regisss/math_qa huggingface dataset:
Problem: a runs twice as fast as b and gives b a start of 71 m . how long should the racecourse be so that a and b might reach in the same time ?
Options: a ) 75 m . , b ) 80 m . , c ) 150 m . , d ) 142 m . , e ) none of the above
Rationale: "ratio of speeds of a and b is 2 : 1 b is 71 m away from a but we know that a covers 1 meter ( 2 - 1 ) more in every second than b the time taken for a to cover 71 m is 71 / 1 = 71 m so the total time taken by a and b to reach = 2 * 71 = 142 m answer : d"
Answer: d
Problem: a and b began business with rs . 3000 and rs . 4000 after 8 months , a withdraws rs . 1000 and b advances rs . 1000 more . at the end of the year , their profits amounted to rs . 630 find the share of b .
Options: a ) 240 , b ) 288 , c ) 277 , d ) 390 , e ) 361
Rationale: "( 3 * 8 + 2 * 4 ) : ( 4 * 8 + 5 * 4 ) 8 : 13 13 / 21 * 630 = 390 answer : d"
Answer: d
Problem: a reduction of 20 % in the price of salt enables a lady to obtain 10 kgs more for rs . 500 , find the original price per kg ?
Options: a ) s . 12.7 , b ) s . 12.4 , c ) s . 12.5 , d ) s . 12.1 , e ) s . 12.9
Rationale: "100 * ( 20 / 100 ) = 20 - - - 10 ? - - - 1 = > rs . 2 500 - - - 80 ? - - - 2 = > rs . 12.5 answer : c"
Answer: c
Problem: evaluate : 59 - 12 * 3 * 2 = ?
Options: a ) 42 , b ) 51 , c ) 62 , d ) 72 , e ) 82
Rationale: "according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 59 - 12 * 3 * 2 = 59 - 8 = 51 correct answer b"
Answer: b
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: if there are 200 questions in a 3 hr examination . among these questions are 50 type a problems , which requires twice as much as time be spent than the rest of the type b problems . how many minutes should be spent on type a problems ?
Options: a ) 72 min , b ) 62 min , c ) 70 min , d ) 74 min , e ) 76 min
Rationale: "x = time for type b prolems 2 x = time for type a problem total time = 3 hrs = 180 min 150 x + 50 * 2 x = 180 x = 180 / 250 x = 0.72 time taken for type a problem = 50 * 2 * 0.72 = 72 min answer : a"
Answer: a
Problem: a person spends 1 / 3 rd of the money with him on clothes , 1 / 5 th of the remaining on food and 1 / 4 th of the remaining on travel . now , he is left with rs 100 . how much did he have with him in the beginning ?
Options: a ) rs 200 , b ) rs 250 , c ) rs 300 , d ) rs 450 , e ) rs 550
Rationale: "suppose the amount in the beginning was rs ’ x ’ money spent on clothes = rs 1 x / 3 balance = rs 2 x / 3 money spent on food = 1 / 5 of 2 x / 3 = rs 2 x / 15 balance = 2 x / 3 - 2 x / 15 = rs 8 x / 15 money spent on travel = 1 / 4 of 8 x / 15 = rs 2 x / 15 = 8 x / 15 - 2 x / 15 = 6 x / 15 = rs 2 x / 5 therefore 2 x / 5 = 100 = 250 answer : b"
Answer: b
Problem: marginal cost is the cost of increasing the quantity produced ( or purchased ) by one unit . if the fixed cost for n products is $ 10,000 and the marginal cost is $ 80 , and the total cost is $ 16,000 , what is the value of n ?
Options: a ) 30 , b ) 50 , c ) 60 , d ) 75 , e ) 100
Rationale: "total cost for n products = fixed cost for n products + n * marginal cost - - > $ 16,000 = $ 10,000 + n * $ 80 - - > n = 75 . answer : d ."
Answer: d
Problem: find the area , diameter = 12 m .
