Cheukting/mathqa huggingface dataset:
Question (general): the average age of a class of 20 students is 22 years . the average increased by 2 when the teacher ' s age also included . what is the age of the teacher ?
Options: a ) 40 years , b ) 41 years , c ) 42 years , d ) 43 years , e ) 44 years
Rationale: "if age of the teacher was 22 , average would not have changed . since average increased by 2 , age of the teacher = 19 + 22 × 1 = 44 answer : e"
Answer: e
Question (geometry): the length of a rectangle is 18 cm and its breadth is 10 cm . when the length is increased to 25 cm , what will be the breadth of the rectangle if the area remains the same ?
Options: a ) 7 cm
b ) 7.1 cm
c ) 7.2 cm
d ) 7.3 cm
e ) none of these
Rationale: solution let the breadth be b . then , ⇒ 25 b = 18 × 10 ⇒ b = ( 18 x 10 / 25 ) cm = 7.2 cm answer c
Answer: c
Question (general): a whale goes on a feeding frenzy that lasts for 9 hours . for the first hour he catches and eats x kilos of plankton . in every hour after the first , it consumes 3 kilos of plankton more than it consumed in the previous hour . if by the end of the frenzy the whale will have consumed a whopping accumulated total 540 kilos of plankton , how many kilos did he consume on the sixth hour ?
Options: a ) 38 , b ) 47 , c ) 50 , d ) 53 , e ) 63
Rationale: "if you list the amount eaten each hour , you ' ll get an equally spaced list , increasing by 3 each hour . in any equally spaced list , the median equals the mean . here , the mean is 540 / 9 = 60 , so the median is also 60 , and that is the amount eaten in the 5 th hour . we need to add 3 to find the total eaten in the next hour , so the answer is 63 . option e ."
Answer: e
Question (physics): walking at 70 % of his usual speed a man takes 24 minutes more to cover a distance . what is his usual time to cover this distance ?
Options: a ) 30 , b ) 36 , c ) 42 , d ) 48 , e ) 56
Rationale: "speed is inversly proprtional to time walking at 70 % of speed meand 7 / 10 s takes 10 / 7 t . it takes 24 minutes extra to cover the distance . then 10 / 7 t = t + 24 10 t = 7 t + 168 3 t = 168 t = 56 . option e is correct"
Answer: e
Question (gain): the profit earned by selling an article for rs . 832 is equal to the loss incurred when the same article is sold for rs . 448 . what should be the sale price for making 40 % profit ?
Options: a ) 220 , b ) 230 , c ) 960 , d ) 780 , e ) 896
Rationale: "c . p . = rs . x . then , 832 - x = x - 448 2 x = 1280 = > x = 640 required s . p . = 140 % of rs . 640 = 140 / 100 * 640 = rs . 896 . e"
Answer: e
Question (general): two employees x and y are paid a total of rs . 880 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?
Options: a ) s . 150 , b ) s . 200 , c ) s . 250 , d ) s . 350 , e ) s . 400
Rationale: "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 880 but x = 120 % of y = 120 y / 100 = 12 y / 10 â ˆ ´ 12 y / 10 + y = 880 â ‡ ’ y [ 12 / 10 + 1 ] = 880 â ‡ ’ 22 y / 10 = 880 â ‡ ’ 22 y = 8800 â ‡ ’ y = 8800 / 22 = 800 / 2 = rs . 400 e )"
Answer: e
Question (physics): two trains start from p and q respectively and travel towards each other at a speed of 50 km / hr and 40 km / hr respectively . by the time they meet , the first train has travelled 1 ookm more than the second . the distance between p and q is
Options: a ) 500 km , b ) 600 km , c ) 700 km , d ) 900 km , e ) 400 km
Rationale: "explanation : at the time of meeting , let the distance travelled by the second train be x km then , distance covered by the first train is ( x + 100 ) km = > x / 40 = ( x + 100 ) / 50 = > 50 x = 40 x + 4000 = > x = 400 km so , distance between p and q = ( x + x + 100 ) km = 900 km answer : option d"
Answer: d
Question (other): a certain store sold pens for $ 0.35 each and pencils for $ 0.25 each . if a customer purchased both pens and pencils from the store for a total of $ 3.50 , what total number of pens and pencils did the customer purchase ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "answer : algebraically , the question looks like this : 2.5 = 0.35 x + 0.25 y there are six possible numbers of pens that fit that requirement : 1 pen : $ 0.35 2 pens : $ 0.70 3 pens : $ 1.05 4 pens : $ 1.40 5 pens : $ 1.75 balance can fetch 7 pencils for $ 0.25 each . that ' s 5 pens and 7 pencils for a total of 12 pens and pencils . choice ( e ) is correct ."
