Cheukting/mathqa huggingface dataset:
Question (general): a cement mixture is composed of 3 elements . by weight , 1 / 5 of the mixture is sand , 3 / 4 of the mixture is water , and the remaining 6 pounds of the mixture is gravel . what is the weight of the entire mixture in pounds ?
Options: a ) 100 , b ) 120 , c ) 130 , d ) 140 , e ) 150
Rationale: "let the total weight be x . sand content = ( 1 / 5 ) x water content = ( 3 / 4 ) x gravel = x - ( 1 / 5 ) x - ( 3 / 4 ) x = ( 1 / 20 ) x = 6 x = 120 then answer will be b = 120"
Answer: b
Question (general): for each month of a given year except december , a worker earned the same monthly salary and donated one - tenth of that salary to charity . in december , the worker earned n times his usual monthly salary and donated one - fifth of his earnings to charity . if the worker ' s charitable contributions totaled one - nineth of his earnings for the entire year , what is the value of n ?
Options: a ) 8 / 5 , b ) 5 / 2 , c ) 3 , d ) 11 / 3 , e ) 22
Rationale: let monthly salary for each of the 11 months except december was x , then 11 x * 1 / 10 + nx * 1 / 5 = 1 / 9 ( 11 x + nx ) ; 11 / 10 + n / 5 = 1 / 9 ( 11 + n ) = > 11 + 2 n / 10 = 11 + n / 9 = > 66 + 12 n = 110 + 10 n = > 2 n = 44 n = 22 answer : e
Answer: e
Question (physics): ajay can walk 3 km in 1 hour . in how many hours he can walk 50 km ?
Options: a ) 5 hrs , b ) 16.6 hrs , c ) 15.6 hrs , d ) 20.4 hrs , e ) 30 hrs
Rationale: "1 hour he walk 3 km he walk 50 km in = 50 / 3 * 1 = 16.6 hours answer is 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: answer let the business value change from a to b . then , 4 % of a = 5 % of b ⇒ 4 a / 100 = 5 b / 100 ⇒ b = 4 a / 5 ∴ change in business = ( a - 4 a / 5 ) = a / 5 percentage slump in business = { ( a / 5 ) / a } x 100 % = 20 % correct option : c
Answer: c
Question (gain): find 44 % of 240
Options: a ) 96 , b ) 105.6 , c ) 86 , d ) 74 , e ) 110
Rationale: "we know that r % of m is equal to r / 100 × m . so , we have 44 % of 240 44 / 100 × 240 = 105.6 answer : b"
Answer: b
Question (gain): there were two candidates in an election . winner candidate received 62 % of votes and won the election by 324 votes . find the number of votes casted to the winning candidate ?
Options: a ) 456 , b ) 837 , c ) 912 , d ) 1200 , e ) 1400
Rationale: "w = 62 % l = 38 % 62 % - 38 % = 24 % 24 % - - - - - - - - 324 62 % - - - - - - - - ? = > 837 answer : b"
Answer: b
Question (physics): r is the set of positive even integers less than 51 , and s is the set of the squares of the integers in r . how many elements does the intersection of r and s contain ?
Options: a ) none , b ) three , c ) four , d ) five , e ) seven
Rationale: "r is the set of positive even integers less than 51 , and s is the set of the squares of the integers in r . how many elements does the intersection of r and s contain ? r = 2,4 , 6,8 , 10,12 . . . s = 4,16 , 36,64 . . . numbers : 4 , 16 , and 36 are even integers ( less than 51 ) that are in both sets . solution : three answer : b"
Answer: b
Question (general): a die is rolled twice . what is the probability of getting a sum equal to 9 ?
Options: a ) 2 / 9 , b ) 5 / 7 , c ) 1 / 7 , d ) 1 / 9 , e ) 3 / 7
Rationale: total number of outcomes possible when a die is rolled = 6 ( ∵ any one face out of the 6 faces ) hence , total number of outcomes possible when a die is rolled twice , n ( s ) = 6 × 6 = 36 e = getting a sum of 9 when the two dice fall = { ( 3 , 6 ) , { 4 , 5 } , { 5 , 4 } , ( 6 , 3 ) } hence , n ( e ) = 4 p ( e ) = n ( e ) / n ( s ) = 4 / 36 = 1 / 9 answer : option d
Answer: d
Question (general): if xy > 0 , 1 / x + 1 / y = 2 , and 1 / xy = 8 , then ( x + y ) / 4 = ?
