Cheukting/mathqa huggingface dataset:
Question (general): on dividing a number by 357 , we get 37 as remainder . on dividing the same number by 17 , what will be the remainder ?
Options: a ) 4 , b ) 3 , c ) 8 , d ) 7 , e ) 2
Rationale: "let x be the number and y be the quotient . then , x = 357 * y + 37 = ( 17 * 21 * y ) + ( 17 * 2 ) + 3 = 17 * ( 21 y + 2 ) + 3 . required number = 3 . answer is b"
Answer: b
Question (general): a certain social security recipient will receive an annual benefit of $ 12,000 provided he has annual earnings of $ 9,360 or less , but the benefit will be reduced by $ 1 for every $ 3 of annual earnings over $ 9,360 . what amount of total annual earnings would result in a 55 percent reduction in the recipient ' s annual social security benefit ? ( assume social security benefits are not counted as part of annual earnings . )
Options: a ) $ 15,360 , b ) $ 17,360 , c ) $ 25,560 , d ) $ 21,360 , e ) $ 27,360
Rationale: "for every $ 3 earn above $ 9360 , the recipient loses $ 1 of benefit . or for every $ 1 loss in the benefit , the recipient earns $ 3 above $ 9360 if earning is ; 9360 + 3 x benefit = 12000 - x or the vice versa if benefit is 12000 - x , the earning becomes 9360 + 3 x he lost 50 % of the benefit ; benefit received = 12000 - 0.55 * 12000 = 12000 - 6600 x = 5400 earning becomes 9360 + 3 x = 9360 + 3 * 5400 = 25560 ans : c"
Answer: c
Question (physics): a vessel of capacity 45 litres is fully filled with pure milk . nine litres of milk is removed from the vessel and replaced with water . nine litres of the solution thus formed is removed and replaced with water . find the quantity of pure milk in the final milk solution ?
Options: a ) 28.8 , b ) 72.9 , c ) 38.3 , d ) 78.3 , e ) 79.3
Rationale: "explanation : let the initial quantity of milk in vessel be t litres . let us say y litres of the mixture is taken out and replaced by water for n times , alternatively . quantity of milk finally in the vessel is then given by [ ( t - y ) / t ] ^ n * t for the given problem , t = 45 , y = 9 and n = 2 . hence , quantity of milk finally in the vessel = [ ( 45 - 9 ) / 45 ] ^ 2 ( 45 ) = 28.8 litres . answer : option a"
Answer: a
Question (geometry): if circles x and y have the same area and circle x has a circumference of 12 π , half of the radius of circle y is :
Options: a ) 16 , b ) 8 , c ) 3 , d ) 2 , e ) 1
Rationale: "x be radius of circle x y be radius of circle y given : pi * x ^ 2 = pi * y ^ 2 also , 2 * pi * x = 12 * pi x = 6 thus y = 6 y / 2 = 3 ans : c"
Answer: c
Question (physics): convert the 18 / 42 m / s into kilometers per hour ?
Options: a ) 3.5 kmph . , b ) 2.5 kmph . , c ) 1.2 kmph . , d ) 1.54 kmph . , e ) 1.9 kmph .
Rationale: "18 / 42 m / s = 18 / 42 * 18 / 5 = 1 ( 27 / 50 ) = 1.54 kmph . answer : d"
Answer: d
Question (gain): if a man lost 1 % by selling oranges at the rate of 16 a rupee at how many a rupee must he sell them to gain 44 % ?
Options: a ) 12 , b ) 14 , c ) 7 , d ) 11 , e ) 10
Rationale: "99 % - - - - 16 144 % - - - - ? 99 / 144 * 16 = 11 answer : d"
Answer: d
Question (general): a certain car uses one gallon of gasoline every 34 miles when it travels on highway , and one gallon of gasoline every 20 miles when it travels in the city . when a car travels 4 miles on highway and 4 additional miles in the city , it uses what percent more gasoline than if it travels 8 miles on the highway ?
