Cheukting/mathqa huggingface dataset:
Question (geometry): for any even integer p , 300 multiplied by p is square of an integer . what is the least value of p ?
Options: a ) 3 , b ) 4 , c ) 10 , d ) 12 , e ) 14
Rationale: p ∗ 3 ∗ 10 ^ 2 = s ^ 2 so , s = √ p ∗ 3 ∗ 10 ^ 2 so , if p = 3 we get a perfect square number ! ! hence answer will be ( a ) 3
Answer: a
Question (gain): if the selling price of 50 articles is equal to the cost price of 45 articles , then the loss or gain percent is :
Options: a ) 45 % , b ) 10 % , c ) 20 % , d ) 60 % , e ) 56 %
Rationale: "c . p . of each article be re . 1 . then , c . p . of 50 articles = rs . 50 ; s . p . of 50 articles = rs . 45 . loss % = 5 / 50 * 100 = 10 % answer b"
Answer: b
Question (general): the average marks of a class of 20 students is 40 and that of another class of 50 students is 60 . find the average marks of all the students ?
Options: a ) 44.28 , b ) 54.28 , c ) 34.28 , d ) 64.28 , e ) 74.28
Rationale: "sum of the marks for the class of 20 students = 20 * 40 = 800 sum of the marks for the class of 50 students = 50 * 60 = 3000 sum of the marks for the class of 70 students = 800 + 3000 = 3800 average marks of all the students = 3800 / 70 = 54.28 answer : b"
Answer: b
Question (geometry): in a certain circle there are 9 points . what is the number of the triangles connecting 3 points of the 9 points ?
Options: a ) 12 , b ) 84 , c ) 108 , d ) 120 , e ) 132
Rationale: "imo : b here we have to select 3 points out of 9 points . order is not important so the answer will be 9 c 3 = 84 answer b"
Answer: b
Question (general): in shop there are 10 bulbs , a total of 4 are defective . if a customer buys 4 bulbs selected at random from the box , what is the probability that neither bulbs will be defective ?
Options: a ) 2 / 19 , b ) 3 / 29 , c ) 4 / 15 , d ) 1 / 15 , e ) 1 / 2
Rationale: first , there are 6 c 4 ways you can select 6 good bulbs from 4 good ones . second , there are 10 c 4 ways you select 4 bulbs from 10 ones in the box . then , the probability that neither bulb will be defective is : 6 c 4 / 10 c 4 = 15 / 210 = 1 / 15 answer is d
Answer: d
Question (general): if x + | x | + y = 2 and x + | y | - y = 6 what is x + y = ?
Options: a ) 1 , b ) - 1 , c ) 3 , d ) 5 , e ) 13
Rationale: "if x < 0 and y < 0 , then we ' ll have x - x + y = 7 and x - y - y = 6 . from the first equation y = 7 , so we can discard this case since y is not less than 0 . if x > = 0 and y < 0 , then we ' ll have x + x + y = 7 and x - y - y = 6 . solving gives x = 4 > 0 and y = - 1 < 0 - - > x + y = 3 . since in ps questions only one answer choice can be correct , then the answer is c ( so , we can stop here and not even consider other two cases ) . answer : c . adding both eqn we get 2 x + ixi + iyi = 13 now considering x < 0 and y > 0 2 x - x + y = 13 we get x + y = 1 hence answer should be a"
Answer: a
Question (general): employees of a certain company are each to receive a unique 5 - digit identification code consisting of the digits 0 , 1 , 2 , 3 , and 4 such that no digit is used more than once in any given code . in valid codes , the second digit in the code is exactly twice the first digit . how many valid codes are there ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: there are 3 ! ways to make codes starting with 12 . there are 3 ! ways to make codes starting with 24 . the number of codes is 2 * 3 ! = 12 . the answer is b .
Answer: b
Question (physics): 36 men can complete a piece of work in 18 days . in how many days will 72 men complete the same work ?
Options: a ) 24 , b ) 17 , c ) 18 , d ) 9 , e ) 11
Rationale: "explanation : less men , means more days { indirect proportion } let the number of days be x then , 72 : 36 : : 18 : x x = 9 answer : d ) 9 days"
Answer: d
Question (general): in a room filled with 7 people , 4 people have exactly 1 sibling in the room and 3 people have exactly 3 siblings in the room . if two individuals are selected from the room at random , what is the probability that those two individuals are not siblings ?
