Cheukting/mathqa huggingface dataset:
Question (gain): the salary of a person was reduced by 14 % . by what percent should his reduced salary be raised so as to bring it at par with his original salary ?
Options: a ) 10 % , b ) 16.3 % , c ) 13.7 % , d ) 15.1 % , e ) 12.3 %
Rationale: let the original salary be $ 100 new salary = $ 86 increase on 86 = 14 increase on 100 = 14 / 86 * 100 = 16.3 % answer is b
Answer: b
Question (general): 11 times a number gives 132 . the number is
Options: a ) 11 , b ) 12 , c ) 13.2 , d ) none , e ) can not be determined
Rationale: "explanation : let the number be ' n ' 11 × n = 132 ⇒ n = 12 correct option : b"
Answer: b
Question (physics): a bullet train covers a distance in 50 min , if it runs at a speed of 48 kmph on an average . the speed at which the bullet train must run to reduce the time of journey to 40 min will be .
Options: a ) 80 kmph , b ) 40 kmph , c ) 60 kmph , d ) 90 kmph , e ) 30 kmph
Rationale: c 60 kmph time = 50 / 60 hr = 5 / 6 hr speed = 48 mph distance = s * t = 48 * 5 / 6 = 40 km time = 40 / 60 hr = 2 / 3 hr new speed = 40 * 3 / 2 kmph = 60 kmph
Answer: c
Question (geometry): the area of a triangle is with base 12 m and height 5 m ?
Options: a ) 88 m 2 , b ) 30 m 2 , c ) 66 m 2 , d ) 77 m 2 , e ) 31 m 2
Rationale: "1 / 2 * 12 * 5 = 30 m 2 answer : b"
Answer: b
Question (probability): what is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular decagon ( 10 - sided polygon ) ?
Options: a ) 3 / 10 , b ) 2 / 5 , c ) 2 / 7 , d ) 10 / 21 , e ) 5 / 11
Rationale: from any vertex , there are two vertices on sides , which do not make a diagonal but a side . so the remaining n - 3 vertices make diagonals . there are 2 of these diagonals which are the shortest . the probability of choosing one of the shortest diagonals is 2 / 7 . the answer is c .
Answer: c
Question (general): one half of a two digit number exceeds its one third by 9 . what is the sum of the digits of the number ?
Options: a ) a ) 3 , b ) b ) 5 , c ) c ) 7 , d ) d ) 9 , e ) e ) 11
Rationale: "x / 2 – x / 3 = 9 = > x = 54 5 + 4 = 9 answer : d"
Answer: d
Question (physics): sheila works 8 hours per day on monday , wednesday and friday , and 6 hours per day on tuesday and thursday . she does not work on saturday and sunday . she earns $ 360 per week . how much does she earn in dollars per hour ?
Options: a ) 11 , b ) 10 , c ) 9 , d ) 8 , e ) 7
Rationale: "let sheila earn x dollars per hour so , on monday , wednesday and friday , she earns 8 x each and , on tuesday and thursday , she earns 6 x each in total , over the week she should earn , 3 ( 8 x ) + 2 ( 6 x ) = 36 x she earns $ 360 per week 36 x = 360 x = 10 correct option : b"
Answer: b
Question (other): the h . c . f . of two numbers is 30 and the other two factors of their l . c . m . are 15 and 12 . the larger of the two numbers is
Options: a ) 476 , b ) 399 , c ) 450 , d ) 322 , e ) none
Rationale: "solution clearly , the numbers are ( 30 x 15 ) and ( 30 x 12 ) . larger number = ( 30 x 15 ) = 450 . answer c"
Answer: c
Question (general): the difference between the place values of two nines in the numerical 62039295 is
Options: a ) 89 , b ) 891 , c ) 8910 , d ) 0 , e ) none of them
Rationale: "required difference = ( 9000 - 90 ) = 8910 . answer is c"
Answer: c
Question (general): dacid obtained 90 , 92 , 85 , 87 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 67 , b ) 26 , c ) 88 , d ) 90 , e ) 75
Rationale: "average = ( 90 + 92 + 85 + 87 + 85 ) / 5 = 439 / 5 = 87.8 . answer : c"
Answer: c
Question (other): in a group of 6 boys and 4 girls , four children are to be selected . in how many different ways can they be selected ?
