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## What is the smallest integer that. . . . .

This topic has 3 expert replies and 0 member replies

### Top Member

Vincen Legendary Member
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#### What is the smallest integer that. . . . .

Wed Sep 27, 2017 6:12 pm
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

The OA is D.

I did not understand the question. What do I need to calculate here? I am confuse.

### GMAT/MBA Expert

Scott@TargetTestPrep GMAT Instructor
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Thu Jan 11, 2018 1:46 pm
Vincen wrote:
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
Since the smallest prime number is 2, the smallest product of a prime number and 7 is 2 x 7 = 14, and the smallest integer that yields a prime number when it is divided by 14 is 28 (notice that 28/14 = 2).

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### GMAT/MBA Expert

Matt@VeritasPrep GMAT Instructor
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Thu Sep 28, 2017 4:30 pm
They're saying that

the answer / (7 * some prime) = another prime

And they want the answer to be the smallest number that solves the equation above.

If we call the answer a, some prime p, and the other prime q, we've got:

a / 7p = q

a = 7pq

To make this as small as possible, make p and q the smallest primes possible: p = 2, q = 2.

From that, a = 7 * 2 * 2 = 28

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### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
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Wed Sep 27, 2017 7:56 pm
Hi Vincen,

We're asked to find the smallest integer that can be DIVIDED by the PRODUCT of a PRIME number and 7 AND will yield a PRIME number as the result. We can answer this question by TESTing THE ANSWERS.

The smallest product that can occur between 7 and a prime is (7)(2) = 14. 7 is NOT divisibly by 14, so we can eliminate Answer A.

While 14 is divisible by 14, the end result is 1 - but that is NOT a prime number. Eliminate Answer B.

24/14 is NOT a prime. The next two products to consider would be (7)(3) = 21 and (7)(5) = 35. However, 24/21 and 24/35 are NOT primes. Eliminate Answer C.

28/14 = 2 - and that IS a prime. This matches everything we were told, so this must be the answer.

GMAT assassins aren't born, they're made,
Rich

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