## QBM039

Q1. There are two vessels, one containing 1 litre of pure milk and the other containing 1 litre of water. If half a litre of the latter is transferred to the former and upon stirring the contents well, half a litre of the former is transferred to the latter, what is the ratio of milk to water in the latter?
1)4 : 5

2) 3 : 4

3) 2 : 3

4) 1 : 2
Q2. What is the remainder when (2222)^{5555}+ (5555)^{2222} is divided by 7 ?
a)3

b)5

c)6

d)0
Q3. P is a prime number greater than 5. What is the remainder when P is divided by 6?
a)5

b)1

c)1 or 5

d) none of these
Q4. Divide 60 into two parts, so that three times the greater may exceed 100 by as much as 8 times the less falls short of 200. What is the greater part?
a)40

b)36

c)32

d) 31
Q5. The average age of a family of 5 members is 20 years. If the age of the youngest member were 10 years then what was the average age of the family at the time of the birth of the youngest member?
A.13.5

B.14

C.15

D.12.5
Q6. The playoffs in Major League Baseball begin in just about a week, culminating in the World Series which selects the champion team. The World Series is a tournament of seven games with the champion being the first team to win four games. How many different ways can the World Series be played?
Q7.Boxes numbered 1, 2, 3, 4, and 5 are kept in a row, and they are to be filled with either a red or a blue ball, such that no two adjacent boxes can be filled with blue balls. How Many different arrangements are possible, given that all balls of a given color are exactly identical in all respects?
(1)8

(2)10

(3)15

(4)22
Q8. A priest and a pirate are shipwrecked on an island with a boat which is large enough to carry only one of them to the mainland. They decide to let Lady Luck decide which one of them will be rescued. On the island they find two coins. Assuming that at least one of the coins is fair -- that is, gives heads or tails 50% of the time -- but not knowing which one that may be, how can they use the coins to decide fairly who gets off the island?
Q9.If you'd like me to notify you by email when the Problem of the Week resumes in the fall, please drop me a line, including your email address. I'll send you a note in late August or early September.
Q10. What is interesting about the following sequence?
1/89, 1/9899, 1/998999, 1/99989999,
Q11. Roll a standard pair of six-sided dice, and note the sum. There is one way of obtaining a 2, two ways of obtaining a 3, and so on, up to one way of obtaining a 12. Find all other pairs of six-sided dice such that:
a. The set of dots on each die is not the standard {1,2,3,4,5,6}.
b. Each face has at least one dot.
c. The number of ways of obtaining each sum is the same as for the standard dice.
Q12. If 0 < x > 9, y>10, 9

C. (x + y + z) > (a + b + c)
(1) All of A, B, and C

(2) only B

(3) only C

(4) only Band C
Q13. A bag contains 40 jellybeans, of which 10 are red, 10 are black, 10 are green, and 10 are yellow. The least number that a blindfolded person must eat to be certain of having eaten at least one of each color is:
a.31

b.22

c.4

d.5

e. None of these
Q14. If the average of three numbers a, b, and c is A. What is the average of the four numbers a, b, c and A?
A. A/4

B. A/2

C. 2A

D. None of these
END

## answer to Q3

Q3. P is a prime number greater than 5. What is the remainder when P is divided by 6?

a)5

b)1

c)1 or 5

d) none of these

**Answer: It is obivouc the answer is either 1 or 5 (example 7 and 11)**

**All the prime numbers can be expressed as 6n + 1 or 6n - 1. **