Cheukting/mathqa huggingface dataset:
Question (general): a taxi owner buys diesel at rs . 8.50 , rs . 9 and rs . 9.50 per litre for 3 successive years . what approximately is the average cost per litre of diesel if he spends rs . 5000 each year ?
Options: a ) 7.98 , b ) 8.98 , c ) 9.98 , d ) 6.98 , e ) 8.12
Rationale: total cost = 5000 × 3 = 15000 total diesel used = 5000 / 8.50 + 5000 / 9 + 5000 / 9.50 = 588 + 555 + 527 = 1670 average cost per litre of diesel = 15000 / 1670 = 8.98 answer : b
Answer: b
Question (gain): a man invests rs . 5,000 at the rate of 5 % per annum . how much more should he invest at the rate of 8 % , so that he can earn a total of 6 % per annum ?
Options: a ) rs . 1200 , b ) rs . 1300 , c ) rs . 2500 , d ) rs . 2000 , e ) none of these
Rationale: "explanation : interest on rs . 5000 at 5 % per annum = ( 5000 × 5 × 1 ) / 100 = rs . 250 let his additional investment at 8 % = x interest on rs . x at 8 % per annum = ( x × 8 × 1 ) / 100 = 2 x / 25 . to earn 6 % per annum for the total , interest = ( 5000 + x ) × 6 × 1 / 100 . = > 250 + 2 x / 25 = ( 5000 + x ) × 6 × 1 / 100 . = > 25000 + 8 x = ( 5000 + x ) × 6 . = > 25000 + 8 x = 30000 + 6 x . = > 2 x = 5000 . = > x = 2500 . answer : c"
Answer: c
Question (general): an ant walks an average of 500 meters in 12 minutes . a beetle walks 15 % less distance at the same time on the average . assuming the beetle walks at her regular rate , what is its speed in km / h ?
Options: a ) 2.215 , b ) 2.5 . , c ) 2.775 , d ) 3.2 , e ) 3.5
Rationale: "the ant walks an average of 500 meters in 12 minutes or , 500 meters in 1 / 5 hours the beetle walks 15 % less distance = 500 - 75 = 425 meters in 12 minutes or , 0.425 km in 12 / 60 = 1 / 5 hours speed = 0.425 * 5 = 2.125 km / h ans should be 2.125 answer : a"
Answer: a
Question (general): when 1 / 10 percent of 5,000 is subtracted from 1 / 10 of 5,000 , the difference is
Options: a ) 0 , b ) 50 , c ) 450 , d ) 495 , e ) 500
Rationale: "1 / 10 of 5,000 is 500 ; 1 / 10 percent of 5,000 is 100 times smaller than the above , so it ' s 5 ; thus the difference is 500 - 5 = 495 . answer : d ."
Answer: d
Question (gain): what will be the fraction of 75 %
Options: a ) 3 / 4 , b ) 1 / 5 , c ) 1 / 10 , d ) 1 / 11 , e ) none of above
Rationale: "explanation : it will 75 * 1 / 100 = 3 / 4 option a"
Answer: a
Question (general): what is the least number which should be added to 2782 so that the sum is exactly divisible by 5 , 6 , 4 , and 3 ?
Options: a ) 26 , b ) 32 , c ) 38 , d ) 46 , e ) 52
Rationale: "l . c . m . of 5 , 6 , 4 and 3 = 60 . when dividing 2782 by 60 , the remainder is 22 . the number to be added = 60 - 22 = 38 . the answer is c ."
Answer: c
Question (general): how much is 35 % of 40 is greater than 4 / 5 of 25 ?
Options: a ) 29 , b ) 776 , c ) 66 , d ) 14 , e ) 99
Rationale: "( 80 / 100 ) * 40 – ( 4 / 5 ) * 25 35 - 20 = 14 answer : d"
Answer: d
Question (physics): two cyclist start from the same places in opposite directions . one is going towards north at 10 kmph and the other is going towards south 10 kmph . what time will they take to be 50 km apart ?
