SajjadAhmad wrote:

If u and v are distinct prime numbers, which of the following CANNOT be a prime number?

A. uv + 3v − 2

B. uv – u + 2v − 2

C. uv + 2u – v − 2

D. uv + 3u − 2v − 6

E. uv + u + v + 1

NOTE: this is one of those questions that require us to check/test each answer choice. In these situations,

always check the answer choices from E to A, because the correct answer is typically closer to the bottom than to the top.

For more on this strategy, see my article:

http://www.gmatprepnow.com/articles/han ... -questions E. uv + u + v + 1

Notice that we can factor this expression IN PARTS.

We get:

uv + u +

v + 1 =

u(v + 1) +

1(v + 1)= (u + 1)(v + 1)

Since we are adding 1 to u and adding 1 to v, we know that (u+1) does not equal 1, and (v+1) does not equal 1

So, we can be CERTAIN that (u + 1)(v + 1) is a COMPOSITE number, which means it is NOT PRIME.

Answer:

Cheers,

Brent

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Brent Hanneson – Founder of gmatprepnow.com