Options: a ) 15 % , b ) 20 % , c ) 22.5 % , d ) 35 % , e ) 50 %
Rationale: 4 miles on the highway = 4 / 34 gallons ; 4 miles in the city = 4 / 20 gallons ; total = 4 / 34 + 4 / 20 = 27 / 85 gallons . 8 miles on the highway = 4 / 17 gallons . the % change = ( 27 / 85 - 4 / 17 ) / ( 4 / 17 ) = 0.35 . answer : d .
Answer: d
Question (geometry): in measuring the sides of a rectangle , one side is taken 9 % in excess , and the other 8 % in deficit . find the error percent in the area calculated from these measurements .
Options: a ) 0.11 % , b ) 0.7 % , c ) 0.4 % , d ) 0.6 % , e ) 0.28 %
Rationale: "let x and y be the sides of the rectangle . then , correct area = xy . calculated area = ( 12 / 11 ) x ( 23 / 25 ) y = ( 358 / 357 ) ( xy ) error in measurement = ( 358 / 357 ) xy - xy = ( 1 / 357 ) xy error percentage = [ ( 1 / 357 ) xy ( 1 / xy ) 100 ] % = ( 7 / 25 ) % = 0.28 % . answer is e ."
Answer: e
Question (gain): there is 50 % increase in an amount in 6 years at s . i . what will be the c . i . of rs . 12,000 after 3 years at the same rate ?
Options: a ) 2160 , b ) 3120 , c ) 17988 , d ) 6240 , e ) 5240
Rationale: "let p = rs . 100 . then , s . i . rs . 50 and t = 6 years . r = ( 100 * 50 ) / ( 100 * 6 ) = 10 % p . a . now , p = rs . 12000 , t = 3 years and r = 8.33 % p . a . c . i . = [ 12000 * { ( 1 + 8.33 / 100 ) 3 - 1 } ] = rs . 17988 answer : c"
Answer: c
Question (gain): if the cost price is 86 % of the selling price , then what is the profit percent ?
Options: a ) 5 % , b ) 11 % , c ) 16 % , d ) 21 % , e ) 19 %
Rationale: "let s . p . = $ 100 c . p . = $ 86 profit = $ 14 profit % = 14 / 86 * 100 = 25 / 6 = 16 % approximately answer is c"
Answer: c
Question (general): find the length of the wire required to go 15 times round a square field containing 69696 m ^ 2 .
Options: a ) 1250 , b ) 2489 , c ) 6398 , d ) 15840 , e ) 2487
Rationale: "explanation : a 2 = 69696 = > a = 264 4 a = 1056 1056 * 15 = 15840 answer : d"
Answer: d
Question (general): the average of 5 quantities is 8 . the average of 3 of them is 4 . what is the average of remaining 2 numbers ?
Options: a ) 14 , b ) 10 , c ) 8 , d ) 9.5 , e ) none of these
Rationale: "answer : a ( 5 x 8 - 3 x 4 ) / 2 = 14"
Answer: a
Question (geometry): the perimeter of one square is 48 cm and that of another is 20 cm . find the perimeter and the diagonal of a square which is equal in area to these two combined ?
Options: a ) 5 cm
b ) 13 √ 2 cm
c ) 12 cm
d ) 6 cm
e ) 8 cm
Rationale: explanation : 4 a = 48 4 a = 20 a = 12 a = 5 a ^ 2 = 144 a ^ 2 = 25 combined area = a ^ 2 = 169 = > a = 13 d = 13 √ 2 cm answer : b
Answer: b
Question (general): in a class of 40 students , 2 students did not borrow any books from the library , 12 students each borrowed 1 book , 14 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: the class borrowed a total of 40 * 2 = 80 books . the 28 students who borrowed 0 , 1 , or 2 books borrowed a total of 12 + 14 * 2 = 40 . to maximize the number of books borrowed by 1 student , let ' s assume that 11 students borrowed 3 books and 1 student borrowed the rest . 80 - 40 - 3 * 11 = 7 the maximum number of books borrowed by any student is 7 . the answer is e .
