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If k is a positive integer, is (1/2)^k > 0.125?

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VyshakhR1995
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If k is a positive integer, is (1/2)^k > 0.125? [#permalink] New post   Updated on: 26 Apr 2017, 01:18
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If k is a positive integer, is \((\frac{1}{2})^k > 0.125\)?

(1) k > 3

(2) \((\frac{1}{2})^{(k-1)} < 0.25\)
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D

Originally posted by VyshakhR1995 on 26 Apr 2017, 00:56.
Last edited by Bunuel on 26 Apr 2017, 01:18, edited 2 times in total.
Renamed the topic, edited the question and the tags.
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Bunuel
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Re: If k is a positive integer, is (1/2)^k > 0.125? [#permalink] New post   26 Apr 2017, 01:03
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VyshakhR1995 wrote:
If k is a positive integer,is (1/2)^k > 0.125?

1)k>3

2)(1/2)^k-1< 0.25


Is the exponent there k or k-1?
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Re: If k is a positive integer, is (1/2)^k > 0.125? [#permalink] New post   26 Apr 2017, 01:13
Bunuel wrote:
VyshakhR1995 wrote:
If k is a positive integer,is (1/2)^k > 0.125?

1)k>3

2)(1/2)^k-1< 0.25


Is the exponent there k or k-1?


exponent is k-1
Edited
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Re: If k is a positive integer, is (1/2)^k > 0.125? [#permalink] New post   18 May 2017, 21:50
" A "alone is sufficient But with B I am getting a different answer for different value of K .
How D is the answer here.
Thanks
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If k is a positive integer, is (1/2)^k > 0.125? [#permalink] New post   18 May 2017, 22:42
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kannu44 wrote:
" A "alone is sufficient But with B I am getting a different answer for different value of K .
How D is the answer here.
Thanks


If k is a positive integer, is \((\frac{1}{2})^k > 0.125\)?

Is \((\frac{1}{2})^k > 0.125\)?

Is \((\frac{1}{2})^k > (\frac{1}{2})^3\)?

Is k < 3?

Since given that k is a positive integer, the question basically asks whether k is 1 or 2.

(1) k > 3. Directly gives a NO answer to the question. Sufficient.

(2) \((\frac{1}{2})^{(k-1)} < 0.25\) --> \((\frac{1}{2})^{(k-1)} < (\frac{1}{2})^2\) --> k - 1 > 2 --> k > 3. The same here. Sufficient.

Answer: D.

Hope it helps.
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Re: If k is a positive integer, is (1/2)^k > 0.125? [#permalink] New post   18 May 2017, 22:50
Thanks Bunuel for your quick response. I was making it too complex but surely your way is much elegant.
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Re: If k is a positive integer, is (1/2)^k > 0.125? [#permalink] New post   19 May 2017, 10:30
Bunuel wrote:
kannu44 wrote:
" A "alone is sufficient But with B I am getting a different answer for different value of K .
How D is the answer here.
Thanks


If k is a positive integer, is \((\frac{1}{2})^k > 0.125\)?

Is \((\frac{1}{2})^k > 0.125\)?

Is \((\frac{1}{2})^k > (\frac{1}{2})^3\)?

Is k < 3?

Since given that k is a positive integer, the question basically asks whether k is 1 or 2.

(1) k > 3. Directly gives a NO answer to the question. Not sufficient.

(2) \((\frac{1}{2})^{(k-1)} < 0.25\) --> \((\frac{1}{2})^{(k-1)} < (\frac{1}{2})^2\) --> k - 1 > 2 --> k > 3. The same here. Sufficient.

Answer: D.

Hope it helps.


Hello. I did not understand could you please explain, how did the inequality sign change?
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Re: If k is a positive integer, is (1/2)^k > 0.125? [#permalink] New post   19 May 2017, 10:43
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sreeste wrote:
Bunuel wrote:
kannu44 wrote:
" A "alone is sufficient But with B I am getting a different answer for different value of K .
How D is the answer here.
Thanks


If k is a positive integer, is \((\frac{1}{2})^k > 0.125\)?

Is \((\frac{1}{2})^k > 0.125\)?

Is \((\frac{1}{2})^k > (\frac{1}{2})^3\)?

Is k < 3?

Since given that k is a positive integer, the question basically asks whether k is 1 or 2.

(1) k > 3. Directly gives a NO answer to the question. Not sufficient.

(2) \((\frac{1}{2})^{(k-1)} < 0.25\) --> \((\frac{1}{2})^{(k-1)} < (\frac{1}{2})^2\) --> k - 1 > 2 --> k > 3. The same here. Sufficient.

Answer: D.

Hope it helps.


Hello. I did not understand could you please explain, how did the inequality sign change?


Consider the following:

Is \((\frac{1}{2})^k > (\frac{1}{2})^3\)

Is \(\frac{1}{2^k} > \frac{1}{2^3}\)

Cross-multiply (notice that we can safely do that since both 2^k and 2^3 are positive): is \(2^3 > 2^k\);

Is \(3 > k\).

The same way with \((\frac{1}{2})^{(k-1)} < (\frac{1}{2})^2\) ;

\(\frac{1}{2^{(k-1)}} < \frac{1}{2^2}\);

\(2^2 < 2^{(k-1)}\)

\(2 < k-1\);

\(3 < k\).

Hope it's clear.
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Re: If k is a positive integer, is (1/2)^k > 0.125? [#permalink] New post   19 Sep 2019, 02:40
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VyshakhR1995 wrote:
If k is a positive integer, is \((\frac{1}{2})^k > 0.125\)?

(1) k > 3

(2) \((\frac{1}{2})^{(k-1)} < 0.25\)



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Re: If k is a positive integer, is (1/2)^k > 0.125? [#permalink]
19 Sep 2019, 02:40
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Bunuel
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