Answer: e
Question (physics): dan ’ s car gets 32 miles per gallon . if gas costs $ 4 / gallon , then how many miles can dan ’ s car go on $ 42 of gas ?
Options: a ) 196 , b ) 284 , c ) 336 , d ) 412 , e ) 572
Rationale: "42 / 4 = 10.5 gallons 10.5 * 32 = 336 miles the answer is c ."
Answer: c
Question (physics): aarti can do a piece of work in 8 days . in how many days will she complete three time of work of same type ?
Options: a ) 6 days , b ) 19 days , c ) 24 days , d ) 3 days , e ) 13 days
Rationale: "we have the important relation , more work , more time ( days ) a piece of work can be done in 8 days . three times of work of same type can be done in 8 x 3 = 24 days answer c"
Answer: c
Question (general): in a box of 11 pencils , a total of 2 are defective . if a customer buys 3 pencils selected at random from the box , what is the probability that neither pencils will be defective ?
Options: a ) 1 / 25 , b ) 28 / 55 , c ) 2 / 35 , d ) 2 / 55 , e ) 1 / 75
Rationale: "first , there are 9 c 3 ways you can select 3 good pencils from 4 good ones . second , there are 11 c 3 ways you select 3 pencils from 6 ones in the box . then , the probability that neither pen will be defective is : 9 c 3 / 11 c 3 = 84 / 165 = 28 / 55 answer is b"
Answer: b
Question (general): the average salary of a person for the months of january , february , march and april is rs . 8000 and that for the months february , march , april and may is rs . 8300 . if his salary for the month of may is rs . 6500 , find his salary for the month of january ?
Options: a ) 2177 , b ) 2876 , c ) 4500 , d ) 5300 , e ) 6711
Rationale: sum of the salaries of the person for the months of january , february , march and april = 4 * 8000 = 32000 - - - - ( 1 ) sum of the salaries of the person for the months of february , march , april and may = 4 * 8300 = 33200 - - - - ( 2 ) ( 2 ) - ( 1 ) i . e . may - jan = 1200 salary of may is rs . 6500 salary of january = rs . 5300 . answer : d
Answer: d
Question (gain): by investing rs . 1800 in 9 % stock , syam earns rs . 120 . find out the stock is then quoted at which rate ?
Options: a ) 130 , b ) 135 , c ) 140 , d ) 150 , e ) 145
Rationale: "assume that face value = rs . 100 . dividend per share = rs . 9 ( as it is a 9 % stock ) by investing rs . 1800 , he earns rs . 120 investment needed to earn rs . 9 = 1800 × 9 / 120 = rs . 135 ie , stock is then quoted ( then market value ) = rs . 135 answer is b ."
Answer: b
Question (general): 65 % of x = 20 % of 552.50 . find the value of x ?
Options: a ) 100 , b ) 170 , c ) 150 , d ) 180 , e ) 199
Rationale: "65 % of x = 20 % of 552.50 then , 65 / 100 * x = 20 / 100 * 5525 / 10 x = 170 answer is b"
Answer: b
Question (general): find the value of y from ( 12 ) ^ 3 x 6 ^ 3 ÷ 432 = y ?
