Cheukting/mathqa huggingface dataset:
Question (general): a , b and c have rs . 500 between them , a and c together have rs . 200 and b and c rs . 330 . how much does c have ?
Options: a ) 50 , b ) 78 , c ) 30 , d ) 29 , e ) 27
Rationale: "a + b + c = 500 a + c = 200 b + c = 330 - - - - - - - - - - - - - - a + b + 2 c = 530 a + b + c = 500 - - - - - - - - - - - - - - - - c = 30 answer : c"
Answer: c
Question (general): when positive integer x is divided by positive integer y , the remainder is 4 . if x / y = 96.16 , what is the value of y ?
Options: a ) 96 , b ) 75 , c ) 48 , d ) 25 , e ) 12
Rationale: "by the definition of a remainder , the remainder here is equal to 4 / y . the remainder in decimal form is given as . 16 therefore , 4 / y = . 16 solve for y and get 25 . d"
Answer: d
Question (general): the present ages of 3 persons are in proportions 4 : 7 : 9 . 7 years ago , the sum of their ages was 79 . find their present ages .
Options: a ) 20 , 28 , b ) 28 , 36 , c ) 35 , 45 , d ) 35 , 55 , e ) of these
Rationale: let their present ages be 4 x , 7 x and 9 x years respectively . then , ( 4 x - 7 ) + ( 7 x - 7 ) + ( 9 x - 7 ) = 79 20 x = 100 = > x = 5 their present ages are 20 , 35 and 45 years respectively . answer : c
Answer: c
Question (other): in a certain large company , the ratio of college graduates with a graduate degree to non - college graduates is 1 : 8 , and ratio of college graduates without a graduate degree to non - college graduates is 2 : 3 . if one picks a random college graduate at this large company , what is the probability e this college graduate has a graduate degree ?
Options: a ) 1 / 11 , b ) 1 / 12 , c ) 1 / 13 , d ) 3 / 19 , e ) 3 / 43
Rationale: in believe the answer is d . please see below for explanation . 0 ) we are told the following ratios cgd - college graduate with degree ncg - non college graduate cgn - college graduate no degree cgd ncg cgn 1 8 3 2 in order to make cgd and cgn comparable we need to find the least common multiple of 8 and 3 and that is 24 multiplying the first ratio by 3 and the second ratio by 8 we get cgd ncg cgn 3 24 16 if one picks a random college graduate at this large company , what is the probability this college graduate has a graduate degree ? nr of cgd = 3 nr of cg = 3 + 16 = 19 probability e of cgd / ( cg ) - > 3 / 19 answer d
Answer: d
Question (geometry): the diagonals of a rhombus are 15 cm and 17 cm . find its area ?
Options: a ) 277 , b ) 127.5 , c ) 150 , d ) 288 , e ) 212
Rationale: "1 / 2 * 15 * 17 = 127.5 answer : b"
Answer: b
Question (gain): a car dealership has 40 cars on the lot , 15 % of which are silver . if the dealership receives a new shipment of 80 cars , 30 % of which are not silver , what percentage of total number of cars are silver ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 40 %
Rationale: "the number of silver cars is 0.15 * 40 + 0.3 * 80 = 30 the percentage of cars which are silver is 30 / 120 = 25 % the answer is b ."
Answer: b
Question (physics): two train each 500 m long , and 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 ) 20 sec , b ) 25 sec , c ) 24 sec , d ) 30 sec , e ) 22 sec
Rationale: speed = ( 45 + 30 ) = 75 * 5 / 18 = = > 125 / 6 req time = 500 * 6 / 125 = 24 sec answer c
Answer: c
Question (physics): geetha ' s home has one tap , working alone at its maximum constant rate , can fill a certain sink in 210 seconds . a second tap , working alone at its maximum constant rate , can fill the same sink in 214 seconds . if both taps work together at their respective maximum constant rates , the time it will take to fill the sink is closest to
Options: a ) 106 seconds , b ) 130 seconds , c ) 177 seconds , d ) 200 seconds , e ) 270 seconds
Rationale: tap 1 : 210 secs tap 2 : 214 secs considering the average of these 2 taps : 212 secs . so 1 tap can fill the tank in 212 secs , so 2 taps can fill the tank in 212 / 2 = 106 secs . closest answer is a .
