Category: math competition

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

Boris has an incredible coin changing machine. When he puts in a quarter, it returns five nickles; when he puts in a nickle, it returns five pennies; and when he puts in a penny, it returns five quarters. Boris starts with just one penny. Which of the following amounts could Boris have after using the machine repeatedly?

(A) $3.63 (B) $5.13 (C) $6.30 (D) $7.45 (E) $9.07

ANSWER: D

If all alligators are ferocious creatures and some creepy crawlers are alligators, which statement(s) must be true?

1. All alligators are creepy crawlers.

2. Some ferocious creatures are creepy crawlers.

3. Some alligators are not creepy crawlers.

(A) 1 only (B) 2 only (C) 3 only (D) 2 and 3 only (E) None must be true

ANSWER: B

Let L,M,and N be nonnegative integers such that L+M+N=10. What is the maximum value of A*M*C+A*M+M*C+C*A?

(A) 49 (B) 59 (C) 69 (D) 79 (E) 89

ANSWER:C

Charlyn walks completely around the boundary of a square whose sides are each 5 km long. From any point on her path she can see exactly 1 km horizontally in all directions. What is the area of the region consisting of all points Charlyn can see during her walk, expressed in square kilometers and rounded to the nearest whole number?

(A) 24 (B) 27 (C) 39 (D) 40 (E) 42

ANSWER: C