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If u and v are distinct prime numbers, which of the following CANNOT b

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Sajjad1994
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If u and v are distinct prime numbers, which of the following CANNOT b [#permalink] New post   15 Apr 2017, 09:06
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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
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E
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umadurga
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Re: If u and v are distinct prime numbers, which of the following CANNOT b [#permalink] New post   16 Apr 2017, 11:55
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Sum of two odd numbers is even and product of two odd numbers is odd.(for prime numbers other than 2)

Sum of one even and one odd is odd and product of one even and one odd is even.(for prime no. 2)

Going by this logic, the last option always gives us the even number as it is added by one. (odd +1 = even)
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Re: If u and v are distinct prime numbers, which of the following CANNOT b [#permalink] New post   16 Apr 2017, 13:26
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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: https://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:
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E


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Brent
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Re: If u and v are distinct prime numbers, which of the following CANNOT b [#permalink] New post   16 Apr 2017, 22:01
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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


    A. uv + 3v – 2 = v(u+3) – 2
      • Could be prime, v= 3 and u = 2
    B. uv – u + 2v – 2 = (u+2)(v-1)
      • Could be prime, v= 2 and u = 3
    C. uv + 2u – v – 2 = (u-1)(v+2)
      • Could be prime, u = 2 and v =3
    D. uv + 3u − 2v – 6 = (u-2) (v+3)
      • Could be prime, u = 3 and v = 2
    E. uv + u + v + 1 = (v+1) (u+ 1) = cannot be prime,
      • v+1 and u + 1 both simultaneously cannot be prime. If v= 2, v+1 = 3 is prime, they are only consecutive prime number. As v and u are distinct, u + 1 will never be prime and hence expression E can never be prime.

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Saquib
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Re: If u and v are distinct prime numbers, which of the following CANNOT b [#permalink] New post   30 Sep 2022, 08:28
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