Cheukting/mathqa huggingface dataset:
Question (physics): the ratio of the first and second class fares between two stations is 3 : 1 and that of the number of passengers travelling between the two stations by the first and the second class is 1 : 50 . if in a day , rs . 1 , 325 are collected from the passengers travelling between the two stations , then the amount collected from the second class from the second class passengers is
Options: a ) 1,250 , b ) 1,000 , c ) 850 , d ) 750 , e ) 350
Rationale: explanation : let the fares be 3 x and x respectively for the first and second class . suppose in a day passengers travelling between the two stations be 1 and 50 . then by given condition , 3 x × 1 + x × 50 = 1,325 = > x = 25 the amount collected from second class = 25 × 50 = rs . 1250 answer : a
Answer: a
Question (geometry): find the area of the quadrilateral of one of its diagonals is 20 cm and its off sets 5 cm and 4 cm ?
Options: a ) 189 cm 2 , b ) 150 cm 2 , c ) 127 cm 2 , d ) 177 cm 2 , e ) 90 cm 2
Rationale: "1 / 2 * 20 ( 5 + 4 ) = 90 cm 2 answer : e"
Answer: e
Question (general): a club wants to mix 20 pounds of candy worth $ 10.00 per pound with candy worth $ 5.00 per pound to reduce the cost of the mixture to $ 6.00 per pound . how many pounds of the $ 5.00 per pound candy should be used ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: "let number of pounds of 5 $ candy to be used be w 6 = ( 20 * 10 + 5 * w ) / ( 20 + w ) = > 120 + 6 w = 200 + 5 w = > w = 80 answer e"
Answer: e
Question (physics): the reciprocal of the hcf and lcm of two are 1 / 12 and 1 / 312 . if one of the number is 24 then other no . is
Options: a ) 126 , b ) 136 , c ) 146 , d ) 156 , e ) 166
Rationale: "reciprocal of the hcf and lcm of two are 1 / 12 and 1 / 312 so , hcf = 12 , lcm = 312 lcm * hcf = product of two numbers = a * b = > b = lcm * hcf / a so , other = 12 * 312 / 24 = 156 answer : d"
Answer: d
Question (physics): a can do a piece of work 20 days . b can do work in 35 days . in how many days they will complete the work together ?
Options: a ) 15 days , b ) 16.32 days , c ) 12.72 days , d ) 17 days , e ) 18 days
Rationale: "lcm = 140 , ratio = 20 : 35 = 4 : 7 no of days = 140 / ( 4 + 7 ) = 90 / 5 = 12.72 days answer : c"
Answer: c
Question (gain): the sale price shirts listed for rs . 1000 after successive discount is 15 % and 2 % is ?
Options: a ) 338 , b ) 823 , c ) 833 , d ) 337 , e ) 733
Rationale: "1000 * ( 85 / 100 ) * ( 98 / 100 ) = 833 answer : c"
Answer: c
Question (general): what is the ratio of 4 / 7 to the product 3 * ( 7 / 3 ) ?
Options: a ) 4 : 49 , b ) 1 : 3 , c ) 3 : 21 , d ) 1 : 7 , e ) 3 : 49
Rationale: "4 / 7 / 21 / 3 = 4 / 49 . . . imo option a ."
Answer: a
Question (gain): exactly 5 % of the reporters for a certain wire service cover local politics in country x . if 30 % of the reporters who cover politics for the wire service do not cover local politics in country x , what percent of the reporters for the wire service do not cover politics ?
Options: a ) 20 % , b ) 42 % , c ) 44 % , d ) 92 % , e ) 90 %
Rationale: "you are correct . people who cover local politics are a subset of people who cover politics . 30 % of reporters who cover politics do not cover local politics so 70 % do cover local politics . reporters covering local politics = 70 % of reporters covering politics = 5 % of all reporters reporters covering politics / all reporters = 5 / 70 = 1 / 14 reporters not covering politics / all reporters = 13 / 14 = 92 % = d"
Answer: d
Question (gain): kanul spent $ 35000 in buying raw materials , $ 40000 in buying machinery and 20 % of the total amount he had as cash with him . what was the total amount ?
