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n is divisible by 14 and 3. Which of the following statement

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Retired Moderator
Joined: 07 Jun 2014
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GRE 1: Q167 V156
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n is divisible by 14 and 3. Which of the following statement [#permalink]  12 Aug 2018, 16:05
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Question Stats:

73% (00:49) correct 26% (00:39) wrong based on 26 sessions
n is divisible by 14 and 3. Which of the following statements must be true?

Indicate all such statements.

A. 12 is a factor of n.
B. 21 is a factor of n.
C. n is a multiple of 42.
[Reveal] Spoiler: OA

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Sandy
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Retired Moderator
Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 171

Kudos [?]: 2915 [0], given: 394

Re: n is divisible by 14 and 3. Which of the following statement [#permalink]  15 Aug 2018, 05:19
Expert's post
Explanation

Since n is divisible by 14 and 3, n contains the prime factors of both 14 and 3, which are 2, 7, and 3. Thus, any numbers that can be constructed using only these prime factors (no additional factors) are factors of n.

Since $$12 = 2 \times 2 \times 3$$, you cannot make 12 by multiplying the prime factors of n (you would need one more 2). However, you can construct 21 by multiplying two of the known prime factors of n ($$7 \times 3 = 21$$), so the second statement is true.

Finally, n must be at least 42 ($$= 2 \times 7 \times 3$$, the least common multiple of 14 and 3), so n is definitely a multiple of 42. That is, n can only be 42, 84, 126, etc.
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Sandy
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Re: n is divisible by 14 and 3. Which of the following statement   [#permalink] 15 Aug 2018, 05:19
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n is divisible by 14 and 3. Which of the following statement

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