meshackb wrote:

This problem took me 8 minutes. Although I got it correct I feel like I must be missing something. Can anyone explain a fast way to arrive at the answer?

I guess that you want to solve this one by using algebric way? No need to do that. In actual GMAT, you could simply find 2 cases satisfied statements but lead to 2 different results. This won't cost much time.

For example:

(1) p is prime.

p=2 so 2p+1=5 is prime

p=3 so 2p+1=7 is also a prime

p=5 so 2p+1=11 is also a prime

It seems good.

Now if p=7 so 2p+1=15 is not a prime. Hence (1) is out.

(2) The units digit of p is not prime.

So units digit of p could be 0, 1, 4, 6, 8, 9.

If p=1 then 2p+1=3 is a prime

If p=4 then 2p+1=9 is not a prime

Hence (2) is also out.

Now, combine (1) and (2).

The smallest positive number which is a prime and its units digit is not a prime is 11.

If p=11 then 2p+1=23 is a prime

The next prime is 13, 17, 19

13, 17 are out because these numbers don't satisfy (2).

Now 19 left. If p=19 then 2p+1=2*19+1=39 is not a prime

Clearly (1) + (2) is insufficient.

_________________

Actual LSAT CR bank by Broall

How to solve quadratic equations - Factor quadratic equations

Factor table with sign: The useful tool to solve polynomial inequalities

Applying AM-GM inequality into finding extreme/absolute value

New Error Log with Timer