Options: a ) $ 87952 , b ) $ 93750 , c ) $ 89542 , d ) $ 95820 , e ) $ 84256
Rationale: "let the total amount be x then , ( 100 - 20 ) % of x = 35000 + 40000 80 % of x = 75000 80 x / 100 = 75000 x = $ 93750 answer is b"
Answer: b
Question (general): the total age of a and b is 18 years more than the total age of b and c . c is how many years younger than a . ?
Options: a ) 16 , b ) 12 , c ) 15 , d ) 18 , e ) 10
Rationale: "( a + b ) - ( b - c ) = 18 a - c = 18 answer is d"
Answer: d
Question (physics): the sector of a circle has radius of 21 cm and central angle 150 o . find its perimeter ?
Options: a ) 91.5 , b ) 91.4 , c ) 97 , d ) 91.3 , e ) 91.1
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 150 / 360 * 2 * 22 / 7 * 21 ) + 2 ( 21 ) = 55 + 42 = 97 cm answer : c"
Answer: c
Question (physics): tom drives from town w to town b , driving at a constant speed of 60 miles per hour . from town b tom immediately continues to town c . the distance between w and b is twice the distance between b and c . if the average speed of the whole journey was 36 mph , then what is tom ' s speed driving from b to c in miles per hour ?
Options: a ) 12 , b ) 20 , c ) 24 , d ) 30 , e ) 36
Rationale: let ' s assume that it takes 4 hours to go from point w to b . then the distance between them becomes 240 which makes distance between b and c 120 . ( 240 + 120 ) / ( 4 + x ) gives us the average speed which is 36 . you find x = 6 . so the question simplifies itself to 120 / 6 = 20 hence the answer is b .
Answer: b
Question (general): the average of first 12 natural numbers is ?
Options: a ) 5.2 , b ) 6.5 , c ) 5.3 , d ) 5.9 , e ) 5.1
Rationale: "sum of 12 natural no . = 156 / 2 = 78 average = 78 / 12 = 6.5 answer : b"
Answer: b
Question (other): if 85 percent of the test takers taking an old paper and pencil gmat exam answered the first question on a given math section correctly , and 65 percent of the test takers answered the second question correctly , and 5 percent of the test takers answered neither question correctly , what percent answered both correctly ?
Options: a ) 60 % , b ) 55 % , c ) 70 % , d ) 75 % , e ) 80 %
Rationale: "{ total } = { first correctly } + { second correctly } - { both correctly } + { neither correctly } 100 = 85 + 65 - { both correctly } + 5 { both correctly } = 55 . answer : b ."
Answer: b
Question (general): what is the average of 12 , 13 , 14 , 51 , 52 , 53 , 1 , 11.5 , 1 , 1.20 , and 11.25 ?
Options: a ) 21.06 , b ) 23 , c ) 26 , d ) 23.69 , e ) 22.56
Rationale: "add 12 , 13 , 14 , 51 , 52 , 53 , 1 , 11.5 , 1,12 , and 11.25 grouping numbers together may quicken the addition sum = 231.75 231.75 / 11 = 21.06 a"
Answer: a
Question (gain): what profit percent is made by selling an article at a certain price , if by selling at 2 / 3 rd of that price , there would be a loss of 5 % ?
Options: a ) 20 % , b ) 29 % , c ) 10 % , d ) 80 % , e ) 42.5 %
Rationale: "sp 2 = 2 / 3 sp 1 cp = 100 sp 2 = 95 2 / 3 sp 1 = 95 sp 1 = 142.5 100 - - - 42.5 = > 42.5 % answer : e"
Answer: e
Question (general): a jewelry store purchased a pair of earrings for $ 240 and was selling it at a price that equaled the purchase price of the earrings plus a markup that was 25 percent of the selling price . after some time a jewelry store owner decided to decrease the selling price by 20 percent . what was the jewelry store ' s gross profit on this sale ?
