Is the prime number p equal to 37?
(1) p = n2 +1, where n is an integer.
(2) p2 is greater than 200.
(1) p = n2 +1, where n is an integer.
(2) p2 is greater than 200.
(1) if n = 6, then p = 37, so the answer could be "yes".smclean23 wrote:Is the prime number p equal to 37?
(1) p = n2 +1, where n is an integer.
(2) p2 is greater than 200.
However, if n=2, then p=5 (another prime), so the answer could be "no".
Could be yes, could be no: insufficient.
(2) 37^2 is greater than 200, so the answer could be "yes"
17^2 is greater than 200, so the answer could be "no".
Could be yes, could be no, insufficient.
Together:
we saw that it's possible to get a "yes" answer for both statements, so now we need to see if we can get a "no" answer.
p=5 is no longer allowed, since 5^2 is NOT greater than 200.
However, p=17 IS still allowed, since 17 = 4^2 + 1. So, p could also equal 17.
At the end of the day, we can still get both a "yes" and a "no" answer: choose (E).