Options: a ) 5 / 21 , b ) 3 / 7 , c ) 4 / 7 , d ) 5 / 7 , e ) 32 / 35
Rationale: "there are suppose a b c d e f g members in the room 4 people who have exactly one sibling . . . . a b c d . . . . ( a is bs ∘ sssibl ∈ g ∘ ssand ∘ ssviceversa ) ∘ ss ( c ∘ ssis ∘ ssds ∘ sssibl ∈ g ∘ ssand ∘ ssviceversa ) ∘ ss ( c ∘ ssis ∘ ssdssibl ∈ gandviceversa ) ( cisds sibling and viceversa ) ( c is ds sibling and viceversa ) . . . now remaning efg are 3 people who have exactly 3 siblings . . . . ( e has f and g as his / her sibling and so on . . ) there are now 3 different set of siblings ( a and b ) ( c and d ) ; ( efg ) now first selecting 3 people out of 7 is 7 c 3 = 35 first sibling pair - - - - ( a and b ) - - selecting 3 people - - 3 c 3 = 1 second sibling pair ( c and d ) - - selecting 3 people - - 3 c 3 = 1 third sibling pair ( e f g ) - - selecting 3 out of 3 - - 3 c 3 = 1 total = 1 + 1 + 1 = 3 but , a / c to formula p ( success ) - 1 - p ( fail ) here , p ( failure ) is selecting 3 people who are siblings = 3 / 35 ( 35 is 7 c 3 ) = 1 - 3 / 35 = 32 / 35 ans e"
Answer: e
Question (general): if p is the product of the integers from 1 to 34 , inclusive , what is the greatest integer k for which 3 ^ k is a factor of p ?
Options: a ) 11 , b ) 13 , c ) 15 , d ) 17 , e ) 19
Rationale: 34 ! has 3 , 6 , 9 , . . . . 30 , 33 as factors , which are 11 multiples of 3 . we need to add 4 more to these 11 because of 9 , 18 , and 27 . the greatest integer of k is 15 . the answer is c .
Answer: c
Question (gain): a present value of a machine is $ 2500 . its value depletiation rate is 5 % per annum then find the machine value after 2 years ?
Options: a ) $ 2100 , b ) $ 2546 , c ) $ 2256 , d ) $ 2451 , e ) $ 2345
Rationale: "p = $ 2500 r = 5 % t = 2 years machine value after 2 years = p [ ( 1 - r / 100 ) ^ t ] = 2500 * 19 / 20 * 19 / 20 = $ 2256 approximately answer is c"
Answer: c
Question (general): the sum of the squares of the first 15 positive integers ( 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + . . . + 15 ^ 2 ) is equal to 1280 . 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 ) 8255 , 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 1280 , we get the answer of 8255 . ( ans d )"
Answer: d
Question (physics): the diameter of the wheel of a car is 120 m . how many revolution / min must the wheel makein order to keep a speed of 60 km / hour approximately ?
Options: a ) 210 , b ) 245 , c ) 230 , d ) 254 , e ) 265
Rationale: distance to be covered in 1 min . = ( 60 x 1000 ) / ( 60 ) m = 1000 m . circumference of the wheel = ( 2 x ( 22 / 7 ) x 0.60 ) m = 3.77 m . number of revolutions per min . = ( 1000 / 3.77 ) = 265 e
Answer: e
Question (gain): each light bulb at a hotel is either incandescent or fluorescent . at a certain moment , thirty percent of the incandescent bulbs are switched on , and eighty percent of the fluorescent bulbs are switched on . if 70 percent of all the bulbs are switched on at this moment , what percent of the bulbs that are switched on are incandescent ?
Options: a ) 4.5 % , b ) 8.6 % , c ) 12.3 % , d ) 16.7 % , e ) 20 %
Rationale: let i be the number of incandescent bulbs . let f be the number of fluorescent bulbs . 0.3 i + 0.8 f = 0.7 ( i + f ) 0.1 f = 0.4 i f = 4 i this means that for every 1 incandescent bulb , there are 4 fluorescent bulbs . the percent of bulbs that are switched on which are incandescent is : 0.3 i / ( 0.3 i + 0.8 f ) = 0.3 i / ( 0.3 i + 0.8 * 4 i ) = 0.3 i / 3.5 i = 3 / 35 which is about 8.6 % . the answer is b .
