regisss/math_qa huggingface dataset:
Problem: what is 990 * 990 ?
Options: a ) 974,169 , b ) 974,219 , c ) 974,549 , d ) 980,100 , e ) 985,369
Rationale: "if you take a base of 1000 then 990 is 10 less than 1000 to get the product of 990 x 990 write like this 990 - 10 ( as 10 less than base 1000 ) 990 - 10 now 10 x 10 = 100 and 990 - 10 = 980 so 990 x 990 = 980100 . . . ( bingo the answer is d . you can even have a shortcut . . . . . . 10 x 10 = 100 . . . only answer choice has last three digits as 100 . . so no need to calculate 990 - 10 . after you get 10 x 10 you can straight way pick answer choice d ."
Answer: d
Problem: jill ' s favorite number is even and has some repeating prime factors . john is guessing jills favorite number , and the only hint she gives is that 7 is a prime factor . what is johns best guess ?
Options: a ) 84 , b ) 105 , c ) 54 , d ) 42 , e ) 70
Rationale: a 84 = 2 * 2 * 2 * 7 b 105 is odd c 54 = 2 * 3 * 3 d 42 = 2 * 3 * 7 e 70 = 2 * 5 * 7 the answer must meet three criteria : odd , have repeating prime factors , and 7 is a prime factor . a is the only answer that meets all criteria
Answer: a
Problem: kamal obtained 76 , 65 , 82 , 67 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 65 , b ) 69 , c ) 72 , d ) 75 , e ) none
Rationale: "sol . average = 76 + 65 + 82 + 67 + 85 / 5 ) = ( 375 / 5 ) = 75 . answer d"
Answer: d
Problem: find the number of factors of 180 that are in the form ( 4 * k + 2 ) , where k is a non - negative integer ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 6
Rationale: make sure to follow posting guidelines ( link in my signatures ) . title of the thread must mention the first few words of the question itself . as for the question , the most straightforward way is to list out the factors ( this is fine for this question as 180 is a relatively small number ) . number of factors of 180 ( = 2 ^ 2 * 3 ^ 2 * 5 ) = 18 . so listing the factors gives us : 1 , 180 2 , 90 3 , 60 4 , 45 5 , 36 6 , 30 9 , 20 10 , 18 12 , 15 as the question asks us about the factors of the form 4 k + 2 - - - > eliminate all odd factors . you are now left with 24 , 610 , 1218 , 2030 , 3660 , 90180 for the form 4 k + 2 , the first few values are 2 , 6 , 10 , 14 , 18 , 22 , 26 , 30 . . . already giving you 5 factors ( = 2 , 610 , 1830 ) . you can stop here and mark 6 ( 6 th one = 90 ) as the correct answer as 5 is not given . for checking any particular factor whether they conform to the form 4 k + 2 - - - > do the following 4 k + 2 = 36 - - - > 4 k = 34 - - > this will not give you an integer value for k - - - > reject . proceed with others until you find all the values asked . e is thus the correct answer .
Answer: e
Problem: every student of a certain school must play an instrument . in last year , 1 / 2 of the students picked a woodwind instrument , 2 / 5 of the students picked a brass instrument , and all of the other students took percussion . in this year , 1 / 2 of the students who play woodwind and 1 / 4 of the students who play brass instruments left school , other students did not leave , and no fresh student come in . what fraction of all students play either a woodwind or brass instrument ?
Options: a ) 7 / 13 , b ) 4 / 5 , c ) 9 / 13 , d ) 11 / 13 , e ) 7 / 10
Rationale: lets pick smart numbers . total number of students : 20 woodwind ( 1 / 2 ) : 10 brass ( 2 / 5 ) : 8 percussion ( 1 / 10 ) : 2 after leaving school woodwind : 5 brass : 6 percussion : 2 new total number of students : 13 woodwind and brass : 11 answer 11 / 13 or d
Answer: d
Problem: a cylinder is being filled with sand weighing 200 kg per cubic foot . the cylinder has a diameter of 1 foot and is 5 feet tall . how much sand is being used ? ?
Options: a ) 250 pi kg
b ) 500 pi kg
c ) 500 pi ^ 2 kg
d ) 1000 pi kg
e ) 1000 pi ^ 2 kg
Rationale: answer is a . volume of cylinder = pi * r ^ 2 * h - - - - - - - - > pi * ( 1 / 2 ) ^ 2 * 5 - - - - - - - - > pi * ( 1 / 4 ) * 5 - - - - - - - - > ( 5 / 4 ) pi cubic feet . 1 cubic feet = 200 kg . so ( 5 / 4 ) pi cubic feet = ( ( 200 * 5 ) / 4 ) pi - - - - - - - - - > 250 pi regards , abhijit answer is a
Answer: a
Problem: a can complete the job in 4 hours and b can complete the same job in 3 hours . a works for 1 hour and then b joins and both complete the job . what fraction of the job did b complete
Options: a ) 1 / 7 , b ) 3 / 10 , c ) 1 / 2 , d ) 5 / 6 , e ) 8 / 9
Rationale: a = 1 / 7
Answer: a
Problem: there is food for 760 men for 22 days . how many more men should join after two days so that the same food may last for 16 days more ?
Options: a ) 122 , b ) 140 , c ) 199 , d ) 188 , e ) 190
Rationale: "760 - - - - 22 760 - - - - 20 x - - - - - 16 x * 16 = 760 * 20 x = 950 760 - - - - - - - 190 answer : e"
Answer: e
Problem: if n = 8 ^ 8 – 8 , what is the units digit of n ?
Options: a ) 0 , b ) 1 , c ) 8 , d ) 2 , e ) 4
Rationale: "8 ^ 8 - 8 = 8 ( 8 ^ 7 - 1 ) = = > 8 ( 2 ^ 21 - 1 ) last digit of 2 ^ 21 is 2 based on what explanation livestronger is saying . 2 ^ 24 - 1 yields 2 - 1 = 1 as the unit digit . now on multiply this with 8 , we get unit digit as 8 answer : c"
Answer: c
Problem: if w is the set of all the integers between 19 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 ) 26 , b ) 32 , c ) 33 , d ) 34 , e ) 54
Rationale: "multiples of 2 from 19 to 99 = multiples of 2 from 1 to 99 - multiples of 2 from 1 to 18 = [ 99 / 2 ] - [ 18 / 2 ] = 49 - 9 = 40 multiples of 3 from 19 to 99 = multiples of 3 from 1 to 99 - multiples of 3 from 1 to 18 = [ 99 / 3 ] - [ 18 / 3 ] = 33 - 6 = 27 multiples of 2 and 3 bothi . e . 6 from 19 to 99 = multiples of 6 from 1 to 99 - multiples of 6 from 1 to 18 = [ 99 / 6 ] - [ 18 / 6 ] = 16 - 3 = 13 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 = 40 + 27 - 13 = 54 answer option e"
Answer: e
Problem: find the curved surface area , if the radius of a cone is 28 m and slant height is 30 m ?
