Cheukting/mathqa huggingface dataset:
Question (gain): walking 7 / 6 of his usual rate , a boy reaches his school 3 min early . find his usual time to reach the school ?
Options: a ) 21 , b ) 28 , c ) 99 , d ) 77 , e ) 66
Rationale: "speed ratio = 1 : 7 / 6 = 6 : 7 time ratio = 7 : 6 1 - - - - - - - - 7 3 - - - - - - - - - ? = 21 m answer : a"
Answer: a
Question (geometry): in a rectangular coordinate system , what is the area of a triangle whose vertices have the coordinates ( - 1 , 0 ) , ( 7 , 4 ) , and ( 7 , - 4 ) ?
Options: a ) 29
b ) 30
c ) 31
d ) 32
e ) 33
Rationale: the triangle is symmetric about the x - axis . the part above the x - axis forms a triangle with a base of 8 and a height of 4 . the area of this part is ( 1 / 2 ) ( 8 ) ( 4 ) . we can double this to find the area of the whole triangle . the total area is ( 2 ) ( 1 / 2 ) ( 8 ) ( 4 ) = 32 . the answer is d .
Answer: d
Question (gain): in a school of 850 boys , 40 % of muslims , 28 % hindus , 10 % sikhs and the remaining of other communities . how many belonged to the other communities ?
Options: a ) a ) 125 , b ) b ) 627 , c ) c ) 187 , d ) d ) 721 , e ) e ) 159
Rationale: "40 + 28 + 10 = 78 % 100 – 78 = 22 % 850 * 22 / 100 = 187 answer : c"
Answer: c
Question (geometry): if a rectangular room measures 9 meters by 5 meters by 4 meters , what is the volume of the room in cubic centimeters ? ( 1 meter = 100 centimeters )
Options: a ) 24,000 , b ) 240,000 , c ) 18 , 000,000 , d ) 24 , 000,000 , e ) 240 , 000,000
Rationale: "c . 180 , 000,000 9 * 100 * 5 * 100 * 4 * 100 = 180 , 000,000"
Answer: c
Question (general): the price of a certain painting increased by 20 % during the first year and decreased by 15 % during the second year . the price of the painting at the end of the 2 - year period was what percent of the original price ?
Options: a ) 102 % , b ) 105 % , c ) 120 % , d ) 135 % , e ) 140 %
Rationale: "assume that price is 100 price at the end of yr 1 : 100 + 20 = 120 price at the end of year 2 = 120 - 120 * 0.15 = 120 * 0.85 = 102 hence required answer = ( 102 / 100 ) * 100 % = 102 % answer is a ."
Answer: a
Question (probability): there are 7 books on a shelf , of which 2 are paperbacks and 5 are hardbacks . how many possible selections of 4 books from this shelf include at least one paperback ?
Options: a ) a ) 30 , b ) b ) 45 , c ) c ) 50 , d ) d ) 55 , e ) e ) 60
Rationale: "approach 1 at - least 1 paper back = total - no paper back 7 c 4 - 5 c 4 = 30 approach 2 at - least 1 paper back = 1 paper back , 3 hard back or 2 paper back 2 hard back = 2 c 1 * 5 c 3 + 2 c 2 * 5 c 2 = 30 answer is a"
Answer: a
Question (gain): a man sold 18 toys for rs . 25200 , gaining thereby the cost price of 3 toy find the cost price of a toy
Options: a ) s . 600 , b ) s . 800 , c ) s . 500 , d ) s . 900 , e ) s . 1200
Rationale: let the cost of one toy = x . then , cost of 18 toys = 18 x . gain = 3 x . sp of 18 toys = rs . 25200 . gain = sp â € “ cp 3 x = 25200 â € “ 18 x 21 x = 25200 x = rs . 1200 . answer : option e
Answer: e
Question (general): a , b and c rents a pasture for rs . 870 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should c pay ?