Options: a ) 113.00 square meter , b ) 113.04 square meter , c ) 113.08 square meter , d ) 113.24 square meter , e ) 113.43 square meter
Rationale: "diameter = 12 meter . radius = diameter / 2 . = 12 / 2 . = 6 meter . area of a circle = π r 2 . here , pi ( π ) = 3.14 meter , radius ( r ) = 6 . area of a circle = 3.14 × 6 × 6 . . = 3.14 × 36 . = 113.04 square meter or 113.04 m 2 . answer : b"
Answer: b
Problem: 765.765 - ? + 46.82 = 437.785
Options: a ) a ) 374.80 , b ) b ) 752.804 , c ) c ) 714.642 , d ) d ) 629.906 , e ) of these
Rationale: "explanation : 374.80 answer : option a"
Answer: a
Problem: sam taken a loan rs . 15000 / - from co - operative society with an interest @ 11.5 % per month . at the same time he deposited rs . 10000 / - as fixed deposit with an interest @ 9.5 % per month . after one week sam asked the manager to calculate the interest to be paid . what is the interest amount for 7 days ?
Options: a ) a ) 165 , b ) b ) 220 , c ) c ) 310 , d ) d ) 185 , e ) e ) 181
Rationale: loan amount : rs . 15000 / - @ 11.5 % interest per month = 15000 / - * 11.5 % = rs . 1725 interest for one day = 1725 / 30 = 57.50 interest for 7 days is = 57.50 * 7 = 403 fd amount is = rs . 10000 / - @ 9.5 % interest per month = 10000 * 9.5 % = 950 / - interest for 7 days = 950 / 30 * 7 = 222 interest amount to be paid by sam = 403 - 222 = 181 / - for 7 days answer is e
Answer: e
Problem: how many integers from 20 to 150 , inclusive , are divisible by 3 but not divisible by 7 ?
Options: a ) 37 , b ) 40 , c ) 42 , d ) 45 , e ) 55
Rationale: "we should find # of integers divisible by 3 but not by 3 * 7 = 21 . # of multiples of 21 in the range from 20 to 150 , inclusive is ( 147 - 21 ) / 21 + 1 = 7 ; 44 - 7 = 37 . answer : a ."
Answer: a
Problem: on a two - dimensional coordinate plane , the line d = x ^ 2 - x ^ 3 touches the x - axis in how many places ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "apparently it ' s d = x ^ 2 - x ^ 3 instead of d = x ^ 2 - d ^ 3 . in this case : the x - intercept is the value ( s ) of x for d = 0 . 0 = x ^ 2 - x ^ 3 ; 0 = x ^ 2 ( 1 - x ) ; x = 0 or x = 1 . answer : c ."
Answer: c
Problem: how many even integers from 1 to 100 ( both inclusive ) have even number of factors ?
Options: a ) 13 , 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 , 64,100 and the corresponding integers are 2 , 4,6 , 8,10 ( more than 4 ) . thus c is the correct answer .
Answer: c
Problem: the ratio of the number of females to males at a party was 1 : 2 but when 4 females and 4 males left , the ratio became 1 : 3 . how many people were at the party originally ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 28
Rationale: "the total number of people are x females + 2 x males . 3 * ( x - 4 ) = 2 x - 4 x = 8 there were 3 x = 24 people at the party originally . the answer is c ."
Answer: c
Problem: if 7875 / 5.25 = 1500 , then 787.5 / 52.5 is equal to ?
Options: a ) 15 , b ) 19 , c ) 12 , d ) 14 , e ) 16
Rationale: "answer given expression 787.5 / 52.5 = 7875 / 525 = 7875 / ( 525 x 100 ) = 1500 / 100 15 correct option : a"
Answer: a
Problem: two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 18 hours and 8 hours respectively . the ratio of their speeds is
Options: a ) 4 : 9 , b ) 4 : 3 , c ) 4 : 12 , d ) 4 : 8 , e ) 4 : 5
Rationale: let us name the trains as a and b . then , ( a ' s speed ) : ( b ' s speed ) = b : a = 8 : 18 = 4 : 9 . answer : a
Answer: a
Problem: when the price of an article is reduced by 30 % , the sales increases by 50 % . the percentage change in the total amount of receipts is ?
Options: a ) 5 % decrease , b ) 5 % increase , c ) 10 % decrease , d ) 15 % decrease , e ) none of these
Rationale: we have , receipts = price x sales therefore , net % change in receipts = ( x + y + xy / 100 ) % = [ - 30 + 50 + ( - 30 x 50 ) / 100 ] % = 5 % increase . answer : b
Answer: b
Problem: find the ratio in which rice at rs . 7.20 a kg be mixed with rice at rs . 5.60 a kg to produce a mixture worth rs . 6.30 a kg
Options: a ) 2 : 0 , b ) 2 : 3 , c ) 2 : 1 , d ) 2 : 2 , e ) 7 : 9
Rationale: "by the rule of alligation : cost of 1 kg rice of 1 st kind cost of 1 kg rice of 2 nd kind required ratio = 70 : 90 = 7 : 9 answer : e"
Answer: e
Problem: two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post . if the length of each train be 140 m , in what time will they cross other travelling in opposite direction ?
