Cheukting/mathqa huggingface dataset:
Question (general): if x ^ 2 + 1 / x ^ 2 = 9 , what is the value of x ^ 4 + 1 / x ^ 4 ?
Options: a ) 10 , b ) 72 , c ) 79 , d ) 16 , e ) 18
Rationale: "important : i notice that if we square x ² , we get x ⁴ , and if we square 1 / x ² , we get 1 / x ⁴ , so let ' s see what happens if we take the equation x ² + 1 / x ² = 9 andsquareboth sides : ( x ² + 1 / x ² ) ² = 81 so , ( x ² + 1 / x ² ) ( x ² + 1 / x ² ) = 81 expand to get : x ⁴ + 1 + 1 + 1 / x ⁴ = 81 simplify : x ⁴ + 1 / x ⁴ = 79 answer : c"
Answer: c
Question (general): a certain no . when divided by 65 leaves a remainder 25 , what is the remainder if the same no . be divided by 15 ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 9
Rationale: "explanation : 65 + 25 = 90 / 15 = 6 ( remainder ) c"
Answer: c
Question (gain): a , b and c started a partnership business by investing rs . 24000 , rs . 32000 , rs . 36000 respectively . at the end of the year , the profit were distributed among them . if c ' s share of profit is 36000 , what is the total profit ?
Options: a ) 70000 , b ) 60000 , c ) 80000 , d ) 92000 , e ) 50000
Rationale: "a : b : c = 24000 : 32000 : 36000 = 6 : 8 : 9 let total profit = p then p ã — 9 / 23 = 36000 p = ( 36000 ã — 23 ) / 9 = 92000 answer is d ."
Answer: d
Question (general): the prices of tea and coffee per kg were the same in june . in july the price of coffee shot up by 20 % and that of tea dropped by 20 % . if in july , a mixture containing equal quantities of tea and coffee costs 60 / kg . how much did a kg of coffee cost in june ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 60
Rationale: "let the price of tea and coffee be x per kg in june . price of tea in july = 1.2 x price of coffee in july = 0.8 x . in july the price of 1 / 2 kg ( 500 gm ) of tea and 1 / 2 kg ( 500 gm ) of coffee ( equal quantities ) = 50 1.2 x ( 1 / 2 ) + 0.8 x ( 1 / 2 ) = 60 = > x = 60 e"
Answer: e
Question (physics): brenda and sally run in opposite direction on a circular track , starting at diametrically opposite points . they first meet after brenda has run 300 meters . they next meet after sally has run 150 meters past their first meeting point . each girl runs at a constant speed . what is the length of the track in meters ?
Options: a ) 250 , b ) 300 , c ) 350 , d ) 700 , e ) 500
Rationale: "nice problem . + 1 . first timetogetherthey run half of the circumference . second timetogetherthey run full circumference . first time brenda runs 300 meters , thus second time she runs 2 * 300 = 600 meters . since second time ( when they run full circumference ) brenda runs 600 meters and sally runs 150 meters , thus the circumference is 600 + 150 = 750 meters . answer : d ."
Answer: d
Question (physics): a person travels equal distances with speeds of 8 km / hr , 9 km / hr and 10 km / hr and takes a total time of 47 minutes . the total distance is ?
Options: a ) 6 km , b ) 3 km , c ) 7 km , d ) 5 km , e ) 2 km
Rationale: "let the total distance be 3 x km . then , x / 8 + x / 9 + x / 10 = 47 / 60 x / 3 = 47 / 60 = > x = 2.33 . total distance = 3 * 2.33 = 6.99 km . answer : c"
Answer: c
Question (general): when positive integer n is divided by positive integer j , the remainder is 16 . if n / j = 127.05 , what is value of j ?