Options: a ) 1.2 hr , b ) 2.5 hrs , c ) 3 hrs , d ) 5.2 hrs , e ) 6 hrs
Rationale: "to be ( 10 + 10 ) km apart , they take 1 hour to be 50 km apart , they take 1 / 20 * 50 = 2.5 hrs answer is b"
Answer: b
Question (general): the value of ( 0.2 × 0.2 + 0.01 ) ( 0.1 × 0.1 + 0.02 ) - 1 is equal to
Options: a ) 5 / 3 , b ) 9 / 5 , c ) 41 / 4 , d ) 41 / 12 , e ) none
Rationale: "solution given expression ( 0.2 × 0.2 + 0.01 ) / ( 0.1 × 0.1 × + 0.02 ) = 0.04 + 0.01 / 0.01 + 0.02 = 0.05 / 0.03 = 5 / 3 . answer a"
Answer: a
Question (gain): a person buys an article at rs . 620 . at what price should he sell the article so as to make a profit of 25 % ?
Options: a ) 600 , b ) 882 , c ) 775 , d ) 662 , e ) 521
Rationale: "cost price = rs . 620 profit = 25 % of 620 = rs . 155 selling price = cost price + profit = 620 + 155 = 775 answer : c"
Answer: c
Question (general): the average of 10 numbers is 7 . if each number is multiplied by 10 , then what is the average of the new set of numbers ?
Options: a ) 7 , b ) 17 , c ) 70 , d ) 100 , e ) 107
Rationale: the sum of the ten numbers is 7 * 10 = 70 if each number is multiplied by 10 , the new sum is 10 * ( 70 ) . the average is then 10 * 7 = 70 the answer is c .
Answer: c
Question (general): if xy = 25 , x / y = 36 , for positive numbers x and y , y = ?
Options: a ) 1 / 2 , b ) 2 , c ) 1 / 3 , d ) 3 , e ) 5 / 6
Rationale: "very easy question . 2 variables and 2 easy equations . xy = 25 - - - > x = 25 / y - ( i ) x / y = 36 - - - > replacing ( i ) here - - - > 25 / ( y ^ 2 ) = 36 - - - > y ^ 2 = 25 / 36 - - - > y = 5 / 6 or - 5 / 6 the question states that x and y are positive integers . therefore , y = 5 / 6 is the answer . answer e ."
Answer: e
Question (probability): there is a 20 % chance sandy will visit china this year , while there is a 70 % chance that she will visit malaysia this year . what is the probability that sandy will visit either china or malaysia this year , but not both ?
Options: a ) 44 % , b ) 48 % , c ) 54 % , d ) 62 % , e ) 70 %
Rationale: "p ( china and not malaysia ) = 0.2 * 0.3 = 0.06 p ( malaysia and not china ) = 0.7 * 0.8 = 0.56 total probability = 0.06 + 0.56 = 0.62 = 62 % the answer is d ."
Answer: d
Question (other): if 80 percent of the test takers taking an old paper and pencil gmat exam answered the first question on a given math section correctly , and 75 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 ) 65 % , c ) 70 % , d ) 75 % , e ) 80 %
Rationale: "{ total } = { first correctly } + { second correctly } - { both correctly } + { neither correctly } 100 = 80 + 75 - { both correctly } + 5 { both correctly } = 60 . answer : a ."
Answer: a
Question (general): dacid obtained 70 , 63 , 80 , 63 and 65 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 67 , b ) 26 , c ) 87 , d ) 26 , e ) 68
Rationale: "average = ( 70 + 63 + 80 + 63 + 65 ) / 5 = 341 / 5 = 68.2 . answer : e"
Answer: e
Question (general): the jogging track in a sports complex is 1000 meters in circumference . deepak and his wife start from the same point and walk in opposite directions at 20 km / hr and 13 km / hr respectively . they will meet for the first time in ?
Options: a ) 50 min , b ) 33 min , c ) 35 min , d ) 25 min , e ) 20 min
Rationale: "clearly , the two will meet when they are 1000 m apart to be 20 + 13 = 33 km apart , they take 1 hour to be 1000 m apart , they take 33 * 1000 / 1000 = 33 min . answer is b"
Answer: b
Question (general): at a recent small town election for mayor a total of 979 votes were cast for the 4 candidates , the winner exceeding his opponents by 53 , 79 and 105 votes , respectively . how many votes were cast for the candidate in fourth place ?
