If F is the prime factorization of N!, how many factors in F have an exponent of 1?

[BTGmoderatorDC]

If F is the prime factorization of N!, how many factors in F have an exponent of 1?

(1) 32 ≤ N ≤ 40

(2) 27 ≤ N ≤ 35


OA E

Source: Magoosh

[Jay@ManhattanReview]

If F is the prime factorization of N!, how many factors in F have an exponent of 1?

(1) 32 ≤ N ≤ 40

(2) 27 ≤ N ≤ 35

OA E

Source: Magoosh

Let's take each statement one by one.

(1) 32 ≤ N ≤ 40

Case 1: Say N = 32, then F would have 17, 19, 23, 29 and 31 as primes that have an exponent of 1. The answer is 5.

Case 2: Say N = 34, then F would have 19, 23, 29 and 31 as primes that have an exponent of 1. The answer is 4.

No unique answer. Insufficient.

(2) 27 ≤ N ≤ 35

Both cases discussed above are applicable here, too. Insufficient.

Even both statements together are Insufficient.

The correct answer: E

Hope this helps!

-Jay
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