Cheukting/mathqa huggingface dataset:
Question (general): jill has 42 gallons of water stored in quart , half - gallon , and one gallon jars . she has equal numbers of each size jar holding the liquid . what is the total number of water filled jars ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 72 , e ) 14
Rationale: let the number of each size of jar = wthen 1 / 4 w + 1 / 2 w + w = 42 1 3 / 4 w = 42 w = 24 the total number of jars = 3 w = 72 answer : d
Answer: d
Question (gain): a sum of money becomes 7 / 6 of itself in 4 years at a certain rate of simple interest . the rate per annum is ?
Options: a ) 25 / 6 , b ) 5 5 / 7 , c ) 5 5 / 2 , d ) 5 5 / 8 , e ) 5 5 / 1
Rationale: let sum = x . then , amount = 7 x / 6 s . i . = 7 x / 6 - x = x / 6 ; time = 4 years . rate = ( 100 * x ) / ( x * 6 * 4 ) = 25 / 6 % . answer : a
Answer: a
Question (general): of the 3 - digit integers greater than 700 , how many have distinct digits ?
Options: a ) 216 , b ) 82 , c ) 80 , d ) 45 , e ) 36
Rationale: three digit number can have only following 3 patterns : a . all digits are distinct ; b . two digits are alike and third is different ; c . all three digits are alike . we need to calculate b . b = total - a - c total numbers from 700 to 999 = 299 ( 3 - digit numbers greater than 700 ) ; a . all digits are distinct = 3 * 9 * 8 = 216 answer : a
Answer: a
Question (physics): a can finish a work in 9 days and b can do the same work in 15 days . b worked for 10 days and left the job . in how many days , a alone can finish the remaining work ?
Options: a ) 3 , b ) 5 1 / 2 , c ) 6 , d ) 8 , e ) none of these
Rationale: "b ' s 10 day ' s work = ( 1 / 15 * 10 ) = 2 / 3 remaining work = ( 1 - 2 / 3 ) = 1 / 3 now , 1 / 18 work is done by a in 1 day 1 / 3 work is done by a in ( 9 * 1 / 3 ) = 3 days . correct option : a"
Answer: a
Question (general): let f ( x ) = x ^ 2 + bx + c . if f ( 6 ) = 0 and f ( - 2 ) = 0 , then b + c =
Options: a ) 18 , b ) 15 , c ) - 16 , d ) - 21 , e ) - 24
Rationale: "f ( x ) = x ^ 2 + bx + c . if f ( 6 ) = 0 and f ( - 2 ) = 0 , then b + c = f ( 6 ) = 0 = 36 + 6 b + c - - - taking 36 to the other side - > 6 b + c = - 36 f ( - 2 ) = 0 = 4 - 2 b + c - - - taking - 2 b + c to the other side - > 2 b - c = 4 when we add these 2 equations , we get 8 b = - 32 - - - > b = - 4 and while substituting b = - 4 we get c = - 12 . b + c = - 16 - - - answer c"
Answer: c
Question (geometry): a wire can be bent in the form of a circle of radius 56 cm . if it is bent in the form of a square , then its area will be
Options: a ) 7744 , b ) 8844 , c ) 5544 , d ) 4444 , e ) 3444
Rationale: "length of wire = 2 pier = 2 * ( 22 / 7 ) * 56 = 352 cm side of the square = 352 / 4 = 88 cm area of the square = 88 * 88 = 7744 sq cm answer : a"
Answer: a
Question (general): if 40 % of a number is equal to two - third of another number , what is the ratio of first number to the second number ?
Options: a ) 2 : 5 , b ) 1 : 4 , c ) 3 : 7 , d ) 5 : 3 , e ) 2 : 3
Rationale: "let 40 % of a = 2 / 3 b then 40 a / 100 = 2 b / 3 2 a / 5 = 2 b / 3 a / b = 5 / 3 a : b = 5 : 3 answer is d"
Answer: d
Question (gain): i bought two books ; for rs . 480 . i sold one at a loss of 15 % and other at a loss of 25 % and then i found each book was sold at the same price . find the cost of the book sold at a lower loss ?
