Question: Also Prime

Comment on Also Prime

If we select p = 2 and q = 3, the options A and D are correct??
greenlight-admin's picture

The key word here is "MUST"

Must it be the case that p+q (answer choice A) is ALWAYS prime? In some cases, p+q CAN be prime (as with the values you chose for p and q), but that doesn't mean that p+q MUST be prime.

As we saw in the video, if p = 3 and q = 5, then p+q is NOT prime. So, p+q is not always prime.

If we select q=5 and p=3, why isn't Option B correct?
greenlight-admin's picture

The key word here is "MUST"

If q=5 and p=3, then answer choice B (q-p) does, indeed, yield a prime number.

So, we've shown that q-p CAN be a prime number, but MUST it be a prime number?

No. If q = 11 and p = 3, then q-p = 8, and 8 is NOT a prime number.

So, we can't conclude that q-p MUST be a prime number.

I tried the numbers 2 & 5 and 11 & 13. Got the answer choice B correct in both the instances but it isn't the correct answer. Obviously, in the actual gre we won't have enough time to test more than 2 possibilities. How likely is that this question will appear on the actual test?
greenlight-admin's picture

Rather than test arbitrary values, it helps to choose numbers wisely.

Answer choice B suggests that q-p must be prime.
Well almost all prime numbers are odd.
If we subtract one odd number from another odd number, the difference will be EVEN.
This is a great hint, since most even numbers are NOT prime.
So, choose 2 odd primes.
If we choose 11 and 5, then q - p = 11 - 5 = 6, which is NOT prime
If we choose 19 and 7 then q - p = 19 - 7 = 12, which is NOT prime
If we choose 13 and 3, then q - p = 13 - 3 = 10, which is NOT prime

Unfortunately, when you chose 13 and 11, the difference is EVEN, but it's a prime.


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