Options: a ) 300 , b ) 320 , c ) 370 , d ) 400 , e ) 450
Rationale: "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 127.05 here 127 is the quotient . given that remainder = 16 so , 127.05 = 127 + 16 / j so , j = 320 answer : b"
Answer: b
Question (general): the ratio of the ages of mini and minakshi is 4 : 3 . the sum of their ages is 28 years . the ratio of their ages after 5 years will be
Options: a ) 22 : 17 , b ) 9 : 11 , c ) 5 : 4 , d ) 4 : 5 , e ) 8 : 11
Rationale: "let mini ’ s age = 4 x and minakshi ’ s age = 3 x then 4 x + 3 x = 28 x = 4 mini ’ s age = 16 years and minakshi ’ s age = 12 years ratio of their ages after 8 years = ( 16 + 5 ) : ( 12 + 5 ) = 22 : 17 answer : a"
Answer: a
Question (general): there is an antique clock exhibition . so many clock are piled up with distinct numbers tagged with them . the person managing it hangs different clocks numbers periodically on the main wall . at 9 : 20 am , he hung the clock number 200 ; at 11 : 00 am , he hung the clock number 30 ; at 4 : 00 pm , he hung the clock number 240 . which numbered clock will he hang on the wall when the time is 7 : 30 pm ?
Options: a ) 313 , b ) 314 , c ) 315 , d ) 316 , e ) 317
Rationale: solution : he will hang clock number 315 at 7 : 30 pm . the person has been hanging the clock number which corresponds with the angle between the hour hand and the minute hand of the clock at that time . answer c
Answer: c
Question (general): the mean of 30 values was 150 . it was detected on rechecking that one value 165 was wrongly copied as 135 for the computation of the mean . find the correct mean .
Options: a ) 151 , b ) 149 , c ) 152 , d ) 148 , e ) none of the above
Rationale: "corrected mean = 150 × 30 − 135 + 165 / 30 = 4500 − 135 + 165 / 30 = 4530 / 30 = 151 answer a"
Answer: a
Question (gain): machine a and machine b are each used to manufacture 550 sprockets . it takes machine a 10 hours longer to produce 660 sprockets than machine b . machine b produces 10 % more sprockets per hour than machine a . how many sprockets per hour does machineaproduce ?
Options: a ) 5.5 , b ) 6.6 , c ) 60 , d ) 100 , e ) 110
Rationale: "time taken by b = t time taken by a = t + 10 qty produced by a = q qty produced by b = 1.1 q for b : t ( 1.1 q ) = 550 qt = 500 for a : ( t + 10 ) ( q ) = 550 qt + 10 q = 550 500 + 10 q = 550 q = 5 so a can produce 5 / hour . then b can produce = 5 ( 1.1 ) = 5.5 / hour . a"
Answer: a
Question (general): a batch of cookies was divided amomg 4 tins : 2 / 3 of all the cookies were placed in either the blue or the green tin , and the rest were placed in the red tin . if 1 / 4 of all the cookies were placed in the blue tin , what fraction of the cookies that were placed in the other tins were placed in the green tin
Options: a ) 15 / 2 , b ) 9 / 4 , c ) 5 / 9 , d ) 7 / 5 , e ) 5 / 8
Rationale: "this will help reduce the number of variables you have to deal with : g + b = 2 / 3 r = 1 / 4 b = 1 / 4 we can solve for g which is 5 / 12 what fraction ( let it equal x ) of the cookies that were placed in the other tins were placed in the green tin ? so . . x * ( g + r ) = g x * ( 5 / 12 + 1 / 4 ) = 5 / 12 x = 5 / 8 answer : e"
Answer: e
Question (general): there are , in a certain league , 8 teams , and each team face another team for a total of 12 times . how many games are played in the season ?
Options: a ) 150 , b ) 121 , c ) 144 , d ) 180 , e ) 1200
Rationale: "by using the formula , t [ n ( n - 1 ) / 2 ] , where t = no . of games between two teams and n = total no . of teams , we get : 144 option c ."
Answer: c
Question (general): a man spends rs . 1700 per month on an average for the first 3 months , rs 1550 for next 4 months and rs . 1800 per month for the last 5 months and saves rs . 5200 a year . what is his average monthly income ?