Answer: a
Question (general): a bucket contains 2 mixtures a and b in the ratio 3 : 2 . if 5 liters of the mixture is replaced by 5 liters of liquid b , then the ratio of the two liquids becomes 3 : 5 . how much of the liquid a was there in the bucket ?
Options: a ) 8 liters , b ) 10 liters , c ) 12 liters , d ) 15 liters , e ) 18 liters
Rationale: "1 st ratio = 3 : 2 2 nd ratio = 3 : 5 difference of cross products ratio = 3 * 5 - 3 * 2 = 9 common factor of the 1 st ratio = ( quantity replaced / sum of terms in 1 st ratio ) + ( quantity replaced * term a in 2 nd ratio / difference ) = ( 5 / 5 ) + ( 5 * 3 / 9 ) = 1 + 5 / 3 = 2.67 quantity of a = 3 * 2.67 = 8 liters approximately answer is a"
Answer: a
Question (general): 34 : 43 : : 25 : ?
Options: a ) 49 , b ) 52 , c ) 36 , d ) 64 , e ) 56
Rationale: "ans 52 reverse of 25 answer : b"
Answer: b
Question (gain): how many liters of water must be evaporated from 50 liters of a 3 - percent sugar solution to get a 2 - percent solution ?
Options: a ) 35 , b ) 33 1 / 3 , c ) 27 , d ) 16 2 / 3 , e ) 18
Rationale: "how many liters of water must be evaporated from 50 liters of a 3 - percent sugar solution to get a 2 - percent solution ? 3 % of a 50 liter solution is 1.5 l . so you are trying to determine how many liters must a solution be for the 1.5 l to represent 2 % of the solution . set up an inequality and solve for x : 1.5 / x = 1 / 2 x = 3 since you need a 15 l solution , you must evaporate 18 of the original 50 l solution to get a 2 % solution . answer is e ."
Answer: e
Question (gain): how much more would rs . 40000 fetch , after two years , if it is put at 20 % p . a . compound interest payable half yearly than if is put at 20 % p . a . compound interest payable yearly ?
Options: a ) 482 , b ) 725 , c ) 964 , d ) 837 , e ) 923
Rationale: "40000 ( 11 / 10 ) 4 - 40000 ( 6 / 5 ) 2 = 964 answer : c"
Answer: c
Question (gain): fresh grapes contain 80 % water by weight and raisins obtained by drying fresh grapes contain 25 % water by weight . how many kgs of fresh grapes are needed to get 20 kgs of raisins ?
Options: a ) 75 kgs , b ) 64 kgs , c ) 72 kgs , d ) 65 kgs , e ) 70 kgs
Rationale: "the weight of non - water in 20 kg of dried grapes ( which is 100 - 25 = 75 % of whole weight ) will be the same as the weight of non - water in x kg of fresh grapes ( which is 100 - 80 = 20 % of whole weight ) , so 20 * 0.75 = x * 0.2 - - > x = 75 . answer : a ."
Answer: a
Question (physics): a can finish a work in 6 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 ) 6 , b ) 5 , c ) 5.5 , d ) 2 , e ) 8
Rationale: "b ' s 10 day ' s work = ( 1 x 10 ) = 2 . 15 3 remaining work = ( 1 - 2 ) = 1 . 3 3 now , 1 work is done by a in 1 day . 6 therefore 1 work is done by a in ( 6 x 1 ) = 2 days . d"
Answer: d
Question (gain): one night 25 percent of the female officers on a police force were on duty . if 500 officers were on duty that night and half of these were female officers , how many female officers were on the police force ?
