Cheukting/mathqa huggingface dataset:
Question (general): what is the tens digit of 6 ^ 10 ?
Options: a ) 7 , b ) 3 , c ) 5 , d ) 1 , e ) 9
Rationale: "( 6 ^ 2 ) = 6 * 6 = 36 ( 6 ^ 3 ) = 36 * 6 = . 16 ( 6 ^ 4 ) = . 16 * 6 = . . 96 ( 6 ^ 5 ) = . . 96 * 6 = . . 76 ( 6 ^ 6 ) = . . 76 * 6 = . . . 56 ( 6 ^ 7 ) = . . . . 56 * 6 = . . . . 36 if you see there is a pattern here in tens digits 3 , 1,9 , 7,5 , 3,1 and so on . . . continue the pattern up to 6 ^ 10 ( dont actually calculate full values ) and answer is a : 7"
Answer: a
Question (gain): a certain sum is invested at simple interest at 18 % p . a . for two years instead of investing at 12 % p . a . for the same time period . therefore the interest received is more by rs . 840 . find the sum ?
Options: a ) 7000 , b ) 2787 , c ) 2799 , d ) 2699 , e ) 2790
Rationale: "let the sum be rs . x . ( x * 18 * 2 ) / 100 - ( x * 12 * 2 ) / 100 = 840 = > 36 x / 100 - 24 x / 100 = 840 = > 12 x / 100 = 840 = > x = 7000 . answer : a"
Answer: a
Question (general): for any number z , z * is defined as the greatest positive even integer less than or equal to y . what is the value of 6.15 – 6.15 * ?
Options: a ) 1.5 , b ) 0.15 , c ) 6.25 , d ) 0.25 , e ) 6.0
Rationale: "since z * is defined as the greatest positive even integer less than or equal to z , then 6.15 * = 6 ( the greatest positive even integer less than or equal to 6.15 is 6 ) . hence , 6.15 – 6.15 * = 6.15 - 6 = 0.15 answer : b ."
Answer: b
Question (general): when positive integer x is divided by positive integer y , the remainder is 9 . if x / y = 96.15 , what is the value of y ?
Options: a ) 96 , b ) 60 , c ) 48 , d ) 25 , e ) 12
Rationale: "guys , one more simple funda . 5 / 2 = 2.5 now . 5 x 2 = 1 is the remainder 25 / 4 = 6.25 now . 25 x 4 = 1 is the remainder 32 / 5 = 6.4 now . 4 x 5 = 2 is the remainder given x / y = 96.15 and remainder is 9 so . 15 x y = 9 hence y = 60 ans b"
Answer: b
Question (geometry): the cost of the paint is rs . 40.00 per kg . if 1 kg of paint covers 20 sq . ft , how much will it cost to paint outside of a cube having 10 feet each side
Options: a ) rs . 1200 , b ) rs . 672 , c ) rs . 546 , d ) rs . 876 , e ) none of these
Rationale: "explanation : surface area of a cube = 6 x 10 ^ 2 = 600 s q . ft quantity of paint required = ( 600 / 20 ) = 30 kg cost of painting = 40 x 30 = rs . 1200 answer : a"
Answer: a
Question (geometry): what is the perimeter of a rectangular field whose diagonal is 10 m and length is 3 m ?
Options: a ) 12 m
b ) 5 m
c ) 10 m
d ) 8 m
e ) 6 m
Rationale: sol : breadth of the rectangular plot is = 10 ^ 2 - 3 ^ 2 = 1 m therefore , perimeter of the rectangular plot = 2 ( 3 + 1 ) = 8 m d ) 8 m
Answer: d
Question (general): cereal a is 10 % sugar by weight , whereas healthier but less delicious cereal b is 2 % sugar by weight . to make a delicious and healthy mixture that is 3 % sugar , what should be the ratio of cereal a to cereal b , by weight ?