Options: a ) 17 sec , b ) 12 sec , c ) 16 sec , d ) 14 sec , e ) 18 sec
Rationale: "speed of the first train = 120 / 10 = 12 m / sec . speed of the second train = 120 / 5 = 8 m / sec . relative speed = 12 + 8 = 20 m / sec . required time = ( 140 + 140 ) / 20 = 14 sec . answer : d"
Answer: d
Problem: at a special sale , 5 tickets can be purchased for the price of 3 tickets . if 5 tickets are purchased at the sale , the amount saved will be what percent of the original price of the 5 tickets ?
Options: a ) 20 % , b ) 33.3 % , c ) 40 % , d ) 60 % , e ) 66.6 %
Rationale: "let the price of a ticket be rs . 100 , so 3 tickets cost 300 & 5 tickets cost 500 5 tickets purchased at price of 3 tickets ie . , for 300 , so amount saved s rs . 200 , % of 5 tickets = ( 200 / 500 ) * 100 = 40 % answer : c"
Answer: c
Problem: the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 20000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is
Options: a ) 20 , b ) 49 , c ) 22 , d ) 23 , e ) none
Rationale: "sol . let the total number of workers be x . then , 8000 x = ( 20000 × 7 ) + 6000 ( x – 7 ) ‹ = › 2000 x = 98000 ‹ = › x = 49 . answer b"
Answer: b
Problem: find the average of all the numbers between 6 and 34 which are divisible by 7 .
Options: a ) 18 , b ) 20 , c ) 17.5 , d ) 30 , e ) 32
Rationale: "solution average = ( 7 + 14 + 21 + 28 ) / 4 ) = 70 / 4 = 17.5 . answer c"
Answer: c
Problem: at what price must an article costing rs . 47.50 be marked in order that after deducting 6 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 63.16 , b ) 62.6 , c ) 62.1 , d ) 62.7 , e ) 62.2
Rationale: "cp = 47.50 sp = 47.50 * ( 125 / 100 ) = 59.375 mp * ( 94 / 100 ) = 59.375 mp = 63.16 answer : a"
Answer: a
Problem: if a mixture is 3 ⁄ 5 alcohol by volume and 4 ⁄ 5 water by volume , what is the ratio of the volume of alcohol to the volume of water in this mixture ?
Options: a ) 1 / 3 , b ) 3 / 2 , c ) 3 / 4 , d ) 3 , e ) 3 / 5
Rationale: "should be a sub - 600 level q . . volume = { 3 / 5 } / { 4 / 5 } = 3 / 4 c"
Answer: c
Problem: what is difference between biggest and smallest fraction among 2 / 3 , 3 / 4 , 4 / 5 and 5 / 6
Options: a ) 2 / 5 , b ) 3 / 5 , c ) 1 / 6 , d ) 1 / 7 , e ) none of these
Rationale: "explanation : 2 / 3 = . 66 , 3 / 4 = . 75 , 4 / 5 = . 8 and 5 / 6 = . 833 so biggest is 5 / 6 and smallest is 2 / 3 their difference is 5 / 6 - 2 / 3 = 1 / 6 option c"
Answer: c
Problem: a reduction of 25 % in the price of salt enables a lady to obtain 10 kgs more for rs . 800 , find the original price per kg ?
Options: a ) 25.67 , b ) 26.67 , c ) 27.2 , d ) 26.98 , e ) 27.76
Rationale: "answer : 800 * ( 25 / 100 ) = 200 - - - 10 ? - - - 1 = > rs . 20 800 - - - 600 ? - - - 20 = > rs . 26.67 . answer : b"
Answer: b
Problem: the compound and the simple interests on a certain sum at the same rate of interest for two years are rs . 11730 and rs . 10200 respectively . find the sum .