Options: a ) a ) 657 , b ) b ) 280 , c ) c ) 225 , d ) d ) 289 , e ) e ) 427
Rationale: "x * ( 85 / 100 ) = ( 480 - x ) 75 / 100 x = 225 answer : c"
Answer: c
Question (general): what is the tens digit of 7 ^ 1213 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "7 ^ 1 = 7 7 ^ 2 = 49 7 ^ 3 = 343 7 ^ 4 = 2401 7 ^ 5 = 16807 7 ^ 6 = 117649 we should see this as pattern recognition . we have a cycle of 4 . ( we can multiply the last 2 digits only as we care about ten ' s digit ) 0 , 4 , 4 , 0 . 1213 = 4 * 304 + 1 the ten ' s digit will be 0 . answer a"
Answer: a
Question (physics): if 5 workers collect 48 kg of cotton in 4 days , how many kg of cotton will 9 workers collect in 2 days ?
Options: a ) 47.6 kg , b ) 52.6 kg , c ) 59.6 kg , d ) 56.6 kg , e ) 57.6 kg
Rationale: "( 3 * 5 ) / 48 = ( 9 * 2 ) / x x = 57.6 kg answer : e"
Answer: e
Question (other): in the third grade of windblown school there are 78 students , one third of them failed the math test and 1 / 6 failed that literature test . at least how many students failed both tests ?
Options: a ) 0 . , b ) 6 . , c ) 8 . , d ) 10 . , e ) 12 .
Rationale: total = 78 failed in math = 78 / 3 = 26 failed in literature = 78 / 6 = 13 the least failed in both can be 0 while max can be 13 answer a
Answer: a
Question (general): david has $ 2,400 at the beginning of his trip , after spending money , he still has exactly $ 800 less than he spent on the trip . how much money does john still have ?
Options: a ) $ 200 , b ) $ 400 , c ) $ 600 , d ) $ 800 , e ) $ 1,200
Rationale: "suppose total money spent = x not spend ( money he still has ) = x - 800 x + x - 800 = 2400 x = 1600 money not spend = 1600 - 800 = 800 answer : d"
Answer: d
Question (gain): a money lender finds that due to a fall in the annual rate of interest from 8 % to 7 3 / 5 % his yearly income diminishes by rs . 61.50 . his capital is
Options: a ) 153.75 , b ) 37.78 , c ) 246.0 , d ) 27.88 , e ) 127.71
Rationale: "explanation : capital = rs . x , then 2 / 5 x = 153.75 answer : a ) rs . 153.75"
Answer: a
Question (general): if 2994 ã · 14.5 = 173 , then 29.94 ã · 1.45 = ?
Options: a ) 17.1 , b ) 17.3 , c ) 17.5 , d ) 17.7 , e ) 17.2
Rationale: "29.94 / 1.45 = 299.4 / 14.5 = ( 2994 / 14.5 ) x 1 / 10 ) [ here , substitute 173 in the place of 2994 / 14.5 ] = 173 / 10 = 17.3 answer is b ."
Answer: b
Question (general): the ages of 2 persons differ by 16 years . if 6 years ago the elder one be 3 times as old as the younger one , find the present age of younger person .
Options: a ) 10 , b ) 14 , c ) 20 , d ) 15 , e ) 32
Rationale: "age of the younger person = x age of the elder person = x + 16 3 ( x - 6 ) = x + 16 - 6 x = 14 answer is b"
Answer: b
Question (general): three numbers are in the ratio 4 : 5 : 6 and their average is 39 . the largest number is :
Options: a ) 28 , b ) 32 , c ) 36 , d ) 42 , e ) 46.8
Rationale: "explanation : let the numbers be 4 x , 5 x and 6 x . therefore , ( 4 x + 5 x + 6 x ) / 3 = 39 15 x = 117 x = 7.8 largest number = 6 x = 46.8 . answer e"
Answer: e
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 262 runs ?
Options: a ) 6.25 , b ) 6.22 , c ) 6.29 , d ) 5.75 , e ) 6.13
Rationale: "required run rate = [ 262 - ( 3.2 * 10 ) ] / 40 = 230 / 40 = 5.75 answer : d"
Answer: d
Question (physics): two pipes can fill a tank in 18 minutes and 60 minutes . an outlet pipe can empty the tank in 45 minutes . if all the pipes are opened when the tank is empty , then how many minutes will it take to fill the tank ?
