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

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Math Expert
Joined: 02 Sep 2009
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Is the integer k a prime number? (1) 2k = 6 (2) 1 < k < 6  [#permalink]

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23 Sep 2018, 05:19
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100% (00:21) correct 0% (00:00) wrong based on 29 sessions

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Is the integer k a prime number?

(1) 2k = 6

(2) 1 < k < 6

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Intern
Joined: 23 Sep 2018
Posts: 3
Is the integer k a prime number? (1) 2k = 6 (2) 1 < k < 6  [#permalink]

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23 Sep 2018, 05:38
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.

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Re: Is the integer k a prime number? (1) 2k = 6 (2) 1 < k < 6  [#permalink]

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23 Sep 2018, 06:50
Top Contributor
Bunuel wrote:
Is the integer k a prime number?

(1) 2k = 6
(2) 1 < k < 6

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

Cheers,
Brent
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Brent Hanneson – GMATPrepNow.com

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Re: Is the integer k a prime number? (1) 2k = 6 (2) 1 < k < 6  [#permalink]

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23 Sep 2018, 07:51
Bunuel wrote:
Is the integer k a prime number?

(1) 2k = 6

(2) 1 < k < 6

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

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

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

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

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

Regards,
Fabio.
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Re: Is the integer k a prime number? (1) 2k = 6 (2) 1 < k < 6 &nbs [#permalink] 23 Sep 2018, 07:51
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