MU-NLPC/Calc-aqua_rat huggingface dataset:
Amit and Ananthu can do a work in 15 days and 90 days respectively. Amit started the work and left after 3 days. Ananthu took over and completed the work. In how many days was the total work completed? Choose the correct choice from the following:
A) 68 days
B) 70 days
C) 73 days
D) 75 days
E) 77 days

Solution: Amit’s one day’s work= 1/15   Amit’s 3 day’s work = 1/15 *3 = 1/5   Work left= 1-1/5 = 4/5   Ananthu’s one day’s work= 1/90   Ananthu can do work in = 4/5 *90= 
4/5 *90 = 72
72 days   So total days= 72+3= 
72+3 = 75
75 days   ANSWER:75 days
Answer: D
The ratio of three numbers is 4:2:5 and their sum is 121. The second number of the three numbers is?  Select.
A) 22  B) 26  C) 27  D) 29  E) 30

Solution: 4:2:5   Total parts = 11   11 parts --> 121   1 part ---->11   The second number of the three numbers is = 2 * 11= 
2 * 11 = 22
22   22nswer : 22
Answer: A
A family made a down payment of $100 and borrowed the balance on a set of encyclopedias that cost $400. The balance with interest was paid in 23 monthly payments of $16 each and a final payment of $9. The amount of interest paid was what percent of the amount borrowed? Choose the most appropriate option:
A) 30%	B) 22%	C) 24%	D) 27%	E) 25.67%

Solution: borrowings = 400-100= 
400-100 = 300
300   total pmt= 23x16 + 9 = 377   so int = 377 - 300= 
377 - 300 = 77
77   interest in terms of borrowing= 77/300 = 25.67%   Answer is 25.67%
Answer: E
The product of the squares of two positive integers is 81. How many pairs of positive integers satisfy this condition?
Choose the correct choice from the following:
A) 0 B) 1 C) 2 D) 3 E) 4

Solution: Ans: C - 2 pairs   (xˆ2)(yˆ2) = 81 [square root both sides]   xy = 9   9 = 1x9, 9x1, 3x3   Cancel the repeats   This leaves us with exactly 2 options.   Hence, 2
Answer: C
What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58?  Select: A) 17 B) 18 C) 19 D) 14 E) 16

Solution: Let the side of the square plot be a ft.   a2 = 289 => a = 17   Length of the fence = Perimeter of the plot = 4a = 68 ft.   Cost of building the fence = 68 * 58 = Rs. 3944.   17nswer: Option 17
Answer: A
2 hours after train A leaves Lucknow a train B leaves the same stationtraveling in the same direction at an average speed of 36 km/hr. After traveling 6 hrsthe train B overtakes the train A. What is the average speed of the train A?  Select the correct option.
A) 22.5 km/hr
B) 16 km/hr
C) 27 km/hr
D) 18 km/hr
E) None of these

Solution: Explanation :   Total distance covered by B=36*6= 
36*6 = 216
216kmTotal time taken by A to cover same distance=2+6= 
2+6 = 8
8 hrsaverage speed of A=216/8= 
216/8 = 27
27 km/hr   Answer : 27 km/hr
Answer: C
The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?	Pick:  A) 2000  B) 2887  C) 2797  D) 1172  E) 1200

Solution: Explanation:   Let C.P. be Rs. x.   Then, (1920 - x)/x * 100 = (x - 1280)/x * 100   1920 - x = x - 1280   2x = 3200 => x = 1600   Required S.P. = 125 % of Rs. 1600 = 125/100 * 1600 = Rs. 2000.   2000nswer:2000
Answer: A
Thabo owns exactly 160 books, and each book is either paperback fiction, paperback nonfiction, or hardcover nonfiction. If he owns 20 more paperback nonfiction books than hardcover nonfiction books, and twice as many paperback fiction books as paperback nonfiction books, how many hardcover books nonfiction books does Thabo own?  Select.
A) 10	B) 25	C) 35	D) 46	E) 50

Solution: I think we can use double-matrix method and solve using only one variable.   Our goal is to find the number of hardcover nonfiction books. Let that number be x. We are given that all 140 books are either paperback fiction, paperback nonfiction, or hardcover nonfiction. This implies that number of hardcover fiction books is 0.   Double-matrix: P = paperback; H = hardcover; F = fiction; NF = nonfiction   P H Total   F 2x+40 0   NF x+20 x   Total 3x+60 x 160   3x + 60 + x = 160   x = 25   Answer (25.)
Answer: B
If x=1/7, which expression has the greatest value?	Choose the correct choice:
A) x^(1/3)
B) x^(1/2)
C) 1/(2x)
D) x/.03
E) x^(-3)