Options: a ) 2550 , b ) 2640 , c ) 3960 , d ) 4280 , e ) 5490
Rationale: "cone curved surface area = ï € rl 22 / 7 ã — 28 ã — 30 = 88 ã — 30 = 2640 m ( power 2 ) answer is b ."
Answer: b
Problem: | 16 - 5 | - | 5 - 12 | = ?
Options: a ) 3 , b ) 2 , c ) 1 , d ) 0 , e ) 4
Rationale: "| 16 - 5 | - | 5 - 12 | = | 11 | - | - 7 | = 11 - 7 = 4 correct answer e"
Answer: e
Problem: if two - third of a bucket is filled in 90 seconds then the time taken to fill the bucket completely will be .
Options: a ) 90 seconds , b ) 70 seconds , c ) 135 seconds , d ) 100 seconds , e ) 120 seconds
Rationale: "2 / 3 filled in 90 seconds 1 / 3 filled in 45 seconds then 2 / 3 + 1 / 3 = 90 + 45 seconds = 135 seconds answer : c"
Answer: c
Problem: if a tire rotates at 400 revolutions per minute when the car is traveling 120 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 = 12,0000 m : c is the circumference c = 5 meters correct answer d
Answer: d
Problem: the population of a town increased from 1 , 75000 to 2 , 62500 in a decade . what is the average percent increase of population per year ?
Options: a ) 4 % , b ) 6 % , c ) 5 % , d ) 50 % , e ) none of these
Rationale: explanation : increase in the population in 10 years = 2 , 62500 - 1 , 75000 = 87500 % ncrease in the population in 10 years = ( 87500 / 175000 ) × 100 = 8750 / 175 = 50 % average % increase of population per year = 50 % / 10 = 5 % answer : option c
Answer: c
Problem: 10 men do a work in 10 days . how many men are needed to finish the work in 2 days ?
Options: a ) 50 , b ) 20 , c ) 30 , d ) 10 , e ) 15
Rationale: "men required to finish the work in 2 days = 10 * 10 / 2 = 50 answer is a"
Answer: a
Problem: the average age of 35 students in a class is 16 years . the average age of 21 students is 14 . what is the average age of remaining 38 students ?
Options: a ) 14 years , b ) 7 years , c ) 19 years , d ) 21 years , e ) none
Rationale: "solution sum of the ages of 14 students = ( 16 x 35 ) - ( 14 x 21 ) = 560 - 294 . = 266 . ∴ required average = 266 / 38 = 7 years . answer b"
Answer: b
Problem: a man can row 8 kmph in still water . if the velocity of the current is 2 kmph and it takes him 2 hours to row to a place and come back . how far is the place ?
Options: a ) 5.5 , b ) 8.5 , c ) 6.5 , d ) 9.5 , e ) 7.5
Rationale: man ' s rate down stream = 8 + 2 = 10 kmph man ' s rate upstream = 8 - 2 = 6 kmph let the required distance be x km then x / 10 + x / 6 = 2 3 x + 5 x = 60 8 x = 60 x = 7.5 km answer is e .
Answer: e
Problem: if x is equal to the sum of the integers from 20 to 40 , inclusive , and y is the number of even integers from 20 to 40 , inclusive , what is the value of x + y ?
Options: a ) 601 , b ) 611 , c ) 621 , d ) 631 , e ) 641
Rationale: "x = 20 + 21 + . . . + 40 = 21 ( 30 ) = 630 y = 11 x + y = 641 the answer is e ."
Answer: e
Problem: the hiker walking at a constant rate of 5 miles per hour is passed by a cyclist traveling in the same direction along the same path at 20 miles per hour . the cyclist stops to wait for the hiker 5 minutes after passing her , while the hiker continues to walk at her constant rate , how many minutes must the cyclist wait until the hiker catches up ?
Options: a ) 15 , b ) 10 , c ) 20 , d ) 30 , e ) 35
Rationale: "after passing the hiker the cyclist travels for 5 minutes at a rate of 20 miles / hour . in those 5 mins the cyclist travels a distance of 5 / 3 miles . in those 5 mins the hiker travels a distance of 5 / 12 miles . so the hiker still has to cover 15 / 12 miles to meet the waiting cyclist . the hiker will need 1 / 4 hours or 15 mins to cover the remaining 15 / 12 miles . so the answer is a ."
Answer: a
Problem: a tank with a volume of 30 cubic feet has one inlet pipe and 2 outlet pipes . the inlet pipe fills water into the tank at the rate of 5 cubic inches / min and the 2 outlet pipes empty it out at the rates of 9 cubic inches / min and 8 cubic inches / min respectively . if all 3 pipes are opened when the tank is full , how many minutes does it take to empty the tank ? ( 1 foot = 12 inches )
Options: a ) 1440 , b ) 2340 , c ) 3240 , d ) 4320 , e ) 5420
Rationale: "the tank is emptied at this rate : 9 + 8 - 5 = 12 cubic inches / min the tank has a volume of 30 * 12 * 12 * 12 = 51840 cubic inches . the time it takes to empty the tank is 51840 / 12 = 4320 minutes . the answer is d ."
Answer: d
Problem: a train consists of 12 boggies , each boggy 15 metres long . the train crosses a telegraph post in 9 seconds . due to some problem , three boggies were detached . the train now crosses a telegraph post in
Options: a ) 6.75 sec , b ) 12 sec , c ) 15 sec , d ) 20 sec , e ) none of these
Rationale: "length of train = 12 ã — 15 = 180 m . then , speed of train = 180 â  „ 9 = 20 m / s now , length of train = 9 ã — 15 = 135 m â ˆ ´ required time = 135 â  „ 20 = 6.75 sec . answer a"
Answer: a
Problem: a 90 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds . what is the length of the other train ?
Options: a ) 220 meter , b ) 225 meter , c ) 230 meter , d ) 410 meter , e ) none of these
Rationale: "explanation : as trains are running in opposite directions so their relative speed will get added so , relative speed = 120 + 80 = 200 kmph = 200 * ( 5 / 18 ) = 500 / 9 m / sec let the length of other train is x meter then x + 90 / 9 = 500 / 9 = > x + 90 = 500 = > x = 410 so the length of the train is 410 meters option d"
Answer: d
Problem: with a uniform speed a car covers the distance in 8 hours . had the speed been increased by 2 km / hr , the same distance could have been covered in 7 1 / 2 hours . what is the distance covered ?
Options: a ) 187 km , b ) 480 km , c ) 278 km , d ) 240 km , e ) 671 km
Rationale: "let the distance be x km . then , x / ( 7 1 / 2 ) - x / 8 = 2 2 x / 15 - x / 8 = 2 = > x = 240 km . answer : d"
Answer: d
Problem: a store ’ s selling price of $ 2240 for a certain computer would yield a profit of 30 percent of the store ’ s cost for the computer . what selling price would yield a profit of 40 percent of the computer ’ s cost ?