Options: a ) $ 14 , b ) $ 2 , c ) $ 10 , d ) $ 16 , e ) $ 18
Rationale: sale price ( sp ) = 240 + markup ( mp ) - - > mp = sp - 240 and given mp = sp / 4 ( 25 % is 1 / 4 th ) so sp / 4 = sp - 240 3 sp / 4 = 240 sp = 320 now a discount of 20 % is given so new sp is . 8 * 320 = 256 profit = 256 - 240 = 16 answer is d
Answer: d
Question (general): if 1 / 4 of the passengers on a ship are from north america , 1 / 8 are europeans , 1 / 12 are from africa , 1 / 6 are from asia and the remaining 36 people are citizens of other continents , then how many passengers are on board the ship ?
Options: a ) 92 , b ) 96 , c ) 100 , d ) 104 , e ) 108
Rationale: "1 / 4 + 1 / 8 + 1 / 12 + 1 / 6 = ( 6 + 3 + 2 + 4 ) / 24 = 15 / 24 let x be the number of passengers on the ship . 36 = ( 9 / 24 ) x = 3 x / 8 x = 96 the answer is b ."
Answer: b
Question (physics): a hare and a tortoise have a race along a circle of 100 yards diameter . the tortoise goes in one direction and the hare in the other . the hare starts after the tortoise has covered 1 / 5 of its distance and that too leisurely . the hare and tortoise meet when the hare has covered only 1 / 8 of the distance . by what factor should the hare increase its speed so as to tie the race ?
Options: a ) 37.9 , b ) 37.2 , c ) 37.1 , d ) 37.82 , e ) 37.8
Rationale: assume the circumference of the circle is 200 meters . hare and tortoise started at the same point but moves in the opposite direction . it is given that by that time tortoise covered 40 m ( 1 / 5 th of the distance ) , hare started and both met after hare has covered 25 . this implies , in the time hare has covered 25 m , hare has covered 200 - 40 - 25 = 135 meters . so hare : tortoise speeds = 25 : 135 = 5 : 27 now hare and tortoise has to reach the starting point means , hare has to cover 175 meters and tortoise has to cover only 25 meters in the same time . as time = distancespeed = 2527 = 1755 × kdistancespeed = 2527 = 1755 × k ie . , hare has to increase its speed by a factor k . solving we get k = 37.8 answer : e
Answer: e
Question (geometry): a certain rectangular crate measures 20 feet by 20 feet by 20 feet . a cylindrical gas tank is to be made for shipment in the crate and will stand upright when the crate is placed on one of its six faces . what should the radius of the tank be if it is to be of the largest possible volume ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 10
Rationale: "for max volume of cylinder ( pi * r ^ 2 * h ) we need to max out r ^ 2 * h . we do n ' t know what the dimensions of the crate refer to . . therefore for max vol base should be 20 x 20 i . e . of radius 20 / 2 = 10 e"
Answer: e
Question (general): jack got paid today for his part - time job as a juggler , and noticed that 20 % of his paycheck went to taxes . jack wants to spend 80 % of what ' s left on a new bike , and put the rest into savings . if jack puts $ 20 into savings , how much was his original paycheck before taxes ?
Options: a ) $ 125 , b ) $ 135 , c ) $ 145 , d ) $ 155 , e ) $ 165
Rationale: let p be jack ' s original paycheck value . the value after taxes t is given by t = p - 20 % p let s be the amount put into savings , given by s = t - 80 % t for s = $ 20 , solve for p $ 20 = ( p - 20 % p ) - 80 % ( p - 20 % p ) p = $ 125 correct answer a
Answer: a
Question (general): find a sum for 1 st 5 prime no . ' s ?
Options: a ) 23 , b ) 28 , c ) 30 , d ) 32 , e ) 34
Rationale: "required sum = ( 2 + 3 + 5 + 7 + 11 ) = 28 note : 1 is not a prime number option b"
Answer: b
Question (general): a canoe has two oars , left and right . each oar either works or breaks . the failure or non - failure of each oar is independent of the failure or non - failure of the other . you can still row the canoe with one oar . the probability that the left oar works is 3 / 5 . the probability that the right oar works is also 3 / 5 . what is the probability w that you can still row the canoe ?
