Cheukting/mathqa huggingface dataset:
Question (probability): two cards are drawn together from a pack of 52 cards . the probability that one is a spade and one is a heart , is :
Options: a ) 2 / 109 , b ) 7 / 109 , c ) 8 / 223 , d ) 14 / 263 , e ) 13 / 102
Rationale: "n ( s ) = ( 52 x 51 ) / ( 2 x 1 ) = 1326 . let e = event of getting 1 spade and 1 heart . n ( e ) = number of ways of choosing 1 spade out of 13 and 1 heart out of 13 = ( 13 x 13 ) = 169 . p ( e ) = n ( e ) / n ( s ) 169 / 1326 = 13 / 102 answer e"
Answer: e
Question (general): how many positive integers less than 50 are there such that they are multiples of 9 ?
Options: a ) 5 , b ) 6 , c ) 4 , d ) 8 , e ) 3
Rationale: "number of multiples of 9 = > 45 - 9 / 9 + 1 = 5 answer is a"
Answer: a
Question (general): pat , kate and mark charged a total of 189 hours to a certain project . if pat charged twice as much time to the project as kate and 1 / 3 as much times as mark , how many more hours did mark charge to the project than kate .
Options: a ) 18 , b ) 36 , c ) 72 , d ) 90 , e ) 105
Rationale: "let kate charge for x hours , then pat charged for 2 x and mat - for 6 x . so , 2 x + 6 x + x = 189 - total hours charged for , x = 21 . mat charged 6 x - x or 5 x for more hours than kate , or for 105 hours . e is correct"
Answer: e
Question (gain): a part of certain sum of money is invested at 9 % per annum and the rest at 18 % per annum , if the interest earned in each case for the same period is equal , then ratio of the sums invested is ?
Options: a ) 4 : 2 , b ) 2 : 1 , c ) 4 : 3 , d ) 4 : 0 , e ) 4 : 9
Rationale: "18 : 9 = 2 : 1 answer : b"
Answer: b
Question (gain): find the amount on rs . 5000 in 2 years , the rate of interest being 10 % per first year and 12 % for the second year ?
Options: a ) 3377 , b ) 6160 , c ) 5460 , d ) 1976 , e ) 1671
Rationale: 5000 * 110 / 100 * 112 / 100 = > 6160 answer : b
Answer: b
Question (general): ray writes a two digit number . he sees that the number exceeds 4 times the sum of its digits by 3 . if the number is increased by 18 , the result is the same as the number formed by reversing the digits . find the sum of the digits of the number .
Options: a ) 2 , b ) 8 , c ) 9 , d ) 3 , e ) 5
Rationale: "let the two digit number be xy . 4 ( x + y ) + 3 = 10 x + y - - - ( 1 ) 10 x + y + 18 = 10 y + x - - - ( 2 ) solving 1 st equation , 4 x + 4 y + 3 = 10 x + y 3 y + 3 = 6 x 6 x – 3 y = 3 therefore , 2 x – y = 1 - - - ( 3 ) solving 2 nd equation , xy + 18 = yx ⇒ ⇒ ( 10 x + b ) + 18 = 10 y + x ⇒ ⇒ 18 = 9 y – 9 x ⇒ ⇒ 2 = y – x we get y - x = 2 - - - ( 4 ) adding 3 and 4 , we get x = 3 by substituting in ( 4 ) , we get y = 5 so the given number is 35 . sum of the digits = 8 . answer : b"
Answer: b
Question (physics): 1000 men have provisions for 15 days . if 200 more men join them , for how many days will the provisions last now ?
Options: a ) 10.5 , b ) 12.5 , c ) 13.5 , d ) 11.5 , e ) 11
Rationale: "1000 * 15 = 1200 * x x = 12.5 answer b"
Answer: b
Question (geometry): a circle graph shows how the budget of a certain company was spent : 15 percent for transportation , 9 percent for research and development , 5 percent for utilities , 4 percent for equipment , 2 percent for supplies , and the remainder for salaries . if the area of each sector of the graph is proportional to the percent of the budget it represents , how many degrees of the circle are used to represent salaries ?