Options: a ) 159 , b ) 194 , c ) 210 , d ) 209 , e ) 166
Rationale: "out of 10 students 4 children should to be selected . so the combination will be 10 c 4 . 10 c 4 = 10 ! / 6 ! * 4 ! = 10 * 9 * 8 * 7 * 6 ! / 6 ! * ( 4 * 3 * 2 * 1 ) 10 c 4 = 210 there are 210 differect possible ways to select 4 children out of 10 students ."
Answer: c
Question (other): in a certain town , the ratio of ny yankees fans to ny mets fans is 3 : 2 , and the ratio of ny mets fans to boston red sox fans is 4 : 5 . if there are 360 baseball fans in the town , each of whom is a fan of exactly one of those three teams , how many ny mets fans are there in this town ?
Options: a ) 96
b ) 108
c ) 120
d ) 132
e ) 140
Rationale: the ratio of yankees : mets : red sox = 6 : 4 : 5 the mets fans are 4 / 15 of the population . ( 4 / 15 ) * 360 = 96 the answer is a .
Answer: a
Question (general): the sum of ages of 5 children born at the intervals of 3 years each is 55 years . what is the age of the youngest child ?
Options: a ) 5 years , b ) 4 years , c ) 6 years , d ) 7 years , e ) 8 years
Rationale: "let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 55 5 x = 25 x = 5 . age of the youngest child = x = 5 years . a )"
Answer: a
Question (gain): a man invested rs . 14,400 in rs . 100 shares of a company at 25 % premium . if the company declares 5 % dividend at the end of the year , then how much does he get ?
Options: a ) rs . 576 , b ) rs . 600 , c ) rs . 650 , d ) rs . 720 , e ) none
Rationale: "solution number of shares = ( 14400 / 125 ) = 115.2 . face value = rs . ( 100 x 115.2 ) = rs . 11520 . annual income = rs . ( 5 / 100 x 11520 ) = rs . 576 . answer a"
Answer: a
Question (gain): a ladder 22 feet long is leaning against a wall that is perpendicular to level ground . the bottom of the ladder is 7 feet from the base of the wall . if the top of the ladder slips down 3 feet , how many feet will the bottom of the ladder slip ?
Options: a ) 12.86 , b ) 15 , c ) 18 , d ) 19 , e ) 25
Rationale: "22 ^ 2 - 7 ^ 2 = 435 it means that the height is equal to 20.85 . since the top of the ladder slips down 4 feet , then the height of the wall = 20.85 - 3 = 17.85 the bottom = sqrt ( 22 ^ 2 - 17.85 ^ 2 ) = sqrt ( 484 - 318.62 ) = 12.86 ans is a"
Answer: a
Question (other): water consists of hydrogen and oxygen , and the approximate ratio , by mass , of hydrogen to oxygen is 2 : 16 . approximately how many grams of hydrogen are there in 117 grams of water ?
Options: a ) 7 , b ) 9 , c ) 11 , d ) 13 , e ) 15
Rationale: ( 2 / 18 ) * 117 = 13 grams the answer is d .
Answer: d
Question (physics): if a tire rotates at 400 revolutions per minute when the car is traveling 24 km / h , what is the circumference of the tire ?
Options: a ) 1 meters , b ) 6 meters , c ) 5 meters , d ) 3 meters , e ) 7 meters
Rationale: "400 rev / minute = 400 * 60 rev / 60 minutes = 24,000 rev / hour 24,000 * c = 24,000 m : c is the circumference c = 1 meters correct answer a"
Answer: a
Question (physics): a can do a work in 15 days and b in 20 days . if they work on it together for 7 days , then the fraction of the work that is left is
Options: a ) 8 / 17 , b ) 7 / 15 , c ) 3 / 15 , d ) 8 / 15 , e ) 11 / 60
Rationale: "person ( a ) ( b ) ( a + b ) time - ( 15 ) ( 20 ) ( - ) rate - ( 20 ) ( 15 ) ( 35 ) work - ( 300 ) ( 300 ) ( 300 ) therefore a + b requires ( 300 / 35 ) days to complete entire work for 1 st 4 days they work 35 * 7 = 245 remaining work is 300 - 245 = 55 remaining fraction of work is = 55 / 300 = 11 / 60 answer e"
Answer: e
Question (general): workers decided to raise rs . 3 lacs by equal contribution from each . had they contributed rs . 50 eachextra , the contribution would have been rs . 3.75 lacs . how many workers were they ?