Options: a ) $ 2400 , b ) $ 2412 , c ) $ 2650 , d ) $ 2732 , e ) $ 2800
Rationale: "1.3 x = 2240 x = 2240 / 1.3 so , 1.4 x = 2240 * 1.4 / 1.3 = 2412 answer : - b"
Answer: b
Problem: three table runners have a combined area of 220 square inches . by overlapping the runners to cover 80 % of a table of area 175 square inches , the area that is covered by exactly two layers of runner is 24 square inches . what is the area of the table that is covered with three layers of runner ?
Options: a ) 18 square inches , b ) 20 square inches , c ) 24 square inches , d ) 28 square inches , e ) 30 square inches
Rationale: "total = a + b + c - ( sum of exactly 2 - group overlaps ) - 2 * ( all three ) + neither 80 % * 175 = 220 - 24 - 2 * ( all three ) + 0 2 * ( all three ) = 220 - 24 - 140 all three = 28 answer : d"
Answer: d
Problem: the youngest of 4 children has siblings who are 2 , 7 , and 11 years older than she is . if the average ( arithmetic mean ) age of the 4 siblings is 25 , what is the age of the youngest sibling ?
Options: a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 21
Rationale: "x + ( x + 2 ) + ( x + 7 ) + ( x + 11 ) = 100 4 x + 20 = 100 4 x = 80 x = 20 the answer is d ."
Answer: d
Problem: addison high school ’ s senior class has 300 boys and 240 girls . if 60 % of the boys attended the college then 60 % of the total class attended college , what percentage of the girls class attended college ?
Options: a ) 60 , b ) 50 , c ) 46 , d ) 55.56 , e ) 65
Rationale: "number of boys attending the party : 0.60 * 300 = 180 total students = 300 + 240 = 540 number of students attending the party : 0.60 * 540 = 324 number of girls attending = 324 - 180 = 144 % of girls attending = 144 / 240 = 60 % . a is the correct answer"
Answer: a
Problem: if 6 ! / 3 ^ x is an integer , what is the greatest possible value of x ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "6 - 2 * 3 3 - 1 * 3 hence max of 3 ^ 2 is allowed . imo a ."
Answer: a
Problem: a person walking at 10 kmph reaches his office 10 minutes late . if he walks at 15 kmph , he reaches there 10 minutes earlier . how far is the office from his house ?
Options: a ) 5 km , b ) 15 km , c ) 8 km , d ) 10 km , e ) 20 km
Rationale: formula = s 1 * s 2 / s 2 - s 1 * t 1 + t 2 / 60 = 10 * 15 / 5 * 20 / 60 = 30 * 20 / 60 = 10 km answer is d
Answer: d
Problem: running at the same rate , 8 identical machines can produce 560 paperclips a minute . at this rate , how many paperclips could 18 machines produce in 6 minutes ?
Options: a ) 1344 , b ) 3360 , c ) 7560 , d ) 50400 , e ) 67200
Rationale: "8 machines produce 560 in 1 min 8 machines produce 560 * 6 in 6 min 18 machine produce 560 * 6 * ( 18 / 8 ) in 6 minutes 560 * 6 * 18 / 8 = 7560 answer is c ."
Answer: c
Problem: two pipes a and b can fill a tank in 25 hours and 35 hours respectively . if both the pipes are opened simultaneously , how much time will be taken to fill the tank ?
Options: a ) 20 hours , b ) 14 6 / 11 hours , c ) 10 hours , d ) 12 hours , e ) 8 hours
Rationale: "part filled by a in 1 hour = 1 / 25 part filled by b in 1 hour = 1 / 30 part filled by ( a + b ) in 1 hour = 1 / 25 + 1 / 30 = 11 / 150 both the pipes together fill the tank in 150 / 11 = 14 6 / 11 hours answer is b"
Answer: b
Problem: tammy climbed a mountain in two days . she spent a total of 14 hours climbing the mountain . on the second day , she walked at an average speed that was half a kilometer per hour faster , but 2 hours less than what she walked on the first day . if the total distance she climbed during the two days is 52 kilometers , how many w kilometers per hour did tammy walk on the second day ?
Options: a ) 3 , b ) 3.5 , c ) 4 , d ) 4.5 , e ) 6
Rationale: "ans : c total time = 14 hrs let time traveled during 1 st day = x let time traveled during 2 nd day = x - 2 total time = 14 x + x - 2 = 14 x = 8 speed * time = distance s * 8 + ( s + 0.5 ) ( 8 - 2 ) = 52 solving s = 4.5 now speed for 2 nd day is 0.5 less than the 1 st day which is 4.5 thus speed for 2 nd day = 4 its simple algebra for s * 8 + ( s + 0.5 ) ( 8 - 2 ) = 52 but for some reason im getting 3.5 and not 4.5 . 8 s + 6 s + 3 = 52 14 s = 49 s = 3.5"
Answer: c
Problem: jolene entered an 14 - month investment contract that guarantees to pay 2 percent interest at the end of 6 months , another 3 percent interest at the end of 12 months , and 4 percent interest at the end of the 18 month contract . if each interest payment is reinvested in the contract , and jolene invested $ 10,000 initially , what will be the total amount of interest paid during the 18 - month contract ?
Options: a ) $ 506.00 , b ) $ 726.24 , c ) $ 900.00 , d ) $ 920.24 , e ) $ 926.24
Rationale: "if interest were not compounded in every six months ( so if interest were not earned on interest ) then we would have ( 2 + 3 + 4 ) = 9 % simple interest earned on $ 10,000 , which is $ 900 . so , you can rule out a , b and c right away . interest earned after the first time interval : $ 10,000 * 2 % = $ 200 ; interest earned after the second time interval : ( $ 10,000 + $ 200 ) * 3 % = $ 300 + $ 6 = $ 306 ; interest earned after the third time interval : ( $ 10,000 + $ 200 + $ 306 ) * 4 % = $ 400 + $ 8 + ( ~ $ 12 ) = ~ $ 420 ; total : 200 + 306 + ( ~ 420 ) = ~ $ 506.00 answer : a ."
Answer: a
Problem: an isosceles triangle with sides 13 13 10 and there is a circle inscribed it . find the radius of circle ?
Options: a ) 1.32
b ) 3.33
c ) 3.58
d ) 4.34
e ) 5.18
Rationale: height of triangle = √ ( 13 ^ 2 - ( 10 / 2 ) ^ 2 ) = 12 area of triangle = r * s where , r = radius of inscribed circle & s = ( a + b + c ) / 2 area of triangle = 1 / 2 * b * h = 1 / 2 * 10 * 12 = 60 s = ( 13 + 13 + 10 ) / 2 = 18 r = area of triangle / s = 60 / 18 = 10 / 3 = 3.33 answer : b
Answer: b
Problem: the diagonals of a rhombus are 10 cm and 15 cm . find its area ?
Options: a ) 75 , b ) 129 , c ) 150 , d ) 123 , e ) 117
Rationale: "1 / 2 * 10 * 15 = 75 answer : a"
Answer: a
Problem: in a can , there is a mixture of milk and water in the ratio 1 : 5 . if it is filled with an additional 2 litres of milk the can would be full and ratio of milk and water would become 3 : 5 . find the capacity of the can ?
