Cheukting/mathqa huggingface dataset:
Question (general): to be considered for “ movie of the year , ” a film must appear in at least 1 / 4 of the top - 10 - movies lists submitted by the cinematic academy ’ s 765 members . what is the smallest number of top - 10 lists a film can appear on and still be considered for “ movie of the year ” ?
Options: a ) 191 , b ) 192 , c ) 193 , d ) 212 , e ) 213
Rationale: "total movies submitted are 765 . as per question we need to take 1 / 4 of 765 to be considered for top 10 movies = 191.25 approximate the value we 192 . answer : option b is the correct answer . ."
Answer: b
Question (geometry): a box measuring 24 inches long by 40 inches wide by 16 inches deep is to be filled entirely with identical cubes . no space is to be left unfilled . what is the smallest number of cubes that can accomplish this objective ?
Options: a ) 28 , b ) 30 , c ) 32 , d ) 35 , e ) 37
Rationale: "least number of cubes will be required when the cubes that could fit in are biggest . 8 is the biggest number that could divide all three , 24 , 40 and 16 . thus side of cube must be 8 , and total number of cubes = 24 / 8 * 40 / 8 * 16 / 8 = 30 ans b"
Answer: b
Question (general): there are 11 baskets numbered from 1 to 11 and filled with apples . 10 children are asked to pick apples one by one from each basket such that the number of apples picked by each child from each basket is equal to the number marked on the basket . if there were 1000 apples in total and the baskets were filled in such a way that none of the basket became empty in the process , how many apples were left in the end ?
Options: a ) 180 , b ) 220 , c ) 260 , d ) 300 , e ) 340
Rationale: each child takes a total of 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 = 11 * 12 / 2 = 66 apples . the total number of apples taken by 10 children is 10 * 66 = 660 the number of apples left in the end is 1000 - 660 = 340 apples . the answer is e .
Answer: e
Question (other): two vessels having volumes in the ratio 3 : 5 are filled with water and milk solutions . the ratio of milk and water in the two vessels are 3 : 1 and 6 : 4 respectively . if the contents of both the vessel are empties into a larger vessel , find the ratio of milk and water in the larger vessel .
Options: a ) 26 : 11 , b ) 23 : 11 , c ) 21 : 11 , d ) 24 : 11 , e ) 25 : 11
Rationale: "vessel a = 300 gallons - - > milk = 225 , water = 75 ; vessel b = 500 gallons - - > milk = 300 , water = 200 ; vessel a + b = 800 gallons - - > milk = 525 , water 275 the ratio = 525 / 275 - - > 21 : 11 answer : c"
Answer: c
Question (general): suzie ’ s discount footwear sells all pairs of shoes for one price and all pairs of boots for another price . on monday the store sold 22 pairs of shoes and 16 pairs of boots for $ 508 . on tuesday the store sold 8 pairs of shoes and 32 pairs of boots for $ 656 . how much more do pairs of boots cost than pairs of shoes at suzie ’ s discount footwear ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 8
Rationale: "let x be pair of shoes and y be pair of boots . 22 x + 16 y = 508 . . . eq 1 8 x + 32 y = 656 . . . . eq 2 . now multiply eq 1 by 2 and sub eq 2 . 44 x = 1016 8 x = 656 . 36 x = 360 = > x = 10 . sub x in eq 2 . . . . we get 80 + 32 y = 656 . . . then we get 32 y = 576 then y = 18 differenece between x and y is 8 answer : e"
Answer: e
Question (geometry): a rectangular block 10 cm by 20 cm by 35 cm is cut into an exact number of equal cubes . find the least possible number of cubes ?
Options: a ) 6 , b ) 56 , c ) 15 , d ) 40 , e ) 22
Rationale: "volume of the block = 10 * 20 * 35 = 7000 cm ^ 3 side of the largest cube = h . c . f of 10 , 20,35 = 5 cm volume of the cube = 5 * 5 * 5 = 125 cm ^ 3 number of cubes = 7000 / 125 = 56 answer is b"
Answer: b
Question (general): the scoring system in a certain football competition goes as follows : 3 points for victory , 1 point for a draw , and 0 points for defeat . each team plays 20 matches . if a team scored 5 points after 5 games , what is the least number of the remaining matches it has to win to reach the 40 - point mark by the end of the tournament ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "to get 40 points as end of season we need another 35 points or more from remaining 15 matches : option a = 6 * 3 + 9 * 1 = 27 option b = 7 * 3 + 8 * 1 = 29 option c = 8 * 3 + 7 * 1 = 31 option d = 9 * 3 + 6 * 1 = 33 option e = 10 * 3 + 5 * 1 = 35 hence option e - 10"
Answer: e
Question (gain): if a lends rs . 2000 to b at 10 % per annum and b lends the same sum to c at 11.5 % per annum then the gain of b in a period of 3 years is ?