Answer: b
Question (gain): a chemist mixes one liter of pure water with x liters of a 40 % salt solution , and the resulting mixture is a 20 % salt solution . what is the value of x ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 1 , e ) 3
Rationale: "concentration of salt in pure solution = 0 concentration of salt in salt solution = 40 % concentration of salt in the mixed solution = 20 % the pure solution and the salt solution is mixed in the ratio of - - > ( 40 - 20 ) / ( 20 - 0 ) = 1 / 1 1 / x = 1 / 1 x = 1 answer : d"
Answer: d
Question (general): the average age of students of a class is 15.8 years . the average age of boys in the class is 16.4 years and that of the girls is 15.5 years . the ration of the number of boys to the number of girls in the class is ?
Options: a ) 2 : 6 , b ) 2 : 3 , c ) 2 : 5 , d ) 2 : 1 , e ) 1 : 2
Rationale: "let the ratio be k : 1 . then , k * 16.4 + 1 * 15.5 = ( k + 1 ) * 15.8 = ( 16.4 - 15.8 ) k = ( 15.8 - 15.5 ) = k = 0.3 / 0.6 = 1 / 2 required ratio = 1 / 2 : 1 = 1 : 2 . answer : e"
Answer: e
Question (geometry): consider a right circular cone of base radius 4 and height 10 cm . a cylinder is to be placed inside the cone with one of the flat surface resting on the base of the cone . find the largest possible total surface area ( in sq cm ) of the cylinder .
Options: a ) 100 π / 3
b ) 80 π / 3
c ) 120 π / 7
d ) 130 π / 9
e ) 110 π / 7
Rationale: explanation : let the radius of cylinder be r and its height is h . so , the height remained above cylinder is 10 - h also , triangles abc and ade are similar . so ratio of corresponding sides must be equal i . e ab / ad = bc / de . i . e . ( 10 - h ) / 10 = r / 4 . so 40 - 4 h = 10 r ( by cross multiply ) h = ( 40 - 10 r ) / 4 = 10 - 2.5 r now we have total surface area of cyl = 2 * π * r * h + 2 * π * r 2 . putting value of h = 10 - 2.5 r here , we get s = 2 * π * r * ( 10 - 2.5 r ) + 2 * π * r 2 . s = 20 * π * r - 5 * π * r 2 + 2 * π * r 2 . s = 20 * π * r - 3 * π * r . now , we have to maximize s , so differentiate it w . r . t r , we get s = 20 * π - 6 * π * r setting it to zero , we get = > 20 * π - 6 * π * r = 0 = > r = 20 / 6 = 10 / 3 . so , h = 10 - 2.5 r = 10 - 2.5 * 10 / 3 = 5 / 3 so , = > s = 2 * π * r * h + 2 * π * r 2 . = > s = 2 * π * 10 / 3 * 5 / 3 + 2 * π * 100 / 9 . = > s = 2 * π * 50 / 9 + 2 * π * 100 / 9 . = > s = 2 π 150 / 9 . = > s = 100 π / 3 . answer : a
Answer: a
Question (geometry): a football field is 10800 square yards . if 1200 pounds of fertilizer are spread evenly across the entire field , how many pounds of fertilizer were spread over an area of the field totaling 3600 square yards ?
Options: a ) 400 , b ) 600 , c ) 750 , d ) 2400 , e ) 3200
Rationale: "answer a ) 10800 yards need 1200 lbs 1 yard will need 1200 / 10800 = 1 / 9 lbs 3600 yards will need 1 / 9 * 3600 yards = 400 lbs"
Answer: a
Question (general): two same glasses are respectively 1 / 4 th 1 / 5 th full of milk . they are then filled with water and the contents mixed in a tumbler . the ratio of milk and water in the tumbler is ?