Options: a ) 216 ° , b ) 222 ° , c ) 228 ° , d ) 234 ° , e ) 240 °
Rationale: "the percent of the budget for salaries is 100 - ( 15 + 9 + 5 + 4 + 2 ) = 65 % 100 % of the circle is 360 degrees . then ( 65 % / 100 % ) * 360 = 234 degrees the answer is d ."
Answer: d
Question (geometry): the area of a rectangular field is equal to 750 square meters . its perimeter is equal to 110 meters . find the width of this rectangle .
Options: a ) 5
b ) 10
c ) 15
d ) 20
e ) 25
Rationale: l * w = 750 : area , l is the length and w is the width . 2 l + 2 w = 110 : perimeter l = 55 - w : solve for l ( 55 - w ) * w = 750 : substitute in the area equation w = 25 and l = 30 correct answer e
Answer: e
Question (gain): a number increased by 10 % gives 660 . the number is ?
Options: a ) 200 , b ) 300 , c ) 500 , d ) 600 , e ) 400
Rationale: "formula = total = 100 % , increase = ` ` + ' ' decrease = ` ` - ' ' a number means = 100 % that same number increased by 10 % = 110 % 110 % - - - - - - - > 660 ( 110 ã — 6 = 660 ) 100 % - - - - - - - > 600 ( 100 ã — 6 = 600 ) option ' d '"
Answer: d
Question (general): working simultaneously and independently at an identical constant rate , 10 machines of a certain type can produce a total of x units of product p in 4 days . how many of these machines , working simultaneously and independently at this constant rate , can produce a total of 3 x units of product p in 6 days ?
Options: a ) 14 , b ) 15 , c ) 18 , d ) 20 , e ) 22
Rationale: "the rate of 10 machines is rate = job / time = x / 4 units per day - - > the rate of 1 machine 1 / 10 * ( x / 4 ) = x / 40 units per day ; now , again as { time } * { combined rate } = { job done } then 6 * ( m * x / 40 ) = 3 x - - > m = 20 . answer : d ."
Answer: d
Question (general): the average of first five prime numbers greater than 3 is ?
Options: a ) 32.2 , b ) 10.6 , c ) 32.3 , d ) 32.8 , e ) 32.4
Rationale: "5 + 7 + 11 + 13 + 17 = 53 / 5 = 10.60 answer = b"
Answer: b
Question (physics): the length of a train and that of a platform are equal . if with a speed of 90 k / hr , the train crosses the platform in one minute , then the length of the train ( in meters ) is ?
Options: a ) 299 , b ) 266 , c ) 299 , d ) 750 , e ) 261
Rationale: "speed = [ 90 * 5 / 18 ] m / sec = 25 m / sec ; time = 1 min . = 60 sec . let the length of the train and that of the platform be x meters . then , 2 x / 60 = 25 è x = 25 * 60 / 2 = 750 answer : d"
Answer: d
Question (general): the average age of students of a class is 15.7 years . the average age of boys in the class is 16.4 years and that of the girls is 15.4 years . the ration of the number of boys to the number of girls in the class is ?
Options: a ) 3 : 7 , b ) 7 : 3 , c ) 2 : 5 , d ) 2 : 1 , e ) 2 : 4
Rationale: "let the ratio be k : 1 . then , k * 16.4 + 1 * 15.4 = ( k + 1 ) * 15.7 = ( 16.4 - 15.7 ) k = ( 15.7 - 15.4 ) = k = 0.3 / 0.7 = 3 / 7 required ratio = 3 / 7 : 1 = 3 : 7 . answer : a"
Answer: a
Question (geometry): in the rectangular coordinate system , points ( 5 , 0 ) and ( – 5 , 0 ) both lie on circle c . what is the maximum possible value of the radius of c ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 16 , e ) none of the above
Rationale: "the answer is b it takes 3 distinct points to define a circle . only 2 are given here . the two points essentially identify a single chord of the circle c . since no other information is provided , however , the radius of the circle can essentially be anything . all this information tell us is that the radius isgreater 5 b"
Answer: b
Question (physics): train a leaves the station traveling at 30 miles per hour . two hours later train в leaves the same station traveling in the same direction at 42 miles per hour . how many miles from the station was train a overtaken by train b ?