Options: a ) 2 : 9 , b ) 2 : 7 , c ) 1 : 7 , d ) 1 : 4 , e ) 1 : 3
Rationale: 2 % is 1 % - point below 3 % and 10 % is 7 % - points above 3 % . the ratio of a : b should be 1 : 7 . the answer is c .
Answer: c
Question (physics): a man can row at 5 kmph in still water . if the velocity of current is 3 kmph and it takes him 1 hour to row to a place and come back , how far is the place ?
Options: a ) 2.4 km , b ) 2.9 km , c ) 3.4 km , d ) 4.4 km , e ) 1.6 km
Rationale: "explanation : speed in still water = 5 kmph speed of the current = 3 kmph speed downstream = ( 5 + 3 ) = 8 kmph speed upstream = ( 5 - 3 ) = 2 kmph let the required distance be x km total time taken = 1 hour â ‡ ’ x / 8 + x / 2 = 1 â ‡ ’ x + 4 x = 8 â ‡ ’ 5 x = 8 â ‡ ’ x = 1.6 km answer : option e"
Answer: e
Question (physics): a 120.00001 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds . what is the length of the other train ?
Options: a ) 220 meter , b ) 225 meter , c ) 380 meter , d ) 435 meter , e ) none of these
Rationale: "explanation : as trains are running in opposite directions so their relative speed will get added so , relative speed = 120 + 80 = 200 kmph = 200 * ( 5 / 18 ) = 500 / 9 m / sec let the length of other train is x meter then x + 120 / 9 = 500 / 9 = > x + 120 = 500 = > x = 380 so the length of the train is 380 meters option c"
Answer: c
Question (geometry): the ratio between the length and the breadth of a rectangular plot is 7 : 5 . if the perimeter of the plot is 288 metres , what is its area ?
Options: a ) 1320 sq . metres
b ) 3260 sq . metres
c ) 4280 sq . metres
d ) 5040 sq . metres
e ) none of these
Rationale: let the length and breadth be 7 x and 5 x respectively . then , p = 2 ( 7 x + 5 x ) = 288 â ‡ ’ x = 12 area = 7 ã — 12 ã — 5 ã — 12 = 5040 sq . m . answer d
Answer: d
Question (general): during the first two weeks of january , the total rainfall in springdale was 20 inches . if the rainfall during the second week was 1.5 times the rainfall during the first week , what was the rainfall during the second week of january ?
Options: a ) 5 inches , b ) 6 inches , c ) 9 inches , d ) 10 inches , e ) 12 inches
Rationale: "total rainfall in 2 weeks = 20 inches . assume the rainfall in second week = 1.5 x rainfall in first week = x total rainfall = 2.5 x = 20 inches x = 8 and 1.5 x = 12 rainfall during second week = 12 inches option e"
Answer: e
Question (probability): the set s consists of 5 numbers : { 1 , 2,3 , 4,5 } . if all possible subsets including the null set are created and one subset is chosen at random , what is the probability that the subset has 3 or 4 as its largest number ?
Options: a ) 3 / 4 , b ) 3 / 8 , c ) 3 / 16 , d ) 5 / 16 , e ) 3 / 32
Rationale: the set s has 2 ^ 5 = 32 subsets . the number 5 is in half of these subsets . of the remaining 16 subsets , 4 is an element in 8 of them . thus 4 is the largest number in 8 subsets of s . of the remaining 8 subsets , 3 is an element in 4 of them . thus 3 is the largest number in 4 subsets of s . the probability that 3 or 4 is the largest number is 12 / 32 = 3 / 8 . the answer is c .
Answer: b
Question (general): an exam consists of 8 true / false questions . brian forgets to study , so he must guess blindly on each question . if any score above 80 % is a passing grade , what is the probability that brian passes ?
