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Sally has five red cards numbered 1 through 5 and four blue cards numbered 3 through 6. She stacks the cards so that the colors alternate and so that the number on each red card divides evenly into the number on each neighboring blue card. What is the sum of the numbers on the middle three cards?
(A) 8 (B) 9 (C) 10 (D) 11 (E) 12
ANSWER:D
Pat is to select six cookies from a tray containing only chocolate chip, oatmeal, and peanut butter cookies. There are at least six of each of these three kinds of cookies on the tray. How many different assortments of six cookies can be selected?
(A) 22 (B) 25 (C) 27 (D) 28 (E) 729
ANSWER:B
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A base-10 three digit number n is selected at random. Which of the following is closest to the probability that the base-9 representation and the base-11 representation of n are both three-digit numerals?
(A) 0.3 (B) 0.4 (C) 0.5 (D) 0.6 (E) 0.7
ANSWER: B
What is the probability that an integer in the set {1,2,3,…,100} is divisible by 2 and not divisible by 3?
(A) 1/6 (B) 33/100 (C) 17/50 (D) 1/2 (E) 18/25
ANSWER:C
Let n be the largest integer that is the product of exactly 3 distinct prime number d,e, and 10d+e, where d and e are single digits. What is the sum of the digits of n?
(A) 12 (B) 15 (C) 18 (D) 21 (E) 24
ANSWER: A
A point (x,y) is randomly picked from inside the rectangle with vertices (0,0), (4,0), (4,1), and (0,1). What is the probability that x< y ?
(A) 1/8 (B) 1/4 (C) 3/8 (D) 1/2 (E) 3/4
ANSWER:B
The sum of the two 5-digit numbers ABC10 and ABC12 is 123422. What is A+B+C ?
(A) 10 (B) 11 (C) 12 (D) 13 (E) 14
ANSWER: E
What is the probability that a randomly drawn positive factor of 60 is less than 7?
(A) 1/10 (B) 1/6 (C) 1/4 (D) 1/3 (E) 1/2
ANSWER: E
How many non-congruent triangles with perimeter 7 have integer side lengths?
(A) 1 (B) 2 (C) 3 (D) 4 (E) 5
ANSWER: C
It takes Mary 30 minutes to walk uphill 1 km from her home to school, but it takes her only 10 minutes to walk from school to her home along the same route. What is her average speed, in km/hr, for the round trip?
(A) 3 (B) 3.125 (C) 3.5 (D) 4 (E) 4.5
ANSWER: A