Options: a ) 2025 , b ) 2125 , c ) 2225 , d ) 2325 , e ) 2425
Rationale: explanation : total expenditure for the first 3 months = 3 ã — 1700 = 5100 total expenditure for 4 months = 4 ã — 1550 = 6200 total expenditure for 5 months = 5 ã — 1800 = 9000 total expenditure and saving ( which is income for one year ) = 5100 + 6200 + 9000 + 5200 = rs . 25500 so , average monthly income = 25500 / 12 = rs . 2125 answer b
Answer: b
Question (general): 25 x 10 + 25 x 11 = ?
Options: a ) 725 , b ) 720 , c ) 600 , d ) 525 , e ) none of them
Rationale: "= 25 x ( 10 + 11 ) ( by distributive law ) = 25 x 21 = 525 answer is d"
Answer: d
Question (general): the average of 25 results is 45 . the average of first 12 of those is 14 and the average of last 12 is 17 . what is the 13 th result ?
Options: a ) 740 , b ) 750 , c ) 690 , d ) 780 , e ) 708
Rationale: "solution : sum of 1 st 12 results = 12 * 14 sum of last 12 results = 12 * 17 13 th result = x ( let ) now , 12 * 14 + 12 * 17 + x = 25 * 45 or , x = 708 . answer : option e"
Answer: e
Question (gain): the sale price sarees listed for rs . 400 after successive discount is 20 % and 15 % is ?
Options: a ) 297 , b ) 272 , c ) 342 , d ) 762 , e ) 269
Rationale: "400 * ( 80 / 100 ) * ( 85 / 100 ) = 272 answer : b"
Answer: b
Question (probability): a bag contains 3 blue and 5 white marbles . one by one , marbles are drawn out randomly until only two are left in the bag . what is the probability q that out of the two , one is white and one is blue ?
Options: a ) 15 / 56 , b ) 41 / 56 , c ) 13 / 28 , d ) 15 / 28 , e ) 5 / 14
Rationale: the required probability q = probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls . ways to select 6 out of total 8 = 8 c 6 ways to select 4 out of 5 white balls = 5 c 4 ways to select 2 out of 3 blue balls = 3 c 2 thus the required probability = ( 5 c 4 * 3 c 2 ) / 8 c 6 = 15 / 28 . d is thus the correct answer .
Answer: d
Question (general): in what proportion must rice at rs 3.10 per kg be mixed with rice at rs 3.60 per kg , so that the mixture be worth rs 3.25 a kg ?
Options: a ) 3 / 5 , b ) 3 / 2 , c ) 5 / 3 , d ) 5 / 7 , e ) 7 / 3
Rationale: "c . p of 1 kg of cheaper rice = rs 3.10 c . p of 1 kg of expensive rice = rs 3.60 the mixture be worth for 1 kg = rs 3.25 by the alligation rule : quantity of cheaper rice / quantity of expensive rice = ( 3.6 - 3.25 ) / ( 3.25 - 3.10 ) = ( 0.35 ) / ( 0.15 ) = 7 / 3 e"
Answer: e
Question (general): of the families in city x in 1994 , 40 percent owned a personal computer . the number of families in city x owning a computer in 1998 was 30 percent greater than it was in 1994 , and the total number of families in city x was 4 percent greater in 1998 than it was in 1994 . what percent of the families in city x owned a personal computer in 1998 ?
Options: a ) 50 % , b ) 52 % , c ) 56 % , d ) 70 % , e ) 74 %
Rationale: "say a 100 families existed in 1994 then the number of families owning a computer in 1994 - 40 number of families owning computer in 1998 = 40 * 130 / 100 = 52 number of families in 1998 = 104 the percentage = 52 / 104 * 100 = 50 % . answer : a"
Answer: a
Question (general): one - third less than 35 % of 180 is equal to :
Options: a ) 15 , b ) 30 , c ) 35 , d ) 42 , e ) 45
Rationale: lots of ways to tackle this . 35 % of 180 = 63 1 / 3 of 63 = 21 so , 1 / 3 less than 63 is equal to 63 - 21 = 42 answer : d
Answer: d
Question (general): country x imported approximately $ 1.44 billion of goods in 1996 . if country x imported $ 420 million of goods in the first two months of 1997 and continued to import goods at the same rate for the rest of the year , by how much would country xs 1997 imports exceed those of 1996 ?