Options: a ) 180 , b ) 270 , c ) 360 , d ) 500 , e ) 550
Rationale: "12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 9 / 29 * 870 = 270 answer b"
Answer: b
Question (gain): sonika deposited rs . 8000 which amounted to rs . 9200 after 3 years at simple interest . had the interest been 3 % more . she would get how much ?
Options: a ) 9920 , b ) 96288 , c ) 26667 , d ) 1662 , e ) 2882
Rationale: "( 8000 * 3 * 3 ) / 100 = 720 9200 - - - - - - - - 9920 answer : a"
Answer: a
Question (general): the average of first five prime numbers greater than 17 is ?
Options: a ) 32.2 , b ) 32.98 , c ) 32.3 , d ) 32.8 , e ) 27.8
Rationale: "19 + 23 + 29 + 31 + 37 = 139 / 5 = 27.8 answer : e"
Answer: e
Question (other): in a graduating class of 232 students , 144 took geometry and 119 took biology . what is the difference between the greatest possible number i and the smallest possible number of students that could have taken both geometry and biology ?
Options: a ) 144 , b ) 119 , c ) 113 , d ) 88 , e ) 31
Rationale: official solution : first of all , notice that since 144 took geometry and 119 took biology , then the number of students who took both geometry and biology can not be greater than 119 . { total } = { geometry } + { biology } - { both } + { neither } ; 232 = 144 + 119 - { both } + { neither } ; { both } = 31 + { neither } . { both } is minimized when { neither } is 0 . in this case { both } = 31 . the greatest possible number i of students that could have taken both geometry and biology , is 119 . thus , the answer is 119 - 31 = 88 . answer : d .
Answer: d
Question (other): two alloys a and b are composed of two basic elements . the ratios of the compositions of the two basic elements in the two alloys are 7 : 5 and 1 : 2 , respectively . a new alloy x is formed by mixing the two alloys a and b in the ratio 4 : 3 . what is the ratio of the composition of the two basic elements in alloy x ?
Options: a ) 1 : 1 , b ) 2 : 3 , c ) 5 : 2 , d ) 10 : 11 , e ) 7 : 9
Rationale: "mixture a has a total of 7 + 5 = 12 parts . if in the final mixture this represents 6 parts , then the total number of parts in mixture b should be ( 12 / 6 ) * 3 = 6 . so , we should take of mixture b a quantity with 3 and 6 parts , respectively . this will give us in the final mixture ( 7 + 3 ) : ( 5 + 6 ) , which means 10 : 11 answer d ."
Answer: d
Question (general): for the past n days , the average ( arithmetic mean ) daily production at a company was 50 units . if today ' s production of 60 units raises the average to 55 units per day , what is the value of n ?
Options: a ) 30 , b ) 18 , c ) 10 , d ) 9 , e ) 1
Rationale: "( average production for n days ) * n = ( total production for n days ) - - > 50 n = ( total production for n days ) ; ( total production for n days ) + 60 = ( average production for n + 1 days ) * ( n + 1 ) - - > 50 n + 60 = 55 * ( n + 1 ) - - > n = 1 . answer : e ."
Answer: e
Question (gain): sue ' s trail mix is 30 % nuts and 70 % dried fruit . jane ' s trail mix is 60 % nuts and 40 % chocolate chips . if the combined mixture of sue and jane ' s trails mix contains 55 % nuts , what percent of the combined mixture is dried fruit ?
Options: a ) 8.5 % , b ) 11.7 % , c ) 14.2 % , d ) 17.6 % , e ) 20.5 %
Rationale: "55 % is 25 % - points above 30 % and 5 % - points below 60 % . so the ratio of sue ' s mix to jane ' s mix is 1 : 5 . 1 / 6 * 70 % = 11.7 % the answer is b ."
Answer: b
Question (general): think of a number , divide it by 4 and add 9 to it . the result is 15 . what is the number thought of ?