Options: a ) 220 , b ) 230 , c ) 500 , d ) 1500 , e ) 590
Rationale: n * 50 = ( 375000 - 300000 ) = 75000 n = 75000 / 50 = 1500 d
Answer: d
Question (gain): 40 % of a number is added to 60 , the result is the same number . find the number ?
Options: a ) 300 , b ) 288 , c ) 270 , d ) 100 , e ) 281
Rationale: "( 40 / 100 ) * x + 60 = x 4 x + 600 = 10 x 6 x = 600 x = 100 answer : d"
Answer: d
Question (geometry): in right triangle abc , ac is the hypotenuse . if ac is 35 and ab + bc = 55 , what is the area of the triangle abc ?
Options: a ) 225 , b ) 450 , c ) 25 √ 2 , d ) 200 , e ) 200 √ 2
Rationale: "square ab + bc = 55 : ( ab ) ^ 2 + 2 * ab * bc + ( bc ) ^ 2 = 3025 . since ( ac ) ^ 2 = ( ab ) ^ 2 + ( bc ) ^ 2 = 35 ^ 2 = 1225 , then ( ab ) ^ 2 + 2 * ab * bc + ( bc ) ^ 2 = 1225 + 2 * ab * bc = 3025 . 1225 + 2 * ab * bc = 3025 . ab * bc = 900 . the area = 1 / 2 * ab * bc = 450 . answer : b ."
Answer: b
Question (general): what is the smallest integer that is multiple of 5 , 711
Options: a ) a ) 70 , b ) b ) 35 , c ) c ) 385 , d ) d ) 280 , e ) e ) 140
Rationale: it is the lcm of 5 , 7 and 11 which is 385 . the answer is c .
Answer: c
Question (physics): jack and jill are marathon runners . jack can finish a marathon ( 42 km ) in 7 hours and jill can run a marathon in 4.2 hours . what is the ratio of their average running speed ? ( jack : jill )
Options: a ) 14 / 15 , b ) 15 / 14 , c ) 5 / 5 , d ) 5 / 4 , e ) can not be determined
Rationale: "average speed of jack = distance / time = 42 / 7 = 6 average speed of jill = 42 / ( 4.2 ) = 10 ratio of average speed of jack to jill = 6 / 10 = 3 / 5 answer c"
Answer: c
Question (general): the average waight of a , b , c is 45 kg . the avgwgt of a & b be 40 kg & that of b , c be 43 kg . find the wgt of b .