Options: a ) 33498 , b ) 17000 , c ) 2665 , d ) 28876 , e ) 313
Rationale: "the simple interest for the first year is 10200 / 2 is rs . 5100 and compound interest for first year also is rs . 5100 . the compound interest for second year on rs . 5100 for one year so rate of the interest = ( 100 * 1530 ) / ( 5100 * 1 ) = 30 % p . a . so p = ( 100 * 10200 ) / ( 30 * 2 ) = rs . 17000 answer : b"
Answer: b
Problem: the length of a room is 5.5 m and width is 3.75 m . what is the cost of paying the floor by slabs at the rate of $ 300 per sq . metre .
Options: a ) $ 2587.50 , b ) $ 3587.50 , c ) $ 4187.50 , d ) $ 6187.50 , e ) $ 8587.50
Rationale: "area = 5.5 × 3.75 sq . metre . cost for 1 sq . metre . = $ 300 hence , total cost = 5.5 × 3.75 × 300 = $ 6187.50 d"
Answer: d
Problem: of the 150 people at a party , 70 were women , and 30 women tried the appetizer . if 60 people did not try the appetizer , what is the total number of men who tried the appetizer ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: "total people at party = 150 women = 70 so men 150 - 70 = 80 no . of pple who tried appetizer = 150 - 60 ( given info ) = 90 no of women who tried appetizer = 30 so remaining ppl ( men ) who tried the appetizer = 90 - 30 = 60 correct option c"
Answer: c
Problem: a man swims downstream 28 km and upstream 12 km taking 2 hours each time , what is the speed of the man in still water ?
Options: a ) 10 , b ) 8 , c ) 5 , d ) 2 , e ) 4
Rationale: "28 - - - 2 ds = 14 ? - - - - 1 12 - - - - 2 us = 6 ? - - - - 1 m = ? m = ( 14 + 6 ) / 2 = 10 answer : a"
Answer: a
Problem: in a restaurant , the profit is 130 % of the cost . if the cost increases by 12 % but the selling price remains constant , approximately what percentage of the selling price is the profit ?
Options: a ) 30 % , b ) 51 % , c ) 90 % , d ) 100 % , e ) none of these
Rationale: "explanation : let c . p . = rs . 100 . then , profit = rs . 130 , s . p . = rs . 230 . new c . p . = 112 % of rs . 100 = rs . 112 new s . p . = rs . 230 . profit = rs . ( 230 - 112 ) = rs . 118 . required percentage = ( 118 / 230 * 100 ) % = 51 % appox answer : b"
Answer: b
Problem: a dog takes 5 leaps for every 6 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 ) 1 : 6 , b ) 5 : 6 , c ) 6 : 1 , d ) 5 : 1 , e ) 9 : 1
Rationale: "explanation : dog : hare = ( 5 * 3 ) leaps of hare : 6 leaps of hare = 15 : 3 - - > 5 : 1 answer : d"
Answer: d
Problem: a mathematics teacher tabulated the marks secured by 35 students of 8 th class . the average of their marks was 72 . if the marks secured by reema was written as 36 instead of 66 then find the correct average marks up to two decimal places .
Options: a ) 72.85 , b ) 74.31 , c ) 72.43 , d ) 73.43 , e ) can not be determined
Rationale: total marks = 35 x 72 = 2520 corrected total marks = 2520 - 36 + 66 = 2550 correct average = 2550 / 35 = 72.85 answer : a
Answer: a
Problem: a bag contains 6 green balls and 7 white balls . if two balls are drawn simultaneously , what is the probability that both balls are the same colour ?
Options: a ) 2 / 7 , b ) 3 / 10 , c ) 5 / 11 , d ) 6 / 13 , e ) 11 / 21
Rationale: "the total number of ways to draw two balls is 13 c 2 = 78 the number of ways to draw two green balls is 6 c 2 = 15 the number of ways to draw two white balls is 7 c 2 = 21 p ( two balls of the same colour ) = 36 / 78 = 6 / 13 the answer is d ."
Answer: d
Problem: in the biology lab of ` ` jefferson ' ' high school there are 0.036 * 10 ^ 5 germs , equally divided among 75000 * 10 ^ ( - 3 ) petri dishes . how many germs live happily in a single dish ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 48
Rationale: "0.036 * 10 ^ 5 can be written as 3600 75000 * 10 ^ ( - 3 ) can be written as 75 required = 3600 / 75 = 48 answer : e"
Answer: e
Problem: set x consists of the integers from 1 to 12 , inclusive , while set y consists of the integers from 0 to 20 , inclusive . how many distinct integers do belong to the both sets at the same time ?
