Cheukting/mathqa huggingface dataset:
Question (general): the income tax in country x is 8 % of any income up to $ 5000 . for incomes over $ 5000 , an 8 % tax is imposed on the first $ 5000 , and a 10 % tax is imposed on the portion of the total income in excess of $ 5000 . if perry paid $ 950 in income tax last month , then what was perry ' s income ?
Options: a ) $ 10500 , b ) $ 11000 , c ) $ 13000 , d ) $ 13500 , e ) $ 14,000
Rationale: given : for incomes over $ 5,000 , an 8 % tax is imposed on the first $ 5,000 , and a 10 % tax is imposed on the portion of the total income in excess of $ 5000 . if perry paid $ 950 in income tax last month , then what was perry ' s income ? for first 5000 , 8 % tax then we get 400 $ as tax . now perry paid 950 $ tax . . . we need to check which option is going to yield 550 $ on the remaining amount . a . $ 10,500 - 5000 = 5500 , then we get 10 % tax , we get 550 $ . . . ( $ 10,500 - 5000 - here already for 5000 $ we have calculated the tax and we need to tally for the remaining amount ) 550 + 400 = 950 $ . . . hence this is the option . answer : option a .
Answer: a
Question (gain): a shopkeeper sold an book offering a discount of 5 % and earned a profit of 23.5 % . what would have been the percentage of profit earned if no discount was offered ?
Options: a ) 140 , b ) 120 , c ) 130 , d ) 110 , e ) 150
Rationale: c 130 % let c . p . be $ 100 . then , s . p . = $ 123.50 let marked price be $ x . then , 95 / 100 x = 123.50 x = 12350 / 95 = $ 130 now , s . p . = $ 130 , c . p . = $ 100 profit % = 30 % .
Answer: c
Question (general): if n = 2 ^ 0.15 and n ^ b = 8 , b must equal
Options: a ) 3 / 80 , b ) 3 / 5 , c ) 20 , d ) 5 / 3 , e ) 80 / 3
Rationale: "15 / 100 = 3 / 20 n = 2 ^ 3 / 20 n ^ b = 2 ^ 3 ( 2 ^ 3 / 20 ) ^ b = 2 ^ 3 b = 20 answer : c"
Answer: c
Question (gain): last year sandy saved 10 % of her annual salary . this year , she made 10 % more money than last year , and she saved 6 % of her salary . the amount saved this year was what percent of the amount she saved last year ?
Options: a ) 66 % , b ) 80 % , c ) 112 % , d ) 136 % , e ) 148 %
Rationale: "let last year ' s salary be x . last year , sandy save 0.1 x this year , sandy saved 0.06 * 1.1 x = 0.066 x 0.066 x / 0.1 x = 0.66 = 66 % the answer is a ."
Answer: a
Question (general): the value of a scooter depreciates in such a way that its value of the end of each year is 3 / 4 of its value of the beginning of the same year . if the initial value of the scooter is rs . 40000 , what is the value at the end of 2 years ?
Options: a ) 3277 , b ) 2977 , c ) 22500 , d ) 6077 , e ) 17112
Rationale: explanation : 40,000 * ( 3 / 4 ) ^ 2 answer : c
Answer: c
Question (general): 5 years ago , paula was 3 times as old as karl . in 6 years , paula will be twice as old as karl . what is the sum of their ages now ?
Options: a ) 42 , b ) 46 , c ) 50 , d ) 54 , e ) 58
Rationale: p - 5 = 3 ( k - 5 ) and so p = 3 k - 10 p + 6 = 2 ( k + 6 ) ( 3 k - 10 ) + 6 = 2 k + 12 k = 16 p = 38 p + k = 54 the answer is d .
Answer: d
Question (gain): one fourth of a solution that was 8 % sugar by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight . the second solution was what percent sugar by weight ?
Options: a ) 74 % , b ) 52 % , c ) 40 % , d ) 18 % , e ) 8.5 %
Rationale: "say the second solution ( which was 1 / 4 th of total ) was x % sugar , then 3 / 4 * 0.08 + 1 / 4 * x = 1 * 0.16 - - > x = 0.4 . alternately you can consider total solution to be 100 liters and in this case you ' ll have : 75 * 0.08 + 25 * x = 100 * 0.16 - - > x = 0.4 . answer : c ."
Answer: c
Question (gain): a and b invests rs . 2000 and rs . 4000 respectively in a business . if a doubles his capital after 6 months . in what ratio should a and b divide that year ' s profit ?