Options: a ) 24 , b ) 77 , c ) 297 , d ) 267 , e ) 29
Rationale: answer : a
Answer: a
Question (general): what number is obtained by adding the units digits of 734 ^ 98 and 347 ^ 81 ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "the units digit of 734 ^ 98 is 6 because 4 raised to the power of an even integer ends in 6 . the units digit of 347 ^ 81 is 7 because powers of 7 end in 7 , 9 , 3 or 1 cyclically . since 81 is in the form 4 n + 1 , the units digit is 7 . then 6 + 7 = 13 . the answer is d ."
Answer: d
Question (geometry): in a new housing development , trees are to be planted along the sidewalk of a certain street . each tree takes up one square foot of sidewalk space , and there are to be 10 feet between each tree . how many trees can be planted if the road is 166 feet long ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 16
Rationale: "let t be the number of trees . then the length required for trees on the sidewalk will be 1 * t = t to maximize the number of trees , the number of 10 feet spaces between trees should be 1 less than total number of trees . for example , if there are 3 trees , then there should be 2 spaces between them . so the number of 10 feet spaces will be t - 1 . then , the length of sidewalk required for 10 feet spaces will be 10 * ( t - 1 ) it is given that total lenght of sidewalk is 166 feet . or 10 ( t - 1 ) + t = 166 or 10 t - 10 + t = 166 or t = 16 answer : - e"
Answer: e
Question (geometry): a cube is painted red on all faces . it is then cut into 27 equal smaller cubes . how many l cubes are painted on only 2 faces ?
Options: a ) 12 , b ) 8 , c ) 6 , d ) 10 , e ) 16
Rationale: "1 ) draw a simple cube 2 ) draw 9 squares on each face of the cube ( so that it looks like a rubik ' s cube ) - this is what the cube will look like when it ' s cut into 27 equal smaller cubes . 3 ) remember that the outside of the cube is the part that ' s painted . . . . the mini - cubes with 2 painted sides are all on the edge of the cube , in themiddleof the edge . there are 4 in front , 4 in back and 4 more on thestripthat runs around the left / top / right / bottom of the cube . l = 4 + 4 + 4 = 12 . answer a"
Answer: a
Question (general): let n be the greatest number that will divide 1305 , 4665 and 6905 , leaving the game remainder in each case . then sum of the digits in n is :
Options: a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: solution n = h . c . f . of ( 4665 - 1305 ) , ( 6905 - 4665 ) and ( 6905 - 1305 ) = h . c . f . of 3360 , 2240 and 5600 = 1120 . sum of digits in n = ( 1 + 1 + 2 + 0 ) = 4 . answer a
Answer: a
Question (geometry): in a rectangular coordinate system , what is the area of a quadrilateral whose vertices have the coordinates ( 3 , - 1 ) , ( 3 , 8 ) , ( 12 , 2 ) , ( 12 , - 7 ) ?
Options: a ) 69 , b ) 75 , c ) 81 , d ) 87 , e ) 93
Rationale: "by graphing the points , we can see that this figure is a trapezoid . a trapezoid is any quadrilateral that has one set of parallel sides , and the formula for the area of a trapezoid is : area = ( 1 / 2 ) × ( base 1 + base 2 ) × ( height ) , where the bases are the parallel sides . we can now determine the area of the quadrilateral : area = 1 / 2 × ( 9 + 9 ) × 9 = 81 . the answer is c ."
Answer: c
Question (physics): a train running at a speed of 36 km / h passes an electric pole in 15 seconds . in how many seconds will the whole train pass a 380 - meter long platform ?
Options: a ) 47 , b ) 49 , c ) 51 , d ) 53 , e ) 55
Rationale: "let the length of the train be x meters . when a train crosses an electric pole , the distance covered is its own length x . speed = 36 km / h = 36000 m / 3600 s = 10 m / s x = 15 * 10 = 150 m . the time taken to pass the platform = ( 150 + 380 ) / 10 = 53 seconds the answer is d ."