Options: a ) 40 , b ) 44 , c ) 48 , d ) 8 , e ) 56
Rationale: "let the capacity of the can be t litres . quantity of milk in the mixture before adding milk = 1 / 6 ( t - 2 ) after adding milk , quantity of milk in the mixture = 3 / 8 t . 3 t / 8 - 2 = 1 / 6 = ( t - 2 ) 10 t = 96 - 16 = > t = 8 answer : d"
Answer: d
Problem: each child has 6 crayons and 12 apples . if there are 12 children , how many crayons are there in total ?
Options: a ) 22 , b ) 65 , c ) 72 , d ) 78 , e ) 90
Rationale: 6 * 12 = 72 . answer is c
Answer: c
Problem: in a certain school , the ratio of boys to girls is 5 to 17 . if there are 72 more girls than boys , how many boys are there ?
Options: a ) 27 , b ) 36 , c ) 45 , d ) 72 , e ) 108
Rationale: "the ratio of b to g is 5 : 13 and the other data point is g are more than boys by 72 . . . looking at the ratio we can say that the 12 ( 17 - 5 ) extra parts caused this diff of 72 . so 1 part corresponds to 72 / 8 = 9 and so 5 parts correspond to 12 * 9 = 108 . e"
Answer: e
Problem: a car takes 8 hours to cover a distance of 540 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 10 kmph , b ) 45 kmph , c ) 60 kmph , d ) 55 kmph , e ) 30 kmph
Rationale: "time = 8 distence = 540 3 / 2 of 8 hours = 8 * 3 / 2 = 12 hours required speed = 540 / 12 = 45 kmph b )"
Answer: b
Problem: in a room with 7 people , 4 people have exactly 1 friend in the room and 3 people have exactly 2 friends in the room ( assuming that friendship is a mutual relationship , i . e . if jane is paul ' s friend , paul is jane ' s friend ) . if two individuals are selected from the room at random , what is the probability that those two individuals are not friends ?
Options: a ) 5 / 21 , b ) 3 / 7 , c ) 4 / 7 , d ) 5 / 7 , e ) 16 / 21
Rationale: "( 4 / 7 ) ( 5 / 6 ) + ( 3 / 7 ) ( 4 / 6 ) if you choose one of the 4 with one other friend , then you have a 5 / 6 chance of not picking their friend 2 nd . if you choose one of the 3 with 2 friends , you have a 4 / 6 chance of not picking one of their friends second . add them up . 20 / 42 + 12 / 42 32 / 42 = 16 / 21 e . 16 / 21"
Answer: e
Problem: assisants are needed to prepare for preparation . each helper can make either 2 large cakes or 35 small cakes / hour . the kitchen is available for 3 hours and 20 large cakes and 700 small cakes are needed . how many helpers are required ?
Options: a ) 9 , b ) 10 , c ) 13 , d ) 16 , e ) 18
Rationale: 20 large cakes will require the equivalent of 10 helpers working for one hour . 700 small cakes will require the equivalent of 20 helpers working for one hour . this means if only one hour were available we would need 30 helpers . but since three hours are available we can use 10 helpers . b
Answer: b
Problem: if the perimeter of a rectangular park is 1000 m , its length when its breadth is 200 m is ?
Options: a ) 50 , b ) 100 , c ) 200 , d ) 300 , e ) 400
Rationale: 2 ( l + 200 ) = 1000 = > l = 300 m answer : d
Answer: d
Problem: a boat running upstream takes 640 min to cover a certain distance , while it takes 280 min to cover the same distance running down stream . what is the ratio between the speed of the boat and speed of water current respectively ?
Options: a ) 23 : 7 , b ) 22 : 9 , c ) 23 : 8 , d ) 23 : 9 , e ) 23 : 11
Rationale: let the speed of the boat = x and speed of the current = y relative speed in upstream = x - y and in downstream = x + y let the distance ' d ' is to be covered in downstream and upstream , then time taken in upstream = d / ( x - y ) = 640 or d = 640 ( x - y ) - - - - ( i ) and time taken in downstream = d / ( x + y ) = 280 or d = 280 ( x + y ) - - - - ( ii ) comparing ( i ) & ( ii ) , 640 ( x - y ) = 280 ( x + y ) = > 16 ( x - y ) = 7 ( x + y ) = > 16 x - 16 y = 7 x - 7 y = > 9 x = 23 y = > x / y = 23 / 9 answer : d
Answer: d
Problem: f ( 1 ) = 1 , where f ( x + y ) = f ( x ) + f ( y ) + 8 xy - 2 . then f ( 7 ) = ?
Options: a ) 162 , b ) 163 , c ) 164 , d ) 165 , e ) 166
Rationale: f ( 1 ) = 1 f ( 2 ) = f ( 1 + 1 ) = 1 + 1 + 8 - 2 = 8 f ( 3 ) = f ( 2 + 1 ) = 8 + 1 + ( 8 * 2 * 1 ) - 2 = 23 f ( 6 ) = f ( 3 + 3 ) = 23 + 23 + ( 8 * 3 * 3 ) - 2 = 116 f ( 7 ) = f ( 6 + 1 ) = 116 + 1 + ( 8 * 6 * 1 ) - 2 = 163 thus ans is 163 answer : b
Answer: b
Problem: what is the largest possible value of cc if 5 c + ( d − 12 ) ^ 2 = 235 ?
Options: a ) 17 , b ) 25 , c ) 35 , d ) 42 , e ) 47
Rationale: to maximize c , we should minimize ( d - 12 ) ^ 2 . ( d - 12 ) ^ 2 is a square of a number , thus its smallest possible value is 0 ( for d = 12 ) . in this case we ' d have 5 c + 0 = 235 - - > c = 47 . answer : e .
Answer: e
Problem: find the cost of fencing around a circular field of diameter 35 m at the rate of rs . 1.50 a meter ?
Options: a ) 287 , b ) 132 , c ) 156 , d ) 115.5 , e ) 267
Rationale: "2 * 22 / 7 * 17.5 = 110 110 * 1 1 / 2 = rs . 115.5 answer : d"
Answer: d
Problem: the sum of all two digit numbers divisible by 5 is
Options: a ) 945 , b ) 3487 , c ) 28 , d ) 279 , e ) 1287
Rationale: "required numbers are 10,15 , 20,25 , . . . , 95 this is an a . p . in which a = 10 , d = 5 and l = 95 . let the number of terms in it be n . then t = 95 so a + ( n - 1 ) d = 95 . 10 + ( n - 1 ) * 5 = 95 , then n = 18 . required sum = n / 2 ( a + l ) = 18 / 2 ( 10 + 95 ) = 945 . answer : a ) 945"
Answer: a
Problem: at the faculty of aerospace engineering , 312 students study random - processing methods , 222 students study scramjet rocket engines and 112 students study them both . if every student in the faculty has to study one of the two subjects , how many students are there in the faculty of aerospace engineering ?
