Cheukting/mathqa huggingface dataset:
Question (general): 8 % people of a village in sri lanka died by bombardment , 15 % of the remainder left the village on account of fear . if now the population is reduced to 3553 , how much was it in the beginning ?
Options: a ) 2988 , b ) 4543 , c ) 4400 , d ) 2871 , e ) 881
Rationale: "x * ( 92 / 100 ) * ( 85 / 100 ) = 3553 x = 4543 answer : b"
Answer: b
Question (physics): 57 persons can repair a road in 12 days , working 5 hours a day . in how many days will 30 persons , working 6 hours a day , complete the work ?
Options: a ) 10 , b ) 13 , c ) 14 , d ) 15 , e ) 19
Rationale: "according to the chain rule , m 1 x t 1 = m 2 x t 2 therefore , 57 x 12 x 5 = 30 x 6 x x x = 19 hence , the number of days = 19 . answer : e"
Answer: e
Question (physics): how many plants will be there in a circular bed whose outer edge measure 30 cms , allowing 4 cm 2 for each plant ?
Options: a ) 18 , b ) 750 , c ) 24 , d ) 120 , e ) none of these
Rationale: "circumference of circular bed = 30 cm area of circular bed = ( 30 ) 2 ⁄ 4 π space for each plant = 4 cm 2 ∴ required number of plants = ( 30 ) 2 ⁄ 4 π ÷ 4 = 17.89 = 18 ( approx ) answer a"
Answer: a
Question (general): the product z of two prime numbers is between 20 and 60 . if one of the prime numbers is greater than 2 but less than 6 and the other is greater than 18 but less than 36 then what is z ?
Options: a ) 21 , b ) 35 , c ) 39 , d ) 51 , e ) 57
Rationale: "the smallest possible product is 57 which is 3 * 19 . all other products are too big . the answer is e ."
Answer: e
Question (physics): a boat goes 100 km downstream in 10 hours , and 60 m upstream in 15 hours . the speed of the stream is ?
Options: a ) 3 , b ) 22 1 / 4 , c ) 22 1 / 2 , d ) 22 1 / 1 , e ) 22 1 / 3
Rationale: "100 - - - 10 ds = 10 ? - - - - 1 60 - - - - 15 us = 4 ? - - - - - 1 s = ( 10 - 4 ) / 2 = 3 kmp answer : a"
Answer: a
Question (general): in how many ways can 16 different gifts be divided among 4 children such that each child receives exactly two gifts ?
Options: a ) 16 ^ 4 , b ) ( 4 ! ) ^ 4 , c ) 16 ! / ( 2 ! ) ^ 4 , d ) 16 ! / 2 ! , e ) 4 ^ 16
Rationale: total 16 different gifts , and 4 children . thus any one child gets 16 c 2 gifts , then the other child gets 14 c 2 gifts ( 16 total - 2 already given ) , then the third one gets 12 c 2 gifts , and the last child gets 10 c 2 gifts . since order in which each child gets the gift is not imp , thus , ans : 16 c 2 * 14 c 2 * 12 c 2 * 10 c 2 = 16 ! / ( 2 ! ) ^ 4 c
Answer: c
Question (general): how many different values of positive integer x , for which | x + 4 | < x , are there ?
Options: a ) 0 , b ) 2 , c ) 3 , d ) 8 , e ) 16
Rationale: answer d i opted to put the random value option . i used 0 , 4 , - 4 and the the extreme of 60 and - 60 . . i was able to solve it in 1 : 09 d
Answer: d
Question (physics): at a certain resort , each of the 39 food service employees is trained to work in a minimum of 1 restaurant and a maximum of 3 restaurants . the 3 restaurants are the family buffet , the dining room , and the snack bar . exactly 15 employees are trained to work in the family buffet , 18 are trained to work in the dining room , and 12 are trained to work in the snack bar . if 4 employees are trained to work in exactly 2 restaurants , how many employees are trained to work in all 3 restaurants ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 1
Rationale: "39 = 15 + 18 + 12 - 4 - 2 x 2 x = 15 + 18 + 12 - 4 - 39 = 41 - 39 = 2 x = 1 e"
Answer: e
Question (physics): the edges of a cuboid are 2 cm , 5 cm and 3 cm . find the volume of the cuboid ?