Options: a ) 2134 , b ) 2234 , c ) 2540 , d ) 2560 , e ) 864
Rationale: "5184 e"
Answer: e
Question (physics): a train 105 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is :
Options: a ) 22 , b ) 50 , c ) 42.8 , d ) 288 , e ) 12
Rationale: speed of the train relative to man = ( 105 / 10 ) m / sec = ( 21 / 2 ) m / sec . [ ( 21 / 2 ) * ( 18 / 5 ) ] km / hr = 37.8 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 37.8 = = > x = 42.8 km / hr . answer : c
Answer: c
Question (general): find the greatest number that will divide 256 , 193 and 210 leaving 6 , 18 and 100 as remainders respectively
Options: a ) 19 , b ) 25 , c ) 23 , d ) 20 , e ) 26
Rationale: "explanation : answer will be hcf of ( 256 - 6 , 193 - 18 , 210 - 10 ) hcf of ( 250 , 175 , 200 ) = 25 option b"
Answer: b
Question (gain): the area of a circle is increased by 1500 % . by what percent has the radius of the circle increased ?
Options: a ) 100 % , b ) 200 % , c ) 300 % , d ) 600 % , e ) 800 %
Rationale: "the area of the circle is increased by 1500 % , thus the area is increased 16 times . the area of a circle it proportional to the square of the radius ( area = π r ^ 2 ) , therefore the radius must increase 4 times ( diameter increase 4 times = area increase 16 times ) , which is increase by 500 % . answer : c"
Answer: c
Question (general): the total price of a basic computer and printer are $ 2,500 . if the same printer had been purchased with an enhanced computer whose price was $ 500 more than the price of the basic computer , then the price of the printer would have been 1 / 6 of that total . what was the price of the basic computer ?
Options: a ) 1500 , b ) 1600 , c ) 1750 , d ) 1900 , e ) 2000
Rationale: let the price of basic computer be c and the price of the printer be p : c + p = $ 2,500 . the price of the enhanced computer will be c + 500 and total price for that computer and the printer will be 2,500 + 500 = $ 3,000 . now , we are told that the price of the printer is 1 / 6 of that new total price : p = 1 / 6 * $ 3,000 = $ 500 . plug this value in the first equation : c + 500 = $ 2,500 - - > c = $ 2000 answer : e .
Answer: e
Question (gain): a certain car ' s price decreased by 2.5 % ( from the original price ) each year from 1996 to 2002 , during that time the owner of the car invested in a new carburetor and a new audio system for the car , which increased car ' s price by $ 1,000 . if the price of the car in 1996 was $ 22,000 , what is the car ' s price in 2002 ?
Options: a ) $ 18,400 , b ) $ 19,700 , c ) $ 20,200 , d ) $ 20,400 , e ) $ 21,100
Rationale: "price in 96 = 22000 price decrease each year = 2.5 / 100 * 22000 = 550 price in 97 = 22000 - 550 price in 98 = 22000 - 2 * 550 price in 99 = 22000 - 3 * 550 price in 00 = 22000 - 4 * 550 price in 01 = 22000 - 5 * 550 price in 02 = 22000 - 6 * 550 = 18700 investment in the car = 1000 net price of the car in 02 = 18700 + 1000 = $ 19700 correct option : b"
Answer: b
Question (general): last week john spent 30 percent of his wages on recreation . this week , his wages are 25 percent less than last week ʼ s wages and he spent 20 percent of his wages on recreation . the amount he spends on recreation this week is what percent of the amount he spent on recreation last week ?
Options: a ) 60 % , b ) 70 % , c ) 80 % , d ) 90 % , e ) 50 %
Rationale: say john ' s wages last week were $ 100 , so he spent 0.30 * 100 = $ 30 on recreation ; this week ' s wages is 0.75 * 100 = $ 75 , so he spends 0.2 * 75 = $ 15 on recreation ; 15 / 30 = 0.50 , hence the amount he spends on recreation this week is 50 % of the amount he spent on recreation last week : 30 * 0.5 = 15 answer : e
Answer: e
Question (general): in 2000 there were 10000 women stockbrokers in the united states . by 2005 the number had increased to 20000 . approximately what was the percent increase ?