Options: a ) 404 , b ) 452 , c ) 444 , d ) 468 , e ) 422
Rationale: "312 + 222 - 112 ( since 112 is counted twice ) = 422 e is the answer"
Answer: e
Problem: a , b and c started a business with capitals of rs . 8000 , rs . 10000 and rs . 12000 respectively . at the end of the year , the profit share of b is rs . 1700 . the difference between the profit shares of a and c is ?
Options: a ) 288 , b ) 266 , c ) 155 , d ) 680 , e ) 441
Rationale: "ratio of investments of a , b and c is 8000 : 10000 : 12000 = 4 : 5 : 6 and also given that , profit share of b is rs . 1700 = > 5 parts out of 15 parts is rs . 1700 now , required difference is 6 - 4 = 2 parts required difference = 2 / 5 ( 1700 ) = rs . 680 answer : d"
Answer: d
Problem: if the operation ø is defined for all positive integers x and w by x ø w = ( 2 ^ x ) / ( 2 ^ w ) then ( 4 ø 2 ) ø 2 = ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 16 , e ) 32
Rationale: "4 ø 2 = 2 ^ 4 / 2 ^ 2 = 4 4 ø 2 = 2 ^ 4 / 2 ^ 2 = 4 the answer is b ."
Answer: b
Problem: a rectangular floor is covered by a rug except for a strip 3 meters wide along each of the four edge . if the floor is 12 meters by 10 meters , what is the area of the rug in square meters ?
Options: a ) 30 , b ) 28 , c ) 36 , d ) 42 , e ) 24
Rationale: "a strip of 3 meters is covering the inner rectangular rug for all 4 sides . length of inner rug = 12 - ( 2 * 3 ) breadth of inner rug = 10 - ( 2 * 3 ) area of rug = 6 * 4 = 24 sq . mt â nswer : e"
Answer: e
Problem: if x , y , and z are positive integers , and 2 x = 5 y = 7 z , then the least possible value of x + y + z is
Options: a ) 15 , b ) 28 , c ) 37 , d ) 42 , e ) 59
Rationale: "take lcm of 2,5 and 7 = 70 now 2 x = 70 = > x = 35 5 y = 70 = > y = 14 7 z = 70 = > z = 10 35 + 14 + 10 = 59 . option e ."
Answer: e
Problem: on a trip , a cyclist averaged 8 miles per hour for the first 16 miles and 10 miles per hour for the remaining 16 miles . if the cyclist returned immediately via the same route and took a total of 6.8 hours for the round trip , what was the average speed ( in miles per hour ) for the return trip ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "the time to go 32 miles was 16 / 8 + 16 / 10 = 2 + 1.6 = 3.6 hours . the average speed for the return trip was 32 miles / 3.2 hours = 10 mph . the answer is b ."
Answer: b
Problem: for how many unique pairs of nonnegative integers { a , b } is the equation a ^ 2 - b ^ 2 = 235 true ?
Options: a ) 1 , b ) 2 , c ) 5 , d ) 7 , e ) 9
Rationale: "answer b ( a + b ) ( a - b ) = 235 2 cases for ( a + b ) , ( a - b ) 235 , 1 47 , 5 answer b"
Answer: b
Problem: on dividing a number by 999 , the quotient is 366 and the remainder is 103 . the number is :
Options: a ) 364724 , b ) 365387 , c ) 365737 , d ) 366757 , e ) none of these
Rationale: "required number = 999 * 366 + 103 = ( 1000 - 1 ) * 366 + 103 = 366000 - 366 + 103 = 365737 . answer : c"
Answer: c
Problem: one - third less than 20 % of 180 is equal to :
Options: a ) 24 , b ) 30 , c ) 35 , d ) 40 , e ) 45
Rationale: "lots of ways to tackle this . 20 % of 180 = 36 1 / 3 of 36 = 12 so , 1 / 3 , less than 36 is equal to 36 - 12 = 24 answer : a"
Answer: a
Problem: the area of a square field is 576 km 2 . how long will it take for a horse to run around at the speed of 12 km / h ?
Options: a ) 12 h , b ) 10 h , c ) 8 h , d ) 6 h , e ) none of these
Rationale: "area of field = 576 km 2 . then , each side of field = √ 576 = 24 km distance covered by the horse = perimeter of square field = 24 × 4 = 96 km ∴ time taken by horse = distances / peed = 96 / 12 = 8 h answer c"
Answer: c
Problem: a and b complete a work in 6 days . a can alone can do it in 10 days . if both can together can do the work in how many days ?
Options: a ) 7 , b ) 3.75 , c ) 2 , d ) 1 , e ) 8
Rationale: 1 / 6 + 1 / 10 = 8 / 30 = 4 / 15 15 / 4 = 3.75 days answer b
Answer: b
Problem: suppose you work for a manufacturing plant that pays you $ 12.50 an hour plus $ 0.16 for each widget you make . how many widgets must you produce in a 40 hour week to earn $ 620 ( before payroll deductions ) ?
Options: a ) 670 , b ) 710 , c ) 750 , d ) 790 , e ) 830
Rationale: total pay = 40 * $ 12.50 + $ 0.16 * x = 620 x = 120 / 0.16 = 750 the answer is c .
Answer: c
Problem: what is the distance covered by a car if it travels with a speed of 160 kmh for 5 hours ?
Options: a ) 350 km , b ) 400 km , c ) 800 km , d ) 600 km , e ) 650 km
Rationale: distance = time x speed 5 x 160 = 800 answer : c
Answer: c
Problem: a cricketer scored 132 runs which included 12 boundaries and 2 sixes . what percent of his total score did he make by running between the wickets .
Options: a ) 46.2 % , b ) 54.54 % , c ) 63 % , d ) 70 % , e ) none of these
Rationale: "explanation : number of runs made by running = 132 - ( 12 x 4 + 2 x 6 ) = 132 - ( 60 ) = 72 now , we need to calculate 72 is what percent of 132 . = > 72 / 132 * 100 = 54.54 % answer : b"
Answer: b
Problem: a can do a piece of work in 80 days and b in 100 days . they work together for 20 days and then b goes away . in how many days will a finish the remaining work ?
Options: a ) 33 days , b ) 44 days , c ) 55 days , d ) 42 days , e ) 32 days
Rationale: "explanation : in this type of questions we first get the finishing of work in 1 minute for both pipes then we will add them to get the result , as : part finished by a in 1 day = 1 / 80 part finished by b in 1 day = 1 / 100 part finished by ( a + b ) in 1 day = 1 / 80 + 1 / 100 = 9 / 400 so ( a + b ) ' s 20 days work = 20 * 9 / 400 = 9 / 20 remaining work = 1 - 9 / 20 = 11 / 20 . number days to finish the remaining work by a = 80 * 11 / 20 = 44 days . option b"
Answer: b
Problem: pumps a , b , and c operate at their respective constant rates . pumps a and b , operating simultaneously , can fill a certain tank in 6 / 5 hours ; pumps a and c , operating simultaneously , can fill the tank in 3 / 2 hours ; and pumps b and c , operating simultaneously , can fill the tank in 1 hours . how many hours does it take pumps a , b , and c , operating simultaneously , to fill the tank .