Options: a ) 20
b ) 60
c ) 80
d ) 30
e ) 45
Rationale: 2 * 5 * 3 = 30 answer : d
Answer: d
Question (general): a computer manufacturer produces a certain electronic component at a cost of $ 60 per component . shipping costs for delivering the components are $ 2 per unit . further , the manufacturer has costs of $ 16,500 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 150 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ?
Options: a ) $ 28 , b ) $ 82 , c ) $ 172 , d ) $ 138 , e ) $ 192
Rationale: "this question can be solved easily using a equation model . 150 * p = 16500 ( fixed cost ) + 150 * 60 + 150 * 2 . = 16500 + 9000 + 300 = p = $ 172 . c"
Answer: c
Question (physics): a beaker contains 180 liters of alcohol . on 1 st day , 60 l of alcohol is taken out and replaced by water . 2 nd day , 60 l of mixture iss taken out and replaced by water and the process continues day after day . what will be the quantity of alcohol in beaker after 3 days
Options: a ) 53.3 , b ) 53.8 , c ) 53.7 , d ) 53.5 , e ) 353.3
Rationale: use the formula , final alcohol = initial alcohol × ( 1 − replacementquantityfinalvolume ) n × ( 1 − replacementquantityfinalvolume ) n final alcohol = 180 ( 1 − 60180 ) 3180 ( 1 − 60180 ) 3 = 180 × ( 23 ) 3 = 53.3 ans : a
Answer: a
Question (general): how many two - digit whole numbers yield a remainder of 1 when divided by 10 and also yield a remainder of 1 when divided by 6 ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: the possible number n can be written as follow : n = multiple of lcm ( 6,10 ) + 1 st such number n = 30 x + 1 possible values = 1 , 31 , 61 , 91 answer : 3 such 2 digit number . answer : d
Answer: d
Question (physics): how long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 150 m in length ?
Options: a ) sec , b ) sec , c ) sec , d ) sec , e ) sec
Rationale: "d = 110 + 150 = 260 m s = 60 * 5 / 18 = 50 / 3 t = 260 * 3 / 50 = 15.6 sec answer : d"
Answer: d
Question (general): a car travels uphill at 30 km / hr and downhill at 70 km / hr . it goes 100 km uphill and 50 km downhill . find the average speed of the car ?
Options: a ) 32 kmph , b ) 33 kmph , c ) 34 kmph , d ) 35 kmph , e ) 37 kmph
Rationale: avg speed = total distance / total time . total distance traveled = 100 + 50 = 150 km ; time taken for uphill journey = 100 / 30 = 10 / 3 ; time taken for down hill journey = 50 / 60 = 5 / 7 ; avg speed = 150 / ( 10 / 3 + 5 / 7 ) = 37 kmph answer : e
Answer: e
Question (general): in the faculty of reverse - engineering , 226 second year students study numeric methods , 423 second year students study automatic control of airborne vehicles and 134 second year students study them both . how many students are there in the faculty if the second year students are approximately 75 % of the total ?
Options: a ) 515 . , b ) 545 . , c ) 618 . , d ) 687 . , e ) 666 .
Rationale: "answer is d : 687 solution : total number of students studying both are 423 + 226 - 134 = 515 ( subtracting the 134 since they were included in the both the other numbers already ) . so 75 % of total is 515 , so 100 % is approx . 687 ."
Answer: d
Question (gain): in a certain boys camp , 20 % of the total boys are from school a and 30 % of those study science . if there are 77 boys in the camp that are from school a but do not study science then what is the total number of boys in the camp ?
Options: a ) 550 , b ) 245 , c ) 150 , d ) 35 , e ) 350
Rationale: "since 30 % of the boys from school a study science , then 70 % of the boys from school a do not study science and since 20 % of the total number of boys are from school a , then 0.2 * 0.7 = 0.14 , or 14 % of the boys in the camp are from school a and do not study science . we are told that this number equals to 77 , so 0.14 * { total } = 77 - - > { total } = 550 . answer : a ."
Answer: a
Question (general): if x = 1 + √ 2 , then what is the value of x 4 - 4 x 3 + 4 x 2 + 1 ?