Options: a ) 150 , b ) 170 , c ) 190 , d ) 210 , e ) 230
Rationale: "after two hours , train a is ahead by 60 miles . train b can catch up at a rate of 12 miles per hour . the time to catch up is 60 / 12 = 5 hours . in 5 hours , train a travels another 30 * 5 = 150 miles for a total of 210 miles . the answer is d ."
Answer: d
Question (gain): what sum of money will produce rs . 70 as simple interest in 5 years at 3 1 / 2 percent ?
Options: a ) 400 , b ) 500 , c ) 367 , d ) 368 , e ) 339
Rationale: "70 = ( p * 5 * 7 / 2 ) / 100 p = 400 answer : a"
Answer: a
Question (general): what is the hcf of 2 / 3 , 5 / 9 and 6 / 5
Options: a ) 1 / 45 , b ) 2 / 45 , c ) 4 / 15 , d ) 8 / 45 , e ) 9 / 45
Rationale: "explanation : hcf of fractions = hcf of numerators / lcm of denominators = ( hcf of 2 , 5 , 6 ) / ( lcm of 3 , 9 , 5 ) = 1 / 45 answer : option a"
Answer: a
Question (other): the h . c . f . of two numbers is 38 and the other two factors of their l . c . m . are 12 and 10 . the larger of the two numbers is :
Options: a ) 678 , b ) 456 , c ) 234 , d ) 476 , e ) 432
Rationale: ": explanation : clearly , the numbers are ( 38 x 12 ) and ( 38 x 10 ) . { \ color { blue } \ therefore } larger number = ( 38 x 12 ) = 456 . answer : b ) 456"
Answer: b
Question (general): robert ate 9 chocolates , nickel ate 2 chocolates . how many more chocolates did robert ate than nickel ?
Options: a ) a ) 4 , b ) b ) 7 , c ) c ) 9 , d ) d ) 5 , e ) e ) 2
Rationale: 9 - 2 = 7 . answer is b
Answer: b
Question (geometry): the area of a circle is increased by 800 % . by what percent has the diameter of the circle increased ?
Options: a ) 100 % , b ) 200 % , c ) 300 % , d ) 600 % , e ) 800 %
Rationale: "a diameter of 2 it ' s radius = 1 it ' s area = ( 1 ^ 2 ) pi = 1 pi answer a : if we increase that diameter 100 % , we have . . . . a diameter of 4 it ' s radius = 2 it ' s area = ( 2 ^ 2 ) pi = 4 pi this area has increased ( 4 pi - 1 pi ) / 1 pi = 3 pi / 1 pi = 3 = 300 % answer b : if we increase the diameter 200 % , we have . . . a diameter of 6 it ' s area = 3 it ' s area = ( 3 ^ 2 ) pi = 9 pi this area has increased ( 9 pi - 1 pi ) / 1 pi = 8 pi / 1 pi = 8 = 800 % answer : e"
Answer: e
Question (general): 3 boys are ages 4 , 6 and 7 respectively . 3 girls are ages 5 , 8 and 9 , respectively . if two of the boys and two of the girls are randomly selected and the sum of the selected children ' s ages is q , what is the difference between the probability that q is even and the probability that q is odd ?
Options: a ) 1 / 9 , b ) 1 / 6 , c ) 2 / 9 , d ) 1 / 4 , e ) 1 / 2
Rationale: age of boys q : 4 , 6 , 7 sum of ages taken 2 at a time : 10 , 13,11 ages of girls : 5 , 8 , 9 sum of ages taken 2 at a time : 13 , 17,14 9 combinations of sum between sets ( 10 , 12,11 ) ( 13 , 17,14 ) = 23 , 27,24 - 16 , 30,17 - 24 , 28,25 prob ( even ) = 5 / 9 prob ( odd ) = 4 / 9 answer = 5 / 9 - 4 / 9 = 1 / 9
Answer: a
Question (general): if 4 xz + yw = 4 and xw + yz = 8 , what is the value of the expression ( 2 x + y ) ( 2 z + w ) ?