Options: a ) 9 / 25 , b ) 10 / 25 , c ) 6 / 10 , d ) 2 / 3 , e ) 21 / 25
Rationale: "simply look at the question from the other side . what is the probability that you can ’ t row the canoe ? this would be 2 / 5 x 2 / 5 = 4 / 25 . using the idea that the probability of something happening is 1 – the probability that it doesn ’ t happen , you can use the following equation to reach the right answer w : 1 – 4 / 25 = 21 / 25 . answer choice e ."
Answer: e
Question (physics): working together , wayne and his son can shovel the entire driveway in three hours . if wayne can shovel two times as fast as his son can , how many hours would it take for his son to shovel the entire driveway on his own ?
Options: a ) 4 , b ) 3 , c ) 8 , d ) 9 , e ) 12
Rationale: "w : the time for wyane to do the job s : the time for his son to do the job we have 1 / w + 1 / s = 1 / 2 and w = 2 s then we have 1 / ( 2 * s ) + 1 / s = 1 / 2 < = > 3 / ( 2 * s ) = 1 / 2 < = > s = 3 ans : b"
Answer: b
Question (physics): if a train , travelling at a speed of 90 kmph , crosses a pole in 5 sec , then the length of train is ?
Options: a ) 135 m , b ) 125 m , c ) 129 m , d ) 120 m , e ) 165 m
Rationale: "explanation : d = 90 * 5 / 18 * 5 = 125 m answer : option b"
Answer: b
Question (general): karthik read 7 / 13 th of a book in 1 st week and 5 / 9 th of the remaining book in 2 nd week . if there were 96 pages unread after 2 nd week , how many pages were there in the book ?
Options: a ) 518 , b ) 452 , c ) 468 , d ) 502 , e ) 396
Rationale: solution 96 pages were unread so on second week have 5 / 9 so unread pages = 1 - 5 / 9 = 4 / 9 96 * 9 / 4 = 216 then , on first week unread pages were 216 total pages = 216 * 13 / 6 = 468 so answer is c
Answer: c
Question (general): find the quotient : 0.0204 / 17
Options: a ) 0.012 , b ) 0.12 , c ) 0.0012 , d ) 0.00012 , e ) none of them
Rationale: 204 / 17 = 12 . dividend contains 4 places of decimal . 0.2040 / 17 = 0.0012 . answer is c .
Answer: c
Question (physics): the consumption of diesel per hour of a bus varies directly as square of its speed . when the bus is travelling at 50 kmph its consumption is 1 litre per hour . if each litre costs $ 30 and other expenses per hous is $ 20 , then what would be the minimum expenditure required to cover a distance of 400 km ?
Options: a ) 300 , b ) 400 , c ) 250 , d ) 350 , e ) 450
Rationale: "50 kmph consumption is 1 lt / hr so 400 km will take 8 hrs and the consumption is 8 lt for entire distance . 1 lt costs $ 30 so 8 lt costs $ 240 extra expenses for 1 hr - $ 20 8 hrs - $ 160 total expense - $ 240 + $ 160 = $ 400 answer : b"
Answer: b
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 . 59.29 , the number of the member is the group is :
Options: a ) 57 , b ) 67 , c ) 77 , d ) 87 , e ) 97
Rationale: "money collected = ( 59.29 x 100 ) paise = 5929 paise . number of members = 5929 = 77 . answer : c"
Answer: c
Question (general): if a ^ 2 + b ^ 2 = 30 and ab = 10 , what is the value of the expression ( a - b ) ^ 2 + ( a + b ) ^ 2 ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 60 , e ) 70
Rationale: "( a - b ) ^ 2 = a ^ 2 + b ^ 2 - 2 ab = 30 - 20 = 10 ( a + b ) ^ 2 = a ^ 2 + b ^ 2 + 2 ab = 30 + 20 = 50 so ( a + b ) ^ 2 + ( a - b ) ^ 2 = 50 + 10 = 60 d"
Answer: d
Question (physics): a can do a work in 30 days , b can do it in 20 days . they together under took to do a piece of work for rs . 1000 , what is the share of b ?