Options: a ) 1 / 16 , b ) 1 / 6 , c ) 1 / 5 , d ) 5 , e ) 6
Rationale: "( 1 / x + 1 / y ) = 2 canbe solved as { ( x + y ) / xy } = 8 . substituting for 1 / xy = 8 , we get x + y = 2 / 8 = = > ( x + y ) / 4 = 2 / ( 8 * 4 ) = 1 / 16 . a"
Answer: a
Question (general): the difference in compound interest earned on a deposit ( compounded annually ) in year 1 and year 2 is $ 40 . had the interest rate been 3 times its present value , the difference a would have been how much ?
Options: a ) 40 / 3 , b ) 40 , c ) 120 , d ) 360 , e ) 420
Rationale: case 1 : deposit = $ x ; rate of increase = r . interest yearned in 1 year = xr . deposit in 1 year = x + xr . interest yearned in 2 year = ( x + xr ) r . the difference a = ( x + xr ) r - xr = xr ^ 2 = 40 . case 2 : deposit = $ x ; rate of increase = 3 r . interest yearned in 1 year = x ( 3 r ) . deposit in 1 year = x + 3 xr . interest yearned in 2 year = ( x + 3 xr ) 3 r . the difference = ( x + 3 xr ) 3 r - 3 xr = 9 xr ^ 2 . since from case 1 we know that xr ^ 2 = 40 , then 9 xr ^ 2 = 9 * 40 = 360 . answer : d .
Answer: d
Question (general): an amount of rs . 3120 was divided among a , b and c , in the ratio 1 / 2 : 1 / 3 : 1 / 4 . find the share of a ?
Options: a ) 1320 , b ) 1196 , c ) 1210 , d ) 1440 , e ) 1050
Rationale: "let the shares of a , b and c be a , b and c respectively . a : b : c = 1 / 2 : 1 / 3 : 1 / 4 let us express each term with a common denominator which is the last number divisible by the denominators of each term i . e . , 12 . a : b : c = 6 / 12 : 4 / 12 : 3 / 12 = 6 : 4 : 3 . share of a = 6 / 13 * 3120 = rs . 1440 answer : d"
Answer: d
Question (general): a number when divided by 5 gives a number which is 8 more than the remainder obtained on dividing the same number by 34 . such a least possible number k is
Options: a ) 74 , b ) k = 75 , c ) k = 175 , d ) k = 680 , e ) 690
Rationale: "i solved this question by plugging in numbers from the answer choices . a . ) 74 starting with answer choice a , i immediately eliminated it because 74 is not even divisible by 5 . b . ) 75 i divide 75 / 5 and get 15 as an answer . i divide 75 / 34 and get a remainder of 7 . 15 - 7 = 8 so i know the correct answer isb"
Answer: b
Question (physics): a circular road runs round a circular ground . if the difference between the circumferences of the outer circle and inner circle is 66 metres , the width of the road is :
Options: a ) 5.25 m
b ) 7 m
c ) 10.5 m
d ) 21 m
e ) 22 m
Rationale: 2 π ( r - r ) = 60 = > 2 * 22 / 7 * ( r - r ) = 60 . therefore , ( r - r ) = ( 66 * 7 / 44 ) = 10.5 m answer : c
Answer: c
Question (general): find 12 × × 19
Options: a ) 238 , b ) 228 , c ) 208 , d ) 277 , e ) 101
Rationale: "mentally imagine this number as ( 10 + 2 ) × × 19 = 190 + 38 = 228 . answer : b"
Answer: b
Question (general): how many integers between 334,700 and 458,600 have tens digit 1 and units digit 3 ?
Options: a ) 10,300 , b ) 10,030 , c ) 1,353 , d ) 1,352 , e ) 1,239
Rationale: "there is one number in hundred with 1 in the tens digit and 3 in the units digit : 13 , 113 , 213 , 313 , . . . the difference between 334,700 and 458,600 is 458,600 - 334,700 = 123,900 - one number per each hundred gives 123,900 / 100 = 1,239 numbers . answer : e ."