Options: a ) 1 / 15 , b ) 1 / 16 , c ) 1 / 20 , d ) 1 / 10 , e ) 1 / 12
Rationale: "part of the filled by all the three pipes in one minute = 1 / 18 + 1 / 60 - 1 / 45 = 1 / 20 so , the tank becomes full in 20 minutes . answer : c"
Answer: c
Question (probability): in a certain animal population , for each of the first 3 months of life , the probability that an animal will die during that month is 1 / 10 . for a group of 400 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ?
Options: a ) 240 , b ) 246 , c ) 252 , d ) 292 , e ) 298
Rationale: "number of newborns that can die in first month = 1 / 10 * 400 = 40 survived = 360 number of newborns that can die in second month = 1 / 10 * 360 = 36 survived = 324 number of newborns that can die in third month = 1 / 10 * 324 = 32 survived = 292 answer : d"
Answer: d
Question (geometry): the length of the rectangular field is double its width . inside the field there is square shaped pond 8 m long . if the area of the pond is 1 / 50 of the area of the field . what is the length of the field ?
Options: a ) 73 , b ) 32 , c ) 34 , d ) 43 , e ) 80
Rationale: "explanation : a / 50 = 8 * 8 = > a = 8 * 8 * 50 x * 2 x = 8 * 8 * 50 x = 40 = > 2 x = 80 answer : option e"
Answer: e
Question (physics): a fill pipe can fill 2 / 3 of cistern in 40 minutes in how many minutes , it can fill full of the cistern ?
Options: a ) 60 min , b ) 36 min , c ) 25 min , d ) 30 min , e ) 50 min
Rationale: 2 / 3 of the cistern can fill in 40 min 3 / 3 of the cistern can fill in = 40 * 3 / 2 * 3 / 3 = 60 min answer is a
Answer: a
Question (general): a “ sophie germain ” prime is any positive prime number p for which 2 p + 1 is also prime . the product of all the possible units digits of sophie germain primes greater than 4 is
Options: a ) 3 , b ) 7 , c ) 189 , d ) 227 , e ) 234
Rationale: "in that case , the sophie prime numbers greater than 5 are 7 , 11,23 , 47,59 , . . which yields units digit as 1 , 3,7 and 9 product would be 1 x 3 x 7 x 9 = 189 answer should be c ."
Answer: c
Question (other): x starts a business with rs . 45000 . y joins in the business after 8 months with rs . 30000 . what will be the ratio in which they should share the profit at the end of the year ?
Options: a ) 1 : 2 , b ) 9 : 2 , c ) 1 : 3 , d ) 3 : 1 , e ) 1 : 1
Rationale: "explanation : ratio in which they should share the profit = ratio of the investments multiplied by the time period = 45000 ã — 12 : 30000 ã — 4 = 45 ã — 12 : 30 ã — 4 = 3 ã — 12 : 2 ã — 4 = 9 : 2 answer : option b"
Answer: b
Question (other): what number has a 5 : 1 ratio to the number 12 ?
Options: a ) 22 , b ) 50 , c ) 88 , d ) 52 , e ) 60
Rationale: "5 : 1 = x : 12 x = 60 answer : e"
Answer: e
Question (gain): a started a business with an investment of rs . 70000 and after 6 months b joined him investing rs . 120000 . if the profit at the end of a year is rs . 50000 , then the share of b is ?
Options: a ) 23077 , b ) 24000 , c ) 24005 , d ) 24009 , e ) 24002
Rationale: "ratio of investments of a and b is ( 70000 * 12 ) : ( 120000 * 6 ) = 7 : 6 total profit = rs . 50000 share of b = 6 / 13 ( 50000 ) = rs . 23076.92 ~ 23077 answer : a"
Answer: a
Question (general): if a * b * c = 130 , b * c * d = 65 , c * d * e = 500 and d * e * f = 250 the ( a * f ) / ( c * d ) = ?
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 3 / 4 , d ) 2 / 3 , e ) 1
Rationale: "explanation : a â ˆ — b â ˆ — c / b â ˆ — c â ˆ — d = 130 / 65 = > a / d = 2 d â ˆ — e â ˆ — f / c â ˆ — d â ˆ — e = 250 / 500 = > f / c = 1 / 2 a / d * f / c = 2 * 1 / 2 = 1 answer : e"
Answer: e
Question (geometry): how many internal diagonals does a heptagon ( seven sided polygon ) have ?