Options: a ) 1 / 16 , b ) 37 / 256 , c ) 1 / 2 , d ) 219 / 256 , e ) 125 / 256
Rationale: "if you have 8 t or f and brian is going to guess then each question he has a 50 % chance of getting correct . if a passing score is 70 % it means brian needs to get 6 / 8 = 75 % , 7 / 8 = 87.5 % , or 8 / 8 = 100 % to pass . each is a possibility . if brian gets a 5 / 8 ( = 62.5 % ) or below he fails . so first figure out the number of ways that brian can get 6 out of 8 , 7 out of 8 , and 8 out of 8 questions correct . which is 8 choose 6 , equals is 28 , 8 choose 7 , equals 8 , and 8 choose 8 , equals 1 . this sums to 37 . the number of possible questions outcomes - the sum of 8 choose 8 , 7 choose 8 , 6 choose 8 … . 2 choose 8 , 1 choose 8 , and 0 choose 8 is 256 , so the chance of him passing is 125 / 256 . e"
Answer: e
Question (probability): in a certain animal population , for each of the first 3 months of life , the probability that an animal will die during that month is 1 / 4 . for a group of 200 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ?
Options: a ) 40 , b ) 46 , c ) 52 , d ) 62 , e ) 85
Rationale: "the probability of survival for each of the first 3 months of life is 1 - 1 / 4 = 3 / 4 , so of 200 newborn 200 * 3 / 4 * 3 / 4 * 3 / 4 = ~ 85 is expected to survive . answer : e ."
Answer: e
Question (physics): how many 4 digit numbers are there , if it is known that the first digit is even , the second is odd , the third is prime , the fourth ( units digit ) is divisible by 4 , and the digit 2 can be used only once ?
Options: a ) 20 , b ) 150 , c ) 225 , d ) 300 , e ) 320
Rationale: "4 options for the first digit : 2 , 4 , 6 , 8 ; 5 options for the second digit : 1 , 3 , 5 , 7 , 9 ; 4 options for the third digit : 2 , 3 , 5 , 7 ; 3 options for the fourth digit : 0 , 4 , 8 . four digit # possible without the restriction ( about the digit 2 ) : 4 * 5 * 4 * 3 = 240 numbers with two 2 - s , 2 x 2 x 1 * 5 * 1 * 3 = 15 . thus there are 240 - 15 = 225 such numbers . answer : c ."
Answer: c
Question (other): a salesman sold twice as much pears in the afternoon than in the morning . if he sold $ 390 kilograms of pears that day , how many kilograms did he sell in the afternoon ?
Options: a ) 120 , b ) 180 , c ) 260 , d ) 280 , e ) 320
Rationale: "3 x = 390 x = 130 therefore , the salesman sold 130 kg in the morning and 2 ⋅ 130 = 260 kg in the afternoon . so answer is c ."
Answer: c
Question (general): if a randomly selected positive single digit multiple of 3 is multiplied by a randomly selected prime number less than 20 , what is the probability q that this product will be a multiple of 45 ?
Options: a ) 1 / 32 , b ) 1 / 28 , c ) 1 / 24 , d ) 1 / 16 , e ) 1 / 14
Rationale: "there are 3 single digit multiple of 3 , that is , 3 , 6,9 . there are 8 prime nos less than 20 - 2,3 , 5,7 , 11,13 , 17,19 total outcome - 8 * 3 = 24 favourable outcome = 1 ( 9 * 5 ) hence required probability q = 1 / 24 . answer c ."
Answer: c
Question (other): a certain high school has 500 students . of these students , 20 are taking music , 20 are taking art , and 10 are taking both music and art . how many students are taking neither music nor art ?
Options: a ) 430 , b ) 440 , c ) 450 , d ) 460 , e ) 470
Rationale: "we ' re given a series of facts to work with : 1 ) a certain high school has 500 students . 2 ) of these students : x are taking music , y are taking art , and z are taking both music and art . we ' re asked how many students are taking neither music nor art ? let ' s test x = 20 y = 20 z = 10 so , we have 20 students taking music , 20 taking art and 10 taking both music and art . that 10 person has been counted twice though ( once in the music ' group ' and once in the art ' group ' ) , so what we really have is . . . 10 student taking just music 10 student taking just art 10 student taking both music and art total = 30 students we ' re asked for the total number of students who are taking neither course . that is 5000 - 30 = 470 . e"
Answer: e
Question (general): a courier charges for packages to a certain destination are 65 cents for the first 250 grams and 10 cents for each additional 100 grams or part thereof . what could be the weight in grams of a package for which the charge is $ 2.15 ?
