Three primes, p, q and r, satisfy p+q=r and 1< p< q. Then p equals

1983 AMC 12 Problem 3

Attempt Problem 3 of the 1983 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1983 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

Three primes,

p,

q

and

r,

satisfy

p+q=r

and

1\lt p\lt q.

Then

p

equals

2

3

7

13

17

Every prime except one is odd

If both addends were odd, their sum would be an even number greater than

2

If both

p

and

q

were odd, then

r=p+q

would be even and greater than

2,

so it would not be prime. Thus one addend is the only even prime,

2.

Since

p\lt q,

that addend is

p.

Therefore, the correct answer is A.