Options: a ) 1 % , b ) 2 % , c ) 1.5 % , d ) 3 % , e ) 4 %
Rationale: the percent increase is ( 20000 - 10000 ) / 10000 = 10000 / 10000 = 1 % so the approximate answer is a
Answer: a
Question (gain): a sum of money at simple interest amounts to rs . 2240 in 2 years and to rs . 2600 in 5 years . what is the principal amount
Options: a ) 1000 , b ) 1500 , c ) 2000 , d ) 2500 , e ) 3500
Rationale: "explanation : si for 3 year = 2600 - 2240 = 360 si for 2 year 360 / 3 * 2 = 240 principal = 2240 - 240 = 2000 answer : option c"
Answer: c
Question (general): if ‘ + ’ means ‘ × ’ , ‘ - ‘ means ‘ + ’ , ‘ × ’ means ‘ ÷ ’ and ‘ ÷ ’ means ‘ - ‘ then find the value of ; 6 – 9 + 8 × 3 ÷ 25 =
Options: a ) 6 , b ) 10 , c ) 12 , d ) 5 , e ) 8
Rationale: d 5
Answer: d
Question (other): a dog takes 3 leaps for every 5 leaps of a hare . if one leap of the dog is equal to 3 leaps of the hare , the ratio of the speed of the dog to that of the hare is :
Options: a ) 9 : 5 , b ) 2 : 3 , c ) 4 : 7 , d ) 5 : 6 , e ) none of these
Rationale: "explanation : dog : hare = ( 3 * 3 ) leaps of hare : 5 leaps of hare = 9 : 5 . answer : a"
Answer: a
Question (geometry): what positive number , when squared , is equal to the cube of the positive square root of 12 ?
Options: a ) 64 , b ) 32 , c ) 8 , d ) 4 , e ) 2
Rationale: "let the positive number be x x ^ 2 = ( ( 12 ) ^ ( 1 / 2 ) ) ^ 3 = > x ^ 2 = 4 ^ 3 = 16 = > x = 4 answer d"
Answer: d
Question (physics): if 20 men can build a wall 112 metres long in 6 days , what length of a similar wall can be built by 10 men in 3 days ?
Options: a ) 65 mtr . , b ) 28 mtr , c ) 70 mtr . , d ) 78 mtr . , e ) 17 mtr .
Rationale: "20 men is 6 days can build 112 metres 10 men in 3 days can build = 112 * ( 10 / 20 ) x ( 3 / 6 ) = 28 meters answer : b ."
Answer: b
Question (physics): a alone can finish a work in 10 days which b alone can finish in 15 days . if they work together and finish it , then out of a total wages of rs . 3200 , a will get :
Options: a ) rs . 1200 , b ) rs . 1500 , c ) rs . 1920 , d ) rs . 2000 , e ) none of these
Rationale: "explanation : ratio of working days of a : b = 10 : 15 therefore , their wages ratio = reverse ratio = 15 : 10 therefore , a will get 15 units of ratio total ratio = 25 1 unit of ratio = 3000 / 25 = 128 so , a ’ s amount = 120 × 15 = rs . 1920 . answer : option c"
Answer: c
Question (physics): triathlete dan runs along a 3 - mile stretch of river and then swims back along the same route . if dan runs at a rate of 10 miles per hour and swims at a rate of 6 miles per hour , what is his average rate for the entire trip in miles per minute ?
Options: a ) 1 / 8 , b ) 2 / 15 , c ) 3 / 15 , d ) 1 / 4 , e ) 3 / 8
Rationale: "dan travels 6 miles round trip . running part : ( 3 / 10 * 60 = 18 minutes ) swimming part : ( 3 / 6 * 60 = 30 minutes ) 6 miles in ( 18 + 30 ) minutes 6 / 48 = 1 / 8 mile per minute answer : 1 / 8 mile per minute a"
Answer: a
Question (physics): i flew my tiny seaplane to visit my mother . on the flight up , i flew at 140 mph . on the way home , i flew 88 mph . what was my average speed for the trip ?