Options: a ) 980 , b ) 1120 , c ) 1260 , d ) 1420 , e ) 1670
Rationale: "the charge is 65 cents for the first 250 grams . this leaves a charge of $ 2.15 - $ 0.65 = $ 1.50 the charge for the next 1400 grams is $ 1.40 which leaves a charge of $ 0.10 the weight is somewhere between 1650 and 1750 . the answer is e ."
Answer: e
Question (gain): if rs . 7500 are borrowed at c . i at the rate of 4 % per annum , then after 1 year the amount to be paid is ?
Options: a ) 3377 , b ) 2688 , c ) 2688 , d ) 7800 , e ) 1268
Rationale: "a = 7500 ( 26 / 25 ) ^ 1 = 7800 answer : d"
Answer: d
Question (gain): a shopkeeper buys mangoes at the rate of 7 a rupee and sells them at 5 a rupee . find his net profit or loss percent ?
Options: a ) 40 % , b ) 90 % , c ) 33 % , d ) 35 % , e ) 30 %
Rationale: "the total number of mangoes bought by the shopkeeper be 35 . if he buys 7 a rupee , his cp = 5 he selling at 5 a rupee , his sp = 7 profit = sp - cp = 7 - 5 = 2 profit percent = 2 / 5 * 100 = 40 % answer : a"
Answer: a
Question (general): the difference between a number and its two - fifth is 510 . what is 12 % of that number ?
Options: a ) 58 , b ) 110 , c ) 76 , d ) 102 , e ) 86
Rationale: "let the number be x . then , x - 2 / 5 x = 510 x = ( 510 * 5 ) / 3 = 850 12 % of 850 = 102 . answer : d"
Answer: d
Question (physics): a car gets 24 miles to the gallon . if it is modified to use a solar panel , it will use only 75 percent as much fuel as it does now . if the fuel tank holds 12 gallons , how many more miles will the car be able to travel , per full tank of fuel , after it has been modified ?
Options: a ) 96 , b ) 100 , c ) 104 , d ) 108 , e ) 112
Rationale: "originally , the distance the car could go on a full tank was 12 * 24 = 288 miles . after it has been modified , the car can go 24 / 0.75 = 32 miles per gallon . on a full tank , the car can go 32 * 12 = 384 miles , thus 96 miles more . the answer is a ."
Answer: a
Question (other): the h . c . f . of two numbers is 15 and the other two factors of their l . c . m . are 11 and 15 . the larger of the two numbers is :
Options: a ) 225 , b ) 300 , c ) 299 , d ) 322 , e ) 345
Rationale: "the numbers are ( 15 x 11 ) and ( 15 x 15 ) . larger number = ( 15 x 15 ) = 225 . answer : a"
Answer: a
Question (physics): in a dance competition the points in each round for the first , second , third and fourth position were 10050 , 2010 . no other points were given . ashita participated in several rounds in the competition and the product of her score was 50000 . in how many rounds did she participate ?
Options: a ) 3 , b ) 2 , c ) 1 , d ) 5 , e ) can not be determined
Rationale: correct answer is e because we are given that there wo n ' t be any points awarded for rounds other than 1 st four position . thus , it may happen that she played 15 rounds out of only 5 rounds were there in which she was awarded some points .