Options: a ) - 1 , b ) 0 , c ) 1 , d ) 2 , e ) 3
Rationale: "answer x = 1 + √ 2 ∴ x 4 - 4 x 3 + 4 x 2 + 5 = x 2 ( x 2 - 4 x + 4 ) + 1 = x 2 ( x - 2 ) 2 + 1 = ( 1 + √ 2 ) 2 ( 1 + √ 2 - 2 ) 2 + 1 = ( √ 2 + 1 ) 2 ( √ 2 - 1 ) 2 + 1 = [ ( √ 2 ) 2 - ( 1 ) 2 ] 2 + 1 = ( 2 - 1 ) 2 = 1 + 1 = 2 correct option : d"
Answer: d
Question (general): vlaudia can choose any two of 4 different candles and any 8 of 9 different flowers for a centerpiece arrangement . given these choices , how many candle + flower groupings can she select ?
Options: a ) 54 , b ) 72 , c ) 96 , d ) 144 , e ) 432
Rationale: vlaudia can choose any two of four different candles and any 8 of 9 different flowers for a centerpiece arrangement . 2 candles from 4 candles : 4 c 2 : 6 8 flowers from 9 flowers : 9 c 8 : 9 so total grouping 9 * 6 = 54 . answer is a .
Answer: a
Question (other): how many odd integers from 1 to 100 ( both inclusive ) have odd number of factors ?
Options: a ) 13 , b ) 14 , c ) 5 , d ) 6 , e ) 7
Rationale: integers having odd number of factors will be perfect squares . odd numbers will have odd perfect squares . thus , the possible values for the perfect squares are : 1 , 9,25 , 49,81 and the corresponding integers are 1 , 3,5 , 7,9 ( more than 4 ) . thus c is the correct answer .
Answer: c
Question (gain): how many litres of pure acid are there in 10 litres of a 25 % solution
Options: a ) 1.5 , b ) 1.6 , c ) 2.5 , d ) 1.8 , e ) 1.9
Rationale: explanation : question of this type looks a bit typical , but it is too simple , as below . . . it will be 10 * 25 / 100 = 2.5 answer : option c
Answer: c
Question (general): there are 15 teams in a soccer league and each team plays each of the other teams once . how many games will be played in total ?
Options: a ) 105 , b ) 110 , c ) 115 , d ) 120 , e ) 125
Rationale: "15 c 2 = 105 the answer is a ."
Answer: a
Question (general): rahim bought 65 books for rs . 6500 from one shop and 35 books for rs . 2000 from another . what is the average price he paid per book ?
Options: a ) 80 , b ) 138 , c ) 100 , d ) 129 , e ) 85
Rationale: "average price per book = ( 6500 + 2000 ) / ( 65 + 35 ) = 8500 / 100 = rs . 85 answer : e"
Answer: e
Question (other): at a certain restaurant , the ratio of the number of cooks to the number of waiters is 3 to 10 . when 12 more waiters are hired , the ratio of the number of cooks to the number of waiters changes to 3 to 13 . how many cooks does the restaurant have ?
Options: a ) 4 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: "originally there were 3 k cooks and 10 k waiters . 13 k = 10 k + 12 k = 4 there are 12 cooks . the answer is d ."
Answer: d
Question (general): a man engaged a servant on the condition that he would pay him rs . 800 and a uniform after one year service . he served only for 9 months and received uniform and rs . 400 , find the price of the uniform ?
Options: a ) s . 800 , b ) s . 85 , c ) s . 90 , d ) s . 100 , e ) s . 120
Rationale: "9 / 12 = 3 / 4 * 800 = 600 400 - - - - - - - - - - - - - 200 1 / 4 - - - - - - - - 200 1 - - - - - - - - - ? = > rs . 800 answer : a"
Answer: a
Question (general): a customer purchased a package of ground beef at a cost of $ 1.96 per pound . for the same amount of money , the customer could have purchased a piece of steak that weighed 30 percent less than the package of ground beef . what was the cost per pound of the steak ?
Options: a ) $ 4.65 , b ) $ 4.10 , c ) $ 3.60 , d ) $ 3.20 , e ) $ 2.80
Rationale: "for simplicity , let ' s assume the customer bought 1 pound of ground beef for $ 1.96 . let x be the price per pound for the steak . then 0.7 x = 196 x = 196 / 0.7 = $ 2.80 the answer is e ."
Answer: e
Question (general): a computer manufacturer produces a certain electronic component at a cost of $ 80 per component . shipping costs for delivering the components are $ 7 per unit . further , the manufacturer has costs of $ 16,500 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 150 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ?
Options: a ) $ 28 , b ) $ 82 , c ) $ 110 , d ) $ 138 , e ) $ 197
Rationale: "by the question , the equation would be 150 p - 87 * 150 - 16500 = 0 p being the price we want to find and equation resulting zero means revenue and costs are equal so we can get the minimum price of the component . solving the equation , we get p = $ 197 . answer e for me ."