Options: a ) 9 : 39 , b ) 9 : 31 , c ) 9 : 36 , d ) 9 : 32 , e ) 9 : 34
Rationale: 1 / 4 : 3 / 4 = ( 1 : 3 ) 5 = 5 : 15 1 / 5 : 4 / 5 = ( 1 : 4 ) 4 = 4 : 16 - - - - - - 9 : 31 answer : b
Answer: b
Question (geometry): the area of a rectangle is 15 square centimeters and the perimeter is 16 square centimeters . what are the dimensions of the rectangle ?
Options: a ) 3 and 5
b ) 3 and 6
c ) 3 and 7
d ) 3 and 8
e ) 3 and 9
Rationale: let x and y be the length and width of the rectangle . using the formulas for the area and the perimeter , we can write two equations . 15 = x y and 16 = 2 x + 2 y solve the second equation for x x = 8 - y substitute x in the equation 15 = x y by 8 - y to rewrite the equation as 15 = ( 8 - y ) y solve for y to find y = 3 and y = 5 use x = 8 - y to find x when y = 3 , x = 5 and when y = 5 , x = 3 . the dimensions of the rectangle are 3 and 5 . as an exercise , check that the perimeter of this rectangle is 16 and its area is 15 . answer a
Answer: a
Question (gain): sales price is $ 91 , gross profit is 160 % of cost , what is the value of gross profit ?
Options: a ) 32 , b ) 33 , c ) 39 , d ) 40 , e ) 56
Rationale: "cost + profit = sales cost + ( 160 / 100 ) cost = 91 cost = 35 profit = 91 - 35 = 56 answer ( e )"
Answer: e
Question (general): a number exceeds by 25 from its 3 / 8 part . then the number is ?
Options: a ) 38 , b ) 29 , c ) 27 , d ) 40 , e ) 91
Rationale: "explanation : x â € “ 3 / 8 x = 25 x = 40 answer : d"
Answer: d
Question (general): in an it company , there are a total of 70 employees including 50 programmers . the number of male employees is 80 , including 35 male programmers . how many employees must be selected to guaranty that we have 3 programmers of the same sex ?
Options: a ) 10 , b ) 25 , c ) 55 , d ) 35 , e ) 65
Rationale: you could pick 70 non - programmers , 2 male programmers , and 2 female programmers , and still not have 3 programmers of the same sex . but if you pick one more person , you must either pick a male or a female programmer , so the answer is 25 . b
Answer: b
Question (gain): in the first 10 overs of a cricket game , the run rate was only 3.2 . what should be the rate in the remaining 40 overs to reach the target of 272 runs ?
Options: a ) 6.25 , b ) 6.22 , c ) 6.29 , d ) 6.39 , e ) 6.0
Rationale: "required run rate = [ 272 - ( 3.2 * 10 ) ] / 40 = 240 / 40 = 6.00 answer : e"
Answer: e
Question (general): a certain basketball team that has played 2 / 3 of its games has a record of 16 wins and 4 losses . what is the greatest number of the remaining games that the team can lose and still win at least 3 / 4 of all of its games ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "16 wins , 4 losses - total 20 games played . the team has played 2 / 3 rd of all games so total number of games = 30 3 / 4 th of 30 is 22.5 so the team must win 23 games and can afford to lose at most 7 total games . it has already lost 4 games so it can lose another 3 at most . answer ( e )"
Answer: e
Question (physics): sari and ken climb up a mountain . at night , they camp together . on the day they are supposed to reach the summit , sari wakes up at 06 : 00 and starts climbing at a constant pace . ken starts climbing only at 08 : 00 , when sari is already 800 meters ahead of him . nevertheless , ken climbs at a constant pace of 500 meters per hour , and reaches the summit before sari . if sari is 50 meters behind ken when he reaches the summit , at what time did ken reach the summit ?
Options: a ) 16.3 , b ) 13 : 30 , c ) 14 : 00 , d ) 15 : 00 , e ) 15 : 30
Rationale: both sari and ken climb in the same direction . speed of sari = 800 / 2 = 400 meters / hr ( since she covers 800 meters in 2 hrs ) speed of ken = 500 meters / hr at 8 : 00 , distance between ken and sari is 800 meters . ken needs to cover this and another 50 meters . time he will take = total distance to be covered / relative speed = ( 800 + 50 ) / ( 500 - 400 ) = 8.5 hrs starting from 8 : 00 , in 8.5 hrs , the time will be 16 : 30 answer ( a )
Answer: a
Question (gain): boy sells a book for rs . 800 he gets a loss of 20 % , to gain 10 % , what should be the sp ?
