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Set S consists of n consecutive positive integers, each less

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Set S consists of n consecutive positive integers, each less

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Set S consists of n consecutive positive integers, each less than 25. If n > 3, what is the value of n?

(1) The number of factors of 2 contained in set S is equal to the number of factors of 3 contained in set S.

(2) n is odd.

Official answer =E
Source = Manhattan Prep.

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ziyuenlau wrote:
Set S consists of n consecutive positive integers, each less than 25. If n > 3, what is the value of n?

(1) The number of factors of 2 contained in set S is equal to the number of factors of 3 contained in set S.

(2) n is odd.

Official answer =E
Source = Manhattan Prep.
Hi ziyuenlau,

We have a set S that has n consecutive positive integers (less than 25). We have to find out the value of n, if n > 3.

Let's discuss each statement one by one.

S1: The number of factors of 2 contained in set S is equal to the number of factors of 3 contained in set S.

One of the approaches to attempt this is by hit and trial. However, you can save your precious time by choosing the starting number wisely.

Since 2 > 3, for four or more consecutive integers, the number of factors of 2 would always be equal or more than the factors of 3. So, the factors of 3 may be less than that of 2 in many cases.

So, let's pick a starting integer that gives two 3s, such as 9.

Case 1: Set S: {9, 10, 11, 12) => we have n > 3. We have factors of 2 = factors of 3 = 3. So, n = 4.

Case 2: Set S: {9, 10, 11, 12, 13) => we have n > 3. We have factors of 2 = factors of 3 = 3. So, n = 5. No unique answer. Insufficient.

S2: n is odd

This is clearly insufficient.

S1 and S2:

We already have case 2: Set S: {9, 10, 11, 12, 13) => we have n > 3. We have factors of 2 = factors of 3 = 3. So, n = 5 (odd).

Let's take another case.

Case 3: Set S: {9, 10, 11, 12, 13, 14, 15) => we have n > 3. We have factors of 2 = factors of 3 = 3. So, n = 7 (odd). No unique answer. Insufficient.

The correct answer: E

Hope this helps!

Relevant book: Manhattan Review GMAT Data Sufficiency Guide

-Jay
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Manhattan Review GMAT Prep

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