Solution: Options A and B are both less than 1.   Option C: 1/(2(1/7)) = 7/2= 
7/2 = 7/2 = around 3.5
3.5   Option D: (1/7) / 0.03= 1/0.21 which is about 4.76   Option x^(-3): (1/7)^(-3) = 7^3 = 343   The answer is x^(-3).
Answer: E
In a manufacturing plant, it takes 36 machines 4 hours of continuous work to fill 8 standard orders. At this rate, how many hours of continuous work by 72 machines are required to fill 24 standard orders?	Choose the correct choice from the following answers
A) 3
B) 6
C) 8
D) 9
E) 12

Solution: the choices give away the answer..   36 machines take 4 hours to fill 8 standard orders..   in next eq we aredoubling the machines from 36 to 72, but thework is not doubling(only 1 1/2 times), = 4*48/72*24/8 = 6   Ans 6
Answer: B
A letter lock consists of three rings each marked with six different letters. The number of distinct unsuccessful attempts to open the lock is at the most?
Choices:	A) 176	B) 178	C) 215	D) 197	E) 172

Solution: Since each ring consists of six different letters, the total number of attempts possible with the three rings is   = 6 * 6 * 6= 
6 * 6 * 6 = 216
216. Of these attempts, one of them is a successful attempt.   Maximum number of unsuccessful attempts= 216 - 1= 
216 - 1 = 215
215.   Answer: 215
Answer: C
If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is? Select
A) 1/98	B) 1/2	C) 1/6	D) 1/2	E) 1/9

Solution: The number of exhaustive outcomes is 36.   Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2   P(E) = 1 - 1/2 = 1/2.   Answer: 1/2
Answer: B
If x and y are positive integers such that x < y and z=x/y, which of the following must be true?
I. z>(x − 1)/(y + 1)
II. z<(x + 1)/(y + 1)
III. z>(x + 1)/(y - 1)  Choices.
A) I only B) I and II C) II and III D) II only E) I and III

Solution: x < y --> Let x = 2 and y = 3 --> z = 2/3   I. z>(x − 1)/(y + 1) --> 2/3 > 1/4 --> True   II. z<(x + 1)/(y + 1) --> 2/3 < 3/4 --> True   III. z>(x + 1)/(y - 1) --> 2/3 > 3/2 --> False   Answer: I and II
Answer: B
The first flight out of Phoenix airport had a late departure. If the next three flights departed on-time, how many subsequent flights need to depart from Phoenix on-time, for the airport's on-time departure rate to be higher than 50%?
I will see what is the quickest way to solve it then I will provide the explanation  Pick.
A) 3
B) 7
C) 9
D) 10
E) 11

Solution: The following approach might be the easiest one and less error prone.   We need on-time departure rate to be higher than 5/10, so it should be at least 6/11, which means that 6 out of 11 flights must depart on time. Since for now 3 out of 4 flights departed on time then  6-3= 
 6-3 = 3
3 subsequent flights need to depart on-time.   3nswer: 3
Answer: A
A number when divided by 296 leaves 75 as remainder. When the same number is divided by 37, the remainder will be: Answers
A) 5  B) 4  C) 1  D) 2  E) 3

Solution: Explanation:   Let x = 296q + 75   = (37 x 8q + 37 x 2) + 1   = 37 (8q + 2) + 1   Thus, when the number is divided by 37, the remainder is 1.   Answer 1
Answer: C
Six years ago Rahul was P times as old as Sachin was. If Rahul is now 17 years old, how old is Sachin now in terms of P ?	Choose the correct option: A) 11/P + 6 B) P/11 +6 C) 17 - P/6 D) 17/P E) 11.5P

Solution: let's call Sachin age six years ago is x   so six years ago Rahul was: 17-6= 
17-6 = 11
11 years old   and six years ago Rahul was P times as old as Sachin was=> 11/x = P   => x = 11/P   => Now Sachin's age will be : x+6 = 11/P+6   => the answer is 11/P + 6
Answer: A
P, Q and R have Rs.7000 among themselves. R has two-thirds of the total amount with P and Q. Find the amount with R?
Choose the correct choice from the following answers.
A) Rs.3000 B) Rs.3600 C) Rs.2400 D) Rs.2800 E) None of these