Options: a ) 1100 , b ) 450 , c ) 550 , d ) 590 , e ) 600
Rationale: cost price = 800 / 80 x 100 = 1000 to gain 10 % = 1000 x 10 / 100 = 100 sp = cp + gain = 1000 + 100 = 1100 answer : a
Answer: a
Question (general): the age of somu is one - third his father ' s . 9 years back he was one - fifth of his father ' s age . what is his persent age ?
Options: a ) 11 , b ) 18 , c ) 14 , d ) 12 , e ) 10
Rationale: explanation : let somu ' s age be x and that of his father be 3 x . so , x - 9 = 3 x - 9 / 5 = x = 18 answer : option b
Answer: b
Question (general): at a certain committee meeting only associate professors and assistant professors are present . each associate professor has brought 2 pencils and 1 chart to the meeting , while each assistant professor has brought 1 pencil and 2 charts . if a total of 11 pencils and 16 charts have been brought to the meeting , how many people are present ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "say there are ' a ' associate professors . so we have 2 a pencils and a charts . say there are ' b ' assistant professors . so we have b pencils and 2 b charts . total pencils are 10 so 2 a + b = 11 total charts are 11 so a + 2 b = 16 add both : 3 a + 3 b = 27 so a + b = 9 total number of people = 9 d"
Answer: d
Question (other): a garrison of 400 men had a provision for 31 days . after 20 days 180 persons re - enforcement leave the garrison . find the number of days for which the remaining ration will be sufficient ?
Options: a ) 65 days , b ) 45 days , c ) 20 days , d ) 16 days , e ) 18 days
Rationale: "400 - - - 31 400 - - - 11 220 - - - ? 400 * 11 = 220 * x = > x = 20 days . answer : c"
Answer: c
Question (physics): a goods train leaves a station at a certain time and at a fixed speed . after ^ hours , an express train leaves the same station and moves in the same direction at a uniform speed of 90 kmph . this train catches up the goods train in 4 hours . find the speed of the goods train .
Options: a ) 15 kmph , b ) 36 kmph , c ) 21 kmph , d ) 17 kmph , e ) 19 kmph
Rationale: let the speed of the goods train be x kmph . distance covered by goods train in 10 hours = distance covered by express train in 4 hours 10 x = 4 x 90 or x = 36 . so , speed of goods train = 36 kmph . ans : b
Answer: b
Question (physics): ram and shakil run a race of 2000 meters . first , ram gives shakil a start of 200 meters and beats him by one minute . if , ram gives shakil a start of 6 minutes ram is beaten by 1000 meters . find the time in minutes in which ram and shakil can run the races separately .
Options: a ) 7,10 , b ) 8,10 , c ) 9,10 , d ) 10,10 , e ) 10,12
Rationale: let x and y are the speeds of ram and shakil . . then by problem we got following equation 2000 / x = ( 1800 / y ) - 1 1000 / x = ( 2000 / y ) - 6 solve equation 1 and 2 , we get x = 250 and y = 200 therefore , time taken by ram and shakilk to complete a race of 2000 m is 8 min and 10 min answer : b
Answer: b
Question (physics): rahul can do a work in 3 days while rajesh can do the same work in 2 days . both of them finish the work together and get $ 355 . what is the share of rahul ?
Options: a ) $ 50 , b ) $ 142 , c ) $ 60 , d ) $ 100 , e ) $ 90
Rationale: "rahul ' s wages : rajesh ' s wages = 1 / 3 : 1 / 2 = 2 : 3 rahul ' s share = 355 * 2 / 5 = $ 142 answer is b"
Answer: b
Question (other): a certain fruit stand sold apples for $ 0.70 each and cherry for $ 0.50 each . if a customer purchased both apples and bananas from the stand for a total of $ 6.30 , what total number of apples and bananas did the customer purchase ?