Options: a ) $ 214 million , b ) $ 1120 million , c ) $ 1144 million , d ) $ 1240 million , e ) $ 1080 million
Rationale: "convert units to millions as answer is in millions 1996 imports = $ 1.44 bill = $ 1440 mill i . e . 1440 / 12 = $ 120 mill / month 1997 imports = $ 420 mill / 2 month i . e . $ 210 mill / month difference / month = 210 - 120 = 90 difference / year = $ 90 mill * 12 = $ 1080 mill answer : e"
Answer: e
Question (physics): a company produces 65000 bottles of water everyday . if a case can hold 13 bottles of water . how many cases are required by the company to hold its one day production
Options: a ) 2000 , b ) 4500 , c ) 5000 , d ) 8000 , e ) 9000
Rationale: "number of bottles that can be held in a case = 13 number of cases required to hold 65000 bottles = 65000 / 13 = 5000 cases . so the answer is c = 5000"
Answer: c
Question (gain): what will be the fraction of 5 %
Options: a ) 1 / 20 , b ) 1 / 50 , c ) 1 / 75 , d ) 1 / 25 , e ) none of these
Rationale: "explanation : 5 * 1 / 100 = 1 / 20 . option a"
Answer: a
Question (general): operation # is defined as adding a randomly selected two digit multiple of 4 to a randomly selected two digit prime number and reducing the result by half . if operation # is repeated 10 times , what is the probability that it will yield at least two integers ?
Options: a ) 0 % , b ) 10 % , c ) 20 % , d ) 30 % , e ) 40 %
Rationale: "any multiple of 4 is even . any two - digit prime number is odd . ( even + odd ) / 2 is not an integer . thus # does not yield an integer at all . therefore p = 0 . answer : a ."
Answer: a
Question (geometry): calculate the area of a triangle , if the sides are 13 cm , 12 cm and 5 cm , what is its area ?
Options: a ) 36 cm 2
b ) 35 cm 2
c ) 30 cm 2
d ) 32 cm 2
e ) 31 cm 2
Rationale: the triangle with sides 13 cm , 12 cm and 5 cm is right angled , where the hypotenuse is 13 cm . area of the triangle = 1 / 2 * 12 * 5 = 30 cm 2 answer : c
Answer: c
Question (general): 1 , 3,5 , 7,9 , . . 50 find term of sequnce for this .
Options: a ) 1356 , b ) 1557 , c ) 1688 , d ) 1700 , e ) 2500
Rationale: "this is an arithmetic progression , and we can write down a = 1 a = 1 , d = 2 d = 2 , n = 50 n = 50 . we now use the formula , so that sn = 12 n ( 2 a + ( n − 1 ) l ) sn = 12 n ( 2 a + ( n − 1 ) l ) s 50 = 12 × 50 × ( 2 × 1 + ( 50 − 1 ) × 2 ) s 50 = 12 × 50 × ( 2 × 1 + ( 50 − 1 ) × 2 ) = 25 × ( 2 + 49 × 2 ) = 25 × ( 2 + 49 × 2 ) = 25 × ( 2 + 98 ) = 25 × ( 2 + 98 ) = 2500 = 2500 . e"
Answer: e
Question (general): if a ^ 2 + b ^ 2 = 177 and ab = 54 then find the value of a + b / a - b ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "( a + b ) ^ 2 = a ^ 2 + b ^ 2 + 2 ab = 117 + 2 * 24 = 225 a + b = 15 ( a - b ) ^ 2 = a ^ 2 + b ^ 2 - 2 ab = 117 - 2 * 54 a - b = 3 a + b / a - b = 15 / 3 = 5 answer is c ."
Answer: c
Question (general): a certain mixture of nuts consists of 5 parts almonds to 2 parts walnuts , by weight . what is the number of pounds of almonds in 210 pounds of the mixture ?
Options: a ) 150 , b ) 84 , c ) 40 , d ) 28 , e ) 20
Rationale: "almonds : walnuts = 5 : 2 total mixture has 7 parts in a 210 pound mixture , almonds are 5 / 7 ( total mixture ) = 5 / 7 * 210 = 150 pounds answer ( a )"
Answer: a
Question (general): the simple interest on a sum of money will be rs . 1200 after 10 years . if the principal is trebled after 5 years what will be the total interest at the end of the tenth year ?