Answer: e
Question (other): if number divisible by both 3 and 2 , then the same number divisible by which number ?
Options: a ) 4 , b ) 5 , c ) 8 , d ) 6 , e ) 9
Rationale: obviously , the answer is 6 option d
Answer: d
Question (geometry): the radii of two cones are in ratio 2 : 1 , their volumes are equal . find the ratio of their heights .
Options: a ) 1 : 4
b ) 1 : 3
c ) 1 : 2
d ) 1 : 5
e ) none of these
Rationale: explanation : let their radii be 2 x , x and their heights be h and h resp . then , volume of cone = 1 / 3 π r 2 h 1 / 3 ∗ π ∗ ( 2 x ) 2 ∗ h / 1 / 3 ∗ π ∗ x 2 ∗ h = > hh = 14 = > h : h = 1 : 4 option a
Answer: a
Question (general): the average of first 50 non - zero positive integers is
Options: a ) 11.5 , b ) 25.5 , c ) 22 , d ) 25 , e ) 27
Rationale: "explanation : sum of first n non - zero positive integers n ( n + 1 ) / 2 so , average of first n non - zero positive integers n ( n + 1 ) / 2 n = ( n + 1 ) / 2 = > ( 50 + 1 ) / 2 = 25.5 answer : b"
Answer: b
Question (physics): excluding stoppages , the speed of the bus is 54 kms / hr and with stoppages , it is 45 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 20
Rationale: by including stoppages , bus will cover 9 km less . . ( 54 km - 45 km = 9 km ) excluding stoppages , x = 54 kmph including stoppages , y = 45 kmph difference , z = 9 km time taken to cover that 9 km ( bus stops per hour ( 60 minutes ) ) = z / x ( 60 minutes ) = 9 / 54 ( 60 ) = 1 / 6 ( 60 ) = 10 minutes . answer : b
Answer: b
Question (general): sanoop bought 8 t - shirts at an average price ( arithmetic mean ) of rs . 526 . if sanoop returned 1 t - shirts to the retailer , and the average price of the remaining t - shirts was rs . 505 , then what is the average price , of the 3 returned t - shirts ?
Options: a ) 560 , b ) 561 , c ) 562 , d ) 563 , e ) 673
Rationale: total price of 8 t - shirts = 8 * 526 = 4208 total price of 7 t - shirts = 7 * 505 = 3535 total price of 1 t - shirts = 4208 - 3535 = 673 average price of 3 t - shirts = 673 correct option answer : e
Answer: e
Question (geometry): in how many q ways can 5 people from a group of 6 people be seated around a circular table
Options: a ) 56
b ) 80
c ) 100
d ) 120
e ) 144
Rationale: q = 6 c 5 * ( 5 - 1 ) ! ( select 5 out of 6 and arrange them in circular manner ) = 6 * 4 ! = 6 * 24 = 144 answer - e
Answer: e
Question (general): a number is doubled and 6 is added . if resultant is trebled , it becomes 72 . what is that number
Options: a ) 8 , b ) 10 , c ) 9 , d ) 14 , e ) 16
Rationale: "explanation : = > 3 ( 2 x + 6 ) = 72 = > 2 x + 6 = 24 = > x = 9 option c"
Answer: c
Question (general): o ( x ) represents the least odd integer greater than x , whereas o ( x ) represents the greatest odd integer less than x . likewise , e ( x ) represents the least even integer greater than x , whereas e ( x ) represents the greatest even integer less than x . according to these definitions , the value of o ( 5.3 ) + e ( – 6.7 ) + o ( – 3.3 ) + e ( 4.7 ) is :
Options: a ) - 3 , b ) - 1 , c ) 0 , d ) 1 , e ) 3
Rationale: "o ( 5.3 ) + e ( – 6.7 ) + o ( – 3.3 ) + e ( 4.7 ) = 7 + ( - 6 ) + ( - 5 ) + 4 = 0 the answer is c ."