Answer: e
Question (general): a picnic attracts 240 persons . there are 30 more men than women , and 30 more adults than children . how many men are at this picnic ?
Options: a ) 240 , b ) 75 , c ) 85 , d ) 130 , e ) 200
Rationale: "adult + children = 240 let , children = y then , adult = y + 30 i . e . y + ( y + 30 ) = 210 i . e . y = 115 i . e . adult = 115 + 30 = 145 adults include only men and women i . e . men + women = 145 let women , w = x then men , m = x + 30 i . e . x + ( x + 30 ) = 2 x + 30 = 145 i . e . x = 55 i . e . men , m = 55 + 30 = 85 answer : option c"
Answer: c
Question (general): find 80 / ? = ? / 20
Options: a ) 40 , b ) 400 , c ) 800 , d ) 1600 , e ) none
Rationale: "answer let 80 / y = y / 20 then , y 2 = 80 x 20 = 1600 ∴ y = √ 1600 = 40 . option : a"
Answer: a
Question (other): what is the greatest positive integer r such that 3 ^ r is a factor of 9 ^ 10 ?
Options: a ) r = 5 , b ) r = 9 , c ) r = 10 , d ) r = 20 , e ) 30
Rationale: "what is the greatest positive integer r such that 3 ^ r is a factor of 9 ^ 10 ? 9 ^ 10 = ( 3 ^ 2 ) ^ 10 = 3 ^ 20 d . 20"
Answer: d
Question (general): find the average of all the numbers between 40 and 80 which are divisible by 3 .
Options: a ) 15 , b ) 70 , c ) 20 , d ) 60 , e ) none
Rationale: "sol . average = ( 42 + 45 + 48 + 51 + 54 + 57 + 60 + 63 + 66 + 69 + 72 + 75 + 78 / 13 ) = 780 / 5 = 60 . answer d"
Answer: d
Question (physics): a can do a job in 18 days and b can do it in 30 days . in how many days will they finish it together ?
Options: a ) 1 / 9 , b ) 4 / 45 , c ) 2 / 7 , d ) 6 / 3 , e ) 5 / 2
Rationale: explanation : 1 / 18 + 1 / 30 = 8 / 90 = 4 / 45 so , both together will finish the work in 4 / 45 days . answer : b
Answer: b
Question (physics): in the xy - plane the point ( - 2 - 3 ) is the centre of a circle , the point ( - 2 , 1 ) lies inside the circle and the point ( 4 , - 3 ) lies outside the circle . if the radius r of the circle r is an integer then diameter ?
Options: a ) 6 , b ) 10 , c ) 4 , d ) 3 , e ) 2
Rationale: "can be solved without much calculations . you are given that ( - 2 , - 3 ) is the center of the circle . point ( 4 , - 3 ) lies inside the circle - - - > the radius is lesser than distance of ( - 2 , - 3 ) from ( 4 , - 3 ) - - - > lesser than 6 units but the radius will also be greater than the distance of ( - 2 , - 3 ) from ( - 2,1 ) - - - - > greater than 4 units . thus the radius is > 4 but < 6 and as it is an integer , the only possible value of radius = 5 units . diameter = 2 r = 10 b is the correct answer ."
Answer: b
Question (geometry): the mass of 1 cubic meter of a substance is 300 kilograms under certain conditions . what is the volume , in cubic centimeters , of 1 gram of this substance under these conditions ? ( 1 kilogram = 1,000 grams and 1 cubic meter = 1 , 000,000 cubic centimeters )
Options: a ) 1.33
b ) 1.25
c ) 8.0
d ) 12.5
e ) 80.0
Rationale: density is mass divided by volume . so density of the given substance will be mass / volume = 800 kg / 1 m ^ 3 = 300 kg / m ^ 3 or 1 g / 1.33 cm ^ 3 = 0.3 g / cm ^ 3 . next , ask yourself if 300,000 g is equivalent to 1 , 000,000 cubic centimeters then 1 g is equivalent to how many cubic centimeters ? - - > 1 g - 1 , 000,000 / 300,000 = 10 / 3 = 1.33 cubic centimeters . answer is a
Answer: a
Question (general): in a 300 member association consisting of men and women , exactly 80 % of men and exactly 15 % women are homeowners . what is the least number of members who are homeowners ?