Options: a ) 8981 , b ) 3799 , c ) 1200 , d ) 2400 , e ) 1732
Rationale: "p - - - 10 - - - - 1200 p - - - 5 - - - - - 600 3 p - - - 5 - - - - - 1800 - - - - - - = > 2400 answer : d"
Answer: d
Question (physics): pipe p can drain the liquid from a tank in 4 / 4 the time that it takes pipe q to drain it and in 2 / 3 the time that it takes pipe r to do it . if all 3 pipes operating simultaneously but independently are used to drain liquid from the tank , then pipe q drains what portion of the liquid from the tank ?
Options: a ) 9 / 29 , b ) 8 / 23 , c ) 3 / 4 , d ) 17 / 29 , e ) 3 / 8
Rationale: "suppose q can drain in 1 hr . so , rq = 1 / 1 = 1 so , rp = 1 / [ ( 4 / 4 ) rq ] = 4 / 4 = 1 also , rp = rr / ( 2 / 3 ) = > 1 = rr / ( 2 / 3 ) = > rr = 2 / 3 let h is the time it takes to drain by running all 3 pipes simultaneously so combined rate = rc = 1 / h = 1 + 1 + 2 / 3 = 8 / 3 = 1 / ( 3 / 8 ) thus running simultaneously , pipe q will drain 3 / 8 of the liquid . thus answer = e ."
Answer: e
Question (general): a number whose fifth part increased by 4 is equal to its fourth part diminished by 4 is ?
Options: a ) 160 , b ) 180 , c ) 200 , d ) 220 , e ) none
Rationale: "answer let the number be n . then , ( n / 5 ) + 4 = ( n / 4 ) - 4 â ‡ ’ ( n / 4 ) - ( n / 5 ) = 8 â ‡ ’ ( 5 n - 4 n ) / 20 = 8 â ˆ ´ n = 160 option : a"
Answer: a
Question (physics): a , b , c together can earn $ 600 per day . while a and c together earn $ 400 and b and c together can earn $ 300 . the daily earnings of c ?
Options: a ) $ 100 , b ) $ 200 , c ) $ 250 , d ) $ 300 , e ) $ 500
Rationale: b ' s daily earnings = 600 - 400 = $ 200 a ' s daily earnings = 600 - 300 = $ 300 c ' s daily earnings = 600 - 200 - 300 = $ 100 answer is a
Answer: a
Question (physics): a can do a piece of work in 3 days of 5 hours each and b alone can do it in 5 days of 3 hours each . how long will they take it to do working together 3 / 4 hours a day ?
Options: a ) 6 days , b ) 5 days , c ) 10 days , d ) 9 days , e ) 8 days
Rationale: a ' s work per hour = 1 / 15 b ' s work per hour = 1 / 15 a & b ' s work per hour together = ( 1 / 15 ) + ( 1 / 15 ) = 2 / 15 so a & b together complete the work in 15 / 2 hours . . . if they work 2 1 / 2 = 5 / 2 hours a day , it will take ( 15 / 2 ) / ( 3 / 4 ) days = 10 days . . . answer : c
Answer: c
Question (general): if the price of a certain bond on may 1 st was 3 / 4 the price of the bond on june 1 st and the price of the bond on july 1 st was 50 % greater than the price of the bond on may 1 st . then the price of the bond on june 1 st st was what percent of the average ( arithmetic mean ) price of the bond on may 1 st and july 1 st ?
Options: a ) 50 % , b ) 114.28 % , c ) 120 % , d ) 133 1 / 3 % , e ) 150 %
Rationale: the price on june 1 st = 12 ( assume ) ; the price on may 1 st = 3 / 4 * 12 = 9 ; the price on july 1 st = 8 * 1.5 = 12 . the average price of the bond on may 1 st and july 1 st = ( 9 + 12 ) / 2 = 10.5 . the price of the bond on june 1 st ( 12 ) is 24 / 21 times ( 114.28 % ) the average price of the bond on may 1 st and july 1 st . answer : b .
