Is the integer k a prime number? (1) k + 1 is prime. (2) k + 2 is not

Question

Is the integer k a prime number?

(1) k + 1 is prime.
(2) k + 2 is not prime.

Trickycaddy13668 · Answer

Answer is E. Take 2 sets of number: 1) 2,3,4 and 2)4,5,6. K can't be ascertained to be prime.

Statement 1 says: We have 2 consequtive numbers out of which the 2 Nd is prime. Apply it to the two sets of numbers. Clearly insufficient. So we are left with B,C,E

Statement 2: K+2 is not prime. Apply to the 2 sets and you will find k can't be ascertained to be prime. Now we are left with C and E.

Combining both statements, K still can't be ascertained. Hence E.

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saurabh9gupta · Answer

My aporoach

We can take numbers such as 0 1 2 3 etc

Stmt A
K+1 is prime..

K can be 1 (non prime) in that case k+1 is prime

K can be 2 (prime) in that case k+1 is prime

Not sufficient

Stmt B
K can be 2 (prime) in that case k+2 is not prime
K can be 3 (prime) in that case k+2 is prime

Not sufficient

Taking both together only k=3 and k=1 are out

So C

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ashudhall · Answer

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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vinayakvaish · Answer

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

Hit Kudos!!

SwamyGali18 · Answer

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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Is the integer k a prime number? (1) k + 1 is prime. (2) k + 2 is not

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