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# What is the smallest integer that can be divided by the prod

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Senior Manager
Joined: 20 May 2014
Posts: 263
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Kudos [?]: 31 [0], given: 181

What is the smallest integer that can be divided by the prod [#permalink]  12 Nov 2017, 00:25
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What is the smallest integer that can be divided by the product of a prime number and 7 while yielding a prime number?

(A) 7

(B) 14

(C) 24

(D) 28

(E) 35

Kudos for correct solution.
[Reveal] Spoiler: OA
Director
Joined: 03 Sep 2017
Posts: 522
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Kudos [?]: 202 [1] , given: 66

Re: What is the smallest integer that can be divided by the prod [#permalink]  12 Nov 2017, 23:35
1
KUDOS
Prime numbers are 2, 3, 5, 7, 11, ...

Since the answer choices are between 7 and 35, and one of the divisors is 7, we know that we have to focus on small prime numbers otherwise we would get fractions.

Now, 7 is divisible only by 7 and 1 and 1 is not a prime, so we exclude it.

14 is divisible by 7 and 2, which are two primes, but the result would be 1 that is not prime.

24 is not divisible even by 7

28 is divisible by 7 and 2 and the result is 28/2*7 = 2 that is still prime. That's our answer!

Re: What is the smallest integer that can be divided by the prod   [#permalink] 12 Nov 2017, 23:35
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