Solution: Let the amount with R be Rs.r   r = 2/3 (total amount with P and Q)   r = 2/3(7000 - r) => 3r = 14000 - 2r   => 5r = 14000 => r = 2800.   ANSWER:Rs.2800
Answer: D
A motorist travels to a place 150 km away at an average speed of 50 km/hr and returns at 30 km/hr. His average speed for the whole journey in km/hr is?
Answers:
A) 37.9
B) 37.2
C) 37.5
D) 37.1
E) 37.8

Solution: Average speed = (2xy) /(x + y) km/hr   = (2 * 50 * 30) / (50 + 30) km/hr.   37.5 km/hr.   Answer: 37.5
Answer: C
Let a,b,c,d,e,f be non-negative real numbers. Suppose that a + b + c + d + e + f = 1 and
ad + be + cf >= 1/18 . Find the maximum value of ab + bc + cd + de + ef + fa.	Pick one:
A) 7/36 B) 6/36 C) 5/36 D) 4/36 E) 3/36

Solution: We partially factor   ab + bc + cd + de + ef + fa = a(b + f) + c(b + d) + e(d + f):   Notice that the terms in the parenthesis are very close to (b+d+f), except each part is missing   one term. We can add ad + cf + eb to this expression to get   a(b + f) + c(b + d)e(d + f) + ad + cf + eb   = a(b + d + f) + c(b + d + f) + e(b + d + f)   = (a + c + e)(b + d + f)   Let x = a+c+e and y = b+d+f. We have x+y = 1, so AM-GM gives us x+y   2   p   xy, hence   (a + c + e)(b + d + f) - 1   4 . Subtracting away ad + be + cf - 1   18 gives us   ab + bc + cd + de + ef + fa -   1/4   -1/18   =   7/36   where equality holds when a + c + e = b + d + f = 1   2 and ad + be + cf = 1/18 . We can verify that   equality holds when a = e = 1/9 , b = d = 1/4 ,c = 5/18, f = 0.   correct answer 7/36
Answer: A
A basket contains 3 blue, 3 red and 3 yellow marbles. If 3 marbles are extracted from the basket at random, what is the probability that a marble of each color is among the extracted?
Select:  A) 2/21  B) 3/25  C) 1/6  D) 9/28  E) 11/24

Solution: Probability of getting each color marble = (3C1*3C1*3C1)/9C3   = (3*3*3)/84   = 27/84 = 9/28   So answer is 9/28
Answer: D
You walk one mile to school every day. You leave home at the same time each
day, walk at a steady speed of 3 miles per hour, and arrive just as school begins. Today you
were distracted by the pleasant weather and walked the first half mile at a speed of only 2
miles per hour. At how many miles per hour must you run the last half mile in order to arrive
just as school begins today? Choose the most appropriate option
A) 4  B) 6  C) 8  D) 10  E) 12

Solution: Recall the formula s = v *t, where in this case, s is distance (in miles) traveled at a   constant speed of v (miles per hour), for a time of t hours. The first statement indicates that   it usually takes you only 20 minutes to go to school (solve for t in 1 = 3 * t and change units)   Today, it took you 15 minutes to cover the first half mile (solve for t in 1=2 = 2 * t and   change units). You only have 5 more minutes to arrive (that is 1/12th of an hour), and need   to cover another half mile. Solve for v in the equation 1/2 = (1/12) *v.   correct answer 6
Answer: B
In how many ways letters of the word LICENSING be arranged? Answers:
A) 362880  B) 12540  C) 65320  D) 48962  E) 62458

Solution: LICENSING has 9 letters, out of which I repeated 2 times, N repeated 2 times. Hence total ways = 10!/(2!*2!)= 362880 ways   362880
Answer: A
A ratio between two numbers is 3 : 4 and their L.C.M. is 180. The first number is Choose the correct choice from the following:
A) 60
B) 45
C) 20
D) 15
E) None

Solution: Sol.   Let the required numbers be 3x and 4x. Then, their L.C.M. is 12x.   ∴ 12x = 180⇔ x = 15. Hence, the first number is 45.   Answer 45
Answer: B
A technician makes a round-trip to and from a certain service center by the same route. If the technician completes the drive to the center and then completes 50 percent of the drive from the center, what percent of the round-trip has the technician completed?	Choose the correct choice from the following answers:
A) 70
B) 65
C) 60
D) 75
E) 80