Answer: d
Question (physics): a train running at the speed of 60 km / hr crosses a pole in 21 sec . what is the length of the train ?
Options: a ) 350 m , b ) 490 m , c ) 115 m , d ) 210 m , e ) 150 m
Rationale: "speed = 60 * 5 / 18 = 50 / 3 m / sec length of the train = speed * time = 50 / 3 * 21 = 350 m answer : a"
Answer: a
Question (general): the sum of the first 70 positive even integers is 4,970 . what is the sum of the first 70 odd integers ?
Options: a ) 4500 , b ) 4600 , c ) 4300 , d ) 4900 , e ) 5000
Rationale: sum of first n even numbers = n ( n + 1 ) = 4970 sum of first n odd numbers = n ^ 2 = 70 * 70 = 4900 ( here n = 70 ) answer : d
Answer: d
Question (general): a family consists of two grandparents , two parents , and 3 grandchildren . the average age of the grandparents is 64 years , the average age of the parents is 39 years , and the average age of the grandchildren is 6 years . what is the average age ( in years ) of the family ?
Options: a ) 31 , b ) 32 , c ) 33 , d ) 34 , e ) 35
Rationale: total age of the grandparents = 64 ã — 2 = 128 total age of the parents = 39 ã — 2 = 78 total age of the grandchildren = 6 ã — 3 = 18 average age of the family = ( 128 + 78 + 18 ) / 7 = 224 / 7 = 32 years the answer is b .
Answer: b
Question (gain): if 0.5 % of a = 70 paise , then the value of a is ?
Options: a ) rs . 170 , b ) rs . 140 , c ) rs . 1.70 , d ) rs . 4.25 , e ) none
Rationale: "answer ∵ 0.5 / 100 of a = 70 / 100 ∴ a = rs . ( 70 / 0.5 ) = rs . 140 correct option : b"
Answer: b
Question (physics): darcy lives 1.5 miles from work . she can walk to work at a constant rate of 3 miles per hour , or she can ride the train to work at a constant rate of 20 miles per hour . if she rides the train , there is an additional x minutes spent walking to the nearest train station , waiting for the train , and walking from the final train station to her work . if it takes darcy a total of 15 more minutes to commute to work by walking than it takes her to commute to work by riding the train , what is the value of x ?
Options: a ) 10.5 , b ) 15 , c ) 25.5 , d ) 30 , e ) 60
Rationale: the time it takes darcy to walk to work is ( 1.5 / 3 ) * 60 = 30 minutes the time it takes darcy to take the train is ( 1.5 / 20 ) * 60 + x = 4.5 + x minutes it takes 15 minutes longer to walk , so 30 = 4.5 + x + 15 x = 10.5 minutes answer : a
Answer: a
Question (general): what is the least common multiple of 5,40 , 36,50
Options: a ) 3698 , b ) 874 , c ) 3692 , d ) 1800 , e ) 3214
Rationale: "the given numbers are 5,40 , 36,50 thus the l . c . m is 5 * 2 * 2 * 1 * 2 * 9 * 5 = 1800 the answer is d"
Answer: d
Question (gain): the sale price of a trolley bag including the sale tax is rs . 280 . the rate of sale tax is 12 % . if the shopkeeper has made a profit of 25 % , the cost price of the trolley bag is :
Options: a ) rs 200 , b ) rs 220 , c ) rs 260 , d ) rs 280 , e ) none of these
Rationale: "explanation : 112 % of s . p . = 280 s . p . = rs . ( 280 x 100 / 112 ) = rs . 250 . c . p . = rs ( 100 / 125 x 250 ) = rs 200 answer : a"
Answer: a
Question (gain): the difference between c . i . and s . i . on an amount of rs . 15,000 for 2 years is rs . 150 . what is the rate of interest per annum ?
