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.
Set S consists of n consecutive positive integers, each less
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Hi ziyuenlau,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.
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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