Answer: e
Question (geometry): a metallic sheet is of rectangular shape with dimensions 46 m x 36 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 8 m , the volume of the box ( in m 3 ) is :
Options: a ) 4830 , b ) 5120 , c ) 6420 , d ) 4800 , e ) 8960
Rationale: "l = ( 46 - 16 ) m = 30 m , b = ( 36 - 16 ) m = 20 m , h = 8 m . volume of the box = ( 30 x 20 x 8 ) m 3 = 4800 m 3 . answer : option d"
Answer: d
Question (gain): in an election between two candidates , one got 60 % of the total valid votes , 30 % of the votes were invalid . if the total number of votes was 9000 , the number of valid votes that the other candidate got , was :
Options: a ) 2500 , b ) 2520 , c ) 3000 , d ) 3100 , e ) none of these
Rationale: "explanation : number of valid votes = 70 % of 9000 = 6300 . valid votes polled by other candidates = 40 % of 6300 ( 40 / 1006300 ) = 2520 . harsh mishra a year ago 0 upvotes answer : b"
Answer: b
Question (gain): on a certain road , 10 % of the motorists exceed the posted speed limit and receive speeding tickets , but 20 % of the motorists who exceed the posted speed limit do not receive speeding tickets . what percent of the motorists on that road exceed the posted speed limit ?
Options: a ) 10.5 % , b ) 12.5 % , c ) 15 % , d ) 22 % , e ) 30 %
Rationale: suppose there are x motorists . 10 % of them exceeded the speed limit and received the ticket , i . e . x / 10 . again , suppose total no . of motorists who exceeded the speed limit are y . 20 % of y exceeded the speed limit but did n ' t received the ticket , i . e . y / 5 . it means 4 y / 5 received the ticket . hence , 4 y / 5 = x / 10 or y / x = 1 / 8 or y / x * 100 = 1 / 8 * 100 = 12.5 % answer : b
Answer: b
Question (general): x and y are two towns . ganesh covers the distance from x to y at an average speed of 60 km / hr . however , he covers the distance from y to x at an average speed of 30 km / hr . his average speed during the whole journey in km / hr . is :
Options: a ) 34 , b ) 43 , c ) 40 , d ) 38 , e ) 29
Rationale: "solution : average speed = 2 xy / x + y = 2 * 60 * 30 / 60 + 30 = 40 answer : c"
Answer: c
Question (general): a drink vendor has 20 liters of maaza , 144 liters of pepsi and 368 liters of sprite . he wants to pack them in cans , so that each can contains the same number of liters of a drink , and does n ' t want to mix any two drinks in a can . what is the least number of cans required ?
Options: a ) 135 , b ) 137 , c ) 142 , d ) 130 , e ) 133
Rationale: "the number of liters in each can = hcf of 20 , 144 and 368 = 4 liters . number of cans of maaza = 20 / 4 = 5 number of cans of pepsi = 144 / 4 = 36 number of cans of sprite = 368 / 4 = 92 the total number of cans required = 5 + 36 + 92 = 133 cans . answer : e"
Answer: e
Question (physics): jonathan can type a 40 page document in 40 minutes , susan can type it in 30 minutes , and jack can type it in 24 minutes . working together , how much time will it take them to type the same document ?
Options: a ) 5 minutes , b ) 10 minutes , c ) 15 minutes , d ) 18 minutes , e ) 20 minutes
Rationale: "you may set up common equation like this : job / a + job / b + job / c = job / x memorize this universal formula , you will need it definitely for gmat . and find x from this equation in this specific case , the equation will look like this : 40 / 40 + 40 / 30 + 40 / 24 = 40 / x if you solve this equation , you get the same answer b ( 10 )"
Answer: b
Question (general): find the least number must be subtracted from 62575 so that remaining number is divisible by 99 .
Options: a ) 93 , b ) 7 , c ) 54 , d ) 9 , e ) 6
Rationale: on dividing 62571 by 99 we get the remainder 7 , so 7 should be subtracted . answer is b
Answer: b
Question (general): a man is 12 years older than his brother . in two years , his age will be twice the age of his brother . the present age of his brother is :
Options: a ) 10 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: let the brother ' s present age be x years . then , man ' s present age = ( x + 12 ) years . ( x + 12 ) + 2 = 2 ( x + 2 ) x + 14 = 2 x + 4 x = 10 . answer : a
Answer: a
Question (general): a certain mixture of nuts consists of 5 parts almonds to 2 parts walnuts , by weight . what is the number of pounds of almonds in 280 pounds of the mixture ?