Answer: b
Question (physics): a 300 m long train crosses a platform in 40 sec while it crosses a signal pole in 18 sec . what is the length of the platform ?
Options: a ) 288 , b ) 350 , c ) 889 , d ) 367 , e ) 234
Rationale: "speed = 300 / 18 = 50 / 3 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 40 = 50 / 3 3 x + 900 = 2000 = > x = 367 m . answer : d"
Answer: d
Question (general): the average age of a class of 25 students is 26 years . the average increased by 1 when the teacher ' s age also included . what is the age of the teacher ?
Options: a ) 40 , b ) 41 , c ) 52 , d ) 62 , e ) 73
Rationale: "total age of all students = 25 ã — 26 total age of all students + age of the teacher = 26 ã — 27 age of the teacher = 27 ã — 26 â ˆ ’ 25 ã — 26 = 26 ( 27 â ˆ ’ 25 ) = 26 ã — 2 = 52 answer is c ."
Answer: c
Question (general): the difference between two numbers is 1356 . when the larger number is divided by the smaller one , the quotient is 6 and the remainder is 15 . the smaller number is
Options: a ) 240 , b ) 270 , c ) 295 , d ) 360 , e ) 340
Rationale: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 15 5 x = 1350 x = 270 smaller number = 270 answer : b"
Answer: b
Question (general): on a test , the boys in the class averaged 90 points and the girls in the class averaged 96 points . if the overall class average was 94 points , what is the ratio of boys to girls in the class ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 3 / 5 , e ) 4 / 5
Rationale: ( 96 g + 90 b ) / ( g + b ) = 94 96 g + 90 b = 94 ( g + b ) 2 g = 4 b b / g = 1 / 2 the answer is a .
Answer: a
Question (general): 9 - 3 ÷ 1 / 3 + 3 = ?
Options: a ) 1 , b ) 3 , c ) 6 , d ) 9 , e ) 12
Rationale: 9 - 3 1 / 3 + 3 = 9 - 3 ÷ 1 / 3 + 3 = 9 - ( 3 x 3 ) + 3 = 9 - 9 + 3 = 3 correct answer : b
Answer: b
Question (general): if n divided by 7 has a remainder of 2 , what is the remainder when 5 times n is divided by 7 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 6
Rationale: "as per question = > n = 7 p + 2 for some integer p hence 5 n = > 35 q + 10 = > remainder = > 10 for some integer q alternatively = > n = 2 > 5 n = > 10 = > 10 divided by 7 will leave a remainder 3 hence c"
Answer: c
Question (general): in the coordinate plane , points ( x , 2 ) and ( 8 , y ) are on line k . if line k passes through the origin and has slope 1 / 2 , then x + y =
Options: a ) 8 , b ) 6 , c ) 5 , d ) 3 , e ) 2
Rationale: "line k passes through the origin and has slope 1 / 2 means that its equation is y = 1 / 2 * x . thus : ( x , 2 ) = ( 4 , 2 ) and ( 8 , y ) = ( 8,4 ) - - > x + y = 4 + 4 = 8 . answer : a"
Answer: a
Question (general): find the ones digit of 73 ^ 355
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 9
Rationale: the units digit of 73 ^ 355 will be the same as the units digit of 3 ^ 355 . 3 ^ 1 = 3 - - > the units digit is 3 ; 3 ^ 2 = 9 - - > the units digit is 9 ; 3 ^ 3 = 27 - - > the units digit is 7 ; 3 ^ 4 = 81 - - > the units digit is 1 ; 3 ^ 5 = 243 - - > the units digit is 3 again ; . . . so , as you can see the units digit repeats in blocks of 4 : { 3 , 9 , 7 , 1 } , { 3 , 9 , 7 , 1 } , . . . now , since 355 = 352 + 3 = ( multiple of 4 ) + 2 , then the units digit of 3 ^ 355 will be the third number in the pattern thus 7 . answer : d .