Answer: c
Question (gain): i gain 70 paise on rs . 70 . my gain percent is :
Options: a ) 0.1 % , b ) 1 % , c ) 7 % , d ) 10 % , e ) noneof these
Rationale: solution 11.1 gain % = ( 0.70 / 70 x 100 ) % = 1 % . answer b
Answer: b
Question (gain): a fruit seller had some oranges . he sells 20 % oranges and still has 400 oranges . how many oranges he had originally ?
Options: a ) 420 , b ) 700 , c ) 220 , d ) 500 , e ) none of these
Rationale: "explanation : he sells 20 % of oranges and still there are 400 oranges remaining = > 80 % of oranges = 400 ⇒ ( 80 × total oranges ) / 100 = 400 ⇒ total oranges / 100 = 5 ⇒ total oranges = 5 × 100 = 500 answer : option d"
Answer: d
Question (general): in a group of 800 people , 3 / 5 play at least one instrument , 96 play two or more . what is the probability that one student play exactly one instrument ?
Options: a ) 2 / 125 , b ) 12 / 25 , c ) c ) 2 / 25 , d ) 3 / 25 , e ) 1 / 5
Rationale: p ( playing 2 or more instruments ) = 96 / 800 = 3 / 25 . then , the probability of playing exactly one instrument is given by : p ( playing 1 or more instruments ) - p ( playing 2 or more instruments ) = 3 / 5 - 3 / 25 = 12 / 25 . answer b .
Answer: b
Question (geometry): the ratio of the volumes of two cubes is 1728 : 2197 . what is the ratio of their total surface areas ?
Options: a ) 12 : 18 , b ) 144 : 169 , c ) 44 : 22 , d ) 28 : 144 , e ) 96 : 12
Rationale: "ratio of the sides = â ³ â ˆ š 1728 : â ³ â ˆ š 2197 = 12 : 13 ratio of surface areas = 144 : 169 answer : b"
Answer: b
Question (gain): in an election between two candidates , the first candidate got 60 % of the votes and the second candidate got 240 votes . what was the total number of votes ?
Options: a ) 400 , b ) 600 , c ) 800 , d ) 1000 , e ) 1200
Rationale: let v be the total number of votes . 0.4 v = 240 v = 600 the answer is b .
Answer: b
Question (physics): a man sitting in a train which is travelling at 50 kmph observes that a goods train travelling in a opposite direction , takes 9 seconds to pass him . if the goods train is 280 m long , find its speed .
Options: a ) 58 , b ) 62 , c ) 74 , d ) 81 , e ) 65
Rationale: "relative speed = ( 280 / 9 ) m / s = ( 280 / 9 ) * ( 18 / 5 ) = 112 kmph speed of goods train = 112 - 50 = 62 kmph answer is b"
Answer: b
Question (general): what is the smallest 6 digit number exactly divisible by 111 ?
Options: a ) 100010 , b ) 100012 , c ) 100011 , d ) 100013 , e ) 120012
Rationale: "smallest 6 digit number = 100000 100000 / 111 = 900 , remainder = 100 . hence 11 more should be added to 100000 to get the smallest 6 digit number exactly divisible by 111 = > smallest 6 digit number exactly divisible by 111 = 100000 + 11 = 100011 answer is c"
Answer: c
Question (other): a bag contains 4 green and 8 white balls . if two balls are drawn simultaneously , the probability that both are of the same colour is
Options: a ) 8 / 15 , b ) 2 / 5 , c ) 3 / 5 , d ) 11 / 15 , e ) 17 / 33
Rationale: "drawing two balls of same color from four green balls can be done in 4 c ₂ ways . similarly from eight white balls two can be drawn in ⁸ c ₂ ways . p = 4 c ₂ / ¹ ⁵ c ₂ + ⁸ c ₂ / ¹ ⁵ c ₂ = 17 / 33 answer : e"
Answer: e
Question (general): jar x is 1 / 2 full of water . jar y , which has half the capacity of jar x , is 1 / 2 full of water . if the water in jar y is poured into jar x , then jar x will be filled to what fraction of its capacity ?
Options: a ) 3 / 4 , b ) 5 / 6 , c ) 7 / 8 , d ) 5 / 8 , e ) 7 / 12
Rationale: let p be the capacity of jar x . the amount of water in jar y is 1 / 2 * p / 2 = p / 4 then the total amount in jar x is p / 2 + p / 4 = 3 p / 4 the answer is a .
