regisss/math_qa huggingface dataset:
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: if a person walks at 12 km / hr instead of 10 km / hr , he would have walked 20 km more . the actual distance traveled by him is :
Options: a ) 50 km , b ) 100 km , c ) 60 km , d ) 70 km , e ) 80 km
Rationale: "let the actual distance travelled be x km . x / 10 = ( x + 20 ) / 12 12 x = 10 x + 200 2 x = 200 x = 100 km . answer : b"
Answer: b
Problem: cara leaves her home and walks toward don ' s house . two hours later , don leaves his home and walks toward cara ' s house . the distance between their homes is 45 kilometers , cara ' s walking speed is 6 km / h , and don ' s walking speed is 5 km / h . how many kilometers will cara walk before she meets don ?
Options: a ) 26 , b ) 27 , c ) 28 , d ) 29 , e ) 30
Rationale: cara walks 12 km in the first two hours so there are 33 km remaining . when don starts walking , they complete a total of 11 km per hour . they will meet three hours after don starts walking . since cara walks for 5 hours , she walks 30 km . the answer is e .
Answer: e
Problem: in a garden , there are yellow and green flowers which are straight and curved . if the probability of picking a green flower is 3 / 4 and picking a straight flower is 1 / 2 , then what is the probability of picking a flower which is yellow and curved
Options: a ) 1 / 8 , b ) 1 / 6 , c ) 1 / 4 , d ) 3 / 4 , e ) 7 / 8
Rationale: good question . so we have a garden where all the flowers have two properties : color ( green or yellow ) and shape ( straight or curved ) . we ' re told that 3 / 4 of the garden is green , so , since all the flowers must be either green or yellow , we know that 1 / 4 are yellow . we ' re also told there is an equal probability of straight or curved , 1 / 2 . we want to find out the probability of something being yellow and straight , pr ( yellow and straight ) . so if we recall , the probability of two unique events occurring simultaneously is the product of the two probabilities , pr ( a and b ) = p ( a ) * p ( b ) . so we multiply the two probabilities , pr ( yellow ) * pr ( curved ) = 1 / 4 * 1 / 2 = 1 / 8 , or a .
Answer: a
Problem: if n is a positive integer , what is the remainder when ( 7 ^ ( 3 n + 3 ) ) ( 6 ^ n ) is divided by 10 ?
Options: a ) 1 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "this one took me bout 3 1 / 2 min . just testin numbers and what not . first notice that n is positive . save time by noticing thati worked out one solution where n = 0 only to find that thats not an option : p . 1 - 7 stands for ^ 1 thru 7 1 : 7 * 1 = 7 2 : 7 * 7 = 9 3 : 7 * 9 = 3 4 : 7 * 3 = 1 5 : 7 * 1 = 7 6 : 7 * 7 = 9 7 : 7 * 9 = 3 pattern repeats every @ 5 . notice every ^ 4 or multiple of 4 is always going to be 1 . this is just for future notice for similar problems . so 7 ^ 4 n + 3 - - - > if n = 1 then its ( ( 7 ^ 7 ) * 6 ) ) / 10 which can say is going to be 3 * 8 - - > 18 / 10 - - > r = 8 now from here if id double check just to make sure . 7 ^ 4 ( 2 ) + 3 * 6 ^ 2 - - - > 7 ^ 11 * 36 or we can just say again 7 ^ 11 * 6 ( b / c we are only interested in the units digit ) . since ^ 12 is going to be 1 that means ^ 11 is going to be 3 ( as taken from our pattern ) so again 3 * 6 = 18 / 10 - - - > r = 6 . d or j in this problem ."
Answer: d
Problem: 10 / 21 of 3 / 5 of a number is greater than 4 / 7 of 1 / 5 of the same number by 36 . what is half of that number ?
Options: a ) 105 , b ) 180 , c ) 210 , d ) 240 , e ) 315
Rationale: "let no . be x 10 / 21 * 3 / 5 * x - 4 / 7 * 1 / 5 * x = 8 by further solving 30 x / 105 - 4 x / 35 = 36 18 x / 105 = 36 x = 210 we have to find x / 2 = 210 / 2 = 105 answer : a"
Answer: a
Problem: the speed of a bus increases by 2 km after every one hour . if the distance travelling in the first one hour was 35 km . what was the total distance travelled in 12 hours ?
