BTGmoderatorDC wrote: ↑Tue May 26, 2020 7:14 pm
If n is an integer greater than 5.3, then n! must be divisible by which of the following numbers?
A. 7
B. 11
C. 12
D. 13
E. 14
OA
C
Source: Princeton Review
Since this is a must be true question, we must take the minimum value of n, i.e., n = 6.
So, we have to choose an option that must divide 6! = 1.2.3.4.5.6. Let's take all options, one by one.
A. 7
Since 7 is a prime number and 6! does not have a 7, it's incorrect.
B. 11
Similarly, since 11 is a prime number and 6! does not have an 11, it's incorrect.
C. 12
Correct. 12 can be factored as 2*2*3. We see that in 6! = 1.2.3.4.5.6, there are ample no. of 2s and 3s. So, 12 must divide 6!.
D. 13
Similarly, since 13 is a prime number and 6! does not have a 13, it's incorrect.
E. 14
14 can be factored as 2*7, and since 7 is a prime number and 6! does not have a 7, it's incorrect.
The correct answer:
C
Hope this helps!
-Jay
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