Options: a ) rs . 500 , b ) rs . 400 , c ) rs . 800 , d ) rs . 600 , e ) rs . 200
Rationale: explanation : share of their work days = 30 : 20 share of their work = 20 : 30 share of b ’ s money = 3 / 5 * 1000 = 600 answer : option d
Answer: d
Question (general): 3 x ^ 2 - 6 x + 3 = 0 find the above equation find the value of x
Options: a ) 0 , b ) 1 , c ) 2 , d ) 4 , e ) 6
Rationale: a = 3 , b = - 6 , c = 3 x 1,2 = ( 6 ± √ ( ( - 6 ) 2 - 4 × 3 × 3 ) ) / ( 2 × 3 ) = ( 6 ± √ ( 36 - 36 ) ) / 6 = ( 6 ± 0 ) / 6 x 1 = x 2 = 1 b
Answer: b
Question (gain): the income of a broker remains unchanged though the rate of commission is increased from 4 % to 5 % . the percentage of slump in business is :
Options: a ) 8 % , b ) 1 % , c ) 20 % , d ) 80 % , e ) none
Rationale: "explanation : let the business value changes from x to y . then , 4 % of x = 5 % of y or 4 / 100 × x = 5 / 100 × y or y = 4 / 5 x change in business = ( x − 4 / 5 x ) = 1 / 5 x percentage slump in business = ( 1 / 5 x × 1 / x × 100 ) % correct option : c"
Answer: c
Question (general): how many gallons of milk that is 10 percent butter - fat must be added to 8 gallons of milk that is 45 percent butterfat to obtain milk that is 20 percent butterfat ?
Options: a ) 6 , b ) 12 , c ) 14 , d ) 16 , e ) 20
Rationale: equate the fat : 0.1 x + 0.45 * 8 = 0.2 ( x + 8 ) - - > x = 20 . answer : e .
Answer: e
Question (geometry): if the length of a certain rectangle is decreased by 4 cm and the width is increased by 3 cm , a square with the same area as the original rectangle would result . find the perimeter of the original rectangle .
Options: a ) 40 cm
b ) 45 cm
c ) 50 cm
d ) 52 cm
e ) 57 cm
Rationale: explanation : let x and y be the length and breadth of the rectangle respectively . then , x - 4 = y + 3 or x - y = 7 - - - - ( 1 ) area of the rectangle = xy ; area of the square = ( x - 4 ) ( y + 3 ) ( x - 4 ) ( y + 3 ) = xy < = > 3 x - 4 y = 12 - - - - ( 2 ) solving 1 & 2 , we get x = 16 and y = 9 . perimeter of the rectangle = 2 ( x + y ) = [ 2 ( 16 + 9 ) ] cm = 50 cm . answer : option c
Answer: c
Question (physics): maxwell leaves his home and walks toward brad ' s house at the same time that brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 110 kilometers , maxwell ' s walking speed is 4 km / h , and brad ' s running speed is 7 km / h , what is the distance traveled by brad ?
Options: a ) 16 , b ) 18 , c ) 20 , d ) 70 , e ) 30
Rationale: "time taken = total distance / relative speed total distance = 110 kms relative speed ( opposite side ) ( as they are moving towards each other speed would be added ) = 7 + 4 = 11 kms / hr time taken = 110 / 11 = 10 hrs distance traveled by brad = brad ' s speed * time taken = 7 * 10 = 70 kms . . . answer - d"
Answer: d
Question (gain): a dress on sale in a shop is marked at $ d . during the discount sale its price is reduced by 15 % . staff are allowed a further 10 % reduction on the discounted price . if a staff member buys the dress what will she have to pay in terms of d ?