Options: a ) 46 , b ) 47 , c ) 48 , d ) 49 , e ) 50
Rationale: "solution simple out of 300 80 % are male i . e 240 and 15 % are female i . e 45 , so total homeowner is 295 . now min number homeowner is 45 and max is 240 so question ask us to find least and 46 has least value among all option . so ans is 46 . ans : a"
Answer: a
Question (geometry): mark has a rectangular driveway with a line painted diagonally across . the length of the driveway is 5 feet longer than its width . if the total area of the driveway is 36 square feet , what is the length of the painted line ( in feet ) ?
Options: a ) between 9 and 10
b ) between 10 and 11
c ) between 11 and 12
d ) between 12 and 13
e ) between 13 and 14
Rationale: to solve this , we first need to set up an equation for the area of the room . if x is the width , then we have x ( x + 5 ) = 36 . by putting the equation in standard form , we get x ^ 2 + 5 x - 36 = 0 . by using the quadratic formula , we get roots of 4 and - 9 . we know that x is the width , and x + 5 is the length , so by using the roots , we get 4 as the width ( x ) , and 9 as the length ( x + 5 ) . once we have this , we can use the pythagorean theorem to solve for the diagonal . plugging in the length and width , we will get d ^ 2 = 4 ^ 2 + 9 ^ 2 = 16 + 81 = 97 the square root of 97 is less than 10 , since 10 ^ 2 = 100 . going down a number , we can compute 9 ^ 2 = 81 < 97 . therefore , the length of the diagonal must be between 9 and 10 . the correct answer is a .
Answer: a
Question (general): tom reads at an average rate of 30 pages per hour , while jan reads at an average rate of 41 pages per hour . if tom starts reading a novel at 3 : 20 , and jan begins reading an identical copy of the same book at 4 : 26 , at what time will they be reading the same page ?
Options: a ) 6 : 26 , b ) 6 : 56 , c ) 7 : 26 , d ) 7 : 56 , e ) 8 : 26
Rationale: since tom reads an average of 1 page every 2 minutes , tom will read 33 pages in the first 66 minutes . jan can catch tom at a rate of 11 pages per hour , so it will take 3 hours to catch tom . the answer is c .
Answer: c
Question (general): a theater charges $ 12 for seats in the orchestra and $ 8 for seats in the balcony . on a certain night , a total of 355 tickets were sold for a total cost of $ 3,320 . how many more tickets were sold that night for seats in the balcony than for seats in the orchestra ?
Options: a ) 90 , b ) 115 , c ) 120 , d ) 130 , e ) 220
Rationale: "orchestra seats - a balcony seats - b a + b = 355 and 12 a + 8 b = 3320 solving equations simultaneously ( multiply equation 1 with 8 and subtract from second equation ) 4 a = 3320 - 8 * 355 = 3320 - 2840 = 480 i . e . a = 120 and b = 355 - 120 = 235 more seats in balcony than orchestra = b - a = 235 - 120 = 115 answer : option b"
Answer: b
Question (general): a certain family has 3 sons : richard is 6 years older than david , and david is 8 years older than scott . if in 8 years , richard will be twice as old as scott , then how old was david 6 years ago ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "let ' s say age of richard isr age of david isd age of scott iss now richard is 6 years older than david , i . e . r = d + 6 david is 8 years older than scott i . e . d = s + 8 if in 8 years , richard will be twice as old as scott i . e . r + 8 = 2 x ( s + 8 ) i . e . r + 8 = 2 s + 16 i . e . r = 2 s + 8 but r = d + 6 = ( s + 8 ) + 6 = s + 14 therefore , 2 s + 8 = s + 14 i . e . s = 6 i . e . r = 20 i . e . d = 14 now , how old was david 6 years ago ? i . e . d - 6 = 14 - 6 = 8 years answer : option a"
Answer: a
Question (physics): a type t machine can complete a job in 5 hours and a type b machine can complete the job in 7 hours . how many hours will it take 2 type t machines and 3 type b machines working together and independently to complete the job ?