Options: a ) 134 , b ) 178 , c ) 199 , d ) 166 , e ) 194
Rationale: the number of votes the winning candidate received was 979 + 53 + 79 + 105 / 4 = 304 . the second received 304 – 53 = 251 the fourth place received 304 – 105 = 199 . c
Answer: c
Question (physics): a train 100 meters long completely crosses a 300 meters long bridge in 30 seconds . what is the speed of the train is ?
Options: a ) 32 kmph , b ) 48 kmph , c ) 34 kmph , d ) 43 kmph , e ) 40 kmph
Rationale: "s = ( 100 + 300 ) / 30 = 400 / 30 * 18 / 5 = 48 answer : b"
Answer: b
Question (gain): a man buys a cycle for rs . 1600 and sells it at a loss of 10 % . what is the selling price of the cycle ?
Options: a ) 1410 , b ) 1420 , c ) 1430 , d ) 1440 , e ) 1540
Rationale: "s . p . = 90 % of rs . 1600 = 90 / 100 x 1600 = rs . 1440 answer : 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 7 m x 6 m x 22.5 cm ?
Options: a ) 6400 , b ) 6410 , c ) 5600 , d ) 6500 , e ) 6800
Rationale: "number of bricks = volume of wall / volume of bricks = 700 x 600 x 22.5 / 25 x 11.25 x 6 = = 5600 answer : c"
Answer: c
Question (physics): walking with 4 / 5 of my usual speed , i arrive at the bus stop 7 minutes later than normal . how many minutes does it take to walk to the bus stop at my usual speed ?
Options: a ) 12 , b ) 16 , c ) 20 , d ) 24 , e ) 28
Rationale: let t = usual time = distance / usual speed t + 7 = distance / ( 4 * usual speed / 5 ) = ( 5 * distance ) / ( 4 * usual speed ) = 5 t / 4 t = 28 the answer is e .
Answer: e
Question (physics): a train 360 m long is running at a speed of 36 km / hr . in what time will it pass a bridge 140 m long ?
Options: a ) 50 sec , b ) 29 sec , c ) 26 sec , d ) 27 sec , e ) 34 sec
Rationale: "speed = 36 * 5 / 18 = 10 m / sec total distance covered = 360 + 140 = 500 m required time = 500 * 1 / 10 = 50 sec answer : a"
Answer: a
Question (general): a primitive village follows a strange custom . they have babies only to have a boy . whenever a boy is born in a family , they stop having babies and whenever a girl is born , they have a baby again and again till a boy is born . the probability of having a boy is same as the probability of having a girl . what will be the proportion of boys to girls in the village after some time ?
Options: a ) 2.1 , b ) 1.3 , c ) 5.1 , d ) 2.3 , e ) 1.1
Rationale: e 1 : 1 ( approx ) explanation : we know that the probability of having a boy or having a girl is same and thus , half of the couples will stop after having a boy child . half of the others will have a girl and will have a baby again . out of those half of the couples , half will have a boy and will stop and half will have a girl again . this will keep on going like this . now , if there are x number of couples , there will be x boys . 1 / 2 have a boy and stop : 0 girls 1 / 4 have a girl , then a boy : x / 4 girls 1 / 8 have 2 girls , then a boy : 2 * x / 8 girls 1 / 16 have 3 girls , then a boy : 3 * x / 16 girls 1 / 32 have 4 girls , then a boy : 4 * x / 32 girls … total : x boys and 1 x 2 x 3 x 4 x – + – + – + — + … = ~ x therefore , the proportion of boys to girls will be extremely close to 1 : 1
Answer: e
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 . 19.36 , the number of the member is the group is :
Options: a ) 57 , b ) 67 , c ) 77 , d ) 87 , e ) 44
Rationale: "money collected = ( 19.36 x 100 ) paise = 1936 paise . number of members = square root of 1936 = 44 answer : option e"
Answer: e
Question (other): compound x contains elements a and b at an approximate ratio , by weight , of 2 : 10 . approximately how many grams of element b are there in 324 grams of compound x ?