Options: a ) 12 , b ) 15 , c ) 10 , d ) 20 , e ) 8
Rationale: x = { 1,2 , 3,4 , 5,6 , 7 , 8 , 9 , 10 , 11 , 12 } y = { 0 , 1,2 , 3,4 , 5,6 , 7 , 8 , 9 , 10 , 11,12 , 13,14 , 15,16 , 17,18 , 19,20 } common elements = { 1,2 , 3,4 , 5,6 , 7,8 , 9,10 , 11,12 } = 12 elements answer : option a .
Answer: a
Problem: a train 160 m long running at 72 kmph crosses a platform in 25 sec . what is the length of the platform ?
Options: a ) 443 m , b ) 354 m , c ) 340 m , d ) 350 m , e ) 250 m
Rationale: "c 340 c = ( 72 * 5 / 18 ) * 25 - 160 = 340"
Answer: c
Problem: a cube of edge 5 cm is cut into cubes each of edge 1 cm . the ratio of the total surface area of one of the small cubes to that of the large cube is equal to :
Options: a ) 1 : 25
b ) 1.225
c ) 1 : 52
d ) 1 : 522
e ) none
Rationale: sol . required ratio = 6 * 1 * 1 / 6 * 5 * 5 = 1 / 25 = 1 : 25 . answer a
Answer: a
Problem: the difference b / w the compound interest payble half yearly and the simple interest on a certain sum lent out at 10 % p . a for 1 year is rs 25 . what is the sum ?
Options: a ) rs . 15000 , b ) rs . 12000 , c ) rs . 10000 , d ) rs . 20000 , e ) none of these
Rationale: in simple words s . i = ptr / 100 = ( p * 1 * 10 ) / 100 p / 10 here amount a = p + s . i = p + p / 10 = 11 p / 10 . . . . now for compound interest when calculated half yearly amount = p [ 1 + r / 200 ] ^ 2 t = p [ 1 + 10 / 200 ] ^ 2 * 1 = 441 p / 400 here its given in the question dat diff btwn simple interest and compound interest half yearly . . . is 25 = > 441 p / 400 - 11 p / 10 = 25 = > p / 400 = 25 = > p = 400 * 25 = 10000 so sum = 10000 answer : c
Answer: c
Problem: how many bricks , each measuring 25 cm x 11 cm x 6 cm , will be needed to build a wall of 2 m x 3 m x 2 cm ?
Options: a ) 5600 , b ) 6000 , c ) 73 , d ) 7200 , e ) 8600
Rationale: "number of bricks = volume of the wall / volume of 1 brick = ( 200 x 300 x 2 ) / ( 25 x 11 x 6 ) = 72.7 = 73 . answer : option c"
Answer: c
Problem: 60 percent of movie theatres in town x have 2 screens or less . 20 % of those theatres sell an average of more than $ 300 worth of popcorn per showing . 56 percent of all the movie theatres in town x sell $ 300 or less of popcorn per showing . what percent of all the stores on the street have 4 or more screens and sell an average of more than $ 300 worth of popcorn per day ?
Options: a ) 12 , b ) 18 , c ) 32 , d ) 40 , e ) 44
Rationale: "lets take numbers here . assume that the total number of movie theaters in the town = 100 then number of movie theaters with 3 screens or less = 60 = > number of movie theaters with 4 screens or more = 40 movie theaters with 3 screens or less selling popcorn at more than $ 300 = 20 % of 60 = 12 number of movie theaters selling popcorn at $ 300 or less = 56 = > number of movie theaters selling popcorn at more than $ 300 = 100 - 56 = 44 of these 44 theaters , 12 are those with 3 screens or less therefore 40 ( 44 - 12 ) must be those with four screens or more d is the answer"
Answer: d
Problem: if w is the set of all the integers between 69 and 99 , inclusive , that are either multiples of 3 or multiples of 2 or multiples of both , then w contains how many numbers ?