Options: a ) 8 , b ) 2 , c ) 10 , d ) 4 , e ) 6
Rationale: "explanation : [ 15000 * ( 1 + r / 100 ) 2 - 15000 ] - ( 15000 * r * 2 ) / 100 = 150 15000 [ ( 1 + r / 100 ) 2 - 1 - 2 r / 100 ] = 150 15000 [ ( 100 + r ) 2 - 10000 - 200 r ] / 10000 = 150 r 2 = ( 159 * 2 ) / 3 = 100 = > r = 10 rate = 10 % answer : option c"
Answer: c
Question (gain): a trader mixes 80 kg of tea at 15 per kg with 20 kg of tea at cost price of 20 per kg . in order to earn a profit of 50 % , what should be the sale price of the mixed tea ?
Options: a ) 23.75 , b ) 22 , c ) 20 , d ) 19.2 , e ) none of these
Rationale: "c . p . of mixture = 80 × 15 + 20 × 20 / 80 + 20 = 16 ∴ s . p . = ( 100 + 50 ) / 100 × 16 = 24 answer e"
Answer: e
Question (other): in a school 10 % of the boys are same in number as 1 / 3 th of the girls . what is the ratio of boys to the girls in the school ?
Options: a ) 5 : 2 , b ) 2 : 3 , c ) 10 : 3 , d ) 3 : 7 , e ) 2 : 5
Rationale: "10 % of b = 1 / 3 g 10 b / 100 = g / 3 b = 10 g / 3 b / g = 10 / 3 b : g = 10 : 3 answer is c"
Answer: c
Question (physics): in what time will a train 120 meters long completely pass an electric pole , if it travels at a speed of 60 kmph .
Options: a ) 6.18 , b ) 5.18 , c ) 4.18 , d ) 4.18 , e ) 7.18
Rationale: "sol . speed = [ 60 x 5 / 18 ] m / sec = 16.7 m / sec . time taken = ( 120 / 16.7 ) sec = 7.18 sec . answer e"
Answer: e
Question (gain): a retailer bought a machine at a wholesale price of $ 90 and later on sold it after a 10 % discount of the retail price . if the retailer made a profit equivalent to 20 % of the whole price , what is the retail price e of the machine ?
Options: a ) 81 , b ) 100 , c ) 120 , d ) 135 , e ) 160
Rationale: "since the wholesale price was $ 90 and the profit was 20 % of the wholesale price ( [ . 2 ] [ 90 ] = $ 18 ) , the retail price would have to be above $ 108 , but not that much greater than that . let ' s start by testing answer c : $ 120 . . . . if . . . . . retail price e = $ 120 10 % discount off = $ 120 - ( . 1 ) ( 120 ) = 120 - 12 = 108 20 % profit on wholesale price = 90 + ( . 2 ) ( 90 ) = 90 + 18 = 108 these two numbers match , so this must be the answer ! final answer : [ reveal ] spoiler : c"
Answer: c
Question (general): how many numbers from 49 to 79 are exactly divisible by 11 ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 3 , e ) 12
Rationale: "49 / 11 = 4 and 79 / 11 = 7 = = > 7 - 4 = 3 numbers answer : d"
Answer: d
Question (general): in a class of 40 students , 5 students did not borrow any books from the library , 15 students each borrowed 1 book , 10 students each borrowed 2 books , and the rest of the students each borrowed at least 3 books . if the average ( arithmetic mean ) number of books borrowed per student was 2 , what is the maximum number of books that any single student could have borrowed ?
Options: a ) 3 , b ) 5 , c ) 8 , d ) 13 , e ) 18
Rationale: "the average number of books per student was 2 means that total of 2 * 40 = 80 books were borrowed ; 5 + 15 + 10 = 30 students borrowed total of 5 * 0 + 15 * 1 + 10 * 2 = 35 books ; so 80 - 35 = 45 books are left to distribute among 40 - 30 = 10 students , these 10 arethe rest who borrowed at least 3 books ; tomaximizethe number of books one student from above 10 could have borrowed we shouldminimizethe number of books other 9 students from 10 could have borrowed . minimum these 9 students could have borrowed is 3 books per student , so total number of books they could have borrowed is 9 * 3 = 27 books . so the 10 th student could have borrowed is 45 - 27 = 18 books . answer : e ."