Options: a ) 90 , b ) 122.5 , c ) 132.5 , d ) 114.5 , e ) 212.5
Rationale: "( 2000 * 1.5 * 3 ) / 100 = > 90 answer : a"
Answer: a
Question (physics): a swimming pool 9 m wide and 12 m long is 1 m deep on the shallow side and 4 m deep on the deeper side . its volume is :
Options: a ) 260
b ) 262
c ) 270
d ) 272
e ) none of these
Rationale: explanation : volume will be length * breadth * height , but in this case two heights are given so we will take average , volume = ( 12 ∗ 9 ∗ ( 1 + 4 / 2 ) ) m 312 ∗ 9 ∗ 2.5 m 3 = 270 m 3 option c
Answer: c
Question (physics): the time taken by mr . dhoni to row his boat upstream is twice the time taken by him to row the same distance downstream . if the speed of the boat in still water is 72 kmph , find the speed of the stream ?
Options: a ) 24 kmph , b ) 25 kmph , c ) 26 kmph , d ) 30 kmph , e ) 28 kmph
Rationale: the ratio of the times taken is 2 : 1 . the ratio of the speed of the boat in still water to the speed of the stream = ( 2 + 1 ) / ( 2 - 1 ) = 3 / 1 = 3 : 1 speed of the stream = 72 / 3 = 24 kmph . answer : a
Answer: a
Question (geometry): a math teacher has 24 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 ) 7 , 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 24 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 24 - 17 = 7 answer ( a )"
Answer: a
Question (gain): increasing the original price of a certain item by 15 percent and then increasing the new price by 15 percent is equivalent to increasing the original price by what percent ?
Options: a ) 31.25 , b ) 37.5 , c ) 30.0 , d ) 32.75 , e ) 32.25
Rationale: "we ' re told that the original price of an item is increased by 15 % and then that price is increased by 15 % . . . . if . . . . starting value = $ 100 + 15 % = 100 + . 15 ( 100 ) = 115 + 15 % = 115 + . 15 ( 115 ) = 115 + 17.25 = 132.25 the question asks how the final price relates to the original price . this is essentially about percentage change , which means we should use the percentage change formula : percentage change = ( new - old ) / old = difference / original doing either calculation will yield the same result : 32.25 / 100 = 32.25 % final answer : e"
Answer: e
Question (general): if a number n is chosen at random from the set of two - digit integers whose digits are both prime numbers , what is the probability t that n is divisible by 3 ?
Options: a ) 1 / 3 , b ) ¼ , c ) 9 / 25 , d ) 5 / 16 , e ) 0
Rationale: "prime digits are : 2 , 3 , 5 , 7 total number of 2 digit # s with both digits prime are : 4 * 4 = 16 out of these numbers divisible by 3 = 33 , 27 , 57 , 72 and 75 . i had to find the numbers manually using the 4 numbers above . = > prob = 5 / 16 . ans d . took me 3 : 20 mins ."
Answer: d
Question (general): raj invests a part of rs . 12000 in 12 % stock at rs . 120 and the remainder in 15 % stock at rs . 125 . if his total dividend per annum is rs . 1360 , how much does he invest in 12 % stock at rs . 120 ?