Options: a ) 114 mph , b ) 110 mph , c ) 88 mph , d ) 100 mph , e ) 99 mph
Rationale: "( 140 mph + 88 mph ) / 2 = 114 mph correct answer is : a"
Answer: a
Question (other): how many even integers from 1 to 50 ( both inclusive ) have even number of factors ?
Options: a ) 3 , b ) 14 , c ) 5 , d ) 6 , e ) 7
Rationale: "integers having even number of factors will be perfect squares . even numbers will have even perfect squares . thus , the possible values for the perfect squares are : 4 , 16,36 and the corresponding integers are 2 , 4,6 ( more than 2 ) . thus a is the correct answer ."
Answer: a
Question (general): the average age of 25 students in a group is 12 years . when teacher ' s age is included to it , the average increases by one . what is the teacher ' s age in years ?
Options: a ) 31 , b ) 38 , c ) 39 , d ) 40 , e ) 57
Rationale: "age of the teacher = ( 26 * 13 - 25 * 12 ) = 38 years . answer : b"
Answer: b
Question (general): a $ 84.95 lawn chair was sold for $ 59.95 at a special sale . by approximately what percent was the price decreased ?
Options: a ) 15 % , b ) 20 % , c ) 25 % , d ) 29 % , e ) 80 %
Rationale: "listed selling price of chair = 84.95 $ discounted selling price of chair = 59.95 $ discount = 84.95 - 59.95 = 25 $ % decrease in price of chair = ( 25 / 84.95 ) * 100 % = 29 % approx answer d"
Answer: d
Question (gain): what is 35 % of 4 / 13 of 845 ?
Options: a ) 58 , b ) 69 , c ) 80 , d ) 91 , e ) 102
Rationale: "this problem can be solved easily if we just use approximation : 35 % is a little over 1 / 3 , while 4 / 13 is a little less than 4 / 12 , which is 1 / 3 . thus , the answer is about 1 / 3 of 1 / 3 of 845 , or 1 / 9 of 845 . since the first 1 / 3 is a slight underestimate and the second 1 / 3 is a slight overestimate , the errors will partially cancel each other out . our estimate will be relatively accurate . the number 845 is a bit more than 810 , so ( 1 / 9 ) * 845 will be a bit more than 90 . keeping track not only of your current estimate , but also of the degree to which you have overestimated or underestimated , can help you pinpoint the correct answer more confidently . the closest answer is 91 , so this is the answer to choose . the answer is c ."
Answer: c
Question (general): a grocer has a sale of rs . 5700 , rs . 8550 , rs . 6855 , rs . 3850 for 4 consecutive months . how much sale must he have in the fifth month so that he gets an average sale of rs . 7800 ?
Options: a ) s . 14991 , b ) s . 49930 , c ) s . 14045 , d ) s . 14999 , e ) s . 14578
Rationale: total sale for 4 months = rs . ( 5700 + 8550 + 6855 + 3850 ) = rs . 24955 required sale = rs . [ ( 7800 x 5 ) - 24955 ] = rs . ( 39000 - 24955 ) = rs . 14045 option c
Answer: c
Question (general): a shop produces sarongs . the daily average production is given by 5 n + 20 , where n is the number of workers aside from the owner . in the first k days , 500 units are produced , and then 5 workers are added to the team . after another k days , the cumulative total is 1200 . how many workers were part of the latter production run ?