Options: a ) 23 kg , b ) 43 kg , c ) 21 kg , d ) 31 kg , e ) 43 kg
Rationale: sol . let a , b , c represent their individual wgts . then , a + b + c = ( 45 * 3 ) kg = 135 kg a + b = ( 40 * 2 ) kg = 80 kg & b + c = ( 43 * 2 ) kg = 86 kg b = ( a + b ) + ( b + c ) - ( a + b + c ) = ( 80 + 86 - 135 ) kg = 31 kg . answer d
Answer: d
Question (general): a father is now 3 times as old as his son . 8 years back , he was 4 times as old as his son . the age of the son ( in years ) is
Options: a ) 12 , b ) 24 , c ) 18 , d ) 27 , e ) 25
Rationale: if father ' s age is f and son ' s age is s , then f = 3 s and f - 8 = 4 * ( s - 8 ) 3 s - 5 = 4 s - 32 s = 24 f = 72 years answer : b
Answer: b
Question (general): a certain social security recipient will receive an annual benefit of $ 12,000 provided he has annual earnings of $ 9,360 or less , but the benefit will be reduced by $ 1 for every $ 3 of annual earnings over $ 9,360 . what amount of total annual earnings would result in a 40 percent reduction in the recipient ' s annual social security benefit ? ( assume social security benefits are not counted as part of annual earnings . )
Options: a ) $ 15,360 , b ) $ 17,360 , c ) $ 18,000 , d ) $ 21,360 , e ) $ 30,960
Rationale: "for every $ 3 earn above $ 9360 , the recipient loses $ 1 of benefit . or for every $ 1 loss in the benefit , the recipient earns $ 3 above $ 9360 if earning is ; 9360 + 3 x benefit = 12000 - x or the vice versa if benefit is 12000 - x , the earning becomes 9360 + 3 x he lost 40 % of the benefit ; benefit received = 12000 - 0.4 * 12000 = 12000 - 4800 x = 7200 earning becomes 9360 + 3 x = 9360 + 3 * 7200 = 30960 ans : e"
Answer: e
Question (general): in a house a hall is 20 m long , 15 m wide and 5 m high . its interior has to be covered with mat . what will be the total expenditure if it costs rs . 40 per square m ?
Options: a ) s . 43000 , b ) s . 50000 , c ) s . 57000 , d ) s . 38000 , e ) s . 62000
Rationale: "length ( l ) = 20 m , breadth ( b ) = 15 m and height ( h ) = 5 m total area of the hall to be covered with mat = 2 ( lb + bh + hl ) = 2 ( 20 * 15 + 15 * 5 + 5 * 20 ) = 2 ( 300 + 75 + 100 ) = 2 * 475 = 950 sq . m total expenditure = 40 * 950 = rs . 38000 d"
Answer: d
Question (general): at a restaurant , glasses are stored in two different - sized boxes . one box contains 12 glasses , and the other contains 16 glasses . if the average number of glasses per box is 15 , and there are 16 more of the larger boxes , what is the total number of glasses e at the restaurant ? ( assume that all boxes are filled to capacity . )
Options: a ) 96 , b ) 240 , c ) e = 256 , d ) e = 384 , e ) e = 480
Rationale: "most test takers would recognize thesystemof equations in this prompt and just do algebra to get to the solution ( and that ' s fine ) . the wording of the prompt and the ' spread ' of the answer choices actually provide an interesting ' brute force ' shortcut that you can take advantage of to eliminate the 4 wrong answers . . . . we ' re told that there are 2 types of boxes : those that hold 12 glasses and those that hold 16 glasses . since the average number of boxes is 15 , we know that there must be at least some of each . we ' re also told that that there are 16 more of the larger boxes . this means , at the minimum , we have . . . 1 small box and 17 large boxes = 1 ( 12 ) + 17 ( 16 ) = 12 + 272 = 284 glasses at the minimum since the question asks for the total number of glasses , we can now eliminate answers a , b and c . . . . the difference in the number of boxes must be 16 though , so we could have . . . . 2 small boxes and 18 large boxes 3 small boxes and 19 large boxes etc . with every additional small box + large box that we add , we add 12 + 16 = 28 more glasses . thus , we can justadd 28 suntil we hit the correct answer . . . . 284 + 28 = 312 312 + 28 = 340 340 + 28 = 368 368 + 28 = 396 at this point , we ' ve ' gone past ' answer d , so the correct answer must be answer e . . . . . but here ' s the proof . . . . 396 + 28 = 424 424 + 28 = 452 452 + 28 = 480 final answer : e"
Answer: e
Question (physics): rajani has to read a book of 445 pages . she has already read the first 157 pages of the book and if she reads 24 pages of the book everyday then how long will she take now to complete the book ?