Solution: round trip means 2 trips i.e.to and fro. He has completed one i.e 50% completed. then he traveled another 50% of 50% i.e 25%. so he completed   50 +25= 
  50 +25 = 75
75 % of total trip.   75
Answer: D
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 9 hours and 16 hours respectively. The ratio of their speeds is? Choose the correct choice
A) 4:9	B) 4:3	C) 4:5	D) 4:1	E) 4:2

Solution: Let us name the trains A and B.   Then, (A's speed) : (4:3's speed)   = √b : √a = √16 : √9   = 4:3   Answer:4:3
Answer: B
Two trains A and B starting from two points and travelling in opposite directions, reach their destinations 9 hours and 4 hours respectively after meeting each other. If the train A travels at 70kmph, find the rate at which the train B runs.
Choose the most appropriate option:
A) 40 B) 60 C) 120 D) 80 E) 105

Solution: If two objects A and B start simultaneously from opposite points and, after meeting, reach their destinations in ‘a’ and ‘b’ hours respectively (i.e. A takes ‘a hrs’ to travel from the meeting point to his destination and B takes ‘b hrs’ to travel from the meeting point to his destination), then the ratio of their speeds is given by:   Sa/Sb = √(b/a)   i.e. Ratio of speeds is given by the square root of the inverse ratio of time taken.   Sa/Sb = √(4/9) = 2/3   This gives us that the ratio of the speed of A : speed of B as 2:3.   Since speed of A is 80 kmph, speed of B must be   70*(3/2)= 
  70*(3/2) = 105
105 kmph   105
Answer: E
A, B and C shared profits in ratio of 3 : 7 : 6. Theypartnered for 14months, 8months and 7months respectively. What was he ratio of their investments ? Select:
A) 12 : 49 : 64	B) 20 : 49 : 64	C) 10 : 19 : 64	D) 20 : 29 : 64	E) 30 : 29 : 63

Solution: Simply multiply profit sharing ratio with investment ratio to get investment amount ratio.   Let X is the total investment   â‡’14 x = 3   â‡’ 8 x = 7   â‡’ 7x = 8   â‡’ Final investment ratio = 12 : 49 : 64   12 : 49 : 64
Answer: A
Machine A can put caps on a set of bottles in 8 hours at a constant rate. If Machine A does the job for 6 hours and Machine B does the rest of the job, which works at 1/4 constant rate of Machine A. How long will it take for Machine B alone to do the rest of the job?	Choose one:
A) 4hrs	B) 6hrs	C) 8hrs	D) 10hrs	E) 16hrs

Solution: machine A will do 6/8 in 6 hrs, so A does 3/4 of the work ..   Therefore, B will do the remaining 1/4 th work alone..   As the speed of B is 1/4 rate of A, B will do the 1/4th work in same time that A takes to complete full job...   ans 8   8hrs
Answer: C
If x is an integer, then x(x - 1)(x - v) must be evenly divisible by three when v is any of the following values EXCEPT
Select:
A) -4
B) -2
C) -1
D) 2
E) 5

Solution: here's another approach   x(x - 1)(x - v)   all three are consecutive, so the product MUST be a multiple of 3   we don't know the value of v just yet ... so let's extend the series ... the extension itself reveals the answers   ..(x-5)..(x-2)(x-1)x(x+1)..(x+4)..   we can see the possible values of v too from the series   v = 2 OR 2+3n [25]   v = -1 OR -1+3n [-1-4]   B i.e. -2 does not fit in any value of v   so -2 it is
Answer: B
One fourth of one third of two fifth of a number is 35. What will be40% of that number	Choose the most appropriate option.
A) A)140 B) B)420 C) C)180 D) D)200 E) E)220

Solution: Explanation:   (1/4) * (1/3) * (2/5) * x = 35   then x = 35 * 30= 
35 * 30 = 1_050
1050   40% of 1050= 420   Answer: Option 420
Answer: B
An internet service provider charges $3.10 for the first 1/5 of a day plus $0.40 for each additional 1/5 of a day. What would this company charge for an internet usage that was 8 days long?  Pick one:  A) $15.60  B) $16.00  C) $17.80  D) $18.70  E) $19.10