Options: a ) a ) 6 , b ) b ) 14 , c ) c ) 11 , d ) d ) 15 , e ) e ) 23.5
Rationale: "the daily average production is given by 5 n + 20 - given in the first k days , 500 units are produced = ( 5 n + 20 ) k = 500 k = 500 / 5 n + 20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 5 workers were added = 5 ( n + 5 ) + 20 = 5 n + 45 cumulative is 1200 . . thus for the current period = 1200 - 500 = 700 ( 5 n + 45 ) k = 700 k = 700 / 5 n + 45 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 equate 1 and 2 500 / 5 n + 20 = 700 / 5 n + 45 500 ( 5 n + 45 ) = 700 ( 5 n + 20 ) 25 n + 225 = 35 n + 140 - 10 n = - 85 n = 8.5 thus n + 5 = 14 hence b"
Answer: b
Question (gain): the cash difference between the selling prices of an book at a profit of 4 % and 8 % is $ 3 . the ratio of the two selling prices is :
Options: a ) 55 : 23 , b ) 26 : 27 , c ) 52 : 53 , d ) 45 : 53 , e ) 51 : 34
Rationale: "let c . p . of the book be $ x . then , required ratio = 104 % of x / 108 % of x = 104 / 108 = 26 / 27 = 26 : 27 b"
Answer: b
Question (general): the ratio of ducks and frogs in a pond is 35 : 39 respectively . the average number of ducks and frogs in the pond is 152 . what is the number of frogs in the pond ?
Options: a ) 160 , b ) 152 , c ) 156 , d ) 144 , e ) none
Rationale: solution : ratio of ducks and frogs in pond , = 35 : 39 . average of ducks and frogs in pond , = 152 . so , total number of ducks and frogs in the pond , = 2 * 152 = 304 . therefore , number of frogs , = ( 304 * 39 ) / 74 = 160 . answer : option a
Answer: a
Question (general): suraj has a certain average of runs for 14 innings . in the 15 th innings he scores 140 runs thereby increasing his average by 8 runs . what is his average after the 15 th innings ?
Options: a ) 48 , b ) 28 , c ) 36 , d ) 72 , e ) 27
Rationale: "to improve his average by 8 runs per innings he has to contribute 14 x 8 = 112 runs for the previous 14 innings . thus , the average after the 15 th innings = 140 - 112 = 28 . answer : b"
Answer: b
Question (physics): a cistern is fille in 8 hours and it takes 12 hours when there is a leak in its bottom . if the cistern is full , in what time shall the leak empty it ?
Options: a ) 22 hours , b ) 21 hours , c ) 24 hours , d ) 23 hours , e ) 25 days
Rationale: explanation : work done by 1 hour by filling pipe = 1 / 8 work done by 1 hour by the leak and the filling pipe = 1 / 12 work done by 1 hour by the leak = 1 / 8 – 1 / 12 = 1 / 24 hence the leak can empty it in 24 hours . answer : option c
Answer: c
Question (physics): if 12 men do a work in 80 days , in how many days will 16 men do it ?
Options: a ) 22 , b ) 87 , c ) 77 , d ) 60 , e ) 85
Rationale: 12 * 80 = 16 * x x = 60 days answer : d
Answer: d
Question (general): how many points ( x , y ) lie on the line segment between ( 22 , 12 2 / 3 ) and ( 16 , 17 2 / 3 ) such that x and y are both integers ?
Options: a ) 1 , b ) 5 , c ) 7 , d ) 8 , e ) 9
Rationale: "slope = ( 17 2 / 3 - 12 2 / 3 ) / ( 16 - 22 ) = - 5 / 6 y = mx + b = > 12 2 / 3 = - 22 * 5 / 6 + b = > b = 31 y = - 5 x / 6 + 31 only integer values work , and the only multiples of 6 between 16 and 22 for x values is 18 , thus 1 point . a"
Answer: a
Question (general): a certain class of students is being divided into teams . the class can either be divided into 15 teams with an equal number of players on each team or 24 teams with an equal number of players on each team . what is the lowest possible number of students in the class ?