Options: a ) 54 , b ) 162 , c ) 250 , d ) 270 , e ) 322
Rationale: "total number of fractions = 2 + 10 = 12 element b constitutes = 10 out of 12 parts of x so in 324 gms of x have 324 * 10 / 12 = 270 gms of b and 324 - 270 = 54 gms of a . cross check : - a / b = 54 / 270 = 2 / 10 ( as given ) ans d"
Answer: d
Question (general): a $ 77.95 lawn chair was sold for $ 59.95 at a special sale . by approximately what percent was the price decreased ?
Options: a ) 15 % , b ) 23 % , c ) 25 % , d ) 60 % , e ) 80 %
Rationale: "listed selling price of chair = 77.95 $ discounted selling price of chair = 59.95 $ discount = 77.95 - 59.95 = 18 $ % decrease in price of chair = ( 18 / 77.95 ) * 100 % = 23 % approx answer b"
Answer: b
Question (geometry): 50 square stone slabs of equal size were needed to cover a floor area of 98 sq . m . find the length of each stone slab ?
Options: a ) 140 cm , b ) 767 cm , c ) 88 cm , d ) 666 cm , e ) 776 cm
Rationale: "area of each slab = 98 / 50 m 2 = 1.96 m 2 length of each slab √ 1.96 = 1.4 m = 140 cm"
Answer: a
Question (general): in a division sum , the divisor is 10 times the quotient and 5 times the remainder . if the remainder is 46 , the divident is
Options: a ) 4236 , b ) 4306 , c ) 4336 , d ) 5336 , e ) none
Rationale: "solution divisor = ( 5 × 46 ) = 230 . also . 10 × q = 230 ‹ = › q = 23 . and , r = 46 . dividend = ( 230 × 23 + 46 ) = 5336 . answer d"
Answer: d
Question (physics): a and b complete a work in 8 days . a alone can do it in 12 days . if both together can do the work in how many days ?
Options: a ) 4.8 days , b ) 3.8 days , c ) 3.65 days , d ) 3.77 days , e ) 5.75 days
Rationale: "1 / 8 + 1 / 12 = 5 / 24 24 / 5 = 4.8 days answer : a"
Answer: a
Question (physics): gary ’ s gas station serves an average of 14 cars per hour on saturdays , 10 cars per hour on sundays , and 9 cars per hour on all other days of the week . if the station is open from 6 a . m . to 10 p . m . every day , how many cars does gary ’ s station serve over the course of a typical week ?
Options: a ) 1,104 , b ) 1,200 , c ) 1,240 , d ) 1,280 , e ) 1,320
Rationale: "6 a . m . to 10 p . m . = 16 hours number of cars serviced on weekdays = ( 16 * 9 * 5 ) number of cars serviced on saturday = ( 16 * 14 ) number of cars serviced on sunday = ( 16 * 10 ) number of cars served in a week = 16 ( 45 + 14 + 10 ) = 16 * 69 = 1104 answer : a"
Answer: a
Question (general): a teacher grades students ’ tests by subtracting twice the number of incorrect responses from the number of correct responses . if student a answers each of the 100 questions on her test and receives a score of 73 , how many questions did student a answer correctly ?
Options: a ) 55 , b ) 60 , c ) 73 , d ) 82 , e ) 91
Rationale: let the number of correct responses be x then the number of incorrect responses = 100 - x according to question x - 2 ( 100 - x ) = 73 ( subtracting twice of incorrect from correct ) 3 x = 273 x = 91 answer : e
Answer: e
Question (general): find the value of 3 / 11 × [ ( 1 + 1 / 3 ) ( 1 + 1 / 4 ) … … … … . ( 1 + 1 / 120 ) ] is
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: 3 / 11 × [ ( 1 + 1 / 3 ) ( 1 + 1 / 4 ) . . . . . . . ( 1 + 1 / 120 ) ] 3 / 11 × [ 4 / 3 + 5 / 4 × . . . . . . . . 121 / 120 ] 3 / 11 × 4 / 3 × 5 / 4 × . . . . 121 / 120 121 / 11 = 11 . a
Answer: a
Question (geometry): 10 meters of wire is available to fence off a flower bed in the form of a circular sector . what must the radius of the circle in meters be , if we wish to have a flower bed with the greatest possible surface area ?