Options: a ) 25 days , b ) 20 days , c ) 46 days , d ) 21 days , e ) none of these
Rationale: remaining pages to read = 445 – 157 = 288 ∴ reqd . number of days = 288 ⁄ 24 = 12 answer e
Answer: e
Question (general): when positive integer n is divided by 3 , the remainder is 1 . when n is divided by 7 , the remainder is 5 . what is the smallest positive integer k such that k + n is a multiple of 21 ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "n = 3 p + 1 = 7 q + 5 n + 2 = 3 p + 3 = 7 q + 7 n + 2 is a multiple of 3 and 7 , so it is a multiple of 21 . the answer is a ."
Answer: a
Question (gain): a sum of money becomes 7 / 6 of itself in 7 years at a certain rate of simple interest . the rate per annum is ?
Options: a ) 50 / 13 , b ) 50 / 17 , c ) 50 / 19 , d ) 50 / 21 , e ) 50 / 23
Rationale: "let sum = x . then , amount = 7 x / 6 s . i . = 7 x / 6 - x = x / 6 ; time = 7 years . rate = ( 100 * x ) / ( x * 6 * 7 ) = 50 / 21 % . answer : d"
Answer: d
Question (general): a ship 77 km from the shore , springs a leak which admits to 9 / 4 tonnes of water in 11 / 2 minutes . 92 tonnes of water would sink it . but the pumps can throw out 12 tonnes of water per hour . find the average rate of sailing so that the ship may just reach the shore as it begins to sink .
Options: a ) 10.5 , b ) 11 , c ) 12 , d ) 13 , e ) 15
Rationale: leak admits 9 / 4 tonnes water in 11 / 2 min = 11 / 2 * 4 / 9 = 22 / 9 leak admits 9 / 22 tonne of water in 5 min in 1 min in thrws 1 / 5 tonne of water = 9 / 22 - 1 / 5 = 23 / 110 92 / 23 / 11 min = 440 min 22 / 3 min = 7 / 22 / 22 / 3 = > 10.5 km / hr answer a
Answer: a
Question (general): a library has an average of 600 visitors on sundays and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is :
Options: a ) 250 , b ) 260 , c ) 300 , d ) 285 , e ) none
Rationale: "since the month begins with sunday , to there will be five sundays in the month average required = ( 600 x 5 + 240 x 25 ) / 30 ) = 300 answer : option c"
Answer: c
Question (physics): the lcm of two numbers is 2310 and hcf is 30 . if one of the numbers is 210 . then what is the other number ?
Options: a ) 715 , b ) 825 , c ) 330 , d ) 582 , e ) 465
Rationale: "first number * second number = lcm * hcf other number = 2310 * 30 / 210 = 11 * 30 = 330 answer : c"
Answer: c
Question (gain): a small college reduced its faculty by approximately 15 percent to 195 professors . what was the original number of faculty members ?
Options: a ) 182 , b ) 208 , c ) 224 , d ) 229 , e ) 302
Rationale: "if x is the original number of faculty members , then after 15 % reduction in faculty members number is . 85 x but we are given . 85 x = 195 x = 229 so the original number of faculty members is 229 correct answer - d"
Answer: d
Question (physics): how many seconds will a train 60 meters long take to cross a bridge 120 meters long if the speed of the train is 30 m / sec ?
Options: a ) 6 sec , b ) 8 sec , c ) 15 sec , d ) 3 sec , e ) 5 sec
Rationale: "d = 60 + 120 = 180 s = 30 mps t = 180 / 30 = 6 sec a ) 6 sec"
Answer: a
Question (geometry): if the sides of a rectangle are increased by 35 % , what is the percentage increase in the area ?
Options: a ) 38.25 % , b ) 40.25 % , c ) 82.25 % , d ) 50 % , e ) 65 %
Rationale: if sides are a and b , after increase sides would be 1.35 a and 1.35 b . percentage increase in area = ( 1.35 a * 1.35 b - ab ) * 100 / ab = 82.25 answer : c
Answer: c
Question (physics): the length of the bridge , which a train 120 m long and traveling at 45 km / hr can cross in 30 sec is ?