Options: a ) 90 , b ) 180 , c ) 270 , d ) 500 , e ) 1,000
Rationale: "let total number of female officers in the police force = f total number of officers on duty on that night = 500 number of female officers on duty on that night = 500 / 2 = 250 ( 25 / 100 ) * f = 250 = > f = 1000 answer e"
Answer: e
Question (physics): two bullet trains of equal lengths take 10 seconds and 50 seconds respectively to cross a telegraph post . if the length of each bullet train be 120 metres , in what time ( in seconds ) will they cross each other travelling in opposite direction ?
Options: a ) 13 sec . , b ) 15 sec . , c ) 12 sec . , d ) 17 sec . , e ) 16.7 sec .
Rationale: "speed of the first bullet train = 120 / 10 m / sec = 12 m / sec . speed of the second bullet train = 120 / 50 m / sec = 2.4 m / sec . relative speed = ( 12 + 2.4 ) = 14.4 m / sec . required time = ( 120 + 120 ) / 14.4 sec = 16.7 sec . e"
Answer: e
Question (other): if $ 935 are divided between worker a and worker b in the ratio 5 : 12 , what is the share that worker b will get ?
Options: a ) 62.15 % , b ) 64.26 % , c ) 66.37 % , d ) 68.48 % , e ) 70.59 %
Rationale: "worker b will get 12 / 17 = 70.59 % the answer is e ."
Answer: e
Question (gain): a shop owner sells 30 mtr of cloth and gains sp of 10 metres . find the gain % ?
Options: a ) 30 % , b ) 40 % , c ) 50 % , d ) 65 % , e ) 72 %
Rationale: "here , selling price of 10 m cloth is obtained as profit . profit of 10 m cloth = ( s . p . of 30 m cloth ) – ( c . p . of 30 m cloth ) selling price of 20 m cloth = selling price of 30 m of cloth let cost of each metre be rs . 100 . therefore , cost price of 20 m cloth = rs . 2000 and s . p . of 20 m cloth = rs . rs . 3000 profit % = 10 × 100 = 50 % 20 profit of 50 % was made by the merchant . c"
Answer: c
Question (general): if n is a positive integer and n ^ 2 is divisible by 50 , then what is the largest positive integer that must divide n ?
Options: a ) 5 , b ) 8 , c ) 10 , d ) 20 , e ) 25
Rationale: "50 = 2 * 5 ^ 2 if 50 divides n ^ 2 , then n must be divisible by 2 * 5 = 10 the answer is c ."
Answer: c
Question (general): the sum of present age of abe and the age before 7 years is 29 . find the present age of abe . what will be his age after 7 years ?
Options: a ) 25 , b ) 26 , c ) 27 , d ) 28 , e ) 29
Rationale: "present age = x before 7 yrs , y = x - 7 after 7 yrs , z = x + 7 by the qn , x + ( x - 7 ) = 29 2 x - 7 = 29 2 x = 29 + 7 x = 36 / 2 x = 18 z = x + 7 = 18 + 7 = 25 answer : a"
Answer: a
Question (other): if both 5 ^ 2 and 3 ^ 3 are factors of the number a * 4 ^ 3 * 6 ^ 2 * 13 ^ 11 , then what is the smallest possible value of a ?
Options: a ) 49 , b ) 75 , c ) 150 , d ) 225 , e ) 343
Rationale: "the number a must include at least 3 * 5 ^ 2 = 75 the answer is b ."
Answer: b
Question (physics): a and b can finish a work in 16 days while a alone can do the same work in 32 days . in how many days b alone will complete the work ?
Options: a ) 76 days , b ) 48 days , c ) 98 days , d ) 32 days , e ) 22 days
Rationale: b = 1 / 16 – 1 / 32 = 1 / 32 = > 32 days answer : d
Answer: d
Question (general): of 60 applicants for a job , 28 had at least 4 years ' experience , 36 had degrees , and 6 had less than 4 years ' experience and did not have a degree . how many of the applicants had at least 4 years ' experience and a degree ?