Options: a ) 200 , b ) 84 , c ) 40 , d ) 28 , e ) 20
Rationale: "almonds : walnuts = 5 : 2 total mixture has 7 parts in a 280 pound mixture , almonds are 5 / 7 ( total mixture ) = 5 / 7 * 280 = 200 pounds answer ( a )"
Answer: a
Question (general): how many 4 - digit numbers that do not contain the digits 2 , 3 , 4 , 5 , 6 , or 7 are there ?
Options: a ) 168 , b ) 176 , c ) 184 , d ) 192 , e ) 200
Rationale: the 1 st digit can be filled up by the numbers : { 1 , 8,9 } = 3 ways the 2 nd digit can be filled up by the numbers : { 0,1 , 8,9 } = 4 ways the 3 rd digit can be filled up by the numbers : { 0,1 , 8,9 } = 4 ways the 4 th digit can be filled up by the numbers : { 0,1 , 8,9 } = 4 ways the total number of such four - digit numbers is 3 * 4 * 4 * 4 = 192 the answer is d .
Answer: d
Question (physics): how many bricks , each measuring 25 cm x 11.25 cm x 6 cm , will be needed to build a wall of 8 m x 6 m x 22.5 cm ?
Options: a ) 5600 , b ) 6000 , c ) 6400 , d ) 7200 , e ) none
Rationale: "solution number of bricks = volume of the wall / volume of 1 brick = ( 800 x 600 x 22.5 / 25 x 11.25 x 6 ) = 6400 . answer c"
Answer: c
Question (general): the average weight of 6 person ' s increases by 1.8 kg when a new person comes in place of one of them weighing 69 kg . what might be the weight of the new person ?
Options: a ) 73 kg , b ) 79.8 kg , c ) 86 kg , d ) data inadequate , e ) none of these
Rationale: "total weight increased = ( 6 x 1.8 ) kg = 10.8 kg . weight of new person = ( 69 + 10.8 ) kg = 79.8 kg . answer : option b"
Answer: b
Question (gain): a man took a loan at rate of 12 % per annum simple interest . after 3 years he had to pay 7200 interest . the principal amount borrowed by him was .
Options: a ) rs 14000 , b ) rs 15000 , c ) rs 16000 , d ) rs 20000 , e ) none of these
Rationale: "explanation : s . i . = p â ˆ — r â ˆ — t / 100 = > p = s . i . â ˆ — 100 / r â ˆ — t = > p = 7200 â ˆ — 100 / 12 â ˆ — 3 = rs 20000 option d"
Answer: d
Question (general): a certain company retirement plan has arule of 70 provision that allows an employee to retire when the employee ' s age plus years of employment with the company total at least 70 . in what year could a female employee hired in 1986 on her 30 nd birthday first be eligible to retire under this provision ?
Options: a ) 2003 , b ) 2004 , c ) 2005 , d ) 2006 , e ) 2007
Rationale: "she must gain at least 70 points , now she has 30 and every year gives her two more points : one for age and one for additional year of employment , so 30 + 2 * ( # of years ) = 70 - - > ( # of years ) = 20 - - > 1986 + 20 = 2006 . answer : d ."
Answer: d
Question (gain): i had rs . 10000 with me . out of this , money i lent some money to a for 2 years at 15 % simple interest . i lent the remaining money to b for an equal number of years at 18 % simple interest . after 2 years , i found that a had given me rs . 360 more as interest as compared to ( b ) the amount of money which i had lent to b must have been
Options: a ) 2000 , b ) 3000 , c ) 4000 , d ) 5000 , e ) 6000
Rationale: explanation : total amount = rs . 10000 let money lent a = rs . x and money lent to b = rs . ( 10000 x ) x = rs . 6000 . so the amount of money lent to b = rs . 4000 answer : c
Answer: c
Question (gain): what percent is 320 gm of 1 kg ?