Options: a ) 7 , b ) 9 , c ) 14 , d ) 20 , e ) 35
Rationale: "number of diagonals in any polygon can be found using this formula : n ( n - 3 ) / 2 here n = 7 no . of diagonals = 7 ( 7 - 3 ) / 2 = 14 ans c"
Answer: c
Question (general): in the coordinate plane , points ( x , 5 ) and ( 7 , y ) are on line k . if line k passes through the origin and has slope 5 / 7 , then x + y =
Options: a ) 13 , b ) 14 , c ) 9 , d ) 10 , e ) 12
Rationale: "line k passes through the origin and has slope 5 / 7 means that its equation is y = 5 / 7 * x . thus : ( x , 5 ) = ( 7,5 ) and ( 7 , y ) = ( 7,5 ) - - > x + y = 7 + 5 = 12 . answer : e"
Answer: e
Question (geometry): a specialized type of sand consists of 40 % mineral x by volume and 60 % mineral y by volume . if mineral x weighs 2.5 grams per cubic centimeter and mineral y weighs 2 grams per cubic centimeter , how many grams does a cubic meter of specialized sand combination weigh ? ( 1 meter = 100 centimeters )
Options: a ) 5 , 500,000 , b ) 2 , 200,000 , c ) 55,000 , d ) 28,000 , e ) 280
Rationale: "let the volume be 1 m ^ 3 = 1 m * 1 m * 1 m = 100 cm * 100 cm * 100 cm = 1 , 000,000 cm ^ 3 by volume 40 % is x = 400,000 cm ^ 3 60 % is y = 600,000 cm ^ 3 by weight , in 1 cm ^ 3 , x is 2.5 gms in 400,000 cm ^ 3 , x = 2.5 * 400,000 = 1 , 000,000 grams in 1 cm ^ 3 , y is 2 gms in 600,000 cm ^ 3 , y = 2 * 600,000 = 1 , 200,000 gms total gms in 1 m ^ 3 = 1 , 000,000 + 1 , 200,000 = 2 , 200,000 answer : b"
Answer: b
Question (physics): if the wheel is 56 cm then the number of revolutions to cover a distance of 1056 cm is ?
Options: a ) 10 , b ) 12 , c ) 3 , d ) 11 , e ) 9
Rationale: "2 * 22 / 7 * 56 * x = 1056 = > x = 3 answer : c"
Answer: c
Question (geometry): a rectangular farm has to be fenced one long side , one short side and the diagonal . if the cost of fencing is rs . 12 per meter . the area of farm is 1200 m 2 and the short side is 30 m long . how much would the job cost ?
Options: a ) 1440 , b ) 1200 , c ) 2832 , d ) 1299 , e ) 1236
Rationale: "explanation : l * 30 = 1200 è l = 40 40 + 30 + 50 = 120 120 * 12 = 1440 answer : option a"
Answer: a
Question (physics): a boat moves upstream at the rate of 1 km in 40 minutes and down stream 1 km in 12 minutes . then the speed of the current is :
Options: a ) 1 kmph , b ) 2 kmph , c ) 1.75 kmph , d ) 2.5 kmph , e ) 3.5 kmph
Rationale: "rate upstream = ( 1 / 40 * 60 ) = 1.5 kmph rate dowm stream = 1 / 12 * 60 = 5 kmph rate of the current = ½ ( 5 - 1.5 ) = 1.75 kmph answer : c"
Answer: c
Question (physics): if 10 bulls can plough 20 identical fields in 3 days working 10 hours a day , then in how many days can 30 bulls plough 32 same identical fields working 8 hours a day ?
Options: a ) 8 , b ) 7 , c ) 5 , d ) 2.0 , e ) 1
Rationale: explanation : m 1 * d 1 * w 2 = m 2 * d 2 * w 1 10 * 3 * 10 * 32 = 30 * d * 8 * 20 d = 2 days answer : d
Answer: d
Question (general): how many numbers from 2 to 7 are exactly divisible by 2 ?