Options: a ) 37 / 20 , b ) 1 / 2 , c ) 1 / 4 , d ) 1 , e ) 5 / 6
Rationale: "a + b = 6 / 5 ; a + c = 3 / 2 , b + c = 1 ; add then 2 * ( a + b + c ) = 6 / 5 + 3 / 2 + 1 = 37 / 10 a + b + c = 37 / 20 hrs a"
Answer: a
Problem: the marks obtained by polly and sandy are in the ratio 4 : 5 and those obtained by sandy and willy are in the ratio of 5 : 2 . the marks obtained by polly and willy are in the ratio of . . . ?
Options: a ) 2 : 1 , b ) 3 : 2 , c ) 4 : 3 , d ) 5 : 4 , e ) 6 : 5
Rationale: "polly : sandy = 4 : 5 sandy : willy = 5 : 2 polly : sandy : willy = 4 : 5 : 2 polly : willy = 4 : 2 = 2 : 1 the answer is a ."
Answer: a
Problem: in a certain supermarket , a triangular display of cans is arranged in 9 rows , numbered 1 through 9 from top to bottom . each successively numbered row contains 3 more cans than the row immediately above it . if there are fewer than 120 cans in the entire display , how many cans are in the six row ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "let x be the number of cans in row 1 . the total number of cans is x + ( x + 3 ) + . . . + ( x + 24 ) = 9 x + 3 ( 1 + 2 + . . . + 8 ) = 9 x + 3 ( 8 ) ( 9 ) / 2 = 9 x + 108 since the total is less than 120 , x must equal 1 . the number of cans in the 6 th row is 1 + 3 ( 5 ) = 16 the answer is c ."
Answer: c
Problem: a man ' s regular pay is $ 3 per hour up to 40 hours . overtime is twice the payment for regular time . if he was paid $ 168 , how many hours overtime did he work ?
Options: a ) 8 , b ) 21 , c ) 14 , d ) 12 , e ) 15
Rationale: "answer is : b at $ 3 per hour up to 40 hours , regular pay = $ 3 x 40 = $ 120 if total pay = $ 168 , overtime pay = $ 168 - $ 120 = $ 48 overtime rate ( twice regular ) = 2 x $ 3 = $ 6 per hour = > number of overtime hours = $ 48 / $ 6 = 8"
Answer: a
Problem: if a is thrice as fast as b and together can do a work in 21 days . in how many days a alone can do the work ?
Options: a ) 36 , b ) 42 , c ) 28 , d ) 54 , e ) 45
Rationale: "a ’ s one day ’ s work = 1 / x b ’ s one day ’ s work = 1 / 3 x a + b ’ s one day ’ s work = 1 / x + 1 / 3 x = 1 / 21 = 3 + 1 / 3 x = 4 / 3 x = 1 / 21 x = 21 * 4 / 3 = 28 answer : c"
Answer: c
Problem: if the number 98348 * 0 is exactly divisible by 72 , then the minimum value of * is ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: 72 = 8 * 9 divisibility 0 f 8 last 3 place should be divisible by 8 lly divisibility of 9 sum of digit should be divisible by 9 840 divisible by 8 nd 36 divisible by 9 answer : d
Answer: d
Problem: at a local appliance manufacturing facility , the workers received a 20 % hourly pay raise due to extraordinary performance . if one worker decided to reduce the number of hours that he worked so that his overall pay would remain unchanged , by approximately what percent would he reduce the number of hours that he worked ?
Options: a ) 83 % , b ) 80 % , c ) 20 % , d ) 17 % , e ) 12 %
Rationale: "let ' s say he works usually 10 hours and earns 100 per hour . 10 * 100 = 1000 10 * 120 = 1200 ( this are the new earnings after the raise ) to figure out how much he needs to work with the new salary in order to earn the original 1000 : 1000 / 120 = 8.3333 so he can reduce his work by 1.6666 hours . which is > 15 % . answer d ."
Answer: d
Problem: a reduction of 12 % in the price of oil enables a house wife to obtain 6 kgs more for rs . 1200 , what is the reduced price for kg ?
Options: a ) 24 , b ) 27 , c ) 40 , d ) 28 , e ) 20
Rationale: "1200 * ( 12 / 100 ) = 144 - - - - 6 ? - - - - 1 = > rs . 24 answer : a"
Answer: a
Problem: find the area of a rhombus whose side is 25 cm and one of the diagonals is 30 cm ?
Options: a ) 600
b ) 881
c ) 767
d ) 261
e ) 121
Rationale: consider the rhombus abcd . let the diagonals intersect at e . since diagonals bisect at right angles in a rhombus . be 2 + ae 2 = ab 2 252 = 152 + ae 2 ae = √ ( 625 - 225 ) = √ 400 = 20 , ac = 20 + 20 = 40 cm . area of a rhombus = 1 / 2 * d 1 d 2 = 1 / 2 * 40 * 30 = 600 sq . cm . answer : a
Answer: a
Problem: dick and jane each saved $ 3,000 in 1989 . in 1990 dick saved 8 percent more than in 1989 , and together he and jane saved a total of $ 5,000 . approximately what percent less did jane save in 1990 than in 1989 ?
Options: a ) 8 % , b ) 25 % , c ) 41 % , d ) 59 % , e ) 70 %
Rationale: "dick saved = $ 3240 jane saved = $ 1760 ( jane saved $ 1240 less than she did the prior year ) jane saved approximately $ 1240 / $ 3000 ( close to 41 % ) less in 1990 answer : c"
Answer: c
Problem: the average of temperatures at noontime from monday to friday is 40 ; the lowest one is 30 , what is the possible maximum range of the temperatures ?
Options: a ) 20 , b ) 25 , c ) 50 , d ) 45 , e ) 75
Rationale: "average = 40 , sum of temperatures = 40 * 5 = 200 as the min temperature is 30 , max would be 200 - 4 * 30 = 80 - - > the range = 80 ( max ) - 30 ( min ) = 50 answer : c"
Answer: c
Problem: in a parallelogram , the length of one diagonal and the perpendicular dropped on that diagonal are 30 and 20 metres respectively . find its area
Options: a ) 600 m 2
b ) 540 m 2
c ) 680 m 2
d ) 574 m 2
e ) none of these
Rationale: in a parallelogram . area = diagonal × length of perpendicular on it . = 30 × 20 = 600 m 2 answer a
Answer: a
Problem: a card is drawn from a pack of 52 cards . the probability of getting a queen of spade or an ace of club is :
Options: a ) 1 / 13 , b ) 1 / 26 , c ) 2 / 13 , d ) 1 / 52 , e ) 1 / 48
Rationale: "explanation : total outcomes = 52 favourable outcomes ( getting a queen of spade or an ace of club ) = 2 probability = 2 / 52 = 1 / 26 . answer : b"
Answer: b
Problem: in a certain game , a large bag is filled with blue , green , purple and red chips worth 1 , 5 , x and 11 points each , respectively . the purple chips are worth more than the green chips , but less than the red chips . a certain number of chips are then selected from the bag . if the product of the point values of the selected chips is 11,000 , how many purple chips were selected ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "11,000 = 1 * 5 ^ 3 * 8 * 11 the factor of 8 must come from the purple point value , so there is 1 purple chip . the answer is a ."