Options: a ) 5 / 2 , b ) 2 √ 5 , c ) 5 , d ) 4 √ 2 , e ) none of these
Rationale: "area of sector , a = x / 360 * pi * r ^ 2 circumference of the sector = 10 = > x / 360 * 2 * pi * r + 2 r = 20 = > 2 a / r + 2 r = 10 or 2 a + 2 r ^ 2 = 10 r = > a = r 5 - r ^ 2 = r 5 - r ^ 2 we will now max using derivations i . e 5 - 2 r = 0 r = 5 / 2 a"
Answer: a
Question (general): what is the sum of all possible 3 - digit numbers that can be constructed using the digits 2 , 3 , and 4 if each digit can be used only once in each number ?
Options: a ) 1776 , b ) 1887 , c ) 1998 , d ) 2332 , e ) 2554
Rationale: "there are 6 possible arrangements of the three numbers . then each number will be in the hundreds , tens , and ones place two times each . the sum is 2 ( 222 ) + 2 ( 333 ) + 2 ( 444 ) = 1998 the answer is c ."
Answer: c
Question (gain): solution y is 30 percent liquid x and 70 percent water . if 2 kilograms of water evaporate from 8 kilograms of solution y and 2 kilograms of solution y are added to the remaining 6 kilograms of liquid , what percent of this new solution is liquid x ?
Options: a ) 30 % , b ) 33 1 / 3 % , c ) 37 1 / 2 % , d ) 40 % , e ) 50 %
Rationale: "initial solution = > 8 kg ( x : w : : 2.4 : 5.6 ) after evaporation initial solution = > 6 kg ( x : w : : 2.4 : 3.6 ) new solution = > 2 kg ( x : w : : 0.6 : 1.4 ) mixing ( initial solution + new solution ) = > 6 kg ( 2.4 : 3.6 ) + 2 kg ( 0.6 : 1.4 ) = = 8 kg [ ( 2.4 + 0.6 ) : ( 3.6 + 1.4 ) ] = 8 kg ( x : water : : 3 kg : 5 kg ) hence % of x = 3 / 8 = 37.5 % answer : c"
Answer: c
Question (gain): tickets to a certain concert sell for $ 20 each . the first 10 people to show up at the ticket booth received a 40 % discount , and the next 20 received a 15 % discount . if 48 people bought tickets to the concert , what was the total revenue from ticket sales ?
Options: a ) $ 600 , b ) $ 820 , c ) $ 850 , d ) $ 980 , e ) $ 1,140
Rationale: "price of 1 ticket = 20 $ revenue generated from sales of first 10 tickets = 10 * ( 60 / 100 * 20 ) = 10 * 12 = 120 revenue generated from sales of next 20 tickets = 20 * ( 85 / 100 * 20 ) = 20 * 17 = 340 revenue generated from sales of last 18 tickets = 20 * 18 = 360 revenue generated from sales of 48 tickets = 120 + 340 + 360 = 820 $ answer b"
Answer: b
Question (general): a , b and c are partners . a receives 2 / 3 of profits , b and c dividing the remainder equally . a ' s income is increased by rs . 200 when the rate to profit rises from 5 to 7 percent . find the capital of b ?
Options: a ) 2888 , b ) 2669 , c ) 2500 , d ) 2762 , e ) 8227
Rationale: "a : b : c = 2 / 3 : 1 / 6 : 1 / 6 = 4 : 1 : 1 x * 2 / 100 * 2 / 3 = 200 b capital = 15000 * 1 / 6 = 2500 answer : c"
Answer: c
Question (geometry): if paint costs $ 3.20 per quart , and a quart covers 60 square feet , how much will it cost to paint the outside of a cube 10 feet on each edge ?