Answer: d
Question (physics): how long will it take a train travelling at 98 kmph to pass an electric pole if the train is 140 m long
Options: a ) 6.15 , b ) 5.15 , c ) 3.15 , d ) 1.15 , e ) 7.15
Rationale: "sol . speed = [ 98 x 5 / 18 ] m / sec = 27.2 m / sec . time taken = ( 140 / 27.2 ) sec = 5.15 sec . answer b"
Answer: b
Question (physics): a train can travel 50 % faster than a car . both start from point a at the same time and reach point b 75 kms away from a at the same time . on the way , however , the train lost about 12.5 minutes while stopping at the stations . the speed of the car is :
Options: a ) 120 kmph , b ) 150 kmph , c ) 50 kmph , d ) 80 kmph , e ) 75 kmph
Rationale: "let speed of the car be x kmph . then , speed of the train = 150 / 100 x = 3 / 2 x kmph . 75 / x - 75 / ( 3 / 2 ) x = 125 / 10 x 60 75 / x - 50 / x = 5 / 24 x = 25 x 24 / 5 = 120 kmph . answer : a"
Answer: a
Question (general): from below option 22 is divisible by which one ?
Options: a ) a ) 3 , b ) b ) 4 , c ) c ) 11 , d ) d ) 9 , e ) e ) 7
Rationale: "22 / 11 = 2 c"
Answer: c
Question (general): by approximately what percent is x greater than 1 / 2 if ( 1 / 2 ) ( x ) = 1 ?
Options: a ) 732 % , b ) 560 % , c ) 641 % , d ) 370 % , e ) 300 %
Rationale: "what percent is x greater than 1 / 2 if ( 1 / 2 ) ( x ) = 1 ? = > x = 2 % change = [ ( 2 - 1 / 2 ) / ( 1 / 2 ) ] * 100 = ( 4 - 1 ) * 100 = 300 % approx ans , e"
Answer: e
Question (general): set x consists of all two - digit primes and set y consists of all positive multiples of 6 less than 100 . if the two sets are combined into one , what will be the range of the new set ?
Options: a ) 84 , b ) 89 , c ) 90 , d ) 92 , e ) 91
Rationale: "set x = { 11 , 13 , 17 , . . . . . . . . . . . . . , 83 , 89 , 97 } set y = { 6 , 12 , 18 , . . . . . . . . . . . . . . . , 84 , 90 , 96 } combining two sets , say set z set z = { 6 , 11 , 12 , 13 , 17 , 18 , . . . . . . . . . . . . . . . . . . . , 83 , 84 , 89 , 90 , 96,97 } range = max value - min value range ( z ) = 97 - 6 = 91 oa e is the answer ."
Answer: e
Question (general): if the median of a list of numbers is m , the first quartile of the list is the median of the numbers in the list that are less than m . what is the first quartile of the list of numbers 42 , 23 , 30 , 22 , 26 , 19 , 33 and 35 ?
Options: a ) 33 , b ) 28 , c ) 22.5 , d ) 24 , e ) 23
Rationale: "it is given that a quartile is the middle number of all numbers less than median . . so lets arrange the number in ascending order - 42 , 23 , 30 , 22 , 26 , 19 , 33 and 35 19 , 22 , 23 , 26 , 30 , 33 , 35 , 42 . . . numbers less than median are 19 , 22 , 23 , 26 . . the median of these numbers = center of 22 and 23 = 22.5 c"
Answer: c
Question (gain): a reduction of 25 % in the price of oil enables a house wife to obtain 5 kgs more for rs . 800 , what is the reduced price for kg ?
Options: a ) 40 , b ) 60 , c ) 70 , d ) 80 , e ) 20
Rationale: "a 800 * ( 25 / 100 ) = 200 - - - - 5 ? - - - - 1 = > rs . 40"
Answer: a
Question (gain): 37 . if the cost price of 15 tables be equal to the selling price of 20 tables , the loss per cent is ?
Options: a ) 20 % , b ) 30 % , c ) 25 % , d ) 37.5 % , e ) 38 %
Rationale: let c . p . of each table = re . 1 c . p . of 20 tables = rs . 20 s . p . of 20 table = c . p . of 15 tables = rs . 15 loss = ( 5 / 20 ) x 100 % = 25 % answer : c
Answer: c