Options: a ) 22 , b ) 20 , c ) 24 , d ) 26 , e ) 28
Rationale: ( 2 x + y ) * ( 2 z + w ) = 4 + 2 ( 8 ) = 20 answer : b
Answer: b
Question (gain): some of 50 % - intensity red paint is replaced with 25 % solution of red paint such that the new paint intensity is 40 % . what fraction of the original paint was replaced ?
Options: a ) 1 / 30 , b ) 1 / 5 , c ) 2 / 5 , d ) 3 / 4 , e ) 4 / 5
Rationale: "40 % is 15 % - points above 25 % and 10 % - points below 50 % . thus the ratio of 25 % - solution to 50 % - solution is 2 : 3 . 2 / 5 of the original paint was replaced . the answer is c ."
Answer: c
Question (general): in 10 years , a will be twice as old 5 as b was 10 years ago . if a is now 7 years older than b , the present age of b is
Options: a ) 35 , b ) 37 , c ) 39 , d ) 41 , e ) 42
Rationale: explanation : let b ' s age = x years . then , as age = ( x + 7 ) years . ( x + 7 + 10 ) = 2 ( x — 10 ) hence x = 37 . present age of b = 37 years answer : option b
Answer: b
Question (physics): the distance between 2 cities a and b is 1000 km . a train starts from a at 9 a . m . and travels towards b at 100 km / hr . another starts from b at 10 a . m . and travels towards a at 150 km / hr . at what time do they meet ?
Options: a ) 11 am . , b ) 12 p . m . , c ) 3 pm . , d ) 2 p . m . , e ) 1 p . m .
Rationale: "suppose they meet x hrs after 9 a . m . distance moved by first in x hrs + distance moved by second in ( x - 1 ) hrs = 1000 100 x + 150 ( x - 1 ) = 1000 x = 4.60 = 5 hrs they meet at 9 + 5 = 2 p . m . answer is d"
Answer: d
Question (other): sachin is younger than rahul by 14 years . if the ratio of their ages is 7 : 9 , find the age of sachin
Options: a ) 48 , b ) 24.8 , c ) 24.21 , d ) 24.88 , e ) 49
Rationale: "explanation : if rahul age is x , then sachin age is x - 14 , so , 9 x - 126 = 7 x 2 x = 126 x = 63 so sachin age is 63 - 14 = 49 answer : e ) 49"
Answer: e
Question (general): the number x of cars sold each week varies with the price y in dollars according to the equation x = 800000 – 50 y . what would be the total weekly revenue w , in dollars , from the sale of cars priced at $ 15000 ?
Options: a ) 50000 , b ) 750000 , c ) 850000 , d ) 7 , 500000 , e ) w = 75000,000
Rationale: number of cars sold = x = 800000 - 50 y y = 15000 x = 800000 - 750000 = 50000 revenue from 50000 cars = 15000 * 50000 = 750000000 e
Answer: e
Question (other): two varieties of steel , a and b , have a ratio of iron to chromium as 5 : 1 and 7 : 2 , respectively . steel c is produced by mixing alloys a and b at a ratio of 3 : 2 . what is the ratio of iron to chromium in c ?