Options: a ) 6 , b ) 36 , c ) 48 , d ) 60 , e ) 120
Rationale: "let total no of students in the class be n so , we are told that n is divisible by both 15 24 so , lets find the least common multiple of 15 24 , ie 120 so our answer is ( e ) 120"
Answer: e
Question (general): a department store perceived a run on a lower priced garment and raised the price by 20 % to keep stock available until another shipment arrived . customers fumed and the department store manager allowed them to purchase the garments at 80 % of the new price to save face . what was the difference in the new retail price and the price the customers were allowed to pay instead ?
Options: a ) 4.0 % , b ) 5.0 % , c ) 6.0 % , d ) 7.0 % , e ) 8.0 %
Rationale: quantity x rate = price 1 x 1 = 1 0.8 x 1.20 = 0.960 decrease in price = ( 0.040 / 1 ) ã — 100 = 4.0 % answer = option a
Answer: a
Question (general): the price of a mobile was increased by 40 percent . the new price was then decreased by 15 percent . a single increase of what percent is equivalent to these two successive changes ?
Options: a ) 25 % , b ) 19 % , c ) 30 % , d ) 22.5 % , e ) 15 %
Rationale: consider base price - $ 100 25 % increase = 1.40 * 100 = $ 140 then a 15 % decrease on new price = 0.85 * 140 = $ 119 so final price of radio - $ 119 therefore a 19 % increase correct option - b
Answer: b
Question (physics): a , b and c completed a piece of work , a worked for 16 days , b for 9 days and c for 4 days . their daily wages were in the ratio of 3 : 4 : 5 . find the daily wages of c , if their total earning was rs . 1480 ?
Options: a ) rs . 80 , b ) rs . 120 , c ) rs . 71.15 , d ) rs . 51.15 , e ) rs . 180
Rationale: "3 x 4 x 5 x 16 9 4 48 x + 36 x + 20 x = 1480 104 x = 1480 = > x = 14.23 5 x = 71.15 rs . answer : c"
Answer: c
Question (probability): there are 20 students in a class . in how many different ways can a committee of 3 students be formed ?
Options: a ) 650 , b ) 730 , c ) 980 , d ) 1140 , e ) 1480
Rationale: "20 c 3 = 20 * 19 * 18 / 6 = 1140 the answer is d ."
Answer: d
Question (general): the closest approximation of w ( 69.28 × 0.004 ) / 0.03 is
Options: a ) 0.092 , b ) 0.92 , c ) 9.2 , d ) 92 , e ) 920
Rationale: "w ( 69.28 × 0.004 ) / 0.03 1 . 0.004 = 4 × 10 ^ ( - 3 ) 2 . 0.03 = 3 × 10 ^ ( - 2 ) 3 . ( a × b ) / c = a × ( b / c ) 4 . 0.004 / 0.03 = 4 × 10 ^ ( - 3 ) / ( 3 × 10 ^ ( - 2 ) ) = 4 × 10 ^ ( - 3 - ( - 2 ) ) / 3 = 4 × 10 ^ ( - 1 ) / 3 = ( 4 / 3 ) × 10 ^ ( - 1 ) = 1.333 × 10 ^ ( - 1 ) therefore , ( 69.28 × 0.004 ) / 0.03 = 69.28 × ( 0.004 / 0.03 ) = 69.28 × 1.33 × 10 ^ ( - 1 ) = 69.28 × 1.33 / 10 = 6.928 * 1.33 now , 7 × 2 = 14 7 × 1 = 7 or better : 6.9 × 1 = 6.9 6.9 × 2 = 13.8 hence , 6.9 < 6.928 × 1.33 < 13.8 9.2 is the only answer that satisfies this condition . c"
Answer: c
Question (general): the least number by which 72 must be multiplied in order to produce a multiple of 112 , is :
Options: a ) 6 , b ) 12 , c ) 14 , d ) 18 , e ) 20
Rationale: required number is divisible by 72 as well as by 112 , if it is divisible by their lcm , which is 1008 . now , 1008 when divided by 72 , gives quotient = 14 . therefore , required number = 14 . answer : c
Answer: c