Let n be a 5-digit number, and let q and r be the quotient and the remainder,respectively, when n is divided by 100. For how many values of n is q+r divisible by 11?
(A) 8180 (B) 8181 (C) 8182 (D) 9000 (E) 9090
Category: Uncategorized
Problem 77
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
Problem 76
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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Problem 75
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
Problem 74
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
Problem 73
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
Problem 71
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
Problem 70
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
Problem 69
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
Problem 68
How many non-congruent triangles with perimeter 7 have integer side lengths?
(A) 1 (B) 2 (C) 3 (D) 4 (E) 5
ANSWER: C