Answer: a
Question (physics): if 1 / 2 of the air in a tank is removed with each stroke of a vacuum pump , what fraction of the original amount of air has been removed after 6 strokes ?
Options: a ) 63 / 64 , b ) 7 / 8 , c ) 1 / 4 , d ) 1 / 8 , e ) 1 / 16
Rationale: "left after 1 st stroke = 1 / 2 left after 2 nd stroke = 1 / 2 * 1 / 2 = 1 / 4 left after 3 rd stroke = 1 / 2 * 1 / 4 = 1 / 8 left after 4 th stroke = 1 / 2 * 1 / 8 = 1 / 16 left after 5 th stroke = 1 / 2 * 1 / 16 = 1 / 32 left after 6 th stroke = 1 / 2 * 1 / 32 = 1 / 64 so removed = 1 - 1 / 64 = 63 / 64"
Answer: a
Question (general): a certain ball team has an equal number of right - and left - handed players . on a certain day , one - third of the players were absent from practice . of the players at practice that day , one - third were left handed . what is the ratio of the number of right - handed players who were not at practice that day to the number of lefthanded players who were not at practice ?
Options: a ) 1 / 5 , b ) 2 / 3 , c ) 5 / 7 , d ) 7 / 5 , e ) 3 / 2
Rationale: say the total number of players is 18 , 9 right - handed and 9 left - handed . on a certain day , two - thirds of the players were absent from practice - - > 6 absent and 12 present . of the players at practice that day , one - third were left - handed - - > 12 * 1 / 3 = 4 were left - handed and 8 right - handed . the number of right - handed players who were not at practice that day is 9 - 8 = 1 . the number of left - handed players who were not at practice that days is 9 - 4 = 5 . the ratio = 1 / 5 . answer : a .
Answer: a
Question (physics): a group of hikers is planning a trip that will take them up a mountain using one route and back down using another route . they plan to travel down the mountain at a rate of one and a half times the rate they will use on the way up , but the time each route will take is the same . if they will go up the mountain at a rate of 4 miles per day and it will take them two days , how many miles long is the route down the mountain ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 12 , e ) 16
Rationale: "d = s * t given condition is for up the mountain hikers takes 4 miles per day and total 2 days . . . miles = 8 miles . . . for down speed they take = 3 / 2 ( 4 ) = 6 miles per day and for the same 2 days . . . miles = 12 miles . . answer : option d is correct answer"
Answer: d
Question (general): rates for having a manuscript typed at a certain typing service are $ 5 per page for the first time a page is typed and $ 3 per page each time a page is revised . if a certain manuscript has 200 pages , of which 80 were revised only once , 20 were revised twice , and the rest required no revisions , what was the total cost of having the manuscript typed ?
Options: a ) $ 1360 , b ) $ 1620 , c ) $ 1650 , d ) $ 680 , e ) $ 770
Rationale: "for 200 - 80 - 20 = 100 pages only cost is 5 $ per page for the first time page is typed - 100 * 5 = 500 $ ; for 80 pages the cost is : first time 5 $ + 3 $ of the first revision - 80 * ( 5 + 3 ) = 640 $ ; for 20 pages the cost is : first time 5 $ + 3 $ of the first revision + 3 $ of the second revision - 20 ( 5 + 3 + 3 ) = 220 $ ; total : 500 + 640 + 220 = 1360 $ . answer : a ."
Answer: a
Question (general): the line y = 5 x / 3 + b goes through the point ( 7 , – 1 ) . what is the value of b ?
Options: a ) 3 , b ) – 5 / 3 , c ) – 7 / 5 , d ) 16 / 3 , e ) – 38 / 3
Rationale: “ finding the equation ” procedure . plug ( x , y ) = ( 7 , – 1 ) into this equation : { - 1 } = { { 5 ( 7 ) } / 3 } + b = { 35 / 3 } + b b = { - 35 / 3 } - 1 = { - 35 / 3 } - { 3 / 3 } = - { 38 / 3 } answer = e
Answer: e
Question (general): the average monthly salary of 20 employees in an organisation is rs . 1700 . if the manager ' s salary is added , then the average salary increases by rs . 100 . what is the manager ' s monthly salary ?