Options: a ) 233 , b ) 552 , c ) 376 , d ) 287 , e ) 166
Rationale: given that distance travelled in 1 st hour = 35 km and speed of the bus increases by 2 km after every one hour hence distance travelled in 2 nd hour = 37 km hence distance travelled in 3 rd hour = 39 km . . . total distance travelled = [ 35 + 37 + 39 + . . . ( 12 terms ) ] this is an arithmetic progression ( ap ) with first term , a = 35 , number of terms , n = 12 and common difference , d = 2 . the sequence a , ( a + d ) , ( a + 2 d ) , ( a + 3 d ) , ( a + 4 d ) , . . . is called an arithmetic progression ( ap ) where a is the first term and d is the common difference of the ap sum of the first n terms of an arithmetic progression ( ap ) , sn = n 2 [ 2 a + ( n − 1 ) d ] where n = number of terms hence , [ 35 + 37 + 39 + . . . ( 12 terms ) ] = s 12 = 122 [ 2 × 35 + ( 12 − 1 ) 2 ] = 6 [ 70 + 22 ] = 6 × 92 = 552 hence the total distance travelled = 552 km answer : b
Answer: b
Problem: a tailor trims 11 feet from opposite edges of a square piece of cloth , and 7 feet from the other two edges . if 84 square feet of cloth remain , what was the length of a side of the original piece of cloth ?
Options: a ) 26 , b ) 27 , c ) 28 , d ) 29 , e ) 30
Rationale: "let the original side of the square be x . ( x - 22 ) * ( x - 14 ) = 84 = 6 * 14 x = 28 the answer is c ."
Answer: c
Problem: an order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth . what be the cost of a carpet whose length and breadth are 40 % more and 25 % more respectively than the first carpet . given that the ratio of carpet is rs . 45 per sq . m ?
Options: a ) rs . 4082.40 , b ) rs . 1024.21 , c ) rs . 2810.6 , d ) rs . 3214 , e ) none of these
Rationale: explanation : length of the first carpet = ( 1.44 ) ( 6 ) = 8.64 cm area of the second carpet = 8.64 ( 1 + 40 / 100 ) 6 ( 1 + 25 / 100 ) = 51.84 ( 1.4 ) ( 5 / 4 ) sq m = ( 12.96 ) ( 7 ) sq m cost of the second carpet = ( 45 ) ( 12.96 x 7 ) = 315 ( 13 - 0.04 ) = 4095 - 12.6 = rs . 4082.40 answer is a
Answer: a
Problem: in a office work is distribute between p persons . if 1 / 7 members are absent then work increased for each person is ?
Options: a ) 13.67 % , b ) 14.67 % , c ) 15.67 % , d ) 16.67 % , e ) 17.67 %
Rationale: "let total % of work is 100 % total person = p 1 / 7 person are absent of total person . so absent person is 1 / 7 p ie p / 7 . left person is , p - p / 7 = 6 p / 7 . p person do the work 100 % 1 person do the work 100 * p % 6 p / 7 person do the work ( 100 * p * 7 ) / 6 p % = 116.67 % work increased for each person is = ( 116.67 - 100 ) % = 16.67 % answer : d"
Answer: d
Problem: a courtyard is 25 meter long and 16 meter board is to be paved with bricks of dimensions 20 cm by 10 cm . the total number of bricks required is ?
Options: a ) 22877 , b ) 27778 , c ) 20000 , d ) 27999 , e ) 17799
Rationale: "number of bricks = courtyard area / 1 brick area = ( 2500 × 1600 / 20 × 10 ) = 20000 answer : c"
Answer: c
Problem: in a school of 700 boys , 44 % of muslims , 28 % hindus , 10 % sikhs and the remaining of other communities . how many belonged to the other communities ?
Options: a ) 173 , b ) 126 , c ) 153 , d ) 143 , e ) 133
Rationale: "44 + 28 + 10 = 82 % 100 – 82 = 18 % 700 * 18 / 100 = 126 answer : b"
Answer: b
Problem: a shop keeper marked 30 % above the cost price and offered 20 % discount then find it ' s net profit ?
Options: a ) 2 % , b ) 2.5 % , c ) 3.7 % , d ) 4.6 % , e ) 5 %
Rationale: "net profit = 30 - 20 + ( 30 * ( - 25 ) / 100 ) = 2.5 % answer is b"
Answer: b
Problem: the speed of a car is 100 km in the first hour and 80 km in the second hour . what is the average speed of the car ?