Answer: a
Problem: find large number from below question the difference of two numbers is 1370 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder
Options: a ) 1245 , b ) 1345 , c ) 1455 , d ) 1577 , e ) 1641
Rationale: "let the smaller number be x . then larger number = ( x + 1370 ) . x + 1370 = 6 x + 15 5 x = 1355 x = 271 large number = 271 + 1370 = 1641 e"
Answer: e
Problem: a , b and c started a partnership business by investing rs . 8000 , rs . 4000 , rs . 2000 respectively . at the end of the year , the profit were distributed among them . if c ' s share of profit is 36000 , what is the total profit ?
Options: a ) 70000 , b ) 60000 , c ) 80000 , d ) 90000 , e ) 252000
Rationale: "a : b : c = 8000 : 4000 : 2000 = 4 : 2 : 1 let total profit = p then p ã — 1 / 7 = 36000 p = ( 36000 ã — 7 ) / 1 = 252000 answer is e ."
Answer: e
Problem: find the area of the quadrilateral of one of its diagonals is 24 cm and its off sets 9 cm and 6 cm ?
Options: a ) 180 cm 2 , b ) 150 cm 2 , c ) 168 cm 2 , d ) 198 cm 2 , e ) 987 cm 2
Rationale: "1 / 2 * 24 ( 9 + 6 ) = 180 cm 2 answer : a"
Answer: a
Problem: the average monthly salary of 18 employees in an organisation is rs . 2000 . if the manager ' s salary is added , then the average salary increases by rs . 200 . what is the manager ' s monthly salary ?
Options: a ) rs . 5800 , b ) rs . 3618 , c ) rs . 3600 , d ) rs . 3619 , e ) rs . 3610
Rationale: "manager ' s monthly salary = rs . ( 2200 * 19 - 2000 * 18 ) = rs . 5800 answer : a"
Answer: a
Problem: what is the leastvalue of x . so that 23 x 57 is divisible by 3 ?
Options: a ) 2 , b ) 5 , c ) 1 , d ) 6 , e ) 7
Rationale: the sum of the digits of the number is divisible by 3 , then the number is divisible by 3 . 2 + 3 + x + 5 + 7 = 17 + x least value of x may be 1 therefore 17 + 1 = 18 is divisible by 3 . c
Answer: c
Problem: a , b and c started a business with capitals of rs . 8000 , rs . 10000 and rs . 12000 respectively . at the end of the year , the profit share of b is rs . 4000 . the difference between the profit shares of a and c is ?
Options: a ) 621 , b ) 276 , c ) 236 , d ) 1600 , e ) 211
Rationale: "explanation : ratio of investments of a , b and c is 8000 : 10000 : 12000 = 4 : 5 : 6 and also given that , profit share of b is rs . 4000 = > 5 parts out of 15 parts is rs . 4000 now , required difference is 6 - 4 = 2 parts required difference = 2 / 5 ( 4000 ) = rs . 1600 answer : d"
Answer: d
Problem: in an election between the two candidates , the candidates who gets 70 % of votes polled is winned by 320 vote ’ s majority . what is the total number of votes polled ?
Options: a ) 750 , b ) 700 , c ) 800 , d ) 850 , e ) none of these
Rationale: "explanation : note : majority ( 40 % ) = difference in votes polled to win ( 70 % ) & defeated candidates ( 30 % ) 40 % = 70 % - 30 % 40 % - - - - - > 320 ( 40 * 8 = 320 ) 100 % - - - - - > 800 ( 100 * 8 = 800 ) answer : option c"
Answer: c
Problem: what least number must be added to 1100 , so that the sum is completely divisible by 23 ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "48 * 23 = 1104 1104 - 1100 = 4 answer : c"
Answer: c
Problem: ( 3136 + 6160 ) / 28
Options: a ) 380 , b ) 350 , c ) 332 , d ) 310 , e ) none of these
Rationale: "explanation : as per bodmas rule , first we will solve the equation in bracket then we will go for division = ( 9296 ) / 28 = 332 option c"
Answer: c
Problem: a train 280 m long , running with a speed of 72 km / hr will pass a tree in
Options: a ) 14 sec , b ) 15 sec , c ) 16 sec , d ) 20 sec , e ) none
Rationale: "sol . speed = ( 72 x 5 / 18 ) m / sec . = 20 m / sec . time taken = ( 280 x 1 / 20 ) sec = 14 sec answer a"
Answer: a
Problem: a man swims downstream 24 km and upstream 12 km taking 6 hours each time , what is the speed of the man in still water ?
Options: a ) 5 , b ) 8 , c ) 10 , d ) 4 , e ) 3
Rationale: "24 - - - 6 ds = 4 ? - - - - 1 12 - - - - 6 us = 2 ? - - - - 1 m = ? m = ( 4 + 2 ) / 2 = 3 answer : e"
Answer: e
Problem: s is a set of 45 consecutive multiples of 5 . if the smallest number in s is 55 , then the greatest number in s is
Options: a ) 198 , b ) 275 , c ) 299 , d ) 402 , e ) 205
Rationale: "last term = first term + ( total no . of terms - 1 ) consecutive difference s is a set of 45 consecutive multiples of 5 . if the smallest number in s is 55 , then the greatest number in s is first term = 55 ; total terms = 45 ; difference = 5 55 + ( 44 ) 5 = 275 ans b"
Answer: b
Problem: the sum of ages of 6 children born at the intervals of 3 years each is 75 years . what is the age of the youngest child ?
Options: a ) 10 , b ) 15 , c ) 6 , d ) 5 , e ) 8
Rationale: "let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) , ( x + 12 ) , ( x + 15 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) + ( x + 15 ) = 75 6 x = 30 x = 5 . age of the youngest child = x = 4 years . answer : d"
Answer: d
Problem: the sum of three consecutive integers is 312 . what is the sum of the next three consecutive integers ?
Options: a ) 315 , b ) 321 , c ) 330 , d ) 415 , e ) 424
Rationale: "a + ( a + 1 ) + ( a + 2 ) = 3 a + 3 = 312 ( a + 3 ) + ( a + 4 ) + ( a + 5 ) = ( 3 a + 3 ) + 9 = 312 + 9 = 321 answer : b ."
Answer: b
Problem: a can fill tank in 9 minutes , b can empty the tank in 18 minutes . . in what time the tank be filled , if both pipes work simultaneously ?
Options: a ) 14 minutes , b ) 15 minutes , c ) 16 minutes , d ) 17 minutes , e ) 18 minutes
Rationale: bigger no = 18 , ratio = 9 : 18 = 1 : 2 time taken to fill the tank = 18 / ( 2 - 1 ) = 18 minutes answer : e
Answer: e
Problem: if you spend 1 / 4 of your salary during the first week of the month and 20 % of it during each of the coming 3 weeks , what part ( fraction ) of your salary will leave unspent at the end of the month ?
