Is the integer k a prime number? (1) 2k = 6 (2) 1

Question

Is the integer k a prime number?

(1) 2k = 6

(2) 1 < k < 6

peon91 · Answer

From (1) k=3 hence k is prime. Sufficient.
From (2) k can be 2, 3, 4 or 5. If k=3, k is prime but if k=4 is not. Insufficient.

The correct answer is A.

BrentGMATPrepNow · Answer

Target question :    Is k a prime number?

Given : k is an integer

Statement 1 : 2k = 6  
Solve to get: k = 3
3 is a prime number, so the answer to the target question is  YES, k IS a prime number 
Since we can answer the  target question  with certainty, statement 1 is SUFFICIENT

Statement 2 : 1 < k < 6 
There are several values of k that satisfy statement 2. Here are two: 
 Case a : k COULD equal 2, in which case, the answer to the target question is  YES, k IS a prime number 
 Case b : k COULD equal 4, in which case, the answer to the target question is  NO, k is NOT a prime number 
Since we cannot answer the  target question  with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent

fskilnik · Answer

k\,\,{\mathop{\rm int}}

k\,\,\mathop = \limits^? \,\,{\rm{prime}}

\left( 1 \right)\,\,\,2k = 6\,\,\,\, \Rightarrow \,\,\,\,k\,\,\,{\rm{unique}}\,\,\,\, \Rightarrow \,\,\,\,{\rm{SUFF}}.\,\,\,\,

\left( 2 \right)\,\,\,1 < k < 6\,\,\,\,\left\{ \matrix{
 \,{\rm{Take}}\,\,k = 2\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \hfill \cr 
 \,{\rm{Take}}\,\,k = 4\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \hfill \cr} \right.

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

Is the integer k a prime number? (1) 2k = 6 (2) 1 < k < 6

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