Options: a ) $ 1.60 , b ) $ 32.00 , c ) $ 96.00 , d ) $ 108.00 , e ) $ 196.00
Rationale: "total surface area = 6 a ^ 2 = 6 * 10 * 10 = 600 each quart covers 20 sqr ft thus total number of quarts = 600 / 60 = 10 cost will be 10 * 3.2 = $ 32 ans : b"
Answer: b
Question (general): how many even number in the range between 10 to 160 inclusive are not divisible by 3
Options: a ) 15 , b ) 30 , c ) 51 , d ) 63 , e ) 76
Rationale: "we have to find the number of terms that are divisible by 2 but not by 6 ( as the question asks for the even numbers only which are not divisible by 3 ) for 2 , 10 , 12,14 . . . 160 using ap formula , we can say 160 = 10 + ( n - 1 ) * 2 or n = 76 . for 6 , 12,18 , . . . 156 using ap formula , we can say 156 = 12 + ( n - 1 ) * 6 or n = 25 . hence , only divisible by 2 but not 3 = 76 - 25 = 51 . hence , answer c"
Answer: c
Question (physics): the delhi express runs @ 144 kilometers per hours and it reaches destination 20 minute ahead of schedule . if it averages 100 km / hour , it reaches 24 minute behind schedule . what is the average speed it should maintain in order to reach the destination on schedule ?
Options: a ) 250 , b ) 240 , c ) 230 , d ) 245 , e ) 235
Rationale: if the destination is d kilometer and the speed in order to reach on schedule is s km / hour , the time taken to reach on schedule is d / s hours thus we get two equations : d / 144 = d / s - 1 / 3 and d / 100 = d / s + 2 / 5 and subtracting the first equation from the second we get : 44 d / 14400 = 11 / 15 thus d = 14400 x 11 / 44 x 15 = 240 answer : b
Answer: b
Question (gain): at a florist shop on a certain day , all corsages sold for either $ 40 or $ 45 . if 8 of the corsages that sold for $ 30 had instead sold for $ 20 , then the store ' s revenue from corsages that day would have been reduced by 20 percent . what was the store ' s actual revenue from corsages that day ?
Options: a ) $ 200 , b ) $ 400 , c ) $ 600 , d ) $ 800 , e ) $ 1000
Rationale: "i am doing it elaborately , hope it will help you . let , no . of corsages @ $ 40 = x , no . of corsages @ $ 45 = y and revenue = r so , 40 x + 45 y = r . . . . . . . . . ( 1 ) now , given the situation , 40 ( x + 8 ) + 45 ( y - 8 ) = r - . 2 r = > 40 x + 320 + 45 y - 360 = . 8 r = > 40 x + 45 y = . 8 r + 40 . . . . . . . . . . . . ( 2 ) so , r = . 8 r + 40 = > r = 200 the answer is a ."
Answer: a
Question (gain): when a laptop is sold for rs . 27000 , the owner loses 10 % . at what price must that laptop be sold in order to gain 10 % ?
Options: a ) 33,000 , b ) 34,000 , c ) 35,000 , d ) 36,000 , e ) 37,000
Rationale: "90 : 27000 = 110 : x x = ( 27000 x 110 ) / 90 = 33000 . hence , s . p . = rs . 33,000 . answer : option a"
Answer: a
Question (geometry): if the radius of a circle is increased by 50 % then the area is increased by :
Options: a ) 44 % , b ) 125 % , c ) 144 % , d ) 40 % , e ) none of the above
Rationale: "initially a = pi * r 2 now r 2 = 150 / 100 r then area = pi * ( 150 r / 100 ) 2 area = 225 r / 100 that is area increases from 100 to 225 = increase in area = 125 % answer : b"
Answer: b
Question (gain): a certain company reported that the revenue on sales increased 40 % from 2000 to 2003 , and increased 60 % from 2000 to 2005 . what was the approximate percent increase in revenue for this store from 2003 to 2005 ?
Options: a ) 50 % , b ) 40 % , c ) 14 % , d ) 32 % , e ) 29 %
Rationale: "assume the revenue in 2000 to be 100 . then in 2003 it would be 140 and and in 2005 160 , so from 2003 to 2005 it increased by ( 160 - 140 ) / 140 = 20 / 140 = 1 / 7 = ~ 14 % . answer : c"
Answer: c
Question (gain): the difference between the compound interest compounded annually and simple interest for 2 years at 20 % per annum is rs . 144 . find the principal ?