Options: a ) 12 , b ) 75 , c ) 88 , d ) 54 , e ) 90
Rationale: "s = ( 100 + 80 ) / 2 = 90 kmph answer : e"
Answer: e
Problem: the average marks of 10 students in a class is 100 . but a student mark is wrongly noted as 60 instead of 10 then find the correct average marks ?
Options: a ) a ) 78 , b ) b ) 82 , c ) c ) 95 , d ) d ) 91 , e ) e ) 85
Rationale: "correct avg marks = 100 + ( 10 - 60 ) / 10 avg = 100 - 5 = 95 answer is c"
Answer: c
Problem: there are 300 seniors at morse high school , and 50 % of them have cars . of the remaining grades ( freshmen , sophomores , and juniors ) , only 10 % of them have cars . if 20 % of all the students at morse have cars , how many students are in the 3 lower grades ?
Options: a ) 600 , b ) 900 , c ) 1200 , d ) 1350 , e ) 1500
Rationale: let x be the number of students in the lower three grades . 0.1 x + 150 = 0.2 ( x + 300 ) 0.1 x = 900 x = 900 the answer is b .
Answer: b
Problem: carrie likes to buy t - shirts at the local clothing store . they cost $ 9.95 each . one day , she bought 20 t - shirts . how much money did she spend ?
Options: a ) $ 150 , b ) $ 248.75 , c ) $ 199 , d ) $ 171.6 , e ) $ 190
Rationale: $ 9.95 * 20 = $ 199 . answer is c .
Answer: c
Problem: a train passes a station platform in 36 sec and a man standing on the platform in 20 sec . if the speed of the train is 90 km / hr . what is the length of the platform ?
Options: a ) 229 , b ) 240 , c ) 400 , d ) 277 , e ) 221
Rationale: "speed = 90 * 5 / 18 = 25 m / sec . length of the train = 25 * 20 = 500 m . let the length of the platform be x m . then , ( x + 500 ) / 36 = 25 = > x = 400 m . answer : c"
Answer: c
Problem: in a mixed college 160 students are there in one class . out of this 160 students 5 / 8 students are girls . how many boys are there ?
Options: a ) a ) 40 , b ) b ) 60 , c ) c ) 80 , d ) d ) 120 , e ) e ) 140
Rationale: "total number of students : 160 total girls : 160 * 5 / 8 = 100 total boys : 160 - 100 = 60 answer is b"
Answer: b
Problem: a ferry can transport 85 tons of vehicles . automobiles range in weight from 1,800 to 3,200 pounds . what is the greatest number of automobiles that can be loaded onto the ferry ?
Options: a ) 23 , b ) 41 , c ) 48 , d ) 90 , e ) 86
Rationale: "to get maximum vehicles we must take into consideration the minimum weight i . e 1800 pounds here since , 1 ton = 2000 pounds 85 tons will be 170,000 pounds from the answer choices : let max number of vehicles be 86 total weight will be = 90 * 1800 = 162000 pounds , which is lesser than the maximum weight allowed . ans : d"
Answer: d
Problem: if 10 gallons of grape juice are added to 50 gallons of a mixture , which contains 10 percent grape juice then what percent of the resulting mixture is grape juice ?
Options: a ) 14 % , b ) 25 % , c ) 28 % , d ) 34 % , e ) 50 %
Rationale: "official solution : if we start with 40 gallons of a mixture that is 10 % grape juice , then we have : 50 × 0.10 = 5 gallons of grape juice . 50 × 0.90 = 45 gallons of other components . if we add 10 gallons of grape juice , we will end up with 15 gallons of grape juice and 45 gallons of other components , and we will have a total of 60 gallons of the mixture . so 15 / 60 of the new mixture is grape juice . now we convert this to a percent : percent grape juice = 25 / 100 = 25 % . the correct answer is choice ( b )"
Answer: b
Problem: an artist who needs to buy only paint and canvas finds that the cost of canvas has decreased by 40 percent and the cost of paint has decreased by 60 percent . if paint previously accounted for 4 times as much of the expense of painting as did canvas , by what percent did the total cost for paint and canvas decrease ?