Options: a ) 17 : 73 , b ) 78 : 14 , c ) 45 : 30 , d ) 73 : 17 , e ) 4 : 9
Rationale: in 6 parts of alloy a , 5 parts are iron , and 1 part is chromium . in 9 parts of alloy b , 7 parts are iron and 2 parts are chromium . first , to compare the two alloys , get the same number of parts in total - we can use 18 . so we have : in 18 parts of alloy a , 15 parts are iron and 3 are chromium . in 18 parts of alloy b , 14 parts are iron and 4 are chromium . so combining 3 of a with 2 of b , we ' d be combining 45 and 28 parts of iron , or 73 parts of iron , with 9 and 8 of chromium , or 17 of chromium , so 73 to 17 is the answer . answer : d
Answer: d
Question (general): what is the last digit in the product ( 3 ^ 65 x 6 ^ 59 x 7 ^ 71 )
Options: a ) 5 , b ) 6 , c ) 4 , d ) 8 , e ) 9
Rationale: explanation : unit digit in 34 = 1 unit digit in ( 34 ) 16 = 1 unit digit in 365 = unit digit in [ ( 34 ) 16 x 3 ] = ( 1 x 3 ) = 3 unit digit in 659 = 6 unit digit in 74 unit digit in ( 74 ) 17 is 1 . unit digit in 771 = unit digit in [ ( 74 ) 17 x 73 ] = ( 1 x 3 ) = 3 required digit = unit digit in ( 3 x 6 x 3 ) = 4 . answer is c
Answer: c
Question (probability): there are 11 boys and 10 girls in a class . if three students are selected at random , in how many ways that 3 girl & 2 boys are selected ?
Options: a ) 6600 , b ) 1300 , c ) 6780 , d ) 1976 , e ) 2448
Rationale: "e = event that 3 girl and 2 boys are selected n ( e ) = we have to select 2 boys from 11 and 3 girl from 10 = 11 c 2 * 10 c 3 = 6600 ans - a"
Answer: a
Question (physics): two goods trains each 400 m long are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 38.4 , b ) 32.6 , c ) 48 , d ) 27.4 , e ) 21
Rationale: "relative speed = 45 + 30 = 75 km / hr . 75 * 5 / 18 = 125 / 6 m / sec . distance covered = 400 + 400 = 800 m . required time = 800 * 6 / 125 = 38.40 sec . answer : a"
Answer: a
Question (physics): find the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 13 cm
Options: a ) 178 cm 2 , b ) 179 cm 2 , c ) 285 cm 2 , d ) 247 cm 2 , e ) 197 cm 2
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 13 ) = 247 cm 2 answer : d"
Answer: d
Question (general): a man purchased 3 blankets @ rs . 200 each , 5 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 150 . find the unknown rate of two blankets ?
Options: a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) 500
Rationale: "10 * 150 = 1500 3 * 200 + 5 * 150 = 1350 1350 – 1050 = 300 answer : c"
Answer: c
Question (general): how many positive integers less than 5,000 are evenly divisible by neither 15 nor 22 ?
Options: a ) 4,514 , b ) 4,475 , c ) 4,521 , d ) 4,428 , e ) 4,349
Rationale: "integers less than 5000 divisible by 15 5000 / 15 = 333 . something , so 333 integers less than 5000 divisible by 22 5000 / 22 = 238 . # # , so 238 we have double counted some , so take lcm of 15 and 22 = 105 and divide by 5000 , we get 47 . so all numbers divisible by 15 and 22 = 333 + 238 - 47 = 524 now subtract that from 4999 . 4999 - 524 = 4514 answer a ."
Answer: a
Question (gain): a man buys a cycle for rs . 1800 and sells it at a loss of 25 % . what is the selling price of the cycle ?
Options: a ) s . 1090 , b ) s . 1160 , c ) s . 1190 , d ) s . 1350 , e ) s . 1256
Rationale: "s . p . = 75 % of rs . 1800 = rs . 75 / 100 x 1800 = rs . 1350 answer : d"
Answer: d
Question (physics): a man goes from a to b at a speed of 60 kmph and comes back to a at a speed of 40 kmph . find his average speed for the entire journey ?
Options: a ) 49 kmph , b ) 58 kmph , c ) 44 kmph , d ) 47 kmph , e ) 48 kmph
Rationale: "distance from a and b be ' d ' average speed = total distance / total time average speed = ( 2 d ) / [ ( d / 60 ) + ( d / 40 ] = ( 2 d ) / [ 5 d / 120 ) = > 48 kmph . answer : e"
Answer: e
Question (general): 5358 x 54 = ?
