Knewton Brutal Math Challenge - Week 17 (Math Edition)

by , Jul 28, 2010

Joanna's doozy from last week will be a tough act to follow, but I certainly tried...

The shirt is in play once again. We have blue and we have white.

A set of positive integers contains twice as many even integers as odd integers. How many integers are in the set?

1. If two integers are chosen at random from the set, the probability that their sum will be even is 26/75 less than the probability that their product will be even.

2. The number of integers in the set has fewer than six factors, and one of these factors is 17.

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

(D) EACH statement ALONE is sufficient.

(E) Statements (1) and (2) TOGETHER are NOT sufficient.