Options: a ) 1 / 5 , b ) 29 / 35 , c ) 5 / 6 , d ) 35 / 29 , e ) 35 / 12
Rationale: now d should be the answer . t need 5 hours to complete and b needs 7 hours to compete so 2 t + 3 b will complete 2 / 5 + 3 / 7 or 29 / 35 portion of the job in 1 hour so the whole job will take 35 / 29 hours . . . . = d
Answer: d
Question (general): on a certain date , pat invested $ 10,000 at x percent annual interest , compounded annually . if the total value of the investment plus interest at the end of 12 years will be $ 40,000 , in how many years , the total value of the investment plus interest will increase to $ 120,000 ?
Options: a ) 15 , b ) 21 , c ) 18 , d ) 20 , e ) 24
Rationale: "if i were to choose during the test , would go for 18 or 20 . probably 18 cuz it wont take too long to get the value doubled . . . . i found a method : rule of 72 . given an x % return , it takes 10,000 to quadralope 12 years . so according to the rule : 72 / x is the no of years 10 , 000.00 took to double 20 , 000.00 . again , 20 , 000.00 took to double 40 , 000.00 same ( 72 / x ) no of years . 72 / x + 72 / x = 12 x = 12 % ( though rate here is not very much required ) . again , 40 , 000.00 takes the same ( 72 / x ) no of years to double 120 , 000.00 . 72 / x = 6 years . so altogather : 10,000 - 20,000 = 6 years 20,000 - 40,000 = 6 years 40,000 - 80,000 = 6 years 80,000 - 120,000 = 3 years total 21 years . answer b"
Answer: b
Question (general): if the sum of two numbers is 16 and the sum of their squares is 200 , then the product of the numbers is
Options: a ) 40 , b ) 44 , c ) 80 , d ) 88 , e ) 28
Rationale: "according to the given conditions x + y = 16 and x ^ 2 + y ^ 2 = 200 now ( x + y ) ^ 2 = x ^ 2 + y ^ 2 + 2 xy so 16 ^ 2 = 200 + 2 xy so xy = 56 / 2 = 28 answer : e"
Answer: e
Question (physics): a and b can do a piece of work in 12 days . with the help of c they finish the work in 6 days . c alone can do that piece of work in ?
Options: a ) 33 , b ) 878 , c ) 30 , d ) 88 , e ) 12
Rationale: "c = 1 / 6 â € “ 1 / 12 = 1 / 12 = > 12 days answer : e"
Answer: e
Question (general): an amount of money is to be divided between p , q and r in the ratio of 3 : 7 : 12 . if the difference between the shares of p and q is rs . 4000 , what will be the difference between q and r ' s share ?
Options: a ) 2788 , b ) 5000 , c ) 7282 , d ) 2782 , e ) 2729
Rationale: "4 - - - 4000 5 - - - ? = > 5000 answer : b"
Answer: b
Question (gain): running at the same constant rate , 6 identical machines can produce a total of 390 bottles per minute . at this rate , how many bottles could 10 such machines produce in 4 minutes ?