Options: a ) 235 , b ) 240 , c ) 245 , d ) 250 , e ) 255
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec . time = 30 sec let the length of bridge be x meters . then , ( 120 + x ) / 30 = 25 / 2 x = 255 m . answer : option e"
Answer: e
Question (general): 4 , 12 , 48 , 240 , 1440 , 10080,80640 ( . . . )
Options: a ) 7620 , b ) 10080 , c ) 6200 , d ) 10020 , e ) 725760
Rationale: "explanation : go on multiplying the given numbers by 3 , 4 , 5 , 6 , 7 , 8,9 answer : option e"
Answer: e
Question (general): if a person walks at 20 km / hr instead of 10 km / hr , he would have walked 40 km more . the actual distance traveled by him is ?
Options: a ) 40 km , b ) 76 km , c ) 18 km , d ) 16 km , e ) 97 km
Rationale: "let the actual distance traveled be x km . then , x / 10 = ( x + 40 ) / 20 10 x - 400 = > x = 40 km . answer : a"
Answer: a
Question (general): there are 840 male and female participants in a meeting . half the female participants and one - quarterof the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ?
Options: a ) 75 , b ) 100 , c ) 125 , d ) 140 , e ) 225
Rationale: "let m be the number of male participants and f be the number of female articipants in the meeting . thetotal number of participants is given as 840 . hence , we have m + f = 840 now , we have that half the female participants and one - quarter of the male participants are democrats . let d equal the number of the democrats . then we have the equation f / 2 + m / 4 = d now , we have that one - third of the total participants are democrats . hence , we have the equation d = 840 / 3 = 280 solving the three equations yields the solution f = 280 , m = 560 , and d = 280 . the number of female democratic participants equals half the female participants equals 280 / 2 = 140 . answer : d"
Answer: d
Question (geometry): the percentage increase in the area of a rectangle , if each of its sides is increased by 20 % is ?
Options: a ) 44 % , b ) 45 % , c ) 50 % , d ) 55 % , e ) 60 %
Rationale: "let original length = x metres and original breadth = y metres . original area = ( xy ) m 2 . new length = 120 x m = 6 x m . 100 5 new breadth = 120 y m = 6 y m . 100 5 new area = 6 x x 6 y m 2 = 36 xy m 2 . 5 5 25 the difference between the original area = xy and new - area 36 / 25 xy is = ( 36 / 25 ) xy - xy = xy ( 36 / 25 - 1 ) = xy ( 11 / 25 ) or ( 11 / 25 ) xy increase % = 11 xy x 1 x 100 % = 44 % . a )"
Answer: a
Question (general): the average temperature for monday , tuesday , wednesday and thursday was 48 degrees and for tuesday , wednesday , thursday and friday was 46 degrees . if the temperature on monday was 40 degrees . find the temperature on friday ?
Options: a ) 65 degrees , b ) 32 degrees , c ) 37 degrees , d ) 34 degrees , e ) 74 degrees
Rationale: "m + tu + w + th = 4 * 48 = 192 tu + w + th + f = 4 * 46 = 184 m = 40 tu + w + th = 192 - 40 = 152 f = 184 – 152 = 32 answer : b"
Answer: b
Question (geometry): difference between the length & breadth of a rectangle is 30 m . if its perimeter is 300 m , then its area is ? ? we have : ( l - b ) = 30 and 2 ( l + b ) = 300 or ( l + b ) = 150 ?
Options: a ) 3 : 5 , b ) 2 : 3 , c ) 3 : 6 , d ) 3 : 4 , e ) 3 : 2
Rationale: solving the two equations , we get : l = 90 and b = 60 . the ratio of length and breath is 90 : 60 = 3 : 2 e
Answer: e
Question (geometry): what is the maximum number e of 27 cubic centimetre cubes that can fit in a rectangular box measuring 8 centimetre x 9 centimetre x 12 centimetre ?