Options: a ) 3 : 5 , b ) 3 : 4 , c ) 9 : 2 , d ) 9 : 9 , e ) 3 : 1
Rationale: "( 2 * 6 + 4 * 6 ) : ( 4 * 12 ) 36 : 48 = > 3 : 4 answer : b"
Answer: b
Question (physics): two trains of equal lengths take 8 sec and 15 sec respectively to cross a telegraph post . if the length of each train be 120 m , in what time will they cross other travelling in opposite direction ?
Options: a ) 22 , b ) 12 , c ) 77 , d ) 10 , e ) 21
Rationale: "speed of the first train = 120 / 8 = 15 m / sec . speed of the second train = 120 / 15 = 8 m / sec . relative speed = 15 + 8 = 23 m / sec . required time = ( 120 + 120 ) / 23 = 10 sec . answer : d"
Answer: d
Question (general): a certain list consists of 21 different numbers . if n is in the list and n is 5 times the average ( arithmetic mean ) of the other 20 numbers in the list , then n is what fraction of the sum of the 21 numbers in the list ?
Options: a ) 1 / 20 , b ) 1 / 6 , c ) 1 / 5 , d ) 4 / 21 , e ) 5 / 21
Rationale: "series : a 1 , a 2 . . . . a 20 , n sum of a 1 + a 2 + . . . + a 20 = 20 * x ( x = average ) so , n = 5 * x hence , a 1 + a 2 + . . + a 20 + n = 25 x so , the fraction asked = 5 x / 25 x = 1 / 5 answer c"
Answer: c
Question (physics): danny and steve are running towards each other , each one from his own house . danny can reach steve ' s house in 27 minutes of running , which is half the time it takes steve to reach danny ' s house . if the two started to run at the same time , how much time longer will it take steve to reach the halfway point between their houses than danny to reach the halfway point between their houses ?
Options: a ) 13.5 minutes , b ) 27 minutes , c ) 35 minutes , d ) 54 minutes , e ) 81 minutes
Rationale: "danny ' s time is 27 minutes . the time to reach halfway is 13.5 minutes . steve ' s time is 54 minutes . the time to reach halfway is 27 minutes . the time difference is 27 - 13.5 = 13.5 minutes the answer is a ."
Answer: a
Question (geometry): mr . loyd wants to fence his square shaped land of 120 sqft each side . if a pole is laid every 12 ft how many poles do he need ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60
Rationale: "if each side is 120 feet . . then total perimeter is 120 * 4 = 480 poles every 12 feet hence no of poles = 480 / 12 = 40 answer : c"
Answer: c
Question (general): a number exceeds by 40 from its 3 / 8 part . then the number is ?
Options: a ) a ) 32 , b ) b ) 24 , c ) c ) 64 , d ) d ) 40 , e ) e ) 45
Rationale: "x – 3 / 8 x = 40 x = 64 answer : c"
Answer: c
Question (physics): amar takes as much time in running 22 meters as a car takes in covering 58 meters . what will be the distance covered by amar during the time the car covers 2.6 km ?
Options: a ) 700 m , b ) 978 m , c ) 970 m , d ) 986 m , e ) 640 m
Rationale: "distance covered by amar = 22 / 58 ( 2.6 km ) = 11 / 29 ( 2600 ) = 986 m answer : d"
Answer: d
Question (gain): a 340 - liter solution of kola is made from 88 % water , 5 % concentrated kola and the rest is made from sugar . if 3.2 liters of sugar , 10 liter of water and 6.8 liters of concentrated kola were added to the solution , what percent of the solution is made from sugar ?
Options: a ) 6 % . , b ) 7.5 % . , c ) 9.2 % . , d ) 10.5 % . , e ) 11 % .
Rationale: "denominator : 340 + 10 + 3.2 + 6.8 = 360 numerator : 340 ( 1 - . 88 - . 05 ) + 3.2 340 ( 0.07 ) + 3.2 23.8 + 3.2 27 ratio : 27 / 360 = 3 / 40 answer : b"
Answer: b
Question (general): the average age of 28 students in a group is 12 years . when teacher â € ™ s age is included to it , the average increases by one . what is the teacher â € ™ s age in years ?
Options: a ) 31 , b ) 36 , c ) 41 , d ) 51 , e ) none
Rationale: "sol . age of the teacher = ( 29 ã — 13 â € “ 28 ã — 12 ) years = 41 years . answer c"
Answer: c
Question (geometry): a rectangular tiled patio is composed of 60 square tiles . the rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles . after the change in layout , the patio will still have 60 tiles , and it will still be rectangular . how many rows are in the tile patio before the change in layout ?
