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M06-26

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Bunuel
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M06-26 [#permalink] New post  16 Sep 2014, 00:28
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70% (01:38) correct 30% (01:33) wrong based on 753 sessions
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If \(m\) is a positive integer, is \(\sqrt{m} \gt 25\)?


(1) \(m\) is divisible by 50

(2) \(m\) is divisible by 52
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Bunuel
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Re M06-26 [#permalink] New post  16 Sep 2014, 00:28
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Official Solution:


If \(m\) is a positive integer, is \(\sqrt{m} \gt 25\)?

Square both sides: is \(m \gt 625\)?

(1) \(m\) is divisible by 50.

\(m\) can be 50, which is less than 625, as well as 5,000, which is more than 625. Not sufficient.

(2) \(m\) is divisible by 52.

\(m\) can be 52, which is less than 625, as