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.
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