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If n is the product of the first 10 prime numbers, which of the follow

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Concentration: General Management, Operations
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If n is the product of the first 10 prime numbers, which of the follow [#permalink]

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New post 13 Sep 2015, 00:02
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If n is the product of the first 10 prime numbers, which of the following is an integer?

I. \(\frac{n}{7}\)

II. \(\frac{n}{4}\)

III. \(\frac{n}{143}\)

A. I only
B. I and II only
C. I and III only
D. III only
E. I, II, and III
[Reveal] Spoiler: OA

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Re: If n is the product of the first 10 prime numbers, which of the follow [#permalink]

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New post 13 Sep 2015, 01:46
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The product of first 10 prime numbers is: 2*3*5*7*11*13*17*19*23*29 = n
I) n/7 is an integer --> Yes (It is a part of the product)
II) n/4 is an integer --> No (2 is present only once in the product, not twice)
III) n/143 is an integer --> Yes (Both 11 and 13 are a part of the product)

Ans: C

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Re: If n is the product of the first 10 prime numbers, which of the follow [#permalink]

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New post 12 Sep 2017, 05:52
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Re: If n is the product of the first 10 prime numbers, which of the follow [#permalink]

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New post 15 Sep 2017, 09:41
shasadou wrote:
If n is the product of the first 10 prime numbers, which of the following is an integer?

I. \(\frac{n}{7}\)

II. \(\frac{n}{4}\)

III. \(\frac{n}{143}\)

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


Looking at each Roman numeral, we see that II is n/2^2 and III is n/(11 x 13).

Since 7 is included in the product of the first 10 prime numbers as well as 11 x 13, while 2^2 is not, only 7 and 143 will divide n.

Answer: C
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Re: If n is the product of the first 10 prime numbers, which of the follow   [#permalink] 15 Sep 2017, 09:41
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