Answer: e
Question (general): what is the sum of the greatest common factor and the lowest common multiple of 24 and 36 ?
Options: a ) 92 , b ) 84 , c ) 24 , d ) 60 , e ) 184
Rationale: "prime factorization of 24 = 2 x 2 x 2 x 3 prime factorization of 36 = 2 x 2 x 3 x 3 gcf = 12 lcm = 72 sum = 84 answer b ."
Answer: b
Question (physics): a car travels at a speed of 65 miles per hour . how far will it travel in 5 hours ?
Options: a ) 125 miles , b ) 225 miles , c ) 325 miles , d ) 425 miles , e ) 525 miles
Rationale: "during each hour , the car travels 65 miles . for 5 hours it will travel 65 + 65 + 65 + 65 + 65 = 5 × 65 = 325 miles correct answer is c ) 325 miles"
Answer: c
Question (general): in a race where 12 cars are running , the chance that car x will win is 1 / 6 , that y will win is 1 / 10 and that z will win is 1 / 8 . assuming that a dead heat is impossible , find the chance that one of them will win .
Options: a ) 1 / 140 , b ) 1 / 180 , c ) 27 / 410 , d ) 47 / 120 , e ) 57 / 120
Rationale: "required probability = p ( x ) + p ( y ) + p ( z ) ( all the events are mutually exclusive ) . = 1 / 6 + 1 / 10 + 1 / 8 = 47 / 120 answer : d"
Answer: d
Question (general): in a box of 12 pens , a total of 3 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that both pen will be defective ?
Options: a ) 1 / 6 , b ) 2 / 9 , c ) 6 / 11 , d ) 9 / 16 , e ) 3 / 4
Rationale: "method - 1 there are 9 fine pieces of pen and 3 defective in a lot of 12 pens i . e . probability of first pen being defective = ( 1 / 3 ) i . e . probability of second pen being defective = ( 1 / 2 ) probability of both pen being defective = ( 1 / 2 ) * ( 1 / 3 ) = 1 / 6 answer : option a"
Answer: a
Question (physics): the timing of a college is from 12 p . m to 4.20 p . m . five lectures are held in the given duration and a break of 5 minutes after each lecture is given to the students . find the duration of each lecture .
Options: a ) 52 minutes , b ) 45 minutes , c ) 30 minutes , d ) 48 minutes , e ) 44 minutes
Rationale: explanation : total time a student spends in college = 4 hours 20 minutes = 260 minutes as there are 5 lectures , the number of breaks between lectures is 4 . total time of the break = 20 minutes hence , the duration of each lecture is = ( 260 – 20 ) / 5 = 48 minutes answer d
Answer: d
Question (gain): after decreasing 50 % in the price of an article costs rs . 1200 . find the actual cost of an article ?
Options: a ) 1200 , b ) 50 , c ) 2400 , d ) 100 , e ) 600
Rationale: "cp * ( 50 / 100 ) = 1200 cp = 24 * 100 = > cp = 2400 answer : c"
Answer: c
Question (general): mary ' s income is 60 % more than tim ' s income and tim ' s income is 30 % less than juan ' s income . what % of juan ' s income is mary ' s income .
Options: a ) 112 % , b ) b . 100 % , c ) 96 % , d ) 80 % , e ) 64 %
Rationale: "even i got 96 % j = 100 t = 100 * 0.7 = 70 m = 70 * 1.6 = 112 if mary ' s income is x percent of j m = j * x / 100 x = m * 100 / j = 112 * 100 / 100 = 112 ans : a"
Answer: a
Question (general): a telephone company needs to create a set of 3 - digit area codes . the company is entitled to use only digits 2 , 4 and 5 , which can be repeated . if the product of the digits in the area code must be even , how many different codes can be created ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 30
Rationale: we have 3 places ( - - - ) to fill & we can use only digits 2 , 4 , 5 first place can be filled in 3 ways 2 nd place can be filled in 3 ways because we can repeat the digits 3 rd place can be filled in 3 ways because we can repeat the digits total no of codes = 3 x 3 x 3 = 27 but one combination ( 555 ) will not be even so total no of even codes = 27 - 1 = 26 answer d
Answer: d
Question (general): which no . need to add to 859622 to get a number exactly divisible by 456 ?
