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M03-17

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Bunuel
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M03-17 [#permalink] New post   16 Sep 2014, 00:20
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89% (00:23) correct 11% (00:31) wrong based on 814 sessions
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What is the value of integer \(k\)?


(1) \(2^k=1\)

(2) \(1^k=1\)
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A
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Bunuel
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Re M03-17 [#permalink] New post   16 Sep 2014, 00:20
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Official Solution:


What is the value of integer \(k\)?

(1) \(2^k=1\).

If a base is neither -1 nor 1, then for exponentiation to yield 1, the exponent must be 0. Consequently, it follows that \(k = 0\). Sufficient.

(2) \(1^k=1\).

This equation holds true for any value of \(k\). Not sufficient.


Answer: A
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chetan2u
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Re: M03-17 [#permalink] New post   22 May 2016, 05:40
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msk0657 wrote:
Bunuel wrote:
Official Solution:


(1) \(2^k=1\). Since any nonzero number to the power of 0 is 1 then \(k=0\). Sufficient.

(2) \(1^k=1\). This equation holds true for any value of \(k\). Not sufficient.


Answer: A



Hi Bunuel,

Can you please explain point number 2. (This equation holds true for any value of \(k\). Not sufficient.)

A. When 2 power K = 2 power 0 = 1...I thought this is fine.. sufficient.

B. When 1 power K = 1 power 0 = 1....thought even this is sufficient. Then I chose D.


Hi,
the reason mentioned by you is the very reason that statement II is NOT suff...
you take any value of K,

(2) \(1^k=1\).
K=1....\(1^1=1\)....
K=2....\(1^2=1\)....
so k can take any value 1,2,3,4..
so insuff
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Re: M03-17 [#permalink] New post   22 May 2016, 04:59
Bunuel wrote:
Official Solution:


(1) \(2^k=1\). Since any nonzero number to the power of 0 is 1 then \(k=0\). Sufficient.

(2) \(1^k=1\). This equation holds true for any value of \(k\). Not sufficient.


Answer: A



Hi Bunuel,

Can you please explain point number 2. (This equation holds true for any value of \(k\). Not sufficient.)

A. When 2 power K = 2 power 0 = 1...I thought this is fine.. sufficient.

B. When 1 power K = 1 power 0 = 1....thought even this is sufficient. Then I chose D.
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Bunuel
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Re: M03-17 [#permalink] New post   07 May 2023, 07:24
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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Re M03-17 [#permalink] New post   12 Aug 2023, 02:04
I think this is a high-quality question and I agree with explanation.
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Re M03-17 [#permalink]
12 Aug 2023, 02:04
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Bunuel
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