Options: a ) 12 , b ) 11 , c ) 13 , d ) 14 , e ) 15
Rationale: some multiple of 7 + some multiple of 5 should yield 63 . to get to a some multiple of 5 , we should ensure that a 3 or 8 ( 5 + 3 ) should be a multiple of 7 . 63 is a direct multiple of 7 , however in this case there wo n ' t be any cherry . hence the next option is to look for a multiple of 7 that has 8 as the unit digit . 28 satisfies this hence no . of apples is 4 and no of bananas is 7 b
Answer: b
Question (general): the element being searched for is not found in an array of 100 elements . what is the average number of comparisons needed in a sequential search to determine that the element is not there , if the elements are completely unordered ?
Options: a ) 25 , b ) 50 , c ) 75 , d ) 100 , e ) 125
Rationale: let us assume k be the element we need to search then let array be n 1 , n 2 , n 3 . . . . . . . . . . . . . . n 100 now to prove that the element searched is not there in the array we have to compare the element k with every element in the array . so , totally we need 100 comparisons . answer : d
Answer: d
Question (gain): what is 15 % of 2 / 3 of 0.7 ?
Options: a ) 0.07 , b ) 0.9 , c ) 9 , d ) 90 , e ) none of the above
Rationale: "the best way to solve these questions is to convert every term into fraction ( 15 / 100 ) * ( 2 / 3 ) * ( 7 / 10 ) = 210 / 3000 = 0.07 option a"
Answer: a
Question (general): what is the greatest integer m for which the number 50 ! / 14 ^ m is an integer ?
Options: a ) 11 , b ) 10 , c ) 9 , d ) 8 , e ) 7
Rationale: "14 ^ m = 2 ^ m * 7 ^ m . let ' s figure out how many 7 ' s are in the prime factorization of 50 ! the multiples of 7 are : 7 , 14 , 21 , 28 , 35 , 42 , 7 * 7 . thus 7 ^ 8 will divide 50 ! but 7 ^ 9 will not . clearly 2 ^ 8 will divide 50 ! so m = 8 is the largest possible integer . the answer is d ."
Answer: d
Question (physics): two printing presses begin printing currency at the same time and at constant speeds . press f produces 5 - dollar bills at the rate of 1,000 bills per minute . press t produces 20 - dollar bills at the rate of 200 bills per minute . once the machines have begun printing , how many seconds does it take for press f to produce 50 dollars more currency than press t ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: press f produces $ 5 bills @ 1000 per minute ( 60 sec ) so $ 500 in 6 secs press t produces $ 20 bills 200 per minute ( 60 sec ) so $ 400 in 6 secs . . so we can see f produces $ 100 in 6 secs or will print $ 50 in 3 secs . . ans 3 secs . . b
Answer: b
Question (gain): last year sandy saved 6 % of her annual salary . this year , she made 10 % more money than last year , and she saved 9 % of her salary . the amount saved this year was what percent of the amount she saved last year ?
Options: a ) 140 % , b ) 152 % , c ) 165 % , d ) 176 % , e ) 190 %
Rationale: let last year ' s salary be x . last year , sandy save 0.06 x this year , sandy saved 0.09 * 1.1 x = 0.099 x 0.099 x / 0.06 x = 99 / 60 = 1.65 = 165 % the answer is c .
Answer: c
Question (physics): rahul can do a work in 3 days while rajesh can do the same work in 2 days . both of them finish the work together and get $ 170 . what is the share of rahul ?
Options: a ) $ 68 , b ) $ 40 , c ) $ 60 , d ) $ 100 , e ) $ 90
Rationale: "rahul ' s wages : rajesh ' s wages = 1 / 3 : 1 / 2 = 2 : 3 rahul ' s share = 170 * 2 / 5 = $ 68 answer is a"
Answer: a
Question (general): the ratio between sumit ' s and prakash ' s age at present is 2 : 3 . sumit is 6 years younger than prakash . the ratio of sumit ' s age to prakash ' s age after 6 years will be :
Options: a ) 1 : 2 , b ) 2 : 3 , c ) 3 : 4 , d ) 3 : 8 , e ) none
Rationale: explanation : let their ages be 2 x and 3 x years . 3 x - 2 x = 6 or x = 6 sumit ' s age = 12 years , prakash ' s age = 24 years ratio of their ages = 18 : 24 = 3 : 4 . correct option : c
Answer: c