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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If a, b, and c are three different positive. . .
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If a=5, b=11 and c=13, then all 3 values are prime, as is their sum: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?
5+11+13 = 29.
Thus, option A could be true.
The correct answer is A.
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We can let a, b, and c be 5, 7, and 11, respectively. We see that 5 + 7 + 11 = 23 is prime, and each of a, b, and c is also a prime.Vincen wrote: ↑Fri Sep 29, 2017 7:03 pmIf 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?
Answer: A
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