Options: a ) 272258 , b ) 272358 , c ) 289332 , d ) 274258 , e ) 274358
Rationale: "5358 x 51 = 5358 x ( 50 + 4 ) = 5358 x 50 + 5358 x 4 = 267900 + 21432 = 289332 . c )"
Answer: c
Question (general): a basketball is dropped from a height of 20 feet . if it bounces back up to a height that is exactly half of its previous height , and it stops bouncing after hitting the ground for the fourth time , then how many total feet will the ball have traveled after 2 full bounces .
Options: a ) 50 , b ) 55 , c ) 60 , d ) 75 , e ) 100
Rationale: initial distance = 40 feet first bounce = 20 feet up + 20 feet down = 40 feet second bouche = 10 feet up + 10 feet down = 20 feet total distance covered = 40 + 40 + 20 = 100 answer is e
Answer: e
Question (physics): a 200 meter long train crosses a man standing on the platform in 9 sec . what is the speed of the train ?
Options: a ) 228 , b ) 108 , c ) 1266 , d ) 188 , e ) 80
Rationale: "s = 200 / 9 * 18 / 5 = 80 kmph answer : e"
Answer: e
Question (geometry): find the area of a parallelogram with base 32 cm and height 14 cm ?
Options: a ) 498 cm 2 , b ) 384 cm 2 , c ) 430 cm 2 , d ) 128 cm 2 , e ) 448 cm 2
Rationale: "area of a parallelogram = base * height = 32 * 14 = 448 cm 2 answer : e"
Answer: e
Question (gain): raman mixed 44 kg of butter at rs . 150 per kg with 36 kg butter at the rate of rs . 125 per kg . at what price per kg should he sell the mixture to make a profit of 40 % in the transaction ?
Options: a ) 129.25 , b ) 287.25 , c ) 194.25 , d ) 188.25 , e ) 112.25
Rationale: "explanation : cp per kg of mixture = [ 44 ( 150 ) + 36 ( 125 ) ] / ( 44 + 36 ) = rs . 138.75 sp = cp [ ( 100 + profit % ) / 100 ] = 138.75 * [ ( 100 + 40 ) / 100 ] = rs . 194.25 answer : c"
Answer: c
Question (general): the average age of 42 students in a group is 16 years . when teacher â € ™ s age is included to it , the average increases by one . what is the teacher â € ™ s age in years ?
Options: a ) 31 , b ) 56 , c ) 41 , d ) 59 , e ) none
Rationale: "sol . age of the teacher = ( 43 ã — 17 â € “ 42 ã — 16 ) years = 59 years . answer d"
Answer: d
Question (physics): the l . c . m of two numbers is 2310 and their h . c . f is 30 . if one number is 231 the other is
Options: a ) 330 , b ) 300 , c ) 270 , d ) 250 , e ) 350
Rationale: "the other number = l . c . m * h . c . f / given number = 2310 * 30 / 231 = 300 answer is b ."
Answer: b
Question (physics): hcf and lcm two numbers are 12 and 396 respectively . if one of the numbers is 24 , then the other number is ?
Options: a ) 36 , b ) 198 , c ) 132 , d ) 264 , e ) 364
Rationale: "12 * 396 = 24 * x x = 198 answer : b"
Answer: b
Question (gain): company kw is being sold , and both company a and company b were considering the purchase . the price of company kw is 30 % more than company a has in assets , and this same price is also 100 % more than company b has in assets . if companies a and b were to merge and combine their assets , the price of company kw would be approximately what percent of these combined assets ?
Options: a ) 66 % , b ) 79 % , c ) 86 % , d ) 116 % , e ) 150 %
Rationale: let the price of company a ' s assets be 100 price of assets of kw is 30 % more than company a ' s assets which is 130 price of assets of kw is 100 % more than company b ' s assets which means price of company b ' s assets is half the price of kw = 65 a + b = 165 kw = 130 kw / ( a + b ) * 100 = 130 / 165 * 100 = 78.78 % or 79 % b
Answer: b
Question (physics): two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 24 kmph and 21 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ?