Answer: e
Question (physics): working together , printer a and printer b would finish the task in 24 minutes . printer a alone would finish the task in 60 minutes . how many pages does the task contain if printer b prints 7 pages a minute more than printer a ?
Options: a ) 600 , b ) 840 , c ) 1000 , d ) 1200 , e ) 1500
Rationale: answer : b .
Answer: b
Question (general): the jogging track in a sports complex is 640 m in circumference . lata and geeta start from the same point and walk in opposite directions at 4.2 km / hr and 3.8 km / hr respectively . they will meet for the first time in ?
Options: a ) 2.9 min , b ) 3.9 min , c ) 4.2 min , d ) 4.8 min , e ) 5.6 min
Rationale: clearly , the two will meet when they are 640 m apart . to be ( 4.2 + 3.8 ) = 8.0 km apart , they take 1 hour . that is 60 min . to be 640 m apart , they take ( 640 / 8000 * 60 ) min = 4.8 min . answer : d
Answer: d
Question (general): village x has a population of 68000 , which is decreasing at the rate of 1200 per year . village y has a population of 42000 , which is increasing at the rate of 800 per year . in how many years will the population of the two villages be equal ?
Options: a ) 15 , b ) 19 , c ) 11 , d ) 18 , e ) 13
Rationale: let the population of two villages be equal after p years then , 68000 - 1200 p = 42000 + 800 p 2000 p = 26000 p = 13 answer is e .
Answer: e
Question (gain): in a certain business school class , p students are accounting majors , q students are finance majors , r students are marketing majors , and s students are strategy majors . if pqrs = 2145 , and if 1 < p < q < r < s , how many students in the class are marketing majors ?
Options: a ) 3 , b ) 5 , c ) 8 , d ) 11 , e ) 17
Rationale: "pqrs = 2145 = 3 * 5 * 11 * 13 since 1 < p < q < r < s , the number of students who are marketing majors is r = 11 . the answer is d ."
Answer: d
Question (gain): if a man lost 4 % by selling oranges at the rate of 16 a rupee at how many a rupee must he sell them to gain 28 % ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 10
Rationale: "96 % - - - - 16 128 % - - - - ? 96 / 128 * 16 = 12 answer : a"
Answer: a
Question (general): the population of a town increased from 1 , 25,000 to 1 , 50,000 in a decade . the average percent increase of population per year is :
Options: a ) 4.37 % , b ) 2 % , c ) 6 % , d ) 8.75 % , e ) none of these
Rationale: "solution increase in 10 year = ( 150000 - 125000 ) = 25000 . increase % = ( 25000 / 125000 x 100 ) % = 20 % â ˆ ´ required average = ( 20 / 10 ) % = 2 % answer b"
Answer: b
Question (general): 40 persons like apple . 7 like orange and mango dislike apple . 10 like mango and apple and dislike orange . 6 like all . how many people like apple ?
Options: a ) 47 , b ) 49 , c ) 54 , d ) 58 , e ) 62
Rationale: "orange + mango - apple = 7 mango + apple - orange = 10 apple = 40 orange + mango + apple = 6 40 + 10 + 6 - 7 = 49 like apple answer : b"
Answer: b
Question (general): a man purchased 15 pens , 12 books , 10 pencils and 5 erasers . the cost of each pen is rs . 36 , each book is rs . 45 , each pencil is rs . 8 , and the cost of each eraser is rs . 40 less than the combined costs of pen and pencil . find the total amount spent ?