Options: a ) 10 , b ) 13 , c ) 9 , d ) 7 , e ) 5
Rationale: "60 - 6 = 54 54 - 28 - 36 = - 10 then 10 are in the intersection between 4 years experience and degree . answer : a"
Answer: a
Question (other): if log 0.317 = 0.3332 and log 0.318 = 0.3364 , then find log 0.319
Options: a ) 0.3396 , b ) 0.3496 , c ) 0.3596 , d ) 0.3696 , e ) 0.3796
Rationale: "log . 318 - log . 317 = . 0032 log . 318 + log . oo 1 = log . 319 . 3364 + . 0032 = . 3396 answer : a"
Answer: a
Question (physics): a bicycle wheel has a diameter of 0.81 m . how many complete revolutions does it make in 1 km ?
Options: a ) 246 , b ) 448 , c ) 393 , d ) 710 , e ) 223
Rationale: "1 revolution = 3.14 * diameter . number of revolutions in 1 km = 1000 m / ( 3.14 * 0.81 m ) = 393.2 . hence 393 complete revolutions . answer c"
Answer: c
Question (general): if there are half as many women as men in a group and an equal number of men and women do not own cars - a group that is 30 % of the total . what fraction of the total is men who own cars ?
Options: a ) 3 ⁄ 20 , b ) 31 ⁄ 60 , c ) 9 ⁄ 40 , d ) 1 ⁄ 3 , e ) 11 ⁄ 20
Rationale: consider a group of 100 women and 200 men , a total of 300 people . 30 % of them , which is 90 , form a group of people who do n ' t own a car . half of them are men , and the other half are women , more precisely 45 . it means that there are 200 - 45 = 155 men who own a car , and this represents 155 / 300 = 31 / 60 of the total . answer b
Answer: b
Question (geometry): 12 business executives and 7 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ?
Options: a ) 150 , b ) 131 , c ) 115 , d ) 90 , e ) 45
Rationale: "there are 12 business exec and in each handshake 2 business execs are involved . hence 12 c 2 = 66 also , each of 12 exec will shake hand with every 7 other chairmen for total of 84 handshake . total = 66 + 84 = 150 ans : a"
Answer: a
Question (general): if the function q is defined by the formula q = 5 w / ( 4 d ( z ^ 2 ) ) , by what factor will q be multiplied if w is quadrupled , d is doubled , and z is tripled ?
Options: a ) 1 / 9 , b ) 2 / 9 , c ) 4 / 9 , d ) 3 / 9 , e ) 2 / 27
Rationale: "we just need to find the factor thats all , w - > quadrupled - > 4 w d - > doubled - > 2 d z - > tripled - > 3 z hence , z ^ 2 = 9 z ^ 2 w is in numerator , and d * z in denominator . hence , additional factor being introduced = 4 / 2 * 9 = 4 / 18 = 2 / 9 = b"
Answer: b
Question (general): what is 982 * 982 ?
Options: a ) 964,169 , b ) 964,219 , c ) 964,324 , d ) 975,019 , e ) 975,369
Rationale: "if you take a base of 1000 then 982 is 18 less than 1000 to get the product of 982 x 982 write like this 982 - 18 ( as 18 less than base 1000 ) 982 - 18 now 18 x 18 = 324 and 982 - 18 = 964 so 982 x 982 = 964324 . . . ( bingo the answer is c . you can even have a shortcut . . . . . . 18 x 18 = 324 . . . only answer choice has last three digits as 324 . . so no need to calculate 982 - 18 . after you get 18 x 18 you can straight way pick answer choice c ."
Answer: c
Question (physics): a pipe can fill a cistern in 88 minutes . find the time in which 1 / 11 part of the cistern will be filled ?
Options: a ) 5 min , b ) 2 min , c ) 8 min , d ) 1 min , e ) 10 min
Rationale: full cistern filled in = 88 minutes 1 / 11 part filled in = 88 * 1 / 11 = 8 minutes answer is c
Answer: c
Question (gain): a man walking at a rate of 15 km / hr crosses a bridge in 20 minutes . the length of the bridge is ?
