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Bunuel
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K+1 is prime
Let's take k = 2 (prime)
K+1 = 3 is prime
Does not mean k is prime as k can be 4 and k+1 =5 is prime hence not sufficient

K+2 is not prime
As above example if k = 4 k+2 = 6is not prime
Also if k=2
K+2 = 4 is not prime
Hence not sufficient
Answer is E

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Statement 1:

k+1 is prime: 3 is prime, 2 is prime- K is prime
5 is prime, 4 is not prime- K is not prime

Insufficient

Statement 2:

K+2 is not prime: 4 is not prime, 2 is prime- K is prime
6 is not prime, 4 is not prime- K is not prime

Insufficient

Combined: 4 is not prime, 3 is prime, 2 is prime- K is prime
6 is not prime, 5 is prime, 4 is not prime- K is not Prime

Insufficient

Ans E

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Statement 1 and 2 are clearly insufficient. The trick to see the combined statements is to note 2 is the starting prime number.

For k = 1 both the statements don't hold true.

Excluding the integer 1, For any positive number if k+1 has to be prime, k+2 won't be prime. Both statements will hold true. Since it fails for 1, both statements are not sufficient. E

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