Options: a ) 0.75 d , b ) 0.76 d , c ) 0.765 d , d ) 0.775 d , e ) 0.805 d
Rationale: "successive doscounts = - a - b + ab / 100 putting the values , total discount = - 15 - 10 + 150 / 100 = - 25 + 1.5 = 23.5 % discount hence the final price of the dress = d - 0.235 d = 0.765 d correct option : c"
Answer: c
Question (general): in a simultaneous throw of a pair of dice , find the probability of getting a total more than 11
Options: a ) 11 / 25 , b ) 7 / 12 , c ) 5 / 13 , d ) 5 / 12 , e ) 6 / 17
Rationale: total number of cases = 10 * 10 = 100 favourable cases = [ ( 2,10 ) , ( 3,9 ) , ( 3,10 ) , ( 4,8 ) , ( 4,9 ) , ( 4,10 ) , ( 5,7 ) , ( 5,8 ) , ( 5,9 ) , ( 5,10 ) , ( 6,6 ) , ( 6,7 ) , ( 6,8 ) , ( 6,9 ) , ( 6,10 ) , ( 7,5 ) , ( 7,6 ) , ( 7,7 ) , ( 7,8 ) , ( 7,9 ) , ( 7,10 ) , ( 8,4 ) , ( 8,5 ) , ( 8,6 ) , ( 8,7 ) , ( 8,8 ) , ( 8,9 ) , ( 8,10 ) , ( 9,3 ) , ( 9,4 ) , ( 9,5 ) , ( 9,6 ) , ( 9,7 ) , ( 9,8 ) , ( 9,10 ) , ( 10,2 ) , ( 10,3 ) , ( 10,4 ) , ( 10,5 ) , ( 10,6 ) , ( 10,7 ) , ( 10,8 ) , ( 10,9 ) , ( 10,10 ) ] = 44 so probability = 44 / 100 = 11 / 25 answer is a
Answer: a
Question (gain): sandy had $ 210 left after spending 30 % of the money she took for shopping . how much money did sandy take along with her ?
Options: a ) $ 240 , b ) $ 300 , c ) $ 360 , d ) $ 420 , e ) $ 480
Rationale: "let the money sandy took for shopping be x . 0.7 x = 210 x = 300 the answer is b ."
Answer: b
Question (general): if a ã — b = 2 a - 3 b + ab , then 2 ã — 5 + 5 ã — 2 is equal to :
Options: a ) 18 , b ) 23 , c ) 24 , d ) 25 , e ) 26
Rationale: "explanation : 2 ã — 5 + 5 ã — 2 = ( 2 ã — 2 - 3 ã — 5 + 2 ã — 5 ) + ( 2 ã — 5 - 3 ã — 2 + 5 ã — 3 ) = ( 4 - 15 + 10 + 10 - 6 + 15 ) = 18 . answer : a"
Answer: a
Question (general): if ( n + 2 ) ! / n ! = 156 , n = ?
Options: a ) 2 / 131 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "( n + 2 ) ! / n ! = 156 rewrite as : [ ( n + 2 ) ( n + 1 ) ( n ) ( n - 1 ) ( n - 2 ) . . . . ( 3 ) ( 2 ) ( 1 ) ] / [ ( n ) ( n - 1 ) ( n - 2 ) . . . . ( 3 ) ( 2 ) ( 1 ) ] = 132 cancel out terms : ( n + 2 ) ( n + 1 ) = 156 from here , we might just test the answer choices . since ( 13 ) ( 12 ) = 156 , we can see that n = 11 d"
Answer: d
Question (general): 18 chess players take part in a tournament . every player plays twice with each of his opponents . how many games are to be played ?
Options: a ) 230 , b ) 274 , c ) 306 , d ) 354 , e ) 424
Rationale: "2 * 18 c 2 = 2 * 153 = 306 the answer is c ."
Answer: c
Question (physics): in a garden , there are 10 rows and 12 columns of mango trees . the distance between the two trees is 2 metres and a distance of three metres is left from all sides of the boundary of the garden . what is the length of the garden ?
Options: a ) 22 , b ) 24 , c ) 26 , d ) 28 , e ) 30
Rationale: "between the 12 mango trees , there are 11 gaps and each gap has 2 meter length also , 3 meter is left from all sides of the boundary of the garden . hence , length of the garden = ( 11 ã — 2 ) + 3 + 3 = 28 meter answer is d ."
Answer: d
Question (general): a 6 - liter solution is 40 % alcohol . how many liters of pure alcohol must be added to produce a solution that is 50 % alcohol ?