Options: a ) 40 % , b ) 44 % , c ) 50 % , d ) 56 % , e ) 60 %
Rationale: paint : canvas cost is 4 : 1 . so , paint accounts for 80 % of cost and canvas accounts for 20 % . canvas , after decrease by 40 % will be ( 100 - 40 ) % of 20 % = > 60 % of 20 % = > 12 % of original paint , after decrease by 60 % will be ( 100 - 60 ) % of 80 % = > 40 % of 80 % = > 32 % of original new cost as a % of old cost = 32 + 12 = 44 % of original . so , overall cost saving = 100 - 44 = 56 % therefore , ( d )
Answer: d
Problem: a man can row upstream at 55 kmph and downstream at 65 kmph , and then find the speed of the man in still water ?
Options: a ) 27 , b ) 70 , c ) 60 , d ) 80 , e ) 24
Rationale: "us = 55 ds = 65 m = ( 55 + 65 ) / 2 = 60 answer : c"
Answer: c
Problem: a rectangular grassy plot 110 m . by 65 m has a gravel path 2.5 m wide all round it on the inside . find the cost of gravelling the path at 60 paise per sq . metre
Options: a ) s 510 , b ) s 780 , c ) s 880 , d ) s 480 , e ) s 980
Rationale: "area of the plot = 110 m * 65 m = 7150 sq . m area of plot excluding gravel = 105 m * 60 m = 6300 sq . m area of gravel = 7150 sq . m - 6300 sq . m = 850 sq . m cost of building it = 850 sq . m * 60 = 51000 p in rs = 51000 / 100 = rs 510 answer : a"
Answer: a
Problem: a train is 360 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length
Options: a ) 20 seconds , b ) 30 seconds , c ) 40 seconds , d ) 50 seconds , e ) none of these
Rationale: "explanation : speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 360 + 140 = 500 meter time = distance / speed = 500 ∗ 2 / 25 = 40 seconds option c"
Answer: c
Problem: in some quantity of ghee , 60 % is pure ghee and 40 % is vanaspati . if 10 kg of pure ghee is added , then the strength of vanaspati ghee becomes 20 % . the original quantity was :
Options: a ) 10 , b ) 27 , c ) 87 , d ) 23 , e ) 93
Rationale: "explanation : let the original quantity be x kg . vanaspati ghee in x kg = ( 40 x / 100 ) kg = ( 2 x / 5 ) kg . now , ( 2 x / 5 ) / ( x + 10 ) = 20 / 100 < = > 2 x / ( 5 x + 50 ) = 1 / 5 < = > 5 x = 50 < = > x = 10 . answer : a ) 10 kg"
Answer: a
Problem: evaluate 926 + 9.026 + 0.926 + 9.0026
Options: a ) 944.9755 , b ) 944.9655 , c ) 944.9565 , d ) 946.9565 , e ) 944.9546
Rationale: "926 + 9.026 + 0.926 + 9.0026 = 944.9546 option e"
Answer: e
Problem: what is the units digit of the expression 17 ^ 7 - 2 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 7 , e ) 9
Rationale: "7 ^ 1 = 7 7 ^ 2 = 49 7 ^ 3 = 343 7 ^ 4 = 1 ( last digit ) 7 ^ 5 = 7 ( last digit ) and the cycle repeats after every 4 powers therefore , last digit of 17 ^ 7 = 3 3 - 2 = 1 answer a"
Answer: a
Problem: if v is the product of the integers from 1 to 30 , inclusive , what is the greatest integer k for which 3 ^ k is a factor of v ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: v = 30 ! 8 v = 30 x 29 x 28 x 27 x 26 x 25 x 24 x 24 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 09 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 out of these 30 , 27 , 24 , 21 , 18 , 15 , 12 , 09 , 06 , 3 are factors of 3 3 x 10 , 3 x 3 x 3 , 3 x 8 , 3 x 3 x 2 , 3 x 5 , 3 x 4 , 3 x 3 x 3 , 3 x 2 , 3 so we have a total of 14 three ' s . . . therefore the maximum value of k can be 14 ( c )
Answer: c
Problem: find the side of the largest possible square slabs which can be paved on the floor of a room 2 m 50 cm long and 1 m 50 cm broad . also find the number of such slabs to pave the floor .