Options: a ) 2 , b ) 3 , c ) 5 , d ) 7 , e ) 8
Rationale: "2 / 2 = 1 and 7 / 2 = 3 3 - 1 = 2 2 + 1 = 3 numbers . b )"
Answer: b
Question (general): the product of two numbers is 120 . the sum of their squares is 289 . the sum of the two numbers is :
Options: a ) 20 , b ) 23 , c ) 169 , d ) 172 , e ) 198
Rationale: "explanation : let the number be x and y . we know that , ( x + y ) 2 = ( x 2 + y 2 ) + 2 xy = 289 + 2 × 120 = 289 + 240 = 529 ⇒ x + y = √ 529 = 23 correct option : b"
Answer: b
Question (general): the least number , which when divided by 8 , 15 , 20 and 54 leaves in each case a remainder of 8 is :
Options: a ) 448 , b ) 488 , c ) 542 , d ) 548 , e ) 1088
Rationale: "required number = ( l . c . m . of 8 , 15 , 20 , 54 ) + 8 = 1080 + 8 = 1088 . answer : e"
Answer: e
Question (other): there are 10 slate rocks , 15 pumice rocks , and 6 granite rocks randomly distributed in a certain field . if 2 rocks are chosen at random and without replacement , what is the probability that both rocks will be slate rocks ?
Options: a ) 2 / 19 , b ) 3 / 31 , c ) 4 / 37 , d ) 5 / 41 , e ) 6 / 53
Rationale: "10 / 31 * 9 / 30 = 3 / 31 the answer is b ."
Answer: b
Question (general): the average of 6 no . ' s is 2.80 . the average of 2 of them is 2.4 , while the average of the other 2 is 2.3 . what is the average of the remaining 2 no ' s ?
Options: a ) 2.3 , b ) 2.6 , c ) 3.6 , d ) 3.7 , e ) 4.6
Rationale: sum of the remaining two numbers = ( 2.80 * 6 ) - [ ( 2.4 * 2 ) + ( 2.3 * 2 ) ] = 16.80 - ( 4.8 + 4.6 ) = 16.80 - 9.40 = 7.40 required average = ( 7.4 / 2 ) = 3.7 answer : d
Answer: d
Question (general): if x and y are integers and | x - y | = 12 , what is the minimum possible value of xy ?
Options: a ) - 12 , b ) - 18 , c ) - 24 , d ) - 36 , e ) - 48
Rationale: "we are given | x - y | = 12 , minimum possible value of xy would be maximum numeric value with a - ive sign . . so one of x or y will be negative and other negative . . | x - y | = 12 in this case means that the numeric sum of x and y is 12 . . various combinations could be - 1 and 11 , - 2 and 10 , - 6 and 6 , - 11 and 1 and so on . . when the sum of two numbers is given , the max product is when both x and y are same numeric value . . . so xy will have max numeric value when numeric value of x and y = 12 / 2 = 6 . . so numeric value of xy = 36 but one of x and y is - ive . . so answer is - 36 answer : d"
Answer: d
Question (geometry): what is the smallest positive perfect square that is divisible by 4 , 10 , and 18 ?
Options: a ) 900
b ) 1,600
c ) 2,500
d ) 3,600
e ) 4,900
Rationale: the number needs to be divisible by 2 ^ 2 , 2 * 5 , and 2 * 3 ^ 2 . the smallest such perfect square is 2 ^ 2 * 3 ^ 2 * 5 ^ 2 = 900 the answer is a .
Answer: a
Question (general): if grapes are 91 % water and raisins are 19 % water , then how many kilograms did a quantity of raisins , which currently weighs 9 kilograms , weigh when all the raisins were grapes ? ( assume that the only difference between their raisin - weight and their grape - weight is water that evaporated during their transformation . )
Options: a ) 63 , b ) 72 , c ) 81 , d ) 90 , e ) 99
Rationale: "let x be the original weight . the weight of the grape pulp was 0.09 x . since the grape pulp is 81 % of the raisins , 0.09 x = 0.81 ( 9 kg ) . then x = 9 * 9 = 81 kg . the answer is c ."
Answer: c
Question (general): a bag contains an equal number of one rupee , 50 paise and 25 paise coins respectively . if the total value is 210 , how many coins of each type are there ?
Options: a ) 20 coins , b ) 50 coins , c ) 100 coins , d ) 120 coins , e ) none of these
Rationale: "let number of each type of coin = x . then , 1 × x + . 50 × x + . 25 x = 210 ⇒ 1.75 x = 210 ⇒ x = 120 coins answer d"
Answer: d
Question (physics): a metallic sphere of radius 12 cm is melted and drawn into a wire , whose radius of cross section is 4 cm . what is the length of the wire ?