Options: a ) 1250 m , b ) 1110 m , c ) 950 m , d ) 1000 m , e ) 1300 m
Rationale: "speed = 15 * 5 / 18 = 15 / 18 m / sec distance covered in 20 minutes = 15 / 18 * 20 * 60 = 1000 m answer is d"
Answer: d
Question (general): a total of 3000 chocolates were distributed among 120 boys and girls such that each boy received 2 chocolates and each girl received 3 chocolates . find the respective number of boys and girls ?
Options: a ) 32 , b ) 60 , c ) 27 , d ) 29 , e ) 21
Rationale: let the number of boys be x . number of girls is 120 - x . total number of chocolates received by boys and girls = 2 x + 3 ( 120 - x ) = 300 = > 360 - x = 300 = > x = 60 . so , the number of boys or girls is 60 . answer : b
Answer: b
Question (general): how many figures are required to number the pages the pages of a book containing 365 pages ?
Options: a ) 987 , b ) 977 , c ) 967 , d ) 897 , e ) 997
Rationale: "1 to 9 = 9 * 1 = 9 10 to 99 = 90 * 2 = 180 100 to 365 = 266 * 3 = 798 - - - - - - - - - - - 987 answer : a"
Answer: a
Question (general): a mixture contains milk and water in the ratio 3 : 2 . on adding 10 liters of water , the ratio of milk to water becomes 2 : 3 . total quantity of milk & water before adding water to it ?
Options: a ) 30 , b ) 40 , c ) 20 , d ) 10 , e ) 25
Rationale: milk : water = 3 : 2 after adding 10 liters of water milk : water = 2 : 3 olny water patrs increase when mixture of water milk : wate = 3 : 2 = 2 * ( 3 : 2 ) = 6 : 4 after adding 10 liters of water milk : water = 2 : 3 = 3 * ( 2 : 3 ) = 6 : 9 option ' c '
Answer: c
Question (physics): 16 men can complete a piece of work in 30 days . in how many days can 20 men complete that piece of work ?
Options: a ) 55 days , b ) 77 days , c ) 20 days , d ) 24 days , e ) 44 days
Rationale: "16 * 30 = 20 * x = > x = 24 days answer : d"
Answer: d
Question (physics): a , b , k start from the same place and travel in the same direction at speeds of 30 km / hr , 40 km / hr , 160 km / hr respectively . b starts two hours after a . if b and k overtake a at the same instant , how many hours after a did k start ?
Options: a ) 5.0 , b ) 5.5 , c ) 6.0 , d ) 6.5 , e ) 7.0
Rationale: "in 2 hours , a travels 60 km . b can catch a at a rate of 10 km / hr , so b catches a 6 hours after b starts . so a and b both travel a distance of 240 km . c needs 1.5 hours to travel 240 km , so c leaves 6.5 hours after a . the answer is d ."
Answer: d
Question (geometry): the length of a rectangular field is 7 / 5 its width . if the perimeter of the field is 384 meters , what is the width of the field ?
Options: a ) 50 , b ) 60 , c ) 11 , d ) 80 , e ) 90
Rationale: "let l be the length and w be the width . l = ( 7 / 5 ) w perimeter : 2 l + 2 w = 384 , 2 ( 7 / 5 ) w + 2 w = 384 solve the above equation to find : w = 80 m and l = 112 m . correct answer d ) 80"
Answer: d
Question (physics): speed of a boat in standing water is 16 kmph and the speed of the stream is 2 kmph . a man rows to a place at a distance of 7740 km and comes back to the starting point . the total time taken by him is :
Options: a ) 914.2 hours , b ) 900 hours , c ) 915 hours , d ) 982.9 hours , e ) 915 hours
Rationale: "explanation : speed downstream = ( 16 + 2 ) = 18 kmph speed upstream = ( 16 - 2 ) = 14 kmph total time taken = 7740 / 18 + 7740 / 14 = 430 + 552.9 = 982.9 hours answer : option d"
Answer: d
Question (general): 72 67 66 61 60 . . . ?