Options: a ) 5 , b ) 6 , c ) 10 , d ) 13 , e ) 8
Rationale: "r * c = 60 and ( r + 4 ) ( c - 2 ) = 60 - - > r = 8 and c = 7 . answer : e ."
Answer: e
Question (physics): when the perimeter of a regular polygon is divided by 5 , the length of a side is 25 . what is the name of the polygon ? what is the perimeter ?
Options: a ) 125
b ) 126
c ) 127
d ) 128
e ) 129
Rationale: regular polygon . a polygon with equal sides and equal sides . divided by 5 to get the length of a side . it is the pentagon since it has 5 sides . so p = 5 × s to get the perimeter , just multiply a side by 5 . since 25 × 5 = 125 , the perimeter is 125 . answer a
Answer: a
Question (physics): a vessel of capacity 60 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 ) 23.89 , b ) 72.9 , c ) 38.3 , d ) 43.35 , 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 = 60 , y = 9 and n = 2 . hence , quantity of milk finally in the vessel = [ ( 60 - 9 ) / 60 ] ^ 2 ( 60 ) = 43.35 litres . answer : option d
Answer: d
Question (gain): an empty wooden vessel weighs 8 % of its total weight when filled with paint . if the weight of a partially filled vessel is one half that of a completely filled vessel , what fraction of the vessel is filled .
Options: a ) 3 / 7 , b ) 5 / 9 , c ) 1 / 24 , d ) 4 / 9 , e ) 2 / 5
Rationale: "an empty wooden vessel weighs 8 % of its total weight when filled with paint : vessel = 0.08 ( vessel + paint ) ; 8 v = v + p ( so the weight of completely filled vessel is 8 v ) p = 7 v ( so the weight of the paint when the vessels is completely filled is 7 v ) . the weight of a partially filled vessel is one half that of a completely filled vessel : v + p ' = 1 / 2 * 8 v ; p ' = 3 v ( so the weight of the paint when the vessels is partially filled is 3 v ) . what fraction of the vessel is filled ? so , we need to find the ratio of the weight of the paint when the vessel iscompletely filledto the weight of the paint when the vessel ispartially filled : p ' / p = 3 v / 7 v = 3 / 7 . answer : a ."
Answer: a
Question (general): in a government institute 20 nos . staffs are employed . in a festival season their boss give festival allowance to all . he says his accountant to calculate for 30 days @ 100 . also he says balance payment will give to driver and cleaning staff and to be adjust from petty cash . he had given rs . 65000 / - to the accountant . how much amount will taken from petty cash ?
Options: a ) a ) 1000 , b ) b ) 3000 , c ) c ) 3500 , d ) d ) 2500 , e ) e ) 2250
Rationale: for 20 staffs : 300 * 100 * 20 = 60000 for driver and cleaning staff : 300 * 100 * 2 = 6000 from petty cash : 1000 answer is a
Answer: a
Question (gain): if $ 5,000 is invested in an account that earns 4 % interest compounded semi - annually , then the interest earned after one year would be how much greater than if the $ 5,000 had been invested at 8 % simple yearly interest ?
Options: a ) $ 4 , b ) $ 8 , c ) $ 12 , d ) $ 16 , e ) $ 432
Rationale: "solution amount ( ci ) = p + ( 1 + r / n ) ^ nt = 5000 + ( 1 + 0.04 / 2 ) ^ 2 = 5404 amount ( si ) = p + ptr / 100 = 5000 + ( 5000 * 1 * 4 / 100 ) = 5400 difference = 5404 - 5400 = 4 $ a"
Answer: a
Question (other): an amount of money is to be distributed among faruk , vasim and ranjith in the ratio 3 : 5 : 7 . if vasims share is rs . 1500 , what is the difference between faruk ' s and ranjith ' s shares ?
Options: a ) rs 1200 , b ) rs 1500 , c ) rs 1600 , d ) rs 1900 , e ) rs 1700
Rationale: "explanation : let p = faruk , q = vasim , r = ranjith let p = 3 x , q = 5 x and r = 7 x . then , 5 x = 1500 ? x = 300 . p = 900 , q = 1500 and r = 2100 . hence , ( r - p ) = ( 2100 - 900 ) = 1200 answer : a"
Answer: a
Question (general): in a company of 10 employees , 5 employees earn $ 30,000 , 3 employees earn $ 40,000 , and the 2 highest - paid employees earn the same amount . if the average annual salary for the 10 employees is $ 65,000 , what is the annual salary for each of the highest - paid employees ?