Options: a ) 3000 , b ) 4000 , c ) 5000 , d ) 5500 , e ) 6000
Rationale: investment in 12 % stock be x then investment 15 % stock = ( 12000 - x ) 12 / 120 * x + 15 / 125 * ( 12000 - x ) = 1360 x = 4000 answer b
Answer: b
Question (general): if 42.24 = k ( 14 + m / 50 ) , where k and m are positive integers and m < 50 , then what is the value of k + m ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: 42.24 = 14 k + km / 50 . . . we can rewrite the number as follows : 42 + 0.24 = 14 k + km / 50 . . . . . . . . since k is integer , then 42 = 14 k . . . . . . . . . . k = 3 0.24 = km / 50 . . . . . . 24 / 100 = 3 m / 50 . . . . . . m = 4 k + m = 3 + 4 = 7 answer : b
Answer: b
Question (general): an engineer designed a ball so that when it was dropped , it rose with each bounce exactly one - half as high as it had fallen . the engineer dropped the ball from a 14 - meter platform and caught it after it had traveled 41.7 meters . how many times did the ball bounce ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "ans : 6 division of total diatance travelled will be 14 + 14 + 7 + 3.5 + 1.75 + 0.9 + 0.5 ans b"
Answer: b
Question (general): a and b are two partially filled buckets of water . if 2 liters are transferred from a to b , then a would contain one - third of the amount of water in b . alternatively , if 2 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 ) 13 , c ) 17 , d ) 21 , e ) 22 / 5
Rationale: "let a contains a , b contains b liters so , ( a - 2 ) / ( b + 2 ) = 1 / 3 . . . . . . . ( 1 ) or 3 a - 6 = b + 2 or 3 a - b = 8 again , ( b - 2 ) / ( a + 2 ) = 1 / 2 . . ( 2 ) or 2 b - 4 = a + 2 or 2 b - a = 6 from ( 1 ) ( 2 ) we find a = 22 / 5 ans : e"
Answer: e
Question (physics): the reciprocal of the hcf and lcm of two are 1 / 14 and 1 / 312 . if one of the number is 24 then other no . is
Options: a ) 126 , b ) 136 , c ) 146 , d ) 156 , e ) 182
Rationale: "reciprocal of the hcf and lcm of two are 1 / 14 and 1 / 312 so , hcf = 14 , lcm = 312 lcm * hcf = product of two numbers = a * b = > b = lcm * hcf / a so , other = 14 * 312 / 24 = 182 answer : e"
Answer: e
Question (general): the average mark of the students of a class in a particular exam is 80 . if 5 students whose average mark in that exam is 30 are excluded , the average mark of the remaining will be 90 . find the number of students who wrote the exam .
Options: a ) 15 , b ) 30 , c ) 35 , d ) 45 , e ) 55
Rationale: "let the number of students who wrote the exam be x . total marks of students = 80 x . total marks of ( x - 5 ) students = 90 ( x - 5 ) 80 x - ( 5 * 30 ) = 90 ( x - 5 ) 300 = 10 x = > x = 30 answer : b"
Answer: b
Question (general): a , b and c have rs . 450 between them , a and c together have rs . 200 and b and c rs . 350 . how much does c have ?
Options: a ) a ) 100 , b ) b ) 110 , c ) c ) 120 , d ) d ) 130 , e ) e ) 140
Rationale: "a + b + c = 450 a + c = 200 b + c = 350 - - - - - - - - - - - - - - a + b + 2 c = 550 a + b + c = 450 - - - - - - - - - - - - - - - - c = 100 answer : a"
Answer: a
Question (geometry): one side of a rectangular field is 15 m and one of its diagonal is 17 m . find the area of field ?
Options: a ) 110 , b ) 120 , c ) 130 , d ) 140 , e ) 150
Rationale: "other side = [ ( 17 x 17 ) - ( 15 x 15 ) ] = ( 289 - 225 ) = 8 m area = 15 x 8 = 120 sq . m answer : b"
Answer: b
Question (general): at a certain paint store forest green is made by mixing 4 parts blue paint with 3 parts yellow paint . verdant green is made by mixing 4 parts yellow paint with 3 parts blue paint . how many liters of yellow paint must be added to 21 liters of forest green to change it to verdant green ?
Options: a ) 1 / 3 , b ) 7 , c ) 1 / 2 , d ) 1 / 7 , e ) 1 / 8
Rationale: "21 liter of forset green have 12 liter of blue and 9 liter of yellow suppose we add x liter of yellow to make it a verdant green so the ratio of blue to yellow in verdant green is ¾ so the equation is blue / yellow = 12 / ( 9 + x ) = ¾ 27 + 3 x = 48 = > x = 7 answer : b"
Answer: b
Question (general): mr . evans will states that each of his children will receive an equal share of his estate and that his grandchildren will split a portion of the estate that is equal to the share received by each of his children . if mr . evans has 4 children and 6 grandchildren , then approximately what percentage of mr . evans estate will each grandchild receive ?