Options: a ) 3629 , b ) 3608 , c ) 3600 , d ) 3613 , e ) 6192
Rationale: "p = 144 ( 100 / 5 ) 2 = > p = 3600 answer : c"
Answer: c
Question (general): if xy > 0 , 1 / x + 1 / y = 6 , and 1 / xy = 5 , then ( x + y ) / 6 = ?
Options: a ) 1 / 25 , b ) 1 / 6 , c ) 1 / 5 , d ) 5 , e ) 6
Rationale: "( 1 / x + 1 / y ) = 6 canbe solved as { ( x + y ) / xy } = 5 . substituting for 1 / xy = 5 , we get x + y = 6 / 5 = = > ( x + y ) / 6 = 6 / ( 5 * 6 ) = 1 / 5 . c"
Answer: c
Question (physics): a train 100 meters long completely crosses a 300 meters long bridge in 12 seconds . what is the speed of the train is ?
Options: a ) 32 kmph , b ) 76 kmph , c ) 120 kmph , d ) 43 kmph , e ) 40 kmph
Rationale: "s = ( 100 + 300 ) / 12 = 400 / 12 * 18 / 5 = 120 answer : c"
Answer: c
Question (gain): a reduction of 30 % in the price of salt enables a lady to obtain 10 kgs more for rs . 200 , find the original price per kg ?
Options: a ) 7.5 , b ) 8.99 , c ) 8.0 , d ) 9.2 , e ) 8.57
Rationale: "answer : 200 * ( 30 / 100 ) = 60 - - - 10 ? - - - 1 = > rs . 6 200 - - - 140 ? - - - 6 = > rs . 8.57 . answer : e"
Answer: e
Question (general): if a is a positive integer and 10 ^ a – 74 in decimal notation has digits whose sum is 440 , what is the value of a ?
Options: a ) 40 , b ) 44 , c ) 45 , d ) 46 , e ) 50
Rationale: answer e = 50 we have ( 10 ^ a ) - 74 , where the sum of the digits is 440 . 100 - 74 = 26 , so we already have 2 + 6 = 8 from the 440 . because we have a power of 10 , we will have numbers like 100 , 1000 , 10000 and so on . this minus 74 rests 26 and a lot of 9 s . e . g : 1000 - 74 = 9926 . so dividing the 432 / 9 = 48 , that ` s the number of 9 s . and we have 2 other numbers ( 2 and 6 ) wich were 00 before the subtraction . so we have 48 + 2 as an a = 50
Answer: e
Question (general): if x = 7 and y = − 2 , what is the value of ( x − 2 y ) ^ y ?
Options: a ) − 100 , b ) 0.001 , c ) 0.25 , d ) 4 , e ) 8
Rationale: quickly we can spot that answer is neither integer nor negative . eliminate a , de by inversing and squaring 0.001 answer : b
Answer: b
Question (gain): a distributor sells a product through an on - line store , which take a commission of 20 % of the price set by the distributor . the distributor obtains the product from a producer at the price of $ 15 per item . what is the price that the buyer observers on - line if the distributor wants to maintain a 10 % profit on the cost of the item ?
Options: a ) 18 , b ) 21.6 , c ) 20 , d ) 22.5 , e ) 27
Rationale: producer price = $ 15 ; the distributor wants to maintain a 20 % profit on the cost of the item , thus he must get $ 15 * 1.2 = $ 18 after the store takes a commission of 10 % of the final price - - > ( final price ) * 0.9 = $ 18 - - > ( final price ) = $ 20 . answer : c .
Answer: c
Question (general): if integer k is equal to the sum of all even multiples of 5 between 300 and 610 , what is the greatest prime factor of k ?
Options: a ) 32 , b ) 7 , c ) 11 , d ) 13 , e ) 17
Rationale: "if we break down what the stem is asking what is the sum of all mult of 10 between 300 and 610 . using arithmetic progression to find n : 610 = 300 + ( n - 1 ) 10 310 + 10 = 10 n 320 = 10 n = > n = 32 the sum would be : 32 * mean mean = [ 610 + 300 ] / 2 = 455 32 * 455 a"
Answer: a