Solution: first 1/5 day = $3.10   rest of the days = 8 - (1/5) = 39/5   charge for the rest of the days = 39 *0.4= 
39 *0.4 = 15.6
15.6   total charge= 3.10+15.6= 
3.10+15.6 = 18.7
18.7   Answer is $18.70.
Answer: D
The ratio of sodium chloride to ammonium in 100 kg of mixed ammonium normally used by three chemists is 1: 3. The amount of sodium chloride to be added to 100 kg of mixed ammonium to make the ratio 9 :25 is
Choose one.
A) 2 kg  B) 6.625 kg  C) 6.25 kg  D) 6.35 kg  E) 6.55 kg

Solution: sodium chloride in 100 kg = 1/4 x 100 = 25 kg   ammonium in 100 kg = 3 / 4 x 100 = 75 kg   Now 75 is 25 parts out of   (25 + 9)= 
  (25 + 9) = 34
34 parts.   Hence 9 parts= 9/25 x 75 = 27   2 kgmount to be added = 27 - 25= 
27 - 25 = 2
2 Kg   2 kgNSWER:2 kg
Answer: A
There are 172 lights which are functional and each is controlled by a separate On/Off switch. Two children A and B start playing with the switches. A starts by pressing every third switch till he reaches the end. B, thereafter, presses every fifth switch till he too reaches the end. If all switches were in Off position at the beggining, How many lights are switched On by the end of this operation?
Choose one: A) 83 B) 85 C) 87 D) 79 E) 89

Solution: Editing my solution:   Number of switches = 172   Number of switches turned on by A: 3, 6, ... 171 = 57   Number of switches turned on by B: 5, 10, ....170 = 34   Few switches are turned on by A and later turned off by B: LCM(3,5) = 15x = 15, 30,....90 = 6.   Subtract the above 6 switches from both A and B as they are turned off.   Number of switches that are turned on = (57- 6) + (34 - 6)= 
(57- 6) + (34 - 6) = 79
79   Answer: 79
Answer: D
Cereal A is 10% sugar by weight, whereas healthier but less delicious Cereal B is 4% sugar by weight. To make a delicious and healthy mixture that is 6% sugar, what should be the ratio of Cereal A to Cereal B, by weight?	Choose the correct choice from the following:	A) 2:9	B) 2:7	C) 1:6	D) 1:4	E) 1:2

Solution: Ratio of A / Ratio of B = (Average Wt of Mixture - Wt of B)/(Wt of A - Average Wt of Mixture)   => Ratio of A / Ratio of B = (6 - 4)/(10 - 6) = 2/4 = 1/2   So they should be mixed in the ratio 1:2   Answer - 1:2
Answer: E
What is the measure of the angle W made by the diagonals of the any adjacent sides of a cube. Choose the correct choice from the following:
A) 30
B) 45
C) 60
D) 75
E) 90

Solution: C.. 60 degrees   All the diagonals are equal. If we take 3 touching sides and connect their diagonals, we form an equilateral Triangle. Therefore, each angle would be 60.60
Answer: C
The average weight of 16 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg. Find the average weights of all the boys in the class.  Choose the correct choice from the following options:
A) 48.55
B) 49
C) 51
D) 61
E) 62

Solution: Required average   = (50.25 x 16 + 45.15 x 8)/(16 + 8)   = (804 + 361.20)/24   = 1165.20/24= 
1165.20/24 = 48.55
48.55   48.55nswer is 48.55
Answer: A
The sum of the heights of two high-rises is x feet. If the second high rise is 37 feet taller than the first, how tall will the first high rise be after they add an antenna with a height of z feet to the top?  Select:
A) (x+z)/2 + 37	B) 2x−(37+z)	C) (x−37)/2 + z	D) x/2 - 37 + z	E) (2x−37)/z

Solution: I will note h1 the height of high-rise 1 and h2 the height of high-rise 2. SO:   h1 + h2 = x   and h2 = h1 + 37 =>   Q: h1+ z = ?   h21+ h1 + 37 = x => 2h1= x-37 =? h1 = (x-37)/2   => h1+ z = (x-37)/2 + z, (x−37)/2 + zORRE(x−37)/2 + zT ANSWER (x−37)/2 + z
Answer: C
In how many ways, a committee of 12 members can be selected from 8 men and 7 ladies, consisting of 7 men and 5 ladies?	Pick one:
A) 150  B) 167  C) 200  D) 168  E) 178