Options: a ) $ 190,000 , b ) $ 170,000 , c ) $ 150,000 , d ) $ 130,000 , e ) $ 110,000
Rationale: "5 * 30,000 + 3 * 40,000 + 2 x = 10 * 65,000 2 x = 650,000 - 150,000 - 120,000 2 x = 380,000 x = 190,000 the answer is a ."
Answer: a
Question (general): a man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph , find his average speed for the total journey ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "m = 45 s = 1.5 ds = 6 us = 3 as = ( 2 * 6 * 3 ) / 9 = 4 answer : a"
Answer: a
Question (gain): if a sum of money doubles itself in 25 years at simple interest , the ratepercent per annum is
Options: a ) 12 , b ) 12.5 , c ) 13 , d ) 13.5 , e ) 4
Rationale: "explanation : let sum = x then simple interest = x rate = ( 100 * x ) / ( x * 25 ) = 4 option e"
Answer: e
Question (physics): a company produces 50000 bottles of water everyday . if a case can hold 25 bottles of water . how many cases are required by the company to hold its one day production
Options: a ) 2000 , b ) 4500 , c ) 5000 , d ) 8000 , e ) 9000
Rationale: "number of bottles that can be held in a case = 25 number of cases required to hold 50000 bottles = 50000 / 25 = 2000 cases . so the answer is a = 2000"
Answer: a
Question (general): a small pool filled only with water will require an additional 700 gallons of water in order to be filled to 80 % of its capacity . if pumping in these additional 700 gallons of water will increase the amount of water in the pool by 30 % , what is the total capacity of the pool in gallons ?
Options: a ) 1000 , b ) 1250 , c ) 1300 , d ) 1600 , e ) 2125
Rationale: "since pumping in additional 700 gallons of water will increase the amount of water in the pool by 30 % , then initially the pool is filled with 1,000 gallons of water . so , we have that 1,000 + 700 = 0.8 * { total } - - > { total } = 2,125 . answer : e ."
Answer: e
Question (general): a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 4356 , the number of the member is the group is :
Options: a ) 57 , b ) 66 , c ) 77 , d ) 87 , e ) 97
Rationale: "money collected = ( 43.56 x 100 ) paise = 4356 paise . number of members = square root of 4356 = 66 . answer : option b"
Answer: b
Question (general): the difference of two numbers is 2 and the difference of their squares is 12 . the sum of the number is
Options: a ) 6 , b ) 8 , c ) 10 , d ) 22 , e ) 24
Rationale: "explanation : let the numbers be a , b ; ⇒ a - b = 2 and a 2 − b 2 = 12 a + b = a 2 − b 2 / a − b = 12 / 2 = 6 correct option : a"
Answer: a
Question (general): a type of extra - large suv averages 12.2 miles per gallon ( mpg ) on the highway , but only 7.6 mpg in the city . what is the maximum distance , in miles , that this suv could be driven on 25 gallons of gasoline ?
Options: a ) 190 , b ) 284.6 , c ) 300 , d ) 305 , e ) 312
Rationale: "to maximize the distance that suv could be driven on 25 gallons of gasoline , we need consider only highway driving . max distance = 25 * 12.2 = 305 answer d"
Answer: d
Question (general): 5 men are equal to as many women as are equal to 8 boys . all of them earn rs . 120 only . men â € ™ s wages are ?
Options: a ) 6 rs , b ) 2 rs , c ) 4 rs , d ) 9 rs , e ) 8 rs
Rationale: "5 m = xw = 8 b 5 m + xw + 8 b - - - - - 120 rs . 5 m + 5 m + 5 m - - - - - 120 rs . 15 m - - - - - - 120 rs . = > 1 m = 8 rs . answer : e"
Answer: e
Question (general): 3 / 5 of all married couples have more than one child . 1 / 4 of all married couples have more than 3 children . what fraction of all married couples have 2 or 3 children ?
Options: a ) 1 / 5 , b ) b . 1 / 4 , c ) 7 / 20 , d ) 3 / 5 , e ) it can not be determined from the given information .