Options: a ) rs . 6003 , b ) rs . 3800 , c ) rs . 1288 , d ) rs . 6108 , e ) rs . 6011
Rationale: "explanation : manager ' s monthly salary rs . ( 1800 * 21 - 1700 * 20 ) = rs . 3800 . answer : b"
Answer: b
Question (general): on dividing 17698 by a certain number , we get 89 as quotient and 14 as remainder . what is the divisor ?
Options: a ) 199 , b ) 154 , c ) 852 , d ) 741 , e ) 785
Rationale: "divisor * quotient + remainder = dividend divisor = ( dividend ) - ( remainder ) / quotient ( 17698 - 14 ) / 89 = 199 answer ( a )"
Answer: a
Question (physics): two trains start from same place at same time at right angles to each other . their speeds are 36 km / hr and 48 km / hr respectively . after 30 seconds the distance between them will be ?
Options: a ) 270 mts , b ) 190 mts , c ) 100 mts , d ) 500 mts , e ) 110 mts
Rationale: explanation : using pythagarous theorem , distance travelled by first train = 36 x 5 / 18 x 30 = 300 m distance travelled by second train = 48 x 5 / 18 x 30 = 400 m so distance between them = â ˆ š ( 90000 + 160000 ) = â ˆ š 250000 = 500 mts . answer : d
Answer: d
Question (general): the sum of the squares of the first 15 positive integers ( 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + . . . + 15 ^ 2 ) is equal to 1290 . what is the sum of the squares of the second 15 positive integers ( 16 ^ 2 + 17 ^ 2 + 18 ^ 2 + . . . + 30 ^ 2 ) ?
Options: a ) 2480 , b ) 3490 , c ) 6785 , d ) 8265 , e ) 9255
Rationale: you ' ll never need a formula for the sums of squares on the actual gmat . you do n ' t need to use that formula here , though it ' s not all that straightforward to solve without one . two different approaches : 16 ^ 2 + 17 ^ 2 + 18 ^ 2 + . . . + 30 ^ 2 = ( 15 + 1 ) ^ 2 + ( 15 + 2 ) ^ 2 + ( 15 + 3 ) ^ 2 + . . . + ( 15 + 15 ) ^ 2 now we can expand each square ; they are all in the ( x + y ) ^ 2 = x ^ 2 + 2 xy + y ^ 2 pattern . = ( 15 ^ 2 + 2 * 15 + 1 ^ 2 ) + ( 15 ^ 2 + 4 * 15 + 2 ^ 2 ) + ( 15 ^ 2 + 6 * 15 + 3 ^ 2 ) + . . . + ( 15 ^ 2 + 30 * 15 + 15 ^ 2 ) now we have fifteen 15 ^ 2 terms , so adding these gives 15 * 15 ^ 2 = 15 ^ 3 = 3375 . we also have the entire sum 1 ^ 2 + 2 ^ 2 + . . . + 15 ^ 2 , which we know is equal to 1240 . finally adding the middle terms , we have : 2 * 15 + 4 * 15 + 6 * 15 + . . . + 30 * 15 = 15 ( 2 + 4 + 6 + . . . . + 30 ) = 15 * 2 * ( 1 + 2 + 3 + . . . + 15 ) = 15 * 2 * 8 * 15 = 3600 so the sum must be 3375 + 1240 + 3600 = 8215 alternatively , we can use a different factoring pattern . we want to find the value of 30 ^ 2 + 29 ^ 2 + . . . + 17 ^ 2 + 16 ^ 2 . well if we subtract 15 ^ 2 + 14 ^ 2 + . . . . + 2 ^ 2 + 1 ^ 2 from this , the answer will be 1240 less than what we want to find . so if we can find the value of 30 ^ 2 + 29 ^ 2 + . . . + 17 ^ 2 + 16 ^ 2 - ( 15 ^ 2 + 14 ^ 2 + . . . . + 2 ^ 2 + 1 ^ 2 ) then we can add 1240 to get the answer . now grouping the terms above to get differences of squares , we have = ( 30 ^ 2 - 15 ^ 2 ) + ( 29 ^ 2 - 14 ^ 2 ) + . . . + ( 16 ^ 2 - 1 ^ 2 ) and factoring each of these using x ^ 2 - y ^ 2 = ( x + y ) ( x - y ) , we have = 45 * 15 + 43 * 15 + 41 * 15 + . . . + 17 * 15 = 15 ( 45 + 43 + 41 + . . . + 17 ) in brackets we have an equally spaced sum with fifteen terms , which we can evaluate using the familiar formula . so the above equals 15 * 15 * 62 / 2 = 6975 and adding back the 1290 , we get the answer of 8265 . ( ans d )
Answer: d
Question (physics): if the population of a certain country increases at the rate of one person every 30 seconds , by how many persons does the population increase in 1 hour ?