Options: a ) 20 , b ) 32 , c ) 33 , d ) 34 , e ) 35
Rationale: "multiples of 2 from 69 to 99 = multiples of 2 from 1 to 99 - multiples of 2 from 1 to 68 = [ 99 / 2 ] - [ 68 / 2 ] = 49 - 34 = 15 multiples of 3 from 69 to 99 = multiples of 3 from 1 to 99 - multiples of 3 from 1 to 68 = [ 99 / 3 ] - [ 68 / 3 ] = 33 - 23 = 10 multiples of 2 and 3 bothi . e . 6 from 69 to 99 = multiples of 6 from 1 to 99 - multiples of 6 from 1 to 68 = [ 99 / 6 ] - [ 68 / 6 ] = 16 - 11 = 5 these 8 numbers have been counted twice in both the above calculation while calculating multiples of 2 and 3 i . e . total numbers in w = 15 + 10 - 5 = 20 answer option a"
Answer: a
Problem: 75 boys can complete a work in 26 days . how many men need to complete twice the work in 20 days
Options: a ) 160 , b ) 195 , c ) 180 , d ) 190 , e ) 200
Rationale: "one man can complete the work in 26 * 75 = 1950 days = one time work to complete the work twice it will be completed in let m be the no . of worker assign for this therefore the eqn becomes m * 20 = 2 * 1950 m = 195 workers answer : b"
Answer: b
Problem: a trader bought a car at 20 % discount on its original price . he sold it at a 55 % increase on the price he bought it . what percent of profit did he make on the original price ?
Options: a ) 17 % , b ) 24 % , c ) 12 % , d ) 82 % , e ) 16 %
Rationale: "original price = 100 cp = 80 s = 80 * ( 155 / 100 ) = 124 100 - 124 = 24 % answer : b"
Answer: b
Problem: how many shots of 1 cm radius can be prepared from a sphere of 2 cm radius ?
Options: a ) 3 , b ) 8 , c ) 27 , d ) 88 , e ) 99
Rationale: "4 / 3 ï € * 2 * 2 * 2 = 4 / 3 ï € * 1 * 1 * 1 * x x = 8 answer : b"
Answer: b
Problem: machine a and machine b are each used to manufacture 660 sprockets . it takes machine a 10 hours longer to produce 660 sprockets than machine b . machine b produces 10 percent more sprockets per hour than machine a . how many sprockets per hour does machine a produces ?
Options: a ) 6 , b ) 6.6 , c ) 60 , d ) 100 , e ) 110
Rationale: b takes x hours a takes x + 10 hours rate of a = 660 / x + 10 rate of b = 660 / x thus , 660 / x = ( 660 / x + 10 ) * 1.10 x = 100 so b = 100 a = 110 sprockets per hour 660 / 110 = 6 answer : a
Answer: a
Problem: what is 50 % of 40 % of 1200 grams ?
Options: a ) 450 gms , b ) 100 gms , c ) 300 gms , d ) 240 gms , e ) none of these
Rationale: "50 / 100 × 40 / 100 × 1200 = 240 answer : d"
Answer: d
Problem: the sum of the squares of the first 15 positive integers ( 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + . . . + 15 ^ 2 ) is equal to 1250 . what is the sum of the squares of the second 15 positive integers ( 16 ^ 2 + 17 ^ 2 + 18 ^ 2 + . . . + 30 ^ 2 ) ?
Options: a ) 2480 , b ) 3490 , c ) 6785 , d ) 8225 , e ) 9255
Rationale: "you ' ll never need a formula for the sums of squares on the actual gmat . you do n ' t need to use that formula here , though it ' s not all that straightforward to solve without one . two different approaches : 16 ^ 2 + 17 ^ 2 + 18 ^ 2 + . . . + 30 ^ 2 = ( 15 + 1 ) ^ 2 + ( 15 + 2 ) ^ 2 + ( 15 + 3 ) ^ 2 + . . . + ( 15 + 15 ) ^ 2 now we can expand each square ; they are all in the ( x + y ) ^ 2 = x ^ 2 + 2 xy + y ^ 2 pattern . = ( 15 ^ 2 + 2 * 15 + 1 ^ 2 ) + ( 15 ^ 2 + 4 * 15 + 2 ^ 2 ) + ( 15 ^ 2 + 6 * 15 + 3 ^ 2 ) + . . . + ( 15 ^ 2 + 30 * 15 + 15 ^ 2 ) now we have fifteen 15 ^ 2 terms , so adding these gives 15 * 15 ^ 2 = 15 ^ 3 = 3375 . we also have the entire sum 1 ^ 2 + 2 ^ 2 + . . . + 15 ^ 2 , which we know is equal to 1240 . finally adding the middle terms , we have : 2 * 15 + 4 * 15 + 6 * 15 + . . . + 30 * 15 = 15 ( 2 + 4 + 6 + . . . . + 30 ) = 15 * 2 * ( 1 + 2 + 3 + . . . + 15 ) = 15 * 2 * 8 * 15 = 3600 so the sum must be 3375 + 1240 + 3600 = 8215 alternatively , we can use a different factoring pattern . we want to find the value of 30 ^ 2 + 29 ^ 2 + . . . + 17 ^ 2 + 16 ^ 2 . well if we subtract 15 ^ 2 + 14 ^ 2 + . . . . + 2 ^ 2 + 1 ^ 2 from this , the answer will be 1240 less than what we want to find . so if we can find the value of 30 ^ 2 + 29 ^ 2 + . . . + 17 ^ 2 + 16 ^ 2 - ( 15 ^ 2 + 14 ^ 2 + . . . . + 2 ^ 2 + 1 ^ 2 ) then we can add 1240 to get the answer . now grouping the terms above to get differences of squares , we have = ( 30 ^ 2 - 15 ^ 2 ) + ( 29 ^ 2 - 14 ^ 2 ) + . . . + ( 16 ^ 2 - 1 ^ 2 ) and factoring each of these using x ^ 2 - y ^ 2 = ( x + y ) ( x - y ) , we have = 45 * 15 + 43 * 15 + 41 * 15 + . . . + 17 * 15 = 15 ( 45 + 43 + 41 + . . . + 17 ) in brackets we have an equally spaced sum with fifteen terms , which we can evaluate using the familiar formula . so the above equals 15 * 15 * 62 / 2 = 6975 and adding back the 1250 , we get the answer of 8225 . ( ans d )"
Answer: d
Problem: there were two candidates in an election . winner candidate received 52 % of votes and won the election by 288 votes . find the number of votes casted to the winning candidate ?
Options: a ) 776 , b ) 3744 , c ) 299 , d ) 257 , e ) 125
Rationale: "w = 52 % l = 48 % 52 % - 48 % = 4 % 4 % - - - - - - - - 288 52 % - - - - - - - - ? = > 3744 answer : b"
Answer: b
Problem: john completes a piece of work in 320 days , rose completes the same work in 480 days . if both of them work together , then the number of days required to complete the work is ?
Options: a ) 190 , b ) 192 , c ) 194 , d ) 196 , e ) 198
Rationale: "if a can complete a work in x days and b can complete the same work in y days , then , both of them together can complete the work in x y / x + y days . that is , the required no . of days = 320 × 480 / 800 = 192 days answer is b"
Answer: b
Problem: in a sports club with 30 members , 18 play badminton and 19 play tennis and 2 do not play either . how many members play both badminton and tennis ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "let x play both badminton and tennis so 18 - x play only badminton and 19 - x play only tennis . 2 play none and there are total 30 students . hence , ( 18 - x ) + ( 19 - x ) + x + 2 = 30 39 - 2 x + x = 30 39 - x = 30 x = 9 so 9 members play both badminton and tennis . c"
Answer: c
Problem: a boat having a length 3 m and breadth 2 m is floating on a lake . the boat sinks by 1.2 cm when a man gets on it . the mass of man is
Options: a ) 72 kg , b ) 60 kg , c ) 72 kg , d ) 96 kg , e ) none
Rationale: "solution volume of water displaced = ( 3 x 2 x 0.012 ) m 3 = 0.072 m 3 . mass of man = volume of water displaced × density of water = ( 0.072 × 1000 ) kg = 72 kg . answer a"
Answer: a
Problem: what is the probability for a family with 5 children to have two boys and 3 girls ( assuming the probability of having a boy or a girl is equal ) ?
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 3 / 8 , d ) 3 / 16 , e ) 5 / 16
Rationale: one possible case is : girl - girl - girl - boy - boy the probability of this is 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 32 there are 5 c 3 = 10 such cases so we should multiply by 10 . p ( two boys and three girls ) = 10 / 32 = 5 / 16 the answer is e .
Answer: e
Problem: the lowest number which should be added to 5915 so that the sum is exactly divisible by 3 , 5 , 8 and 7 is :
Options: a ) 705 , b ) 825 , c ) 805 , d ) 905 , e ) 810
Rationale: "l . c . m . of 3 , 5 , 8 and 7 = 840 . on dividing 5915 by 840 , the remainder is 35 . number to be added = ( 840 - 35 ) = 805 . answer : option ' c '"
Answer: c