Options: a ) 345652 , b ) 547678 , c ) 356789 , d ) 778990 , e ) 859622
Rationale: "dividend = quotient * divisor + reminder 859622 / 456 gives quotient = 1885 and reminder = 62 . so , the next number divisible by 456 is 456 places infront of 456 * 1885 which means 456 – 62 = 394 should be added to 859622 . e"
Answer: e
Question (physics): a 250 meter long train crosses a man standing on the platform in 12 sec . what is the speed of the train ?
Options: a ) 228 , b ) 108 , c ) 1266 , d ) 75 , e ) 211
Rationale: "s = 250 / 12 * 18 / 5 = 75 kmph answer : d"
Answer: d
Question (physics): in what time will a train 120 m long cross an electric pole , it its speed be 185 km / hr ?
Options: a ) 2.3 sec , b ) 2.9 sec , c ) 2.7 sec , d ) 8.7 sec , e ) 8.5 sec
Rationale: "speed = 185 * 5 / 18 = 51 m / sec time taken = 120 / 51 = 2.3 sec . answer : a"
Answer: a
Question (gain): a dishonest dealer professes to sell goods at the cost price but uses a weight of 750 grams per kg , what is his percent ?
Options: a ) 25 % , b ) 33 % , c ) 29 % , d ) 55 % , e ) 45 %
Rationale: "750 - - - 250 100 - - - ? = > 33.33 % answer : b"
Answer: b
Question (general): what ratio must a shopkeeper mix peas and soybean of rs . 16 and rs . 25 / kg , as to obtain a mixture of rs . 21 ?
Options: a ) 10 : 7 , b ) 9 : 8 , c ) 4 : 5 , d ) 13 : 11 , e ) 14 : 8
Rationale: "correct option : ( c ) use rule of alligation , to determine the ratio the required ratio of soybean and peas = 4 : 5"
Answer: c
Question (general): a part - time employee whose hourly wage was decreased by 20 percent decided to increase the number of hours worked per week so that the employee ' s total income did not change . by what percent e should the number of hours worked be increased ?
Options: a ) 12.5 % , b ) 20 % , c ) 25 % , d ) 50 % , e ) 100 %
Rationale: "correct answer : c solution : c . we can set up equations for income before and after the wage reduction . initially , the employee earns w wage and works h hours per week . after the reduction , the employee earns . 8 w wage and works x hours . by setting these equations equal to each other , we can determine the increase in hours worked : wh = . 8 wx ( divide both sides by . 8 w ) 1.25 h = x we know that the new number of hours worked e will be 25 % greater than the original number . the answer is c ."
Answer: c
Question (physics): the side of a cube is 8 m , find the voiume ?
Options: a ) 515 , b ) 509 , c ) 502 , d ) 508 , e ) 512
Rationale: "cube volume = a ( power ) 3 a ( power ) 3 = 8 ( power ) 3 = 512 m ( power ) 3 . answer is e ."
Answer: e
Question (geometry): a rectangle has 20 meter length and 15 meter breadth . find ratio between area of rectangle and square whose side is same with rectangle ' s length .
Options: a ) 3 : 2
b ) 3 : 4
c ) 4 : 5
d ) 2 : 3
e ) 2 : 5
Rationale: area of rectangle = 20 * 15 = 300 area of square = 20 ^ 2 = 400 ratio of rectangle ' area and square ' s area = 300 : 400 = 3 : 4 answer : b
Answer: b
Question (general): a number when divided by 221 gives a remainder 43 , what remainder will be obtained by dividing the same number 17 ?
Options: a ) 9 , b ) 11 , c ) 15 , d ) 5 , e ) 20
Rationale: 221 + 43 = 264 / 17 = 9 answer a
Answer: a
Question (general): george went to a fruit market with certain amount of money . with this money he can buy either 50 oranges or 40 mangoes . he retains 8 % of the money for taxi fare and buys 20 mangoes . how many oranges can he buy ?
Options: a ) 21 , b ) 30 , c ) 20 , d ) 16 , e ) 12
Rationale: "let the amount of money be 200 let cost of 1 orange be 4 let cost of 1 mango be 5 he decides to retain 8 % of 200 = 16 for taxi fare , so he is left with 184 he buys 20 mangoes ( @ 5 ) so he spends 100 money left is 84 ( 184 - 100 ) no of oranges he can buy = 84 / 4 = > 21 so , george can buy 21 oranges . a"
Answer: a
Question (gain): a sum of 14,400 amounts to 16,600 in 3 years at the rate of simple interest . what is the rate of interest ?
