that sp = rs . 153 and loss = 15 % cp = [ 100 ( sp ) ] / ( 100 - l % ) = ( 100 * 153 ) / 85 = rs . 180 . to get 20 % profit , new sp = [ ( 100 + p % ) cp ] / 100 = ( 180 * 120 ) / 100 = rs . 216 answer : e
Answer: e
Question (general): the sum of two numbers is 45 . sum of their quotient and reciprocal is 2.05 , find the product of the numbers .
Options: a ) 339 , b ) 500 , c ) 288 , d ) 277 , e ) 112
Rationale: sol : let a , b be the numbers . a + b = 45 ab + baab + ba = 2.05 ⇒ a 2 + b 2 ab ⇒ a 2 + b 2 ab = 2.05 ⇒ ( a + b ) 2 − 2 abab = 2.05 ⇒ ( a + b ) 2 − 2 abab = 2.05 ⇒ ( a + b ) 2 ⇒ ( a + b ) 2 = 2.05 ab + 2 ab = 4.05 ab ⇒ ⇒ ab = 4524 . 054524.05 = 500 answer : b
Answer: b
Question (general): in smithtown , the ratio of right - handed people to left - handed people is 3 to 1 and the ratio of men to women is 3 to 2 . if the number of right - handed men is maximized , then what q percent of all the people in smithtown are left - handed women ?
Options: a ) 50 % , b ) 40 % , c ) 25 % , d ) 20 % , e ) 10 %
Rationale: "looking at the ratio we can take total number of people q = 20 . . ans 5 / 20 or 25 % c"
Answer: c
Question (gain): company p had 15 percent more employees in december than it had in january . if company p had 500 employees in december , how many employees did it have in january ?
Options: a ) 391 , b ) 435 , c ) 410 , d ) 423 , e ) 445
Rationale: "d = number of employees in december j = number of employees in january j x 1.15 = d j x 1.15 = 500 j = 500 / 1.15 j = 50,000 / 115 = 435 thus b is the correct answer ."
Answer: b
Question (general): at a certain fruit stand , the price of each apple is 50 cents and the price of each orange is 60 cents . mary selects a total of 10 apples and oranges from the fruit stand , and the average ( arithmetic mean ) price of the 10 pieces of fruit is 56 cents . how many oranges must mary put back so that the average price of the pieces of fruit that she keeps is 52 cents ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "let number of apples = a number of oranges = b a + b = 10 - - - 1 . 56 = ( . 5 a + . 6 b ) / 10 = > 56 = 5 a + 6 b - - - - 2 solving 1 and 2 , we get a = 4 b = 6 let the number of oranges put back = c 52 * ( 10 - c ) = 50 * 4 + 60 ( 6 - c ) = > c = 5 answer e"
Answer: e
Question (physics): mary can do a piece of work in 28 days . rosy is 40 % more efficient than mary . the number of days taken by rosy to do the same piece of work is ?
Options: a ) 22 , b ) 24 , c ) 20 , d ) 25 , e ) 27
Rationale: "ratio of times taken by mary and rosy = 140 : 100 = 14 : 10 suppose rosy takes x days to do the work . 14 : 10 : : 28 : x = > x = 20 days . hence , rosy takes 20 days to complete the work . answer : c"
Answer: c
Question (general): company x provides bottled water to its employees in 5 liter bottles , $ 5 each . at least how many 5 l bottles must company x buy monthly , so that new contract with $ 40 fixed monthly rate and $ 2 for 20 l bottle each paid off ? ( assume that no other costs apply )
Options: a ) 4 , b ) 9 , c ) 12 , d ) 20 , e ) 25
Rationale: let the no . of 5 liter bottles be x , so the no . of 20 l bottles will be x / 4 ( to equate the vol . ) since the total cost will be equal , 5 x = 40 + 2 * x / 4 so x = 8.88 or 9 . answer is ( b ) .
Answer: b
Question (gain): a reduction of 15 % in the price of oil enables a house wife to obtain 5 kgs more for rs . 800 , what is the reduced price for kg ?
Options: a ) 12 , b ) 16 , c ) 24 , d ) 28 , e ) 32
Rationale: "800 * ( 15 / 100 ) = 120 - - - - 5 ? - - - - 1 = > rs . 24 answer : c"
Answer: c
Question (general): a certain number when divided by 39 leaves a remainder 18 , what is the remainder when the same number is divided by 13 ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 6 , e ) 5
Rationale: "explanation : 39 + 18 = 57 / 13 = 5 ( remainder ) answer : e"
Answer: e
Question (probability): the membership of a committee consists of 4 english teachers , 2 mathematics teachers , and 2 social studies teachers . if 2 committee members are to be selected at random to write the committee ’ s report , what is the probability that the two members selected will both be english teachers ?
