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by abhasjha » Mon Oct 13, 2014 12:18 am
If a, b, and c are three different positive integers whose sum is prime, which of the following statements could be true?

(A) Each of a, b, and c is prime.
(B) Each of a + 3, b + 3, and c + 3 is prime.
(C) Each of a + b, a + c, and b + c is prime.
(D) The average (arithmetic mean) of a, b, and c is prime.
(E) a + b = c
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by [email protected] » Mon Oct 13, 2014 12:57 am
Hi abhasjha,

This question has some interesting "restrictions" to it, but it's perfect for TESTing VALUES (even though you'll have to do a bit more work than normal to find a TEST that "fits").

We're told that A, B and C are 3 DIFFERENT positive integers whose SUM is PRIME.

Since the sum has to be prime, we should be looking for an ODD total. Since the answer choices emphasize the idea of prime numbers, you should think about "brute force-ing" a series of 3 odd numbers (likely primes) to see if you can get a match.

Without too much trouble, I got to 3, 5 and 11....

3+5+11 = 19 = a sum that is prime

Using these values, only one answer is true....

Final Answer: A

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by GMATinsight » Wed Oct 15, 2014 4:49 am
abhasjha wrote:If a, b, and c are three different positive integers whose sum is prime, which of the following statements could be true?

(A) Each of a, b, and c is prime.
(B) Each of a + 3, b + 3, and c + 3 is prime.
(C) Each of a + b, a + c, and b + c is prime.
(D) The average (arithmetic mean) of a, b, and c is prime.
(E) a + b = c
The phrase to catch here is "could be true?"

We have to try several possibilities to find the right option

(A) 3+7+9 = 19 PRIME therefore Possible
No need to try other options else we would have have tried values for other options in similar way

Answer: Option A
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