Options: a ) 20 % , b ) 17 % , c ) 4.0 % , d ) 3.3 % , e ) 2.8 %
Rationale: "20 / 6 = 3.33 answer : d"
Answer: d
Question (gain): a and b invests rs . 4000 and rs . 6000 in a business . after 4 months , a withdraws three - fourth of his capital and 4 months later , b withdraws half of his capital . in what ratio should they share the profits at the end of the year ?
Options: a ) 2 : 5 , b ) 3 : 5 , c ) 4 : 5 , d ) 3 : 7 , e ) 5 : 7
Rationale: "a : b ( 4000 * 4 ) + ( 1000 * 8 ) : ( 6000 * 8 ) + ( 3000 * 4 ) 24000 : 60000 2 : 5 answer : a"
Answer: a
Question (gain): a trader marked the selling price of an article at 10 % above the cost price . at the time of selling , he allows certain discount and suffers a loss of 1 % . he allowed a discount of :
Options: a ) 10 % , b ) 10.5 % , c ) 11 % , d ) 12.5 % , e ) none
Rationale: "sol . let c . p . = rs . 100 . then , marked price = rs . 110 , s . p . = rs . 99 . ∴ discount % = [ 11 / 110 * 100 ] % = 10 % answer a"
Answer: a
Question (physics): a goods train runs at the speed of 72 kmph and crosses a 280 m long platform in 26 seconds . what is the length of the goods train ?
Options: a ) 230 m , b ) 270 m , c ) 240 m , d ) 832 m , e ) 270 m
Rationale: "speed = ( 72 x 5 / 18 ) m / sec = 20 m / sec . time = 26 sec . let the length of the train be x metres . then , x + 280 / 26 = 20 x + 280 = 520 x = 240 . answer : c"
Answer: c
Question (physics): two cars start at the same time from opposite ends of a highway that is 500 miles long . one car is riding at 40 mph and the second car is riding at 60 mph . how long after they begin will they meet ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: as cars are moving in opposite directions their speeds will be added . so their relative speeds : 60 + 40 = 100 mph total distance to be covered = 500 miles . time taken would be : 500 miles / 100 mph = 5 hours e is the answer .
Answer: e
Question (geometry): the area of circle o is added to its diameter . if the circumference of circle o is then subtracted from this total , the result is 12 . what is the radius of circle o ?
Options: a ) – 2 / pi
b ) 2
c ) 3
d ) 4
e ) 6
Rationale: pi * r ^ 2 + 2 r - 2 * pi * r = 12 simplifying the equation : pi * r ( r - 2 ) + 2 r = 12 without much algebraic : we can test the answers quickly , then 6 is the only possible answer that will eliminate pi from equation . answer is e
Answer: e
Question (general): linda spent 2 / 3 of her savings on furniture and the rest on a tv . if the tv cost her $ 250 , what were her original savings ?
Options: a ) $ 750 , b ) $ 350 , c ) $ 650 , d ) $ 550 , e ) $ 850
Rationale: "if linda spent 2 / 3 of her savings on furniture , the rest 3 / 3 - 2 / 3 = 1 / 3 on a tv but the tv cost her $ 250 . so 1 / 3 of her savings is $ 250 . so her original savings are 3 times $ 250 = $ 750 correct answer a"
Answer: a
Question (gain): in an election only two candidates contested . a candidate secured 70 % of the valid votes and won by a majority of 188 votes . find the total number of valid votes ?
Options: a ) 430 , b ) 438 , c ) 436 , d ) 470 , e ) 422
Rationale: "let the total number of valid votes be x . 70 % of x = 70 / 100 * x = 7 x / 10 number of votes secured by the other candidate = x - 7 x / 100 = 3 x / 10 given , 7 x / 10 - 3 x / 10 = 188 = > 4 x / 10 = 188 = > 4 x = 1880 = > x = 470 . answer : d"
Answer: d
Question (other): in a classroom , 12 students brought apples and 8 students brought bananas . if exactly 10 students brought only one of the two types of fruits , how many students brought both types of fruits ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 12 , e ) 14
Rationale: say x students brought both fruits . ( 12 - x ) + ( 8 - x ) = 10 - - > x = 5 . answer : a .
Answer: a
Question (general): the average ( arithmetic mean ) of the even integers from 20 to 60 inclusive is how much greater than the average ( arithmetic mean ) of the even integers from 10 to 140 inclusive ?