Options: a ) 52 , b ) 53 , c ) 54 , d ) 55 , e ) 56
Rationale: "sequence = 72 67 66 61 60 55 there is 2 series : 1 st series = 72 66 60 ( decreasing by 6 ) 2 nd series = 67 61 55 ( decreasing by 6 ) answer : d"
Answer: d
Question (physics): a train is running at a speed of 40 km / hr and it crosses a post in 25.2 seconds . what is the length of the train ?
Options: a ) 190 metres , b ) 160 metres , c ) 280 metres , d ) 120 metres , e ) 250 metres
Rationale: "speed of the train , v = 40 km / hr = 40000 / 3600 m / s = 400 / 36 m / s time taken to cross , t = 25.2 s distance covered , d = vt = ( 400 / 36 ) ã — 25.2 = 280 m distance covered is equal to the length of the train = 280 m correct answer is 280 metres c"
Answer: c
Question (physics): speed of a boat in standing water is 8 kmph and the speed of the stream is 6 kmph . a man rows to place at a distance of 210 km and comes back to the starting point . the total time taken by him is :
Options: a ) 120 hours , b ) 240 hours , c ) 160 hours , d ) 480 hours , e ) none
Rationale: "sol . speed upstream = 2 kmph ; speed downstream = 14 kmph . ∴ total time taken = [ 210 / 2 + 210 / 2 ] hours = 120 hours . answer a"
Answer: a
Question (geometry): a rectangular garden is to be twice as long as it is wide . if 300 yards of fencing , including the gate , will completely enclose the garden , what will be the length of the garden , in yards ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 100
Rationale: "alternate approach backsolving ( using answer options to reach the correct answer ) can work wonders here if one is fast in calculations . given perimeter is 300 so , 2 ( l + b ) = 300 or , l + b = 150 now use the answer options ( given length ; breath will be half the length ) ( a ) 40 l = 40 ; b = 20 l + b = 60 ( b ) 50 l = 50 ; b = 25 l + b = 75 ( c ) 60 l = 60 ; b = 30 l + b = 90 ( d ) 70 l = 70 ; b = 35 l + b = 105 ( e ) 100 l = 100 ; b = 50 l + b = 150 thus you see no , need of any calculations , u can reach the correct option only by checking options ; correct answer will be ( e )"
Answer: e
Question (general): the average age of 35 students in a class is 16 years . the average age of 21 students is 14 . what is the average age of remaining 19 students ?
Options: a ) 14 years , b ) 17 years , c ) 19 years , d ) 21 years , e ) none
Rationale: "solution sum of the ages of 14 students = ( 16 x 35 ) - ( 14 x 21 ) = 560 - 294 . = 266 . ∴ required average = 266 / 19 = 14 years . answer a"
Answer: a
Question (geometry): if each side of a right triangle is increased by 10 % and the base ( b ) is half of the height , find the percentage change in its area ?
Options: a ) 26 %
b ) 21 %
c ) 15 %
d ) 18 %
e ) 12 %
Rationale: a = 1 / 2 x b x h or 1 / 2 x 2 a x a ( for simplification ) new h = 220 a / 100 = 22 a / 10 new b = ( 110 a x 100 ) = = 11 a / 10 new area = 1 / 2 ( 22 a x 11 a ) / ( 10 x 10 ) = ( 121 a ² / 100 ) increased area = = ( 121 a ² / 100 ) - a ² increase % = [ ( 21 a ² / 100 ) x ( 1 / a ² ) x 100 ] % = 21 % answer : b
Answer: b
Question (gain): the calendar of the year 2032 can be used again in the year ?
Options: a ) 2060 , b ) 2050 , c ) 2040 , d ) 2033 , e ) 2034
Rationale: explanation : given year 2032 when divided by 4 , leaves a remainder 0 . note : when remainder is 0 , 28 is added to the given year to get the result . so , 2032 + 28 = 2060 answer : a
Answer: a
Question (gain): a sum of money at simple interest amounts to rs . 825 in 3 years and to rs . 840 in 4 years . the sum is ?