Options: a ) 116 cm , b ) 144 cm , c ) 168 cm , d ) 173 cm , e ) 189 cm
Rationale: "volume of the wire ( in cylindrical shape ) is equal to the volume of the sphere . π ( 4 ) ^ 2 * h = ( 4 / 3 ) π ( 12 ) ^ 3 = > h = 144 cm answer : b"
Answer: b
Question (physics): a train crosses a platform of 150 m in 15 sec , same train crosses another platform of length 250 m in 20 sec . then find the length of the train ?
Options: a ) 150 m , b ) 188 m , c ) 267 m , d ) 268 m , e ) 287 m
Rationale: "length of the train be ‘ x ’ x + 150 / 15 = x + 250 / 20 4 x + 600 = 3 x + 750 x = 150 m answer : a"
Answer: a
Question (general): find √ ? / 19 = 4 ?
Options: a ) 76 , b ) 5776 , c ) 304 , d ) 1296 , e ) none
Rationale: "answer let √ n / 19 = 4 then √ n = 19 x 4 = 76 ∴ n = 76 x 76 = 5776 . correct option : b"
Answer: b
Question (general): a certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint . if 2 gallons of the mixture is needed and the individual colors can be purchased only in one gallon or half gallon cans , what is the least amount of paint , in gallons , that must be purchased in order to measure out the portions needed for the mixture ?
Options: a ) 2 , b ) 2 1 / 2 , c ) 3 , d ) 3 1 / 2 , e ) 4
Rationale: "ratio ; white : black : gray = 3 : 5 : ( 3 + 5 ) = 3 : 5 : 8 if 2 gallons of the mixture is needed < = = > need 2 gallons of gray paint . then , 3 : 5 : 8 = x : y : 2 3 / 8 = x / 2 ; x = 3 / 4 5 / 8 = y / 2 ; y = 5 / 4 you need 3 / 4 gallon of white . you have to buy 1 gallons . you need 5 / 4 gallons of black . you have to buy 1 gallon and another 1 / 2 gallon of black . the least amount of paint = 1 + 1 + 1 / 2 = 2.5 . answer : b"
Answer: b
Question (geometry): if the radius of a circle that centers at the origin is 5 , how many j points on the circle have integer coordinates ?
Options: a ) 4
b ) 8
c ) 12
d ) 15
e ) 20
Rationale: i understand this might not be required but i used the equation of a circle . since the origin is at 0 , x ^ 2 + y ^ 2 = 5 ^ 2 . x , y could be + / - ( 0,5 or 5,0 ) - 4 possibilities . x , y could be + / - ( 3,4 or 4,3 ) - 8 possibilities . ans : j = c
Answer: c
Question (general): an automobile parts supplier charges $ 25 per package of gaskets . when a customer orders more than 10 packages of gaskets , the supplier charges 4 / 5 the price for each package in excess of 10 . during a certain week , the supplier sold 50 packages of gaskets . if 20 percent of the gaskets went to company x , 15 percent to company y , and the rest to company z , what was the total amount , in dollars , that the parts supplier received in payment for the gaskets ?
Options: a ) 1105 , b ) 1245 , c ) 1275 , d ) 1215 , e ) 1150
Rationale: "$ 25 per packet of gasket in case a customer orders less than 10 in case a customer orders > 10 price per gasket = 25 * 4 / 5 = 20 a certain week the supplier sold 60 gasket 1 . he sold 20 % of the gaskets to x = 10 gaskets = 25 * 10 = 250 2 . he sold 30 % of the gaskets to y = 15 gaskets = 25 * 10 + 20 * 5 = 350 3 . he sold remaining 50 % to z = 25 gaskets = 25 * 10 = 250 + 20 * 15 = 550 thus , total money earned 250 + 350 + 550 = 1150 answer is e"
Answer: e
Question (physics): ravi can do a piece of work in 15 days while prakash can do it in 30 days . in how many days will they finish it together ?
Options: a ) 11 days , b ) 9 days , c ) 8 days , d ) 12 days , e ) 10 days
Rationale: "1 / 15 + 1 / 30 = 3 / 30 10 / 1 = 10 days answer : e"
Answer: e
Question (general): ( 1000 ) 7 ÷ ( 10 ) 16 = ?