Solution: (7 men out 8) and (5 ladies out of 7) are to be chosen   Required number of ways = 8C7*7C5 = 168   Answer is 168
Answer: D
61 small identical cubes are used to form a large cube. How many more cubes are needed to add one top layer of small cube all over the surface of the large cube ? Choose the correct option:
A) 64 B) 128 C) 152 D) 155 E) 256

Solution: 61 small cube will make a large cube with 4 cubes in each line i.e.   Adding one layer will require one cube at each end and hence new cube will have 6 cubes in each line.   Total number of small cubes in new cube = 6^3 = 216   Extra cube required = 216 - 61= 
216 - 61 = 155
155   Hence, 155 is the answer.
Answer: D
A card game called “high-low” divides a deck of 52 playing cards into 2 types, “high” cards and “low” cards. There are an equal number of “high” cards and “low” cards in the deck and “high” cards are worth 2 points, while “low” cards are worth 1 point. If you draw cards one at a time, how many ways can you draw “high” and “low” cards to earn 6 points if you must draw exactly 3 “low” cards?	Options:  A) 1  B) 20  C) 3  D) 4  E) 5

Solution: Great question Ravih. This is a permutations problem (order matters) with repeating elements. Given thatlowcards are worth 1 pt andhigh cards2 pts, and you must draw 3 low cards, we know that you must also draw 1 high card. The formula for permutations problems with repeating elements isN!/A!B!...where N represents the number of elements in the group and A, B, etc. represent the number of times that repeating elements are repeated. Here there are 4 elements and thelowcard is repeated 3 times. As a result, the formula is:   5!/3! which represents (5*4*3*2*1)/(3*2*1) which simplifies to just 20, giving you answer 20.
Answer: B
A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 3 employees to 3 different offices?	Choose the correct choice from the following options:
A) 5 B) 6 C) 27 D) 8 E) 9

Solution: Ans. Each employee can go into any of the two offices. Thus we have   => 3 * 3 * 3= 
3 * 3 * 3 = 27
27   Answer : 27
Answer: C
A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 1800. He sold both the items together for Rs. 31150. What percentage of profit did he make?	Select:
A) 30%
B) 75%
C) 40%
D) 70%
E) None of these

Solution: The total CP = Rs. 16000 + Rs. 1800 = Rs. 17800 and SP = Rs. 31150   Profit(%) = (31150 - 17800)/17800* 100= 
(31150 - 17800)/17800* 100 = 75
75%   ANSWER:75%
Answer: B
In a colony of 70 residents, the ratio of the number of men and women is 4:3. Among the women, the ratio of the educated to the uneducated is 1:4. If the ratio of the number of education to uneducated persons is 8:27, then find the ratio of the number of educated and uneducated men in the colony?	Choose the correct choice from the following choices.
A) 1:4	B) 3:5	C) 3:9	D) 3:7	E) 1:3

Solution: Number of men in the colony = 4/7 (70) = 40   Number of women in the colony = 3/7 (70) = 30   Number of educated women in the colony = 1/5 (30) = 6   Number of uneducated women in the colony = 4/5 (30) = 24   Number of educated persons in the colony = 8/35 (70) = 16   As 6 females are educated, remaining 10 educated persons must be men.   Number of uneducated men in the colony = 40 - 10= 
40 - 10 = 30
30   Number of educated men and uneducated men are in the ratio 10:30=> 1:3   Answer:1:3
Answer: E
A drink vendor has 80 liters of Maaza, 144 liters of Pepsi and 368 liters of Sprite. He wants to pack them in cans, so that each can contains the same number of liters of a drink, and doesn't want to mix any two drinks in a can. What is the least number of cans required? Pick one
A) 35
B) 37
C) 42
D) 30
E) 38

Solution: The number of liters in each can = HCF of 80, 144 and 368 = 16 liters.   Number of cans of Maaza = 80/16= 
80/16 = 5
5   Number of cans of Pepsi= 144/16= 
144/16 = 9
9   Number of cans of Sprite= 368/16= 
368/16 = 23
23   The total number of cans required= 5 + 9 + 23= 
5 + 9 + 23 = 37
37 cans.   ANSWER:37
Answer: B
If the product of two numbers is 84942 and their H.C.F. is 33, find their L.C.M.	Choose one:
A) 2574 B) 2500 C) 1365 D) 1574 E) None of these

Solution: Explanation:   HCF * LCM = 84942, because we know   Product of two numbers = Product of HCF and LCM   LCM = 84942/33= 
84942/33 = 2_574
2574   Option 2574
Answer: A