Problem Solving

BTGmoderatorDC wrote: ↑

Wed Aug 05, 2020 5:35 pm

Which of the following is NOT a factor of 20!?

I. 29
II. 85
III. 121

A. I only
B. II only
C. III only
D. I and II
E. I and III

OA E

Source: Magoosh

We know that 20! = 1.2.3....20.

Let's take each statement one by one.

I. 29: Since 29 is a prime number and is greater than 20, we see that 29 is NOT a factor of 20!.

II. 85: Note that 85 = 17*5. Since 5 and 17 are less than 20, 20! has at least one 5 and 17, 85 is factor of 20!.

III. 121: Note that 121 = 1*11. Since 20! has only one 11, 20! does not have 121 as a factor of 20!.

Correct answer: E

Hope this helps!

-Jay
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BTGmoderatorDC wrote: ↑

Wed Aug 05, 2020 5:35 pm

Which of the following is NOT a factor of 20!?

I. 29
II. 85
III. 121

A. I only
B. II only
C. III only
D. I and II
E. I and III


OA E

Solution:

Since 20! does not contain a prime factor of 29, 29 is not a factor of 20!

Since 85 = 17 x 5, and 20! contains both prime factors of 17 and 5, 85 is a factor of 20!.

Since 121 = 11^2, and 20! does not have 2 prime factors of 11, 121 is not a factor 20!.

Answer: E