Options: a ) 648 , b ) 1800 , c ) 2600 , d ) 10800 , e ) 10900
Rationale: "let the required number of bottles be x . more machines , more bottles ( direct proportion ) more minutes , more bottles ( direct proportion ) machines 6 : 10 : : 390 : x time ( in minutes ) 1 : 4 6 x 1 x x = 10 x 4 x 390 x = ( 10 x 4 x 390 ) / ( 6 ) x = 2600 . answer : c"
Answer: c
Question (general): a certain pair of used shoes can be repaired for $ 14.50 and will last for 1 year . a pair of the same kind of shoes can be purchased new for $ 32.00 and will last for 2 years . the average cost per year of the new shoes is what percent greater than the cost of repairing the used shoes ?
Options: a ) 16 , b ) 10.34 , c ) 12.46 , d ) 11.2 , e ) 14
Rationale: 1 ) cost of repairing = 14.5 ( for one year ) , therefore for 2 years it would be $ 29 . 2 ) cost of new pair which will last for 2 years is $ 32 . percentage change formula = ( final value - initial value ) / ( initial value ) * 100 . in this case the final value would be the price of new shoeinitial value would be the cost of repairing the old shoe . i . e ( 32 - 29 ) / ( 29 ) * 100 = 10.34 % . ans is b
Answer: b
Question (geometry): if length of rectangle is increased by 10 % , and breadth is decreased by 10 % . what will it effect on area of rectangle ?
Options: a ) it will have no effect
b ) 1 % increase
c ) 1 % decrease
d ) 2 % increase
e ) 2 % decrease
Rationale: let initial length = l , and breadth = b area = l * b new length = l * 110 % = [ l * 110 / 100 ] = 11 l / 10 , new breadth = 9 b / 10 new area = 11 l / 10 * 9 b / 10 = 99 / 100 lb decrease in area = [ lb - 99 / 100 lb ] = lb / 100 = % decrease = [ lb / 100 * 1 / lb * 100 ] = 1 % answer c
Answer: c
Question (physics): what is the ratio of 12 minute to 1 hour ?
Options: a ) 1 / 4 , b ) 3 / 4 , c ) 1 / 5 , d ) 2 / 2 , e ) 3 / 1
Rationale: c 1 / 5
Answer: c
Question (general): 8 * 8 * 8 * 8 = 2 ^ ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: "solution : 2 ^ 3 * 2 ^ 3 * 2 ^ 3 * 2 ^ 3 = 2 ^ ( 3 + 3 + 3 + 3 ) = 2 ^ 12 answer : 12 option : e"
Answer: e
Question (general): what is the smallest no . which must be added to 53403977 so as to obtain a sum which is divisible by 11 ?
Options: a ) 5 , b ) 4 , c ) 0 , d ) 1 , e ) 2
Rationale: "for divisibility by 11 , the difference of sums of digits at even and odd places must be either zero or divisible by 11 . for 53403977 , difference = ( 5 + 4 + 3 + 7 ) - ( 3 + 0 + 9 + 7 ) = 19 - 19 = 0 . = > 53403977 is also divisible by 11 c"
Answer: c
Question (general): each child has 8 crayons and 15 apples . if there are 7 children , how many crayons are there in total ?
Options: a ) 22 , b ) 56 , c ) 12 , d ) 36 , e ) 10
Rationale: 8 * 7 = 56 . answer is b .
Answer: b
Question (general): a student took 6 courses last year and received an average ( arithmetic mean ) grade of 100 points . the year before , the student took 5 courses and received an average grade of 60 points . to the nearest tenth of a point , what was the student ’ s average grade for the entire two - year period ?
Options: a ) 79 , b ) 89 , c ) 95 , d ) 81.81 , e ) 97.2
Rationale: "let the 6 courses that were taken last year be a 1 , a 2 , a 3 , a 4 , a 5 , a 6 a 1 + a 2 + a 3 + a 4 + a 5 + a 6 = 100 * 6 = 600 the year before , the 5 courses be b 1 , b 2 , b 3 , b 4 , b 5 b 1 + b 2 + b 3 + b 4 + b 5 = 60 * 5 = 300 student ' s average = ( 600 + 300 ) / 11 = 81.81 answer d"
Answer: d
Question (physics): a person is traveling at 20 km / hr and reached his destiny in 2.5 hr then find the distance ?
