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

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shasadou
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If n is the product of the first 10 prime numbers, which of the follow [#permalink] 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
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C
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Re: If n is the product of the first 10 prime numbers, which of the follow [#permalink] 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] New post   15 Sep 2017, 09:41
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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] New post   14 Jan 2019, 05:07
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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


Product of first 10 prime numbers will look something like this: 2 * 3 * 5 * 7 * 11 * 13 * ... = n

I. \(\frac{n}{7}\)
n is a multiple of 7 so n/7 will be an integer.

II. \(\frac{n}{4}\)
Since n is a product of only prime numbers, it will have only one 2. It will not have any other 2 and hence it will not be divisible by 4.

III. \(\frac{n}{143}\)
n is a product of both 11 and 13. So n/143 will be an integer.

Answer (C)
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Re: If n is the product of the first 10 prime numbers, which of the follow [#permalink] New post   13 May 2022, 03:27
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Re: If n is the product of the first 10 prime numbers, which of the follow [#permalink]
13 May 2022, 03:27
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