Options: a ) 100 , b ) 120 , c ) 150 , d ) 180 , e ) 160
Rationale: "answer = 2 * 60 = 120 answer is b"
Answer: b
Question (general): the total age of a and b is 10 years more than the total age of b and c . c is how many year younger than
Options: a ) 14 years , b ) 12 years , c ) 56 years , d ) 10 years , e ) 55 years
Rationale: "given that a + b = 10 + b + c = > a â € “ c = 10 + b â € “ b = 10 = > c is younger than a by 10 years answer : d"
Answer: d
Question (general): at 1 : 00 pm , there were 10.0 grams of bacteria . the bacteria increased to x grams at 4 : 00 pm , and 22.5 grams at 7 : 00 pm . if the amount of bacteria present increased by the same fraction during each of the 3 - hour periods , how many grams of bacteria were present at 4 : 00 pm ?
Options: a ) 14.4 , b ) 14.7 , c ) 15.0 , d ) 15.3 , e ) 15.6
Rationale: "let x be the factor by which the bacteria increases every three hours . at 4 : 00 pm , the amount of bacteria was 10 x and at 7 : 00 pm it was 10 x ^ 2 . 10 x ^ 2 = 22.5 x ^ 2 = 2.25 x = 1.5 at 4 : 00 pm , the amount of bacteria was 10 ( 1.5 ) = 15 grams . the answer is c ."
Answer: c
Question (general): if 6 x ^ 2 + x - 12 = ( ax + w ) ( cx + d ) , then | a | + | w | + | c | + | d | = for a complete solution and more practice problems , see this blog : http : / / magoosh . com / gmat / 2012 / algebra - on . . . to - factor /
Options: a ) 10 , b ) 12 , c ) 15 , d ) 18 , e ) 20
Rationale: 6 x ^ 2 + x - 12 = 6 x ^ 2 + 9 x - 8 x - 12 = > 3 x ( 2 x + 3 ) - 4 ( 2 x + 3 ) = > ( 2 x + 3 ) ( 3 x - 4 ) = ( ax + w ) ( cx + d ) hence a = 2 , w = c = 3 , d = - 4 so , 2 + 3 + 3 + | - 4 | = 2 + 3 + 3 + 4 = 12 answer b .
Answer: b
Question (general): the average of first four prime numbers greater than 10 is ?
Options: a ) 10 , b ) 20 , c ) 15 , d ) 40 , e ) 50
Rationale: "11 + 13 + 17 + 19 = 60 / 4 = 15 answer : c"
Answer: c
Question (gain): a and b started a business investing rs . 60,000 and rs 45,000 respectively . in what ratio the profit earned after 2 years be divided between a and b respectively ?
Options: a ) 3 : 2 , b ) 4 : 3 , c ) 18 : 20 , d ) 1 : 4 , e ) 18 : 4
Rationale: "a : b = 60000 : 45000 = 4 : 3 answer : b"
Answer: b
Question (physics): the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 400 resolutions .
Options: a ) 561.68 m , b ) 562.68 m , c ) 563.68 m , d ) 564.68 m , e ) 565.68 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 400 resolutions . = 500 * 2 * 22 / 7 * 22.4 = 56268 cm = 562.68 m answer : b"
Answer: b
Question (general): what is the remainder when you divide 2 ^ 200 - 2 by 7 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: answer is b . this is very similar to the 32 ^ 32 ^ 32 - 2 divided by 7 question .
Answer: b