Options: a ) 2 / 3 , b ) 1 / 3 , c ) 2 / 9 , d ) 1 / 12 , e ) 3 / 28
Rationale: "probability of first member an english teacher = 3 / 8 probability of second member an english teacher = 2 / 8 probability of both being english teacher = 3 / 8 x 2 / 7 = 3 / 28 ( e )"
Answer: e
Question (physics): a train 360 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 215 m long ?
Options: a ) 40 , b ) 46 , c ) 88 , d ) 77 , e ) 21
Rationale: ": speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 360 + 215 = 575 m required time = 575 * 2 / 25 = 46 sec answer : b"
Answer: b
Question (physics): a and b complete a work in 5 days . a alone can do it in 10 days . if both together can do the work in how many days ?
Options: a ) 3.33 days , b ) 3.99 days , c ) 2.99 days , d ) 2.98 days , e ) 2.44 days
Rationale: "1 / 5 + 1 / 10 = 3 / 10 10 / 3 = 3.33 days answer : a"
Answer: a
Question (physics): when tom works alone he chops 2 lb . salad in 3 minutes , and when tammy works alone she chops 3 lb . salad in 2 minutes . they start working together , and after some time finish chopping 65 lb . of salad . of those 80 lb . , the salad quantity chopped by tom is what percent lesser than the quantifying chopped by tammy ? .
Options: a ) 44 % , b ) 100 % , c ) 105 % , d ) 225 % , e ) 125 %
Rationale: "tom chops 4 lbs in 6 minutes tammy chops 9 lbs in 6 minutes so in the same amount of time , tom chops 125 % less than tammy , since 9 is 125 % greater than 4 . so 125 % is the answer . note that the actual time does n ' t matter . if you multiply the time each work by x , you ' ll multiply the work each does by x , and 9 x is still 125 % greater than 4 x . ans : e"
Answer: e
Question (physics): suresh can complete a job in 15 hours . ashutosh alone can complete the same job in 35 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 ) 14 , 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 — 35 = 14 hours answer c"
Answer: c
Question (physics): a and b can together finish a work in 40 days . they worked together for 10 days and then b left . after another 9 days , a finished the remaining work . in how many days a alone can finish the job ?
Options: a ) 12 , b ) 25 , c ) 60 , d ) 30 , e ) 20
Rationale: "a + b 10 days work = 10 * 1 / 40 = 1 / 4 remaining work = 1 - 1 / 4 = 3 / 4 3 / 4 work is done by a in 9 days whole work will be done by a in 9 * 4 / 3 = 12 days answer is a"
Answer: a
Question (physics): two trains of length 90 m and 95 m are 250 m apart . they start moving towards each other on parallel tracks , at speeds 64 kmph and 92 kmph . after how much time will the trains meet ?
Options: a ) 53 / 10 , b ) 55 / 10 , c ) 56 / 10 , d ) 57 / 10 , e ) 58 / 10
Rationale: "they are moving in opposite directions , relative speed is equal to the sum of their speeds . relative speed = ( 64 + 92 ) * 5 / 18 = 43.3 mps . the time required = d / s = 250 / 43.3 = 58 / 10 sec . answer : e"
Answer: e
Question (general): what is the greatest 6 - digit number when divided by 6 , 7 , 8 , 9 , and 10 leaves a remainder of 4 , 5 , 6 , 7 , and 8 respectively ?
Options: a ) 456780 , b ) 678910 , c ) 997479 , d ) 997918 , e ) 997920
Rationale: when you divide a positive integer by 10 , the remainder will just be the units digit . we know the remainder is 8 when we divide by 10 , so d is the only possible answer .
Answer: d
Question (gain): in one alloy there is 12 % chromium while in another alloy it is 10 % . 15 kg of the first alloy was melted together with 35 kg of the second one to form a third alloy . find the percentage of chromium in the new alloy .
Options: a ) 8.8 % , b ) 9 % , c ) 9.2 % , d ) 8.6 % , e ) 10.6 %
Rationale: "the amount of chromium in the new 15 + 35 = 50 kg alloy is 0.12 * 15 + 0.10 * 35 = 5.3 kg , so the percentage is 5.3 / 50 * 100 = 10.6 % . answer : e ."
Answer: e
Question (gain): a baseball card decreased in value 10 % in its first year and 10 % in its second year . what was the total percent decrease of the card ' s value over the two years ?
Options: a ) 19 % , b ) 30 % , c ) 32 % , d ) 36 % , e ) 72 %
Rationale: "consider the initial value of the baseball card as $ 100 after first year price = 100 * 0.9 = 90 after second year price = 90 * 0.9 = 81 final decrease = [ ( 100 - 81 ) / 100 ] * 100 = 19 % correct answer - a"
Answer: a