Options: a ) 2 / 20 , b ) 3 / 20 , c ) 4 / 20 , d ) 5 / 20 , e ) none
Rationale: solution : 1 / 4 + 3 ( 20 / 100 ) = 1 / 4 + 3 / 5 = 5 + 12 / 20 = 17 / 20 the sallary that will be spent = 17 / 20 unspend will be = 1 − 17 / 20 = 20 − 17 / 20 = 3 / 20 answer b
Answer: b
Problem: find the l . c . m of 16 , 25 , 24 and 10 .
Options: a ) 1000 , b ) 1400 , c ) 1320 , d ) 1200 , e ) 1650
Rationale: "explanation : 4 x 5 x 2 x 3 x 5 x 2 = 1200 answer : option d"
Answer: d
Problem: a bag contains 6 green and 8 white balls . if two balls are drawn simultaneously , the probability that both are of the same colour is
Options: a ) 8 / 15 , b ) 2 / 5 , c ) 3 / 5 , d ) 11 / 15 , e ) 43 / 91
Rationale: "drawing two balls of same color from six green balls can be done in 6 c ₂ ways . similarly from eight white balls two can be drawn in ⁸ c ₂ ways . p = 6 c ₂ / ¹ ⁵ c ₂ + ⁸ c ₂ / ¹ ⁵ c ₂ = 43 / 91 answer : e"
Answer: e
Problem: in an election between two candidates , one got 55 % of the total valid votes , 20 % of the votes were invalid . if the total number of votes was 2000 , the number of valid votes that the other candidate got , was :
Options: a ) 900 , b ) 750 , c ) 250 , d ) 600 , e ) 800
Rationale: "number of valid votes = 80 % of 2000 = 1600 valid votes polled by other candidate = 45 % of 2000 = ( 45 / 100 ) x 2000 = 900 answer = a"
Answer: a
Problem: a man â € ™ s current age is ( 2 / 5 ) of the age of his father . after 14 years , he will be ( 1 / 2 ) of the age of his father . what is the age of father at now ?
Options: a ) 40 , b ) 45 , c ) 38 , d ) 50 , e ) 70
Rationale: let , father â € ™ s current age is a years . then , man â € ™ s current age = [ ( 2 / 5 ) a ] years . therefore , [ ( 2 / 5 ) a + 14 ] = ( 1 / 2 ) ( a + 14 ) 2 ( 2 a + 70 ) = 5 ( a + 14 ) a = 70 e
Answer: e
Problem: at a certain committee meeting only associate professors and assistant professors are present . each associate professor has brought 2 pencils and 1 chart to the meeting , while each assistant professor has brought 1 pencil and 2 charts . if a total of 10 pencils and 5 charts have been brought to the meeting , how many people are present ?
Options: a ) 5 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "say there are ' a ' associate professors . so we have 2 a pencils and a charts . say there are ' b ' assistant professors . so we have b pencils and 2 b charts . total pencils are 10 so 2 a + b = 10 total charts are 11 so a + 2 b = 5 add both : 3 a + 3 b = 15 so a + b = 5 total number of people = 5 a"
Answer: a
Problem: a set of consecutive positive integers beginning with 1 is written on the blackboard . a student came along and erased one number . the average of the remaining numbers is 35 7 / 17 . what was the number erased ?
Options: a ) seven 7 , b ) 8 , c ) 9 , d ) 15 , e ) 17
Rationale: "2 ) the average of the new group of numbers is 35 7 / 17 . the denominator of that fraction tells us that the total number of terms in the new list must be a multiple of 17 : 17 , 34 , 51 , 68 , 85 , etc . 3 ) since we ' re removing 1 number from a list of consecutive positive integers , we could quickly limit down the possible number of terms in the original list : if new = 17 , old = 18 , but the numbers from 1 to 18 would not have an average in the mid - 30 s ( it would be much smaller ) . eliminate this option . if new = 34 , old = 35 , but we run into the same problem . the average wo n ' t match here either . eliminate this option . if new = 51 , old = 52 , same problem here . eliminate this option . if new = 68 , old = 69 . . . . here we have a group of numbers that might just be what we ' re looking for . in theold group , the average is themiddle term = 35 , which is really close to the new average once we remove a number . now , we just have to figure out which of the 5 answers was removed ( and that changed the new average to 35 7 / 17 ) . there are a couple of ways to do this math , but i ' m going to use the answers to save myself some steps : sum of 1 to 69 , inclusive = 69 ( 35 ) = 2415 remove answer b . . . . 2415 - 8 = 2407 new average = 2407 / 68 = 35 27 / 68 now , we can compare 27 / 68 to 7 / 17 27 / 68 and 28 / 68 this is really close , but is not the answer . eliminate b . the answer is either a or c . since 28 / 68 is a bigger fraction than 27 / 68 , we need the sum ( of the 68 integers ) to be bigger . . . which means we need to remove a smaller number . final answer : a"
Answer: a
Problem: a rectangular photograph is surrounded by a border that is 1 inch wide on each side . the total area of the photograph and the border is m square inches . if the border had been 4 inches wide on each side , the total area would have been ( m + 90 ) square inches . what is the perimeter of the photograph , in inches ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: "let x and y be the width and length of the photograph . ( x + 2 ) ( y + 2 ) = m and so ( 1 ) xy + 2 x + 2 y + 4 = m ( x + 8 ) ( y + 8 ) = m and so ( 2 ) xy + 8 x + 8 y + 64 = m + 90 let ' s subtract equation ( 1 ) from equation ( 2 ) . 6 x + 6 y + 60 = 90 2 x + 2 y = 10 , which is the perimeter of the photograph . the answer is a ."
Answer: a
Problem: manoj borrowed rs . 3900 from anwar at 6 % p . a . simple interest for 3 years . he then added some more money to the borrowed sum and lent it to ramu for the same time at 9 % p . a . simple interest . if manoj gains rs . 824.85 by way of interest on the borrowed sum as well as his own amount from the whole transaction , then what is the sum lent by him to ramu ?
Options: a ) 22877 , b ) 5655 , c ) 2778 , d ) 6787 , e ) 1771
Rationale: let the sum lent by manoj to ramu be rs . p . amount gained by manoj = p . 3.9 / 100 = 3900 . 3.6 / 100 = rs . 824.85 27 p = 70200 = 82485 p = ( 82485 + 70200 ) / 27 = 3055 + 2600 = rs . 5655 answer : b
Answer: b
Problem: two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 2.10 km and 1.4 km respectively . the time taken by the slower train to cross the faster train in seconds is ?
Options: a ) 99 , b ) 277 , c ) 84 , d ) 96 , e ) 22
Rationale: "relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 2.10 + 1.4 = 3.5 km = 3500 m . required time = 3500 * 3 / 125 = 84 sec . answer : c"
Answer: c