Options: a ) 2388 , b ) 2337 , c ) 1192 , d ) 2827 , e ) 1180
Rationale: explanation : cost of each eraser = ( 36 + 8 - 40 ) = rs . 4 required amount = 15 * 36 + 12 * 45 + 10 * 8 + 5 * 4 540 + 540 + 80 + 20 = rs . 1180 answer : e
Answer: e
Question (general): john was 22 years old when he married betty . they just celebrated their fifth wedding anniversary , and betty ' s age is now 7 / 9 of john ' s . how old is betty ?
Options: a ) 24 , b ) 26 , c ) 28 , d ) 21 , e ) 32
Rationale: assume betty ' s age on marriage = x years . john ' s age on marriage = 22 john ' s age after 5 years = 27 years . betty ' s age after 5 years = x + 5 given : x + 5 = 7 / 9 ( 27 ) = 21 therefore betty ' s current age = 21 option d
Answer: d
Question (gain): the profit earned by selling an article for rs . 832 is equal to the loss incurred when the same article is sold for rs . 448 . what should be the sale price for making 60 % profit ?
Options: a ) 1024 , b ) 960 , c ) 277 , d ) 266 , e ) 121
Rationale: let c . p . = rs . x . then , 832 - x = x - 448 2 x = 1280 = > x = 640 required s . p . = 160 % of rs . 640 = 160 / 100 * 640 = rs . 1024 . answer : a
Answer: a
Question (physics): workers at a campaign office have 1000 fliers to send out . if they send out 1 / 5 of them in the morning and 1 / 4 of the remaining ones out during the afternoon , how many are left for the next day ?
Options: a ) 300 , b ) 800 , c ) 1100 , d ) 600 , e ) 1900
Rationale: "( 1 / 5 ) * 1000 = 200 remaining = 1000 - 200 = 800 ( 1 / 4 ) of remaining = ( 1 / 4 ) * 800 = 200 remaining now = 800 - 200 = 600 answer : option d"
Answer: d
Question (gain): a cycle is bought for rs . 1000 and sold for rs . 1080 , find the gain percent ?
Options: a ) 11 , b ) 20 , c ) 12 , d ) 40 , e ) 8
Rationale: "1000 - - - - 80 100 - - - - ? = > 8 % answer : e"
Answer: e
Question (gain): a corporation paid $ 7 million in federal taxes on its first $ 50 million of gross profits and then $ 30 million in federal taxes on the next $ 100 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 $ 100 million in profits ?
Options: a ) 6 % , b ) 14 % , c ) 114 % , d ) 23 % , e ) 43 %
Rationale: "difference in ratios = ( 30 / 100 ) - ( 7 / 50 ) = ( 8 / 50 ) % change = ( change ( 8 / 50 ) / original ratio ( 7 / 50 ) ) * 100 = 114 % answer - c"
Answer: c
Question (general): if x ^ 2 + ( 1 / x ^ 2 ) = 2 , x ^ 4 + ( 1 / x ^ 4 ) = ?
Options: a ) 10 , b ) 2 , c ) 12 , d ) 14 , e ) 15
Rationale: - > x ^ 4 + ( 1 / x ^ 4 ) = ( x ^ 2 ) ^ 2 + ( 1 / x ^ 2 ) ^ 2 = ( x ^ 2 + 1 / x ^ 2 ) ^ 2 - 2 x ^ 2 ( 1 / x ^ 2 ) = 2 ^ 2 - 2 = 2 . thus , the answer is b .
Answer: b
Question (other): the ratio of two quantities is 5 : 8 . if each of the quantities is increased by 10 , what is the ratio of the new quantities ?
Options: a ) 5 : 8 , b ) 50 : 78 , c ) 2 : 3 , d ) it can not be determined from the information given . , e ) 6 : 7
Rationale: since the ratio is 5 : 8 we can put the quantities as 5 k and 8 k . moreover increasing quantities implies that the quantities become 5 k + 10 and 8 k + 10 . so the ratio is ( 5 k + 10 ) : ( 8 k + 10 ) . the ratio value depend on the value of k . so it can not be determined from the information given . the answer is d
Answer: d