What is the smallest integer that. . . . .

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pm; Thanked: 6 times; Followed by:5 members

What is the smallest integer that. . . . .

by Vincen » 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.

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Source: Beat The GMAT — Problem Solving | Wed Sep 27, 2017 6:12 pm

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by [email protected] » 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.

Since we're asked for the SMALLEST number that will fit the above information, we should start with Answer A: 7....

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.

Answer B: 14...

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

Answer C: 24

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.

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

Final Answer: D

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

Contact Rich at [email protected]

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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pm; Location: East Bay all the way; Thanked: 625 times; Followed by:119 members; GMAT Score:780

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by Matt@VeritasPrep » 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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by Scott@TargetTestPrep » 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).

Answer: D

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