The four numbers A, B, A+B and A-B are all prime. The sum of these four numbers is

A) Even

B) Divisible by 3

C) Divisible by 5

D) Divisible by 7

E) Prime

Source: 2002 AMC 10/12B #15

The four numbers A, B, A+B and A-B are all prime. The sum of these four numbers is

A) Even

B) Divisible by 3

C) Divisible by 5

D) Divisible by 7

E) Prime

Source: 2002 AMC 10/12B #15

Got it. Piece of Cake.

On a math blog, you say “Easy as pie”

Yah, yah. Which brings me to a question my students were asking. Pi Day is traditionally celebrated on 3-14 and more specifically at 1:59 (generally PM). BUT, in the year 2015, with the date itself being 3-14-15, will the time be ‘officially’ changed to 9:26? Or will there have to be some international symposium where we all vote on that?

Considering that a large portion of the international community wouldn’t recognize 3-14-15 but instead 14-3-15, it’s going to be hard to get a consensus on the matter. But you make a good point. ðŸ˜‰

Didn’t think about time formats. So what about April 31st?

Hahhaaha! I think it would confuse a lot of people to claim that May 1st was now Pi Day.

WoopS! Forgot to count my knuckles….There aren’t 31 days in April, are there? May 1st would be pretty great. It’s already a federal holiday in most European countries, isn’t it? This could be a good ploy to get Pi Day declared a national holiday.

The answer is A, for prime are all odd, and odd adds odd equals even!

The answer for puzzle 8 is A), for all prime are odd, and odd adds odd equals even.

Fairly certain the answer is E.

I would say none…

If A and B are prime, A+B can’t be prime.

Woops, I forgot 2… It’s prime then…

Hi, nice posts there thank’s for the interesting information

Got it. Easy as pi/pie. A + B can be prime as long as you remember that there is one prime even number.

Forgot to say, the answer is E.

Since A, B, A+B and A-B are all primes, we know they are all integers > 1.

A+B is only prime if either A or B is 2, otherwise odd+odd = even (and > 2) and therefore not prime. They can’t both be 2, as 2+2=4 (not prime).

A-B is prime, so A>B, so B must be 2, A must be odd (all primes > 2 are odd…), and A >= 5 so that A-B >= 2.

A + 2 + (A+2) + (A-2) = A + 2 + 2A = 3A + 2.

Since A is odd, 3A + 2 is odd.

So the sum is odd, and we can dismiss answer (A). 3A+2 is not divisible by 3, so we can dismiss (B).

Since B is 2, then the sequence A-2, A, A+2 is a triplet of primes, like 3,5,7. But if A-2 is not divisible by 3, then either A-1 or A is. Assuming it is A-1, then A-1+3=A+2 must be divisible by 3. The result is that one of these three primes A-2,A,A+2 must be 3 itself. Since 1 is not prime, the triplet must be 3,5,7.

So now we know that A is 5 and B is 2, then the sum is 5+2+3+7 = 17, which is prime.

Answer: E.

What is the short version?