Options: a ) 10 , b ) 100 , c ) 1000 , d ) 100000 , e ) none of these
Rationale: "explanation : = ( 103 ) 7 / ( 10 ) 16 = ( 10 ) 21 / ( 10 ) 16 = 10 ( 5 ) = 100000 option d"
Answer: d
Question (general): what is remainder of the division ( 1425 * 1427 * 1429 ) / 12 ?
Options: a ) 5 , b ) 0 , c ) 1 , d ) 2 , e ) 3
Rationale: "remainder will be number / 100 here as the divisor is two digit number = 12 . hence checking for the last two digits = 5 * 7 * 9 = 15 thus remainder = 3 . answer : e"
Answer: e
Question (physics): two men a and b start from place x walking at 4 ½ kmph and 5 ¾ kmph respectively . how many km apart they are at the end of 5 ½ hours if they are walking in the same direction ?
Options: a ) 7 km , b ) 6 km , c ) 6 7 / 8 km , d ) 9 km , e ) 5 km
Rationale: "rs = 5 ¾ - 4 ½ = 1 ¼ t = 3 ½ h . d = 5 / 4 * 11 / 2 = 55 / 8 = 6 7 / 8 km answer : c"
Answer: c
Question (gain): a man walking at a rate of 10 km / hr crosses a bridge in 10 minutes . the length of the bridge is ?
Options: a ) 1521 , b ) 1492 , c ) 1667 , d ) 1254 , e ) 1112
Rationale: "speed = 10 * 5 / 18 = 50 / 18 m / sec distance covered in 10 minutes = 50 / 18 * 10 * 60 = 1667 m answer is c"
Answer: c
Question (physics): the distance from steve ' s house to work is 40 km . on the way back steve drives twice as fast as he did on the way to work . altogether , steve is spending 6 hours a day on the roads . what is steve ' s speed on the way back from work ?
Options: a ) 5 . , b ) 10 . , c ) 14 . , d ) 15 . , e ) 20 .
Rationale: "time is in the ratio 2 : 1 : : to : fro office therefore , 2 x + 1 x = 6 hrs time take to come back - 2 hrs , distance travelled - 40 km = > speed = 20 kmph e"
Answer: e
Question (general): the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 67 kg . what is the weight of the new person ?
Options: a ) 75 , b ) 65 , c ) 87 , d ) 95 , e ) 80
Rationale: "total increase in weight = 8 × 2.5 = 20 if x is the weight of the new person , total increase in weight = x − 67 = > 20 = x - 67 = > x = 20 + 67 = 87 answer is c ."
Answer: c
Question (general): if a # b = ab – b + b ^ 2 , then 3 # 8 =
Options: a ) 80 , b ) 8 , c ) 15 , d ) 21 , e ) 35
Rationale: "solution - simply substitute 3 and 8 in equation in the place of a and b respectively . 3 # 8 = 3 * 8 - 8 + 8 ^ 2 = 24 - 8 + 64 = 80 . ans a"
Answer: a
Question (general): a marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each . there can be no less than 8 musicians per row and no more than 30 musicians per row . how many different rectangular formations z are possible ?
Options: a ) 3 , b ) z = 4 , c ) z = 5 , d ) z = 6 , e ) z = 8
Rationale: "the combinations could be { ( 1,240 ) , ( 2,120 ) , ( 3,80 ) , ( 4,60 ) , ( 5,48 ) , ( 6,40 ) , ( 8,30 ) , ( 10,24 ) , ( 12,20 ) , ) 15,16 ) , ( 16,15 ) , ( 20,12 ) , ( 24,10 ) , ( 30,8 ) , ( 40,6 ) , ( 48,5 ) , ( 60,4 ) , ( 80,3 ) , ( 120,2 ) , ( 240,1 ) } of these we are told 8 < = t < = 30 so we can remove these pairs , and we are left only with . { ( 8,30 , ( 10,24 ) , ( 12,20 ) , ( 15,16 ) , ( 16,15 ) , ( 20,12 ) , ( 24,10 ) , ( 30,8 ) } hence 8 . e"
Answer: e
Question (general): find the sum of first 10 odd numbers
Options: a ) 10 , b ) 40 , c ) 200 , d ) 100 , e ) 540
Rationale: "explanation : n 2 = 102 = 100 answer : option d"
Answer: d