Options: a ) 2 % , b ) 1 % , c ) 6 % , d ) 5 % , e ) 8 %
Rationale: "d 5 % s . i . = ( 16600 - 14400 ) = 2200 . rate = ( 100 x 2200 ) / ( 14400 x 3 ) % = 5 %"
Answer: d
Question (gain): a particular library has 75 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 70 percent of books that were loaned out are returned and there are 66 books in the special collection at that time , how many books of the special collection were loaned out during that month ?
Options: a ) 20 , b ) 30 , c ) 35 , d ) 40 , e ) 55
Rationale: total = 75 books . 65 % of books that were loaned out are returned - - > 100 % - 70 % = 30 % of books that were loaned out are not returned . now , there are 66 books , thus 76 - 68 = 7 books are not returned . { loaned out } * 0.30 = 7 - - > { loaned out } = 30 . answer : b .
Answer: b
Question (physics): if a tire rotates at 400 revolutions per minute when the car is traveling 168 km / h , what is the circumference of the tire ?
Options: a ) 7 meters , b ) 9 meters , c ) 8 meters , d ) 5 meters , e ) 3 meters
Rationale: "400 rev / minute = 400 * 60 rev / 60 minutes = 24,000 rev / hour 24,000 * c = 168,000 m : c is the circumference c = 3 meters correct answer a"
Answer: a
Question (general): in a bus left side are 15 seats available , 3 few seats in right side because in rear exit door . each seat hold 3 people . in addition , there is a seat back can sit 7 people all together . how many people can sit in a bus ?
Options: a ) 52 , b ) 49 , c ) 95 , d ) 88 , e ) 66
Rationale: "right side = 15 seat left side = 15 - 3 ( 3 few seat in right side ) = 12 seat total = 15 + 12 = 27 people can seat in 27 seat = 27 * 3 = 81 people can seat in last seat = 7 total people can seat = 81 + 7 = 88 answer : d"
Answer: d
Question (general): a worker ' s take - home pay last year was the same each month , and she saved the same fraction of her take - home pay each month . the total amount of money that she had saved at the end of the year was 2 times the amount of that portion of her monthly take - home pay that she did not save . if all the money that she saved last year was from her take - home pay , what fraction of her take - home pay did she save each month ?
Options: a ) 1 / 7 , b ) 1 / 6 , c ) 1 / 5 , d ) 1 / 4 , e ) 1 / 3
Rationale: "let x be the fraction of her take - home pay that the worker saved . let p be the monthly pay . 12 xp = 2 ( 1 - x ) p 12 xp = 2 p - 2 xp 14 xp = 2 p x = 1 / 7 the answer is a ."
Answer: a
Question (general): what is the sum of all remainders obtained when the first 120 natural numbers are divided by 9 ?
Options: a ) 397 , b ) 401 , c ) 403 , d ) 405 , e ) 399
Rationale: "a positive integer can give only the following 9 remainders when divided by 9 : 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , and 0 . 1 divided by 9 gives the remainder of 1 ; 2 divided by 9 gives the remainder of 2 ; . . . 8 divided by 9 gives the remainder of 8 ; 9 divided by 9 gives the remainder of 0 . we ' ll have 11 such blocks , since 99 / 9 = 11 . the last will be : 91 divided by 9 gives the remainder of 1 ; 92 divided by 9 gives the remainder of 2 ; . . . 98 divided by 9 gives the remainder of 8 ; 99 divided by 9 gives the remainder of 0 . the last number , 100 , gives the remainder of 1 when divided by 9 , thus the sum of all remainders will be : 11 ( 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 0 ) + 1 = 405 . answer : d ."
Answer: d
Question (physics): if a certain number of labours can dig earth 100 m deep , 25 m long , and 30 m broad in 12 days , then find the number of days the same number of labours will require to dig earth 75 m deep , 20 m long and 50 m broad .
Options: a ) 12 , b ) 18 , c ) 6 , d ) 1 , e ) 2
Rationale: explanation : more number of days means more length , more depth and more width . hence , its a direct proportion . ( 100 * 25 * 30 ) : ( 75 * 20 * 50 ) : : 12 : x 75000 : 75000 : : 12 : x x = 12 answer : a
Answer: a