Options: a ) 1.2 , b ) 1.5 , c ) 1.8 , d ) 2.1 , e ) 2.4
Rationale: let x be the amount of pure alcohol required . 0.4 ( 6 ) + x = 0.5 ( x + 6 ) 0.5 x = 3 - 2.4 x = 1.2 liters the answer is a .
Answer: a
Question (gain): the present population of a town is 2100 . population increase rate is 5 % p . a . find the population of town before 1 years ?
Options: a ) 1500 , b ) 1600 , c ) 2000 , d ) 2100 , e ) 2500
Rationale: "p = 2100 r = 5 % required population of town = p / ( 1 + r / 100 ) ^ t = 2100 / ( 1 + 5 / 100 ) = 2100 / ( 21 / 20 ) = 2000 ( approximately ) answer is c"
Answer: c
Question (geometry): a math teacher has 25 cards , each of which is in the shape of a geometric figure . half of the cards are rectangles , and a third of the cards are rhombuses . if 8 cards are squares , what is the maximum possible number of cards that re circles .
Options: a ) 8 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "a square is a special kind of rhombus ( sides are perpendicular ) a square is a special kind of rectangles ( sides with same length ) among the 25 cards with have : 15 rectangles 10 rhombus 8 squares among the 15 rectangles , there could be 8 special ones ( with sides of same length ) that are squares . that lets at least 7 rectangles that are not square . among the 10 rectangles , there could be 8 special ones ( with sides perpendicular ) that are squares . that lets at least 2 rhombus that are not square . we have 8 squares . so the minimum different cards that represent a square , a rhombus or a rectangle is 2 + 7 + 8 = 17 which means that the maximum number of circles that you could have is 25 - 17 = 8 answer ( a )"
Answer: a
Question (general): in the graduating class of a certain college , 48 percent of the students are male and 52 percent are female . in this class 40 percent of the male and 30 percent of the female students are 25 years old or older . if one student in the class is randomly selected , approximately what is the probability that he or she will be less than 25 years old ?
Options: a ) a ) 0.9 , b ) b ) 0.6 , c ) c ) 0.45 , d ) d ) 0.3 , e ) e ) 0.25
Rationale: "percent of students who are 25 years old or older is 0.4 * 48 + 0.3 * 52 = ~ 34 , so percent of people who are less than 25 years old is 100 - 34 = 66 . answer : b ."
Answer: b
Question (general): when the positive integer x is divided by 9 , the remainder is 5 . what is the remainder when 7 x is divided by 9 ?
Options: a ) 0 , b ) 1 , c ) 3 , d ) 4 , e ) 8
Rationale: i tried plugging in numbers x = 9 q + 5 x = 14 7 x = 98 7 x / 9 = 9 * 10 + 8 remainder is 8 answer is e .
Answer: e
Question (gain): an alloy weighing 26 ounces is 70 percent gold . how many ounces of pure gold must be added to create an alloy that is 90 percent gold ?
Options: a ) 6 , b ) 9 , c ) 12 , d ) 34 , e ) 48
Rationale: in 24 ounces , gold is 26 * ( 70 / 100 ) = 18.2 ounces . now we add x ounces of pure gold to make it 90 % gold . so 18.2 + x = ( 24 + x ) * 90 / 100 = > x = 34 . answer is d .
Answer: d
Question (gain): an inspector rejects 10 % of the meters as defective . how many will he examine to reject 15 ?
Options: a ) a ) 100 , b ) b ) 150 , c ) c ) 250 , d ) d ) 200 , e ) e ) 160
Rationale: "then , 10 % of x = 15 ( 10 / 100 ) x = 15 x = ( 15 * 100 * ) / 10 = 150 answer is b"
Answer: b
Question (gain): the sale price sarees listed for rs . 400 after successive discount is 25 % and 20 % is ?
Options: a ) 297 , b ) 879 , c ) 342 , d ) 240 , e ) 269
Rationale: "400 * ( 75 / 100 ) * ( 80 / 100 ) = 240 answer : d"
Answer: d