If a, b, and c are three different positive. . .

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

If a, b, and c are three different positive. . .

by Vincen » Fri Sep 29, 2017 7:03 pm

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 OA is A.

How can I prove that option A is the correct choice?

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Source: Beat The GMAT — Problem Solving | Fri Sep 29, 2017 7:03 pm

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Sat Sep 30, 2017 3:09 am

Vincen 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 OA is A.

How can I prove that option A is the correct choice?

If a=5, b=11 and c=13, then all 3 values are prime, as is their sum:
5+11+13 = 29.

Thus, option A could be true.

The correct answer is A.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8089; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

Re: If a, b, and c are three different positive. . .

by Scott@TargetTestPrep » Wed Jan 29, 2020 5:20 am

Vincen wrote: ↑
Fri Sep 29, 2017 7:03 pm
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 OA is A.

How can I prove that option A is the correct choice?