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

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by Vincen » Tue Dec 12, 2017 10:30 am
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

The OA is E.

Is there a fast way to get the correct answer here? Experts, can you show me how would you solve it? Thanks in advanced.
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by EconomistGMATTutor » Tue Dec 12, 2017 11:22 am
Hello Vincen.

Let's take a look at your question.

Option 1) 29.

This is a prime number and it does not appear in 20! So, this is not be a factor.

Option 2) 85.

85=5*17, and 5 and 17 are in 20! So, 85 is a factor.

Option 3) 121.

121=11*11, but in 20! there is only one 11. So, this is not be a factor.

Therefore, the correct answer is E.

I hope this explanation may help you.

I'm available if you'd like a follow-up.

Regards.
GMAT Prep From The Economist
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by Jeff@TargetTestPrep » Tue Jan 02, 2018 9:28 am
Vincen wrote: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
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

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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