Options: a ) 288 , b ) 540 , c ) 877 , d ) 278 , e ) 178
Rationale: "1 h - - - - - 5 ? - - - - - - 60 12 h rs = 24 + 21 = 45 t = 12 d = 45 * 12 = 540 answer : b"
Answer: b
Question (general): what is the sum of the greatest common factor and the lowest common multiple of 48 and 72 ?
Options: a ) 192 , b ) 120 , c ) 168 , d ) 160 , e ) 184
Rationale: "prime factorization of the given numbers 72 = 2 ^ 3 * 3 ^ 2 48 = 2 ^ 4 * 3 greatest common factor = 2 ^ 3 * 3 = 24 lowest common multiple = 2 ^ 4 * 3 ^ 2 = 144 sum = 24 + 144 = 168 answer c"
Answer: c
Question (gain): the ration of the number of boys and girls in a college is 2 : 3 . if the percentage is increase in the number of boys and girls be 10 % and 20 % respectively . what will be the new ration ?
Options: a ) 21 : 22 , b ) 13 : 17 , c ) 15 : 43 , d ) 11 : 18 , e ) 15 : 23
Rationale: "let the number of boys and girls be 2 x and 3 x their increased number is 110 % of 2 x and 120 % of 3 x 2 x * 110 / 100 and 3 x * 120 / 100 11 x / 5 and 18 x / 5 required ratio = 11 x / 5 : 18 x / 5 = 11 : 18 answer is d"
Answer: d
Question (general): how many positive integers between 1 and 100 are there such that they are multiples of 13 ?
Options: a ) 6 , b ) 5 , c ) 4 , d ) 7 , e ) 3
Rationale: "multiples of 13 = 13 , 26,39 , - - - - - 91 number of multiples of 13 = > 13 * 7 = 91 answer is d"
Answer: d
Question (general): in the xy - coordinate plane , the graph of y = - x ^ 2 + 9 intersects line l at ( p , 4 ) and ( t , - 7 ) . what is the least possible value of the slope of line l ?
Options: a ) 6 , b ) 2 , c ) - 2 , d ) - 6 , e ) - 5.5
Rationale: "we need to find out the value of p and l to get to the slope . line l and graph y intersect at point ( p , 5 ) . hence , x = p and y = 5 should sactisfy the graph . soliving 5 = - p 2 + 9 p 2 = 4 p = + or - 2 simillarly point ( t , - 7 ) should satisfy the equation . hence x = t and y = - 7 . - 7 = - t 2 + 9 t = + or - 4 considering p = - 2 and t = 4 , the least slope is ( - 7 - 4 ) / ( 4 - 2 ) = - 5.5 imo option e is correct answer ."
Answer: e
Question (gain): a chemist mixes one liter of pure water with x liters of a 45 % salt solution , and the resulting mixture is a 15 % 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 = 45 % concentration of salt in the mixed solution = 15 % the pure solution and the salt solution is mixed in the ratio of - - > ( 45 - 15 ) / ( 15 - 0 ) = 2 / 1 1 / x = 2 / 1 x = 1 / 2 answer : c"
Answer: c
Question (general): the average weight of 5 person ' s increases by 10.0 kg when a new person comes in place of one of them weighing 40 kg . what might be the weight of the new person ?
Options: a ) 76 kg , b ) 76.5 kg , c ) 90 kg , d ) data inadequate , e ) none of these
Rationale: "explanation : total weight increased = ( 5 x 10.00 ) kg = 50 kg . weight of new person = ( 40 + 50 ) kg = 90 kg . answer : c"
Answer: c
Question (physics): two trains 140 m and 170 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
Options: a ) 10.9 sec , b ) 10.1 sec , c ) 10.6 sec , d ) 10.8 sec , e ) 11.16 sec
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 140 + 170 = 310 m . required time = 310 * 9 / 250 = 11.16 sec . answer : e"
Answer: e