Anaira Mitch wrote:All the terms in Set S are integers. Five terms in S are even, and four terms are multiples of 3. How many terms in S are even numbers that are not divisible by 3?

(1) The product of all the even terms in Set S is a multiple of 9.

(2) The integers in S are consecutive.

Hi Anaira Mitch,

We are given that there are 5 even terms and 4 terms that are multiples of 3 (These all can be even, all can be odd, a few can be odd). We have to find out how many terms in set S are even numbers that are not divisible by 3.

Let's see each statement one by one.

S1: The product of all the even terms in Set S is a multiple of 9.

The statement is clearly insufficient as the product of all the 5 even terms in Set S can be 9, 18, 27, 81, etc.

Since 4 terms are multiples of 3, four even terms out of five even terms can be a multiple of 9 or even only one even term out of five even terms can be a multiple of 9. Insufficient.

S2: The integers in S are consecutive.

To accommodate 5 even integers in a set that is a set of consecutive integers, there could be 4, 5, or 6 odd integers.

Let's take all three cases.

A case of 5 even and 4 odd with the constraint that there must be 5 even and 4 multiples of 3 is not possible.

Case 1: (5 even and 5 odd): {3, 4, 5, 6, 7, 8, 9, 10, 11, 12}; we see that 4, 8, and 10 are not divisible by 3. The count of terms = 3.

Case 2: (5 even and 6 odd): {3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}; we see that 4, 8, and 10 are not divisible by 3. The count of terms = 3.

We get a unique answer '3'. Sufficient.

The correct answer: B

Hope this helps!

Relevant book: Manhattan Review GMAT Data Sufficiency Guide

-Jay
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