Options: a ) 40 , b ) 15 , c ) 35 , d ) 20 , e ) 25
Rationale: so , according to a mean of a set of even numbers from 20 to 60 = ( 20 + 60 ) / 2 = 40 and mean of a set of even numbers from 10 to 140 = ( 10 + 140 ) / 2 = 75 difference = 75 - 40 = 35 answer : c .
Answer: c
Question (other): ratio between rahul and deepak is 4 : 3 , after 6 years rahul age will be 26 years . what is deepak present age .
Options: a ) 14 , b ) 15 , c ) 20 , d ) 22 , e ) 24
Rationale: "explanation : present age is 4 x and 3 x , = > 4 x + 6 = 26 = > x = 5 so deepak age is = 3 ( 5 ) = 15 option b"
Answer: b
Question (physics): train a leaves the station traveling at 30 miles per hour . two hours later train в leaves the same station traveling in the same direction at 38 miles per hour . how many miles from the station was train a overtaken by train b ?
Options: a ) 205 , b ) 245 , c ) 285 , d ) 325 , e ) 365
Rationale: after two hours , train a is ahead by 60 miles . train b can catch up at a rate of 8 miles per hour . the time to catch up is 60 / 8 = 7.5 hours . in 7.5 hours , train a travels another 30 * 7.5 = 225 miles for a total of 285 miles . the answer is c .
Answer: c
Question (gain): the length of a rectangular floor is more than its breadth by 200 % . if rs . 100 is required to paint the floor at the rate of rs . 2 per sq m , then what would be the length of the floor ?
Options: a ) 12.25 , b ) 44 , c ) 18 , d ) 16 , e ) 14
Rationale: let the length and the breadth of the floor be l m and b m respectively . l = b + 200 % of b = l + 2 b = 3 b area of the floor = 100 / 2 = 50 sq m l b = 50 i . e . , l * l / 3 = 150 l 2 = 150 = > l = 12.25 answer : a
Answer: a
Question (general): if | x + 10 | = 10 what is the sum of all the values of x .
Options: a ) 20 , b ) 40 , c ) - 20 , d ) 0 , e ) - 40
Rationale: "there will be two cases x + 10 = 10 and x + 10 = - 10 solve for x = > x = 10 - 10 = > x = 0 or x = - 10 - 10 = > x = - 20 the sum of both values will be 0 + - 20 = - 20 answer is c"
Answer: c
Question (general): anne bought doughnuts for a class breakfast party . she bought 12 chocolate doughnuts , 12 coconut doughnuts , and 10 jam - filled doughnuts . how many doughnuts did anne buy in all ?
Options: a ) 25 , b ) 34 , c ) 39 , d ) 21 , e ) 11
Rationale: "add the numbers of doughnuts . 12 + 12 + 10 = 34 . answer is b ."
Answer: b
Question (gain): a bowl was filled with 10 ounces of water , and 0.014 ounce of the water evaporated each day during a 50 - day period . what percent of the original amount of water evaporated during this period ?
Options: a ) 0.004 % , b ) 0.04 % , c ) 0.40 % , d ) 7 % , e ) 40 %
Rationale: "total amount of water evaporated each day during a 50 - day period = . 014 * 50 = . 014 * 100 / 2 = 1.4 / 2 = . 7 percent of the original amount of water evaporated during this period = ( . 7 / 10 ) * 100 % = 7 % answer d"
Answer: d
Question (other): a and b play a game where each is asked to select a number from 1 to 16 . if the two numbers match , both of them win a prize . find the probability that they will not win a prize in a single trial .
Options: a ) 15 / 16 , b ) 1 / 16 , c ) 7 / 8 , d ) 9 / 8 , e ) none of these
Rationale: explanation : a and b win a prize , only if both a and b select the number . so , if a chooses a number , b has to select the same number . hence , it is problem on dependent event . let a select a number . , then p ( a ) = 1 / 16 = probability of a . now , b selects the same number after a has already selected that number . then , p ( b / a ) = 1 / 1 = dependent probability of b given a has occurred . p ( ab ) = probability of winning a prize by both a and b is : - = > p ( a ) x p ( ab ) . = > ( 1 / 16 ) x 1 = 1 / 16 . hence , the probability of not winning a prize is : - = 1 - ( 1 / 16 ) . = 15 / 16 . answer : a
Answer: a
Question (general): a family pays $ 700 per year for an insurance plan that pays 60 percent of the first $ 1,000 in expenses and 100 percent of all medical expenses thereafter . in any given year , the total amount paid by the family will equal the amount paid by the plan when the family ' s medical expenses total how much ?