Rationale: "plug in simple numbers . take 100 couples for example . 3 / 5 of 100 couples have more than one child = 60 couples . 1 / 4 of 100 couples have more than 3 kids = 25 couples . this implies that 25 couples are a subset of 60 couples and the complement of 60 couples within those 100 couples , which equals 40 couples have either one or no kids at all . we need to find couples that have 2 or 3 kids , so essentially , it is 60 - 25 = 35 . fraction will be 35 / 100 = 7 / 20 . option c"
Answer: c
Question (general): a and b are two partially filled buckets of water . if 5 liters are transferred from a to b , then a would contain one - third of the amount of water in b . alternatively , if 4 liters are transferred from b to a , b would contain one - half of the amount of water in a . bucket a contains how many liters of water ?
Options: a ) 11 , b ) 52 / 5 , c ) 17 , d ) 21 , e ) 23
Rationale: "let a contains a , b contains b liters so , ( a - 5 ) / ( b + 5 ) = 1 / 3 . . . . . . . ( 1 ) again , ( b - 4 ) / ( a + 4 ) = 1 / 2 . . . . . . . . . . ( 2 ) from ( 1 ) ( 2 ) we find a = 52 / 5 ans : ( b )"
Answer: b
Question (gain): a company pays 12.5 % dividend to its investors . if an investor buys rs . 60 shares and gets 25 % on investment , at what price did the investor buy the shares ?
Options: a ) 25 , b ) 66 , c ) 30 , d ) 19 , e ) 01
Rationale: explanation : dividend on 1 share = ( 12.5 * 60 ) / 100 = rs . 7.5 rs . 25 is income on an investment of rs . 100 rs . 7.5 is income on an investment of rs . ( 7.5 * 100 ) / 25 = rs . 30 answer : c
Answer: c
Question (general): of the 13 employees in a certain department , 1 has an annual salary of 38,000 , 2 have an annual salary of 45,500 each , 2 have an annual salary of 42,500 each , 3 have an annual salary of 40,000 each and 5 have an annual salary of 48,500 each . what is the median annual salary for the 13 employees ?
Options: a ) 38,000 , b ) 40,000 , c ) 42,500 , d ) 45,500 , e ) 48,500
Rationale: "median is just the value in the middle when you arrange all values in the ascending order in this question , the 7 th value would be the median ( since there are 13 employees ) 38 , 40 , 40 , 40 , 42.5 , 42.5 , 45.5 so , answer is d ."
Answer: d
Question (general): what is the 10 digit to the right of the decimal point , in the decimal expansion of ( 1 / 2 ) ^ 10 ?
Options: a ) 9 , b ) 4 , c ) 2 , d ) 1 , e ) 5
Rationale: step 1 convert fraction to decimal with two decimal places 1 / 2 = 0.50 then convert to scientific number = 5 * 10 ^ - 1 step 2 multiply 5 ^ 10 by 10 ^ - 10 step 3 5 has the sequence 5 , 25 , 125 answer is e
Answer: e
Question (geometry): find the curved surface area , if the radius of a cone is 35 m and slant height is 30 m ?
Options: a ) 1100 , b ) 2200 , c ) 3300 , d ) 4400 , e ) 5500
Rationale: "cone curved surface area = ï € rl 22 / 7 ã — 35 ã — 30 = 110 ã — 30 = 3300 m ( power 2 ) answer is c ."
Answer: c
Question (general): the sum of two numbers is 20 and the sum of their squares is 140 . find the product of the two numbers .
Options: a ) 130 , b ) 140 , c ) 120 , d ) 145 , e ) 150
Rationale: let a and b be the two numbers ( a + b ) ^ 2 = a ^ 2 + 2 ab + b ^ 2 given ( a + b ) = 20 a ^ 2 + b ^ 2 = 140 so , 20 ^ 2 = 140 + 2 ab 2 ab = 400 - 140 2 ab = 260 ab = 130 ans a
Answer: a
Question (general): a man have 8 t - shirt and some pant . he can dress in 72 ways . then tell me the no . of pant that man have .
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: let he have x pant . by fundamental principle total no . of ways in which he can dress = 8 x 8 x = 72 x = 9 pants answer b
Answer: b
Question (general): on average , machine a will produce a completed item once every 4 minutes , and machine b will produce a completed item once every 5 minutes . the number of items machine a produces in a 24 - hour period is approximately what percent greater than the number of items machine b would produce in that same period ?
Options: a ) 25 % , b ) 15 % , c ) 45 % , d ) 33 % , e ) 55 %
Rationale: machine a : 1 item in 4 minutes - - > 1 / 4 items in 1 minute ; machine b : 1 item in 5 minutes - - > 1 / 5 items in 1 minute . in the same time period , machine a produces ( 1 / 4 - 1 / 5 ) / ( 1 / 5 ) * 100 = ~ 25 % more items than machine b . answer : a .
