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Suppose that n is the product of three consecutive integers and that n is divisible by 7. Which of the following is not necessarily a divisor of n ?

(A) 6 (B) 14 (C) 21 (D) 28 (E) 42

ANSWER: D

If x,y,and z are positive with xy=24,xz=48,and yz=72, then x+y+z is

(A) 18 (B) 19 (C) 20 (D) 22 (E) 24

ANSWER: D

Wanda, Darren, Bratrice, and Chi are tutors in the school math club. Their schedule is as follows: Darren works every third school day, Wanda works every fourth school day, Beatrice works every sixth school day, and Chi works every seventh school day. Today they are all working in the math club. In how many school days from today will they next be together tutoring in the lab ?

(A) 42 (B) 84 (C) 126 (D) 178 (E) 252

ANSWER: B

When the decimal point of a certain positive decimal number is moved four places to the right, the new number is four times the reciprocal of the original number. What is the original number ?

(A) 0.0002 (B) 0.002 (C) 0.02 (D) 0.2 (E) 2

ANSWER: C

Let P(n) and S(n) denote the product and the sum, respectively, of the digits of the integer n. for example, P(23)=6 and S(23)=5. Suppose N is a two-digit number such that N=P(N)+S(N). What is the unit digit of N ?

(A) 2 (B) 3 (C) 6 (D) 8 (E) 9

ANSWER:E

What is the maximum number for the possible points of intersection of a circle and a triangle ?

(A) 2 (B) 3 (C) 4 (D) 5 (E) 6

ANSWER: E

The sum of two number is S. Suppose 3 is added to each number and then each of the resulting number is doubled. What is the sum of the final two numbers?

(A) 2S+3 (B) 3S+2

(C) 3S+6 (D) 2S+6

(E) 2S+12

ANSWER: E

In year N, the 300th day of the year is a Tuesday. In year N+1, the 200th day is also a Tuesday. On what day of the week did the 100th day of year N-1 occur ?

(A) Thursday (B) Friday

(C) Saturday (D) Sunday

(E) Monday

ANSWER: A

One morning each member of Angela’s family drank an 8-ounce mixture of coffee with milk. The amounts of coffee and milk varied from cup to cup, but were never zero. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. How many people are in the family?

(A) 3 (B) 4 (C) 5 (D) 6 (E) 7

When the mean, median, and mode of the list

10,2,5,2,4,2,x

are arranged in increasing order, they form a non-constant arithmetic progression. What is the sum of all possible real values of x?

(A) 3 (B) 6 (C) 9 (D) 17 (E) 20

ANSWER: E