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For an integer n, the function f(n) is defined as the product of all

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For an integer n, the function f(n) is defined as the product of all  [#permalink]

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New post 30 Oct 2017, 22:14
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For an integer n, the function f(n) is defined as the product of all integers from 1 to n, where n is greater than 10. Which of the following is NOT a factor of f(n)+1?

I. 2
II. 3
III. 10


A. None
B. II only
C. I and II only
D. I and III only
E. I, II and III

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Re: For an integer n, the function f(n) is defined as the product of all  [#permalink]

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New post 30 Oct 2017, 23:08
nkmungila wrote:
For an integer n, the function f(n) is defined as the product of all integers from 1 to n, where n is greater than 10. Which of the following is NOT a factor of f(n)+1?

I. 2
II. 3
III. 10


A. None
B. II only
C. I and II only
D. I and III only
E. I, II and III


f(n) = n!, where n > 10. So, f(n) is even, a multiple of 3 and a multiple of 10.

Therefore, f(n) + 1 is odd, 1 more than a multiple of 3 and 1 more than a multiple of 10, which means that f(n) + 1 is not divisible by 2, 3, or 10.

Answer: E.
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Re: For an integer n, the function f(n) is defined as the product of all  [#permalink]

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New post 30 Oct 2017, 23:10
Bunuel wrote:
nkmungila wrote:
For an integer n, the function f(n) is defined as the product of all integers from 1 to n, where n is greater than 10. Which of the following is NOT a factor of f(n)+1?

I. 2
II. 3
III. 10


A. None
B. II only
C. I and II only
D. I and III only
E. I, II and III


f(n) = n!, where n > 10. So, f(n) is even, a multiple of 3 and a multiple of 10.

Therefore, f(n) + 1 is odd, 1 more than a multiple of 3 and 1 more than a multiple of 10, which means that f(n) + 1 is not divisible by 2, 3, or 10.

Answer: E.


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Re: For an integer n, the function f(n) is defined as the product of all  [#permalink]

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New post 06 Feb 2019, 19:38
nkmungila wrote:
For an integer n, the function f(n) is defined as the product of all integers from 1 to n, where n is greater than 10. Which of the following is NOT a factor of f(n)+1?

I. 2
II. 3
III. 10


A. None
B. II only
C. I and II only
D. I and III only
E. I, II and III


We must remember that f(n) and f(n) + 1 WON’T SHARE ANY OF THE SAME PRIME FACTORS because they are consecutive integers.

So, since n is greater than 10, we see that f(n) will have prime factors of at least 2, 3, 5, and 7. Thus, 2, 3, and 10 won’t be factors of f(n) + 1.

Answer: E
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Re: For an integer n, the function f(n) is defined as the product of all  [#permalink]

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New post 15 May 2019, 11:14
how to study if I dont know math at all? but I want at least 700?
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Re: For an integer n, the function f(n) is defined as the product of all  [#permalink]

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New post 17 May 2019, 19:39
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Hi nuraliibodulla,

I’m happy to provide advice; however, you should start a new thread in the Ask GMAT Experts section: https://gmatclub.com/forum/gmat-prep-pa ... 6/?fl=menu.

Once you repost your question, I’ll provide some specific advice.
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Scott Woodbury-Stewart

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Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
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self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

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Re: For an integer n, the function f(n) is defined as the product of all   [#permalink] 17 May 2019, 19:39
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