Answer: a
Question (general): what is the divisor ? the dividend is 76 , the remainder is 8 , the quotient is 4
Options: a ) 32 , b ) 48 , c ) 67 , d ) 17 , e ) 26
Rationale: divisor = dividend - remainder divided by the quotient divisor = 76 - 8 divided by 4 divisor = 68 / 4 divisor = 17
Answer: d
Question (other): in a certain corporation , there are 300 male employees and 150 female employees . it is known that 30 % of the male employees have advanced degrees and 40 % of the females have advanced degrees . if one of the 450 employees is chosen at random , what is the probability this employee has an advanced degree or is female ?
Options: a ) 2 / 3 , b ) 3 / 5 , c ) 3 / 10 , d ) 8 / 15 , e ) 11 / 30
Rationale: "p ( female ) = 150 / 450 = 1 / 3 p ( male with advanced degree ) = 0.3 * 300 / 450 = 90 / 450 = 1 / 5 the sum of the probabilities is 8 / 15 the answer is d ."
Answer: d
Question (gain): at what rate percent per annum will a sum of money double in 6 years .
Options: a ) 12.5 % , b ) 13.5 % , c ) 11.5 % , d ) 14.5 % , e ) 16.6 %
Rationale: "let principal = p , then , s . i . = p and time = 8 years rate = [ ( 100 x p ) / ( p x 6 ) ] % = 16.6 % per annum . answer : e"
Answer: e
Question (general): if 8 gallons of gasoline are added to a tank that is already filled to 3 / 4 of its capacity , the tank is then filled to 9 / 10 of its capacity . how many gallons does the tank hold ?
Options: a ) 20 , b ) 24 , c ) 36 , d ) 48 , e ) 60
Rationale: "let the capacity of the tank = c ( 3 / 4 ) c + 8 = ( 9 / 10 ) c = > ( 9 / 10 ) c - ( 3 / 4 ) c = 8 = > ( 3 / 20 ) c = 8 = > c = ( 8 * 20 ) / 3 = 53.33 number of gallons of gasoline that the tank currently holds = 3 / 4 * c + 8 = 39.99 + 8 = 47.99 = 48 answer d"
Answer: d
Question (gain): a certain company ’ s profit in 1996 was 15 percent greater than its profit in 1995 , and its profit in 1997 was 20 percent greater than its profit in 1996 . the company ’ s profit in 1997 was what percent greater than its profit in 1995 ?
Options: a ) 5 % , b ) 18 % , c ) 33 % , d ) 35 % , e ) 38 %
Rationale: "soln : - profit in 1995 - 100 profit in 1996 - 115 % increase profit in 1997 in comparison to 1995 = 15 + 115 * 20 % = 38 % answer : e"
Answer: e
Question (gain): what percent of 250 is 45 ?
Options: a ) 0.25 % , b ) 18 % , c ) 25 % , d ) 40 % , e ) 250 %
Rationale: "250 * x / 100 = 45 x = 45 * 10 / 25 x = 18 ans : b"
Answer: b
Question (general): i chose a number and divide it by 2 . then i subtracted 100 from the result and got 4 . what was the number i chose ?
Options: a ) 200 , b ) 208 , c ) 400 , d ) 500 , e ) 100
Rationale: "let x be the number i chose , then x / 2 − 100 = 4 x / 2 = 104 x = 208 answer is b ."
Answer: b
Question (geometry): the perimeter of an isosceles right triangle is 12 + 12 sq rt 2 . what is the length of the hypotenuse of the triangle ?
Options: a ) 5
b ) 6
c ) 7
d ) 8.485
e ) 8
Rationale: side of triangle is a then perimeter = a + a + a . sqrt 2 ( right angle and pythagorus ) = 2 a + a . sqrt 2 = 12 + 12 sqrt 2 or , a . ( 2 + sqrt 2 ) = 12 ( 1 + sqrt 2 ) , a = 12 * ( 1 + sqrt 2 ) / 2 + sqrt 2 = 12 * 2.414 / 3.414 = then hypotenuse = 8.485 d
Answer: d
Question (general): what is the sum of all possible solutions to | x - 3 | ^ 2 + | x - 3 | = 12 ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "denote | x - 3 | as y : y ^ 2 + y = 12 - - > y = - 4 or y = 3 . discard the first solution since y = | x - 3 | , so it ' s an absolute value and thus can not be negative . y = | x - 3 | = 3 - - > x = 6 or x = - 1 . the sum = 5 . answer : a ."
Answer: a