Options: a ) $ 1,000 , b ) $ 1,200 , c ) $ 1,500 , d ) $ 1,800 , e ) $ 2,200
Rationale: "assuming the medical expenses are $ 1000 or more , the family pays $ 700 + $ 400 = $ 1100 . the total amount paid by insurance plan for the first $ 1000 of expenses is $ 600 . the insurance will pay another $ 500 when the medical expenses are $ 1500 . the answer is c ."
Answer: c
Question (general): the price of commodity x increases by 30 cents every year , while the price of commodity y increases by 20 cents every year . if in 2001 , the price of commodity x was $ 4.20 and the price of commodity y was $ 4.50 , in which year will commodity x cost 90 cents more than the commodity y ?
Options: a ) 2010 , b ) 2011 , c ) 2012 , d ) 2013 , e ) 2014
Rationale: "the cost of commodity x increases by 10 cents per year relative to commodity y . the price of x must gain 30 + 90 = $ 1.20 cents on commodity y , which will take 12 years . the answer is d ."
Answer: d
Question (physics): there are 20 poles with a constant distance between each pole . a car takes 20 second to reach the 12 th pole . how much will it take to reach the last pole .
Options: a ) 34.4543 , b ) 34.5455 , c ) 34.45128 , d ) 34.51288 , e ) 34.41222
Rationale: "assuming the car starts at the first pole . to reach the 12 th pole , the car need to travel 11 poles ( the first pole does n ' t count , as the car is already there ) . 11 poles 20 seconds 1 pole ( 20 / 11 ) seconds to reach the last ( 20 th ) pole , the car needs to travel 19 poles . 19 pole 19 x ( 20 / 11 ) seconds = 34.5455 seconds answer : b"
Answer: b
Question (general): for any positive integer n , the sum of the first n positive integers equals n ( n + 1 ) / 2 . what is the sum of all the even integers between 99 and 301 ?
Options: a ) 10,100 , b ) 20,200 , c ) 22,650 , d ) 40,200 , e ) 45,150
Rationale: firstly calculate the number of even integers between 99 and 301 : no of even integers = ( 300 - 100 ) / 2 + 1 = 101 avg of the even integers is ( 100 + 300 ) / 2 = 200 . the sum would be = no of even integers * avg . = = > 101 * 202 = 20,200 answer b .
Answer: b
Question (gain): what percent of 500 is 125 ?
Options: a ) 0.25 % , b ) 4 % , c ) 25 % , d ) 40 % , e ) 250 %
Rationale: "500 * x / 100 = 125 x = 125 / 5 x = 25 ans : c"
Answer: c
Question (general): a number is increased by 40 % and then decreased by 40 % . find the net increase or decrease per cent .
Options: a ) 19 % , b ) 18 % , c ) 17 % , d ) 13 % , e ) 16 %
Rationale: "let the number be 100 . increase in the number = 40 % = 40 % of 100 = ( 40 / 100 × 100 ) = 40 therefore , increased number = 100 + 40 = 140 this number is decreased by 40 % therefore , decrease in number = 40 % of 140 = ( 40 / 100 × 140 ) = 5600 / 100 = 56 therefore , new number = 140 - 56 = 84 thus , net decreases = 100 - 84 = 16 hence , net percentage decrease = ( 16 / 100 × 100 ) % = ( 1600 / 100 ) % = 16 % answer : e"
Answer: e
Question (gain): a man buys an article for $ 20 . and sells it for $ 25 . find the gain percent ?
Options: a ) 25 % , b ) 50 % , c ) 20 % , d ) 15 % , e ) 30 %
Rationale: "c . p . = $ 20 s . p . = $ 25 gain = $ 5 gain % = 5 / 20 * 100 = 25 % answer is a"
Answer: a
Question (gain): add 20 % of 40 and 25 % of 60 .
Options: a ) 9.5 , b ) 23 , c ) 25 , d ) 22 , e ) 15
Rationale: "20 % of 40 + 25 % of 60 40 * 20 / 100 + 60 * 25 / 100 8 + 15 = 23 answer b"
Answer: b