Options: a ) 53 km , b ) 55 km , c ) 52 km , d ) 60 km , e ) 50 km
Rationale: "t = 2.5 hrs = 5 / 2 hrs d = t * s = 20 * 5 / 2 = 50 km answer is e"
Answer: e
Question (geometry): the parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 12 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places )
Options: a ) 22 cm , b ) 47.14 cm , c ) 84.92 cm , d ) 94.94 cm , e ) 23.57 cm
Rationale: "let the side of the square be a cm . parameter of the rectangle = 2 ( 16 + 12 ) = 56 cm parameter of the square = 56 cm i . e . 4 a = 56 a = 14 diameter of the semicircle = 14 cm circimference of the semicircle = 1 / 2 ( ∏ ) ( 14 ) = 1 / 2 ( 22 / 7 ) ( 14 ) = 308 / 14 = 22 cm answer : a"
Answer: a
Question (physics): a motorcyclist goes from bombay to pune , a distance of 192 kms at an average of 32 kmph speed . another man starts from bombay by car 2 ½ hours after the first , and reaches pune ½ hour earlier . what is the ratio of the speed of the motorcycle and the car ?
Options: a ) 2 : 8 , b ) 1 : 2 , c ) 2 : 5 , d ) 6 : 9 , e ) 6 : 2
Rationale: b 1 : 2 t = 192 / 32 = 6 h t = 6 - 3 = 3 time ratio = 6 : 3 = 2 : 1 speed ratio = 1 : 2
Answer: b
Question (gain): a corporation paid $ 8 million in federal taxes on its first $ 50 million of gross profits and then $ 30 million in federal taxes on the next $ 150 million in gross profits . by approximately what percent did the ratio of federal taxes to gross profits increase from the first $ 50 million in profits to the next $ 150 million in profits ?
Options: a ) 6 % , b ) 14 % , c ) 20 % , d ) 23 % , e ) 86 %
Rationale: "difference in ratios = ( 30 / 150 ) - ( 8 / 50 ) = ( 6 / 50 ) % change = ( change ( 6 / 50 ) / original ratio ( 7 / 50 ) ) * 100 = 86 % answer - e"
Answer: e
Question (geometry): what is the measure of the radius of the circle that circumscribes a triangle whose sides measure 9 , 40 and 41 ?
Options: a ) 6 , b ) 4 , c ) 24.5 , d ) 20.5 , e ) 12.5
Rationale: "explanatory answer 9 , 40 and 41 is pythagorean triplet . so , the triangle is right angled . key property about right triangles in a right angled triangle , the radius of the circle that circumscribes the triangle is half the hypotenuse . in the given triangle , the hypotenuse = 41 . therefore , the radius of the circle that circumscribes the triangle = 41 / 2 = 20.5 units . choice d"
Answer: d
Question (general): 70 , 75 , 80 , 85 , 90 , 105 , 105 , 130 , 130 , 130 the list shown consists of the times , in seconds , that it took each of 10 schoolchildren to run a distance of 400 on of meters . if the standard devastation of the 10 running times is 25.4 seconds , rounded to the nearest tenth of a second , how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times ?
Options: a ) one , b ) two , c ) three , d ) four , e ) five
Rationale: the most time consuming part in this question is to define the mean . under exam pressure and time pressure it is very easy to make mistake . it is easier to group numbers : 130 * 3 = 390 ; 105 * 2 = 210 ; 75 + 85 = 160 ; 70 + 80 = 150 ; 90 ; next stage combine results , again using more convenient ways to calculate : 390 + 210 = 600 ; 160 + 150 = 310 ; 90 . 600 + 310 + 90 = 1000 . since there are 10 numbers the mean is 100 . questions asks to find the quantity of numbers one sd below the mean , which is 100 - 25,4 = 74,6 . there are only two numbers below 74,6 . the answer is b
Answer: b