Options: a ) s . 738 , b ) s . 638 , c ) s . 777 , d ) s . 730 , e ) s . 735
Rationale: "s . i . for 1 year = ( 841 - 825 ) = rs . 16 s . i . for 3 years = 16 * 3 = rs . 48 principal = ( 825 - 48 ) = rs . 777 . answer : c"
Answer: c
Question (general): if p is the product of the integers from 1 to 35 , inclusive , what is the greatest integer k for which 3 ^ k is a factor of p ?
Options: a ) 11 , b ) 13 , c ) 15 , d ) 17 , e ) 19
Rationale: "35 ! has 3 , 6 , 9 , . . . . 30 , 33 as factors , which are 11 multiples of 3 . we need to add 4 more to these 11 because of 9 , 18 , and 27 . the greatest integer of k is 15 . the answer is c ."
Answer: c
Question (other): the simple form of the ratio 4 / 5 : 8 / 9 is ?
Options: a ) 5 : 8 , b ) 4 : 9 , c ) 5 : 9 , d ) 5 : 3 , e ) 9 : 10
Rationale: 4 / 5 : 8 / 9 = 9 : 10 answer : e
Answer: e
Question (general): what is the difference between the c . i . on rs . 6000 for 1 1 / 2 years at 4 % per annum compounded yearly and half - yearly ?
Options: a ) s . 2.04 , b ) s . 2.08 , c ) s . 2.02 , d ) s . 2.83 , e ) s . 2.45
Rationale: "c . i . when interest is compounded yearly = [ 6000 * ( 1 + 4 / 100 ) * ( 1 + ( 1 / 2 * 4 ) / 100 ] = 6000 * 26 / 25 * 51 / 50 = rs . 6364.8 c . i . when interest is compounded half - yearly = [ 6000 * ( 1 + 2 / 100 ) 2 ] = ( 6000 * 51 / 50 * 51 / 50 * 51 / 50 ) = rs . 6367.25 difference = ( 6367.25 - 6364.8 ) = rs . 2.45 . answer : e"
Answer: e
Question (general): in a village there are 150 men and 90 women in present time . if in next year population will be p = ( a ^ 2 + b ^ 2 ) ^ 1 / 2 , and in every year men are reduces 8 % . what is population of after 2 year .
Options: a ) 140 , b ) 141 , c ) 142 , d ) 143 , e ) 144
Rationale: "next year total population = [ 150 ^ 2 + 90 ^ 2 ] ^ . 5 = 174.92 = 175 man decreased by 8 % so total man = 150 * . 92 = 138 women will be = 175 - 138 = 37 so population after two years = [ 135 ^ 2 + 37 ^ 2 ] ^ . 5 = 142.87 = 143 so population after two year = 143 answer : d"
Answer: d
Question (general): i chose a number and divide it by 9 . then i subtracted 100 from the result and got 10 . what was the number i chose ?
Options: a ) 600 , b ) 700 , c ) 990 , d ) 900 , e ) none
Rationale: "solution : let x be the number i chose , then x / 9 â ˆ ’ 100 = 10 x / 9 = 110 x = 990 answer c"
Answer: c
Question (physics): the length of a rectangular plot is 20 metres more than its breadth . if the cost of fencing the plot @ rs . 26.50 per metre is rs . 6625 , what is the length of the plot in metres ?
Options: a ) 333 , b ) 250 , c ) 288 , d ) 276 , e ) 1999
Rationale: "let length of plot = l meters , then breadth = l - 20 meters and perimeter = 2 [ l + l - 20 ] = [ 4 l - 40 ] meters [ 4 l - 40 ] * 26.50 = 6625 [ 4 l - 40 ] = 6625 / 26.50 = 250 4 l = 290 l = 240 / 4 = 72.5 meters . answer : b"
Answer: b
Question (gain): after giving a discount of rs . 50 the shopkeeper gets a profit of 20 % , if the cost price is rs . 500 . find the marked price % ?
Options: a ) 450 , b ) 500 , c ) 650 , d ) 600 , e ) 650
Rationale: "cost price = 500 s . p = 500 * 120 / 100 = 600 disc = 50 so . . . mark price = 600 + 50 = 650 . . . . . . answer : e"
Answer: e