Options: a ) 36
b ) 32
c ) 24
d ) 21
e ) 15
Rationale: 27 cubic centimetre cubes gives side = 3 cm so if : l * w * h is 9 * 12 * 8 , then max . cube we can have are 3 * 4 * 2 = 24 l * w * h is 9 * 8 * 12 , then max . cube we can have are 3 * 2 * 4 = 24 l * w * h is 12 * 8 * 9 , then max . cube we can have are 4 * 2 * 3 = 24 l * w * h is 12 * 9 * 8 , then max . cube we can have are 4 * 3 * 2 = 24 l * w * h is 8 * 12 * 9 , then max . cube we can have are 2 * 4 * 3 = 24 l * w * h is 8 * 9 * 12 , then max . cube we can have are 2 * 3 * 4 = 24 in all cases we get e = 24 cubes . ans . c
Answer: c
Question (geometry): if the area of a circle is 16 pi square feet , find its circumference .
Options: a ) 8 pi feet , b ) 28 pi feet , c ) 38 pi feet , d ) 48 pi feet , e ) 58 pi feet
Rationale: "the area is given by pi * r * r . hence pi * r * r = 16 pi r * r = 16 ; hence r = 16 feet the circumference is given by 2 * pi * r = 2 * pi * 4 = 8 pi feet correct answer a"
Answer: a
Question (general): 892.7 – 573.07 – 95.007 = ?
Options: a ) 224.623 , b ) 224.777 , c ) 233.523 , d ) 414.637 , e ) none of these
Rationale: "solution given expression = 892.7 - ( 573.07 + 95.007 ) = 892.7 - 668.077 = 224.623 . answer a"
Answer: a
Question (general): find k if 64 / k = 4 .
Options: a ) 16 , b ) 17 , c ) 18 , d ) 14 , e ) 13
Rationale: since 64 / k = 4 and 64 / 16 = 4 , then k = 16 correct answer a
Answer: a
Question (general): if 1 + 3 = 10 ; 3 + 5 = 52 ; 5 + 7 = 174 then 7 + 11 = ?
Options: a ) 354 , b ) 225 , c ) 654 , d ) 741 , e ) 464
Rationale: "1 ^ 3 + 3 ^ 2 = 1 + 9 = 10 3 ^ 3 + 5 ^ 2 = 27 + 25 = 52 5 ^ 3 + 7 ^ 2 = 125 + 49 = 174 and 7 ^ 3 + 11 ^ 2 = 343 + 121 = 464 answer : e"
Answer: e
Question (general): 10 play kabadi , 30 play kho kho only , 5 play both gmaes . then how many in total ?
Options: a ) 30 , b ) 35 , c ) 38 , d ) 40 , e ) 45
Rationale: 10 play kabadi = > n ( a ) = 10 , 5 play both gmaes . = > n ( anb ) = 5 30 play kho kho only , = > n ( b ) = n ( b only ) + n ( anb ) = 30 + 5 = 35 total = > n ( aub ) = n ( a ) + n ( b ) - n ( anb ) = 10 + 35 - 5 = 40 answer : d
Answer: d
Question (physics): 14 men make 1400 toy in 5 days 1 day after work 14 more worker join now how may days work can finish
Options: a ) 1 day , b ) 2 days , c ) 3 days , d ) 4 days , e ) 5 days
Rationale: 14 men make toy in 5 days after 1 day 14 more worker join m 1 / m 2 = d 2 / d 1 14 / 28 = d 2 / 4 = 2 day answer : b
Answer: b
Question (general): what ratio must a shopkeepermix peas and soybean of rs . 16 and rs . 25 / kg , as to obtain a mixture of rs . 19.50 ?
Options: a ) 10 : 7 , b ) 9 : 8 , c ) 11 : 7 , d ) 13 : 11 , e ) 14 : 8
Rationale: "correct option : ( c ) use rule of alligation , to determine the ratio the required ratio of soybean and peas = 5.50 : 3.50 = 11 : 7"
Answer: c
Question (gain): a sum of rs 468.75 was lent out at simple interest and at the end of 1 year and 8 months , the total amount of rs 500 is received . find the rate of interest ?
Options: a ) 3 % , b ) 4 % , c ) 5 % , d ) 6 % , e ) 7 %
Rationale: here p = 468.75 which is the principle . amount = rs 500 amount = si + p 500 = [ 468.75 * ( 20 / 12 ) * r ] / 100 + 468.75 31.25 = 156.25 * 5 r / 100 r = 4 % answer : b
Answer: b