Options: a ) 25 , 20 , b ) 30 , 15 , c ) 50 , 15 , d ) none of these , e ) 75,35
Rationale: explanation : hcf ( 250 , 150 ) = 50 cm the number slabs = 250 * 150 / 50 * 50 = 15 answer : c
Answer: c
Problem: a train speeds past a pole in 25 seconds and a platform 200 m long in 30 seconds . its length is :
Options: a ) 1200 m , b ) 2000 m , c ) 1500 m , d ) 1000 m , e ) 4000 m
Rationale: "let the length of the train be x meters and its speed be y m / sec . they , x / y = 25 = > y = x / 25 x + 200 / 30 = x / 25 x = 1000 m . answer : option d"
Answer: d
Problem: two cubes have their volumes in the ratio 1 : 27 . find the ratio of their surface areas .
Options: a ) 1 : 9
b ) 2 : 9
c ) 3 : 9
d ) 5 : 9
e ) none of them
Rationale: let their edges be a and b . then , = a ^ 3 / b ^ 3 = 1 / 27 ( or ) ( a / b ) ^ 3 = ( 1 / 3 ) 3 ( or ) ( a / b ) = ( 1 / 3 ) . therefore , ratio of their surface area = 6 a ^ 2 / 6 b ^ 2 = a ^ 2 / b ^ 2 = ( a / b ) ^ 2 = 1 / 9 , i . e . 1 : 9 . answer is a .
Answer: a
Problem: one fourth of a solution that was 14 % salt by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight . the second solution was what percent salt by weight ?
Options: a ) 24 % , b ) 34 % , c ) 22 % , d ) 18 % , e ) 8.5 %
Rationale: "consider total solution to be 100 liters and in this case you ' ll have : 75 * 0.14 + 25 * x = 100 * 0.16 - - > x = 0.22 . answer : c ."
Answer: c
Problem: a certain fraction has the same ratio to 1 / 18 , as 2 / 5 does to 2 / 9 . what is this certain fraction ?
Options: a ) 1 / 5 , b ) 1 / 7 , c ) 1 / 10 , d ) 1 / 12 , e ) 1 / 15
Rationale: "x / ( 1 / 18 ) = ( 2 / 5 ) / ( 2 / 9 ) x = 2 * 9 * 1 / 18 * 5 * 2 = 1 / 10 the answer is c ."
Answer: c
Problem: how many odd numbers between 10 and 2000 are the squares of integers ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "the numbers are the squares of 5 , 7 , 9 , . . . , 43 which includes 20 numbers . the answer is e ."
Answer: e
Problem: for a certain exam , a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean . what was the mean score e for the exam ?
Options: a ) 74 , b ) 76 , c ) 78 , d ) 80 , e ) 82
Rationale: "a score of 58 was 2 standard deviations below the mean - - > 58 = mean - 2 d a score of 98 was 3 standard deviations above the mean - - > 98 = mean + 3 d solving above for mean e = 74 . answer : a ."
Answer: a
Problem: walking at the rate of 3 kmph a man cover certain distance in 3 hr 20 min . running at a speed of 9 kmph the man will cover the same distance in .
Options: a ) 45 min , b ) 50 min , c ) 40 min , d ) 48 min , e ) 54 min
Rationale: "distance = speed * time 3 * 10 / 3 = 10 km new speed = 9 kmph therefore time = d / s = 10 / 9 = 54 min answer : e ."
Answer: e
Problem: what percent is 25 gm of 1 kg ?
Options: a ) 0.5 % , b ) 1 % , c ) 1.5 % , d ) 2.5 % , e ) 3 %
Rationale: "1 kg = 1000 gm 25 / 1000 × 100 = 2500 / 1000 = 5 / 2 = 2.5 % d )"
Answer: d
Problem: an airplane covers 50 miles in 1 / 5 hours . how many miles can the airplane cover in 5 hours ?
Options: a ) 800 , b ) 600 , c ) 1250 , d ) 950 , e ) 1000
Rationale: divide 5 by 1 / 5 = 5 ÷ 1 / 5 = 5 / 1 ÷ 1 / 5 = 5 / 1 * 5 / 1 = 25 . then , multiply 50 by 25 to get 1250 in 5 hours , the airplane will cover 1250 miles answer is c .
Answer: c
Problem: evaluate 35 / . 07
Options: a ) 400 , b ) 500 , c ) 505 , d ) none of these , e ) 506
Rationale: "explanation : 35 / . 07 = 3500 / 7 = 500 option b"
Answer: b
Problem: a shopkeeper sold an article offering a discount of 5 % and earned a profit of 19.7 % . what would have been the percentage of profit earned if no discount was offered ?