Options: a ) 25 % , b ) 40 % , c ) 10 % , d ) 8 % , e ) 32 %
Rationale: "1 kg = 1000 gm 320 / 1000 ã — 100 = 32000 / 1000 = 32 % answer is e"
Answer: e
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 785 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 ) 197 , c ) 193 , d ) 212 , e ) 213
Rationale: "total movies submitted are 785 . as per question we need to take 1 / 4 of 785 to be considered for top 10 movies = 196.25 approximate the value we 197 . imo option b is the correct answer . . ."
Answer: b
Question (general): the number 0.5 is how much greater than 1 / 3 ?
Options: a ) 1 / 6 , b ) 2 / 10 , c ) 1 / 50 , d ) 1 / 500 , e ) 2 / 500
Rationale: "let x be the difference then . 5 - 1 / 3 = x 5 / 10 - 1 / 3 = x x = 1 / 6 ans a"
Answer: a
Question (other): the concentration of spirit in 3 different vessels a , b and c are 45 % , 30 % and 10 % respectively . if 4 litres from vessel a , 5 litres from vessel b and 6 litres from vessel c are mixed , find the concentration of spirit in the resultant solution .
Options: a ) 26 % , b ) 33 % , c ) 34 % , d ) 35 % , e ) 24 %
Rationale: quantity of spirit in new solution = ( 4 * 45 / 100 ) + ( 5 * 30 / 100 ) + ( 6 * 10 / 100 ) = 1.8 + 1.5 + 0.6 = 3.9 liters so % concentration of spirit = 100 * 3.9 / ( 4 + 5 + 6 ) = 26 % answer : a
Answer: a
Question (general): there are 2 sections a and b in a class , consisting of 50 and 70 students respectively . if the average weight of section a is 50 kg and that of section b is 70 kg , find the average of the whole class ?
Options: a ) 50.78 kg , b ) 49.32 kg , c ) 61.67 kg , d ) 69.15 kg , e ) 70.89 kg
Rationale: "total weight of 50 + 70 students = 50 * 50 + 70 * 70 = 7400 average weight of the class is = 7400 / 120 = 61.67 kg answer is c"
Answer: c
Question (general): a number is increased by 20 % and then decreased by 20 % . find the net increase or decrease per cent .
Options: a ) 9 % , b ) 8 % , c ) 7 % , d ) 3 % , e ) 4 %
Rationale: "let the number be 100 . increase in the number = 20 % = 20 % of 100 = ( 20 / 100 ã — 100 ) = 20 therefore , increased number = 100 + 20 = 120 this number is decreased by 20 % therefore , decrease in number = 20 % of 120 = ( 20 / 100 ã — 120 ) = 2400 / 100 = 24 therefore , new number = 120 - 24 = 96 thus , net decreases = 100 - 96 = 4 hence , net percentage decrease = ( 4 / 100 ã — 100 ) % = ( 400 / 100 ) % = 4 % answer : e"
Answer: e
Question (general): if x ^ 2 – 3 x = 18 , then one possible value of x – 4 =
Options: a ) - 9 , b ) - 5 , c ) - 3 , d ) - 1 , e ) 2
Rationale: x ^ 2 – 3 x = 18 i . e . x ^ 2 – 3 x - 18 = 0 i . e . x ^ 2 – 6 x + 3 x - 18 = 0 i . e . ( x - 6 ) ( x + 3 ) = 0 i . e . x = 6 or - 3 i . e . x - 4 = 6 - 4 or - 3 - 4 i . e . x - 4 = 2 or - 7 answer : option e
Answer: e
Question (general): if 4 x + y = 8 and 3 x - 4 y = 5 , then what is the value of 7 x - 3 y ?
Options: a ) 23 , b ) 3 , c ) 15 , d ) 52 / 7 , e ) 60 / 7
Rationale: 4 x + y = 8 . . . equation 1 3 x - 4 y = 5 . . . equation 2 adding both the equations 7 x - 3 y = 23 correct answer option a
Answer: a