Options: a ) 60 % , b ) 26 % , c ) 30 % , d ) 56 % , e ) 73 %
Rationale: "let c . p . be rs . 100 . then , s . p . = rs . 19.70 let marked price be rs . x . then , 95 / 100 x = 119.70 x = 11970 / 95 = rs . 126 now , s . p . = rs . 126 , c . p . = rs . 100 profit % = 26 % . answer : b"
Answer: b
Problem: 0.003 x 0.2 = ?
Options: a ) 0.0006 , b ) 0.006 , c ) 0.06 , d ) 0.6 , e ) 6.0
Rationale: "3 x 2 = 6 . sum of decimal places = 4 0.003 x 0.2 = 0.0006 answer : option a"
Answer: a
Problem: a candidate who gets 30 % of the marks fails by 60 marks . but another candidate who gets 45 % marks gets 30 marks more than necessary for passing . find the number of marks for passing ?
Options: a ) 100 marks , b ) 240 marks , c ) 280 marks , d ) 371 marks , e ) 827 marks
Rationale: "30 % - - - - - - - - - - - - 60 45 % - - - - - - - - - - - - 30 - - - - - - - - - - - - - - - - - - - - - - 15 % - - - - - - - - - - - - - 90 30 % - - - - - - - - - - - - - - 180 180 + 60 = 240 marks answer : b"
Answer: b
Problem: in may , the groundskeeper at spring lake golf club built a circular green with an area of 80 π square feet . in august , the groundskeeper doubled the distance from the center of the green to the edge of the green . what is the total area of the renovated green ?
Options: a ) 160 π , b ) 320 π , c ) 400 π , d ) 540 π , e ) 640 π
Rationale: "area = π r ^ 2 , so doubling the radius results in an area that is 4 times the original area . 4 ( 80 π ) = 320 π the answer is b ."
Answer: b
Problem: 80 pie square inches of material of negligible thickness are required to construct a 1 / 16 scale model of a cylindrical barrel . if the diameter of the base of the barrel is 160 inches , then what is the volume of the barrel , to the nearest cubic foot ?
Options: a ) 2 pie
b ) 11 pie
c ) 178 pie
d ) 711 pie
e ) 1280 pie
Rationale: radius of barrel , r = 80 radius of model , r = 80 / 16 = 5 surface area of the model = 2 ∗ pi ∗ r ( r + h ) = 80 ∗ pi which gives h = 3 and h = 3 ∗ 16 = 48 so , volume of the barrel = pi ∗ r 2 ∗ h = pi ∗ ( 80 ) 2 ∗ ( 48 ) in cubic inches converting in cubic ft results : volume = pi ∗ ( 80 ) 2 ∗ ( 48 ) / ( 12 ) 3 = 178 pi cubic ft approximately answer [ c ]
Answer: c
Problem: the average weight of 20 girls increases by 2 kg when a new girl comes in place of one of them weighing 40 kg . what might be the weight of the new girl ?
Options: a ) 85 kg , b ) 90 kg , c ) 80 kg , d ) 75 kg , e ) 70 kg
Rationale: "total weight increased = 20 x 2 kg = 40 kg . weight of new person = 40 + 40 kg = 80 kg answer : c"
Answer: c
Problem: a ( 5 , w ^ 3 ) is the ( x , y ) coordinate of point located on the parabola y = x ^ 2 + 2 . what is the value of w ?
Options: a ) 3 . , b ) 4 . , c ) 5 . , d ) 6 . , e ) 9
Rationale: "y = x ^ 2 + 2 x = 5 y = 5 ^ 2 + 2 = 27 y is in the form w ^ 3 w ^ 3 = 27 w = 3 answer : a"
Answer: a
Problem: in a graduating class of 232 students , 144 took geometry and 119 took biology . what is the difference between the greatest possible number t and the smallest possible number of students that could have taken both geometry and biology ?
Options: a ) 144 , b ) 119 , c ) 113 , d ) 88 , e ) 31
Rationale: "official solution : first of all , notice that since 144 took geometry and 119 took biology , then the number of students who took both geometry and biology can not be greater than 119 . { total } = { geometry } + { biology } - { both } + { neither } ; 232 = 144 + 119 - { both } + { neither } ; { both } = 31 + { neither } . { both } is minimized when { neither } is 0 . in this case { both } = 31 . the greatest possible number t of students that could have taken both geometry and biology , is 119 . thus , the answer is 119 - 31 = 88 . answer : d ."
Answer: d
Problem: a certain fruit stand sold apples for $ 0.80 each and bananas for $ 0.70 each . if a customer purchased both apples and bananas from the stand for a total of $ 6.50 , what total number of apples and bananas did the customer purchase ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: let ' s start with 1 apple for $ 0.80 . let ' s subtract $ 0.80 from $ 6.50 until we get a multiple of $ 0.70 . $ 6.50 , $ 5.70 , $ 4.90 = 7 * $ 0.70 the customer purchased 7 bananas and 2 apples . the answer is b .
Answer: b
Problem: what is the thousandths digit in the decimal equivalent of 62 / 5000 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 5 , e ) 6
Rationale: "62 / 5000 = 62 / ( 5 * 10 ^ 3 ) = ( 62 / 5 ) * 10 ^ - 3 = 12.4 * 10 ^ - 3 = . 0124 thousandths digit = 2 answer c"
Answer: c
Problem: in how many seconds will a train 180 meters long pass an oak tree , if the speed of the train is 36 km / hr ?
Options: a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22
Rationale: "speed = 36 * 5 / 18 = 10 m / s time = 180 / 10 = 18 seconds the answer is c ."
Answer: c
Problem: what number should replace the question mark ? 10 , 30 , 14 , 25 , 18 , 20 , - - - ?
Options: a ) 19 , b ) 21 , c ) 25 , d ) 22 , e ) 20
Rationale: "answer : d 10 , 30 , 14 , 25 , 18 , 20 , 22 ? there are two alternate sequences : + 4 and - 5 ."
Answer: d
Problem: a train of length 250 m crosses a bridge of length 180 m in 20 seconds . what is the speed of train ?
Options: a ) 33 , b ) 77.4 , c ) 25 , d ) 22 , e ) 72
Rationale: "sol : ( length of train + length of bridge ) = speed of train x time ( 250 + 180 ) = 20 x speed speed = 430 / 20 = 21.5 m / s = 77.4 km / h answer = b"
Answer: b
Problem: what is the perimeter , in meters , of a rectangular garden 24 meters wide that has the same area as a rectangular playground 16 meters long and 12 meters wide ?
Options: a ) 48 , b ) 56 , c ) 64 , d ) 76 , e ) 192
Rationale: "say length of garden is l meters . then ( l * 24 ) = 16 * 12 [ given area is same . area = l * b ] therefore l works out to 8 meters . perimeter of garden = 2 * ( 8 + 24 ) = 64 meter . answer is c"
Answer: c
Problem: a can do a work in 12 days . when he had worked for 3 days , b joinedhim . if they complete the work in 3 more days , in how manydays can balone finish the work ?
Options: a ) 2 days , b ) 4 days , c ) 5 days , d ) 6 days , e ) 9 days
Rationale: sax work done by afar 3 days : i j . . remzming war — 1 . work done by ( a + b ) for 1 day : . work done by a for 1 day 6 days d
Answer: d
Problem: if k is an integer and 0.0010101 x 10 ^ k is greater than 100 , what is the least possible value of k ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "0.0010101 * 10 ^ k > 100 we need to move the decimal point to the right 5 places to get 101.01 this is equivalent to multiplying by 10 ^ 5 . the answer is d ."
Answer: d
Problem: gold is 19 times as heavy as water and copper is 9 times as heavy as water . in what ratio should these be mixed to get an alloy 18 times as heavy as water ?
Options: a ) 1 : 2 , b ) 3 : 2 , c ) 9 : 1 , d ) 5 : 2 , e ) 6 : 5
Rationale: "g = 19 w c = 9 w let 1 gm of gold mixed with x gm of copper to get 1 + x gm of the alloy 1 gm gold + x gm copper = x + 1 gm of alloy 19 w + 9 wx = x + 1 * 18 w 19 + 9 x = 18 ( x + 1 ) x = 1 / 9 ratio of gold with copper = 1 : 1 / 9 = 9 : 1 answer is c"
Answer: c
Problem: find the ones digit of 73 ^ 350
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 9
Rationale: "3,9 , 7,1 repeats after every four times therefore 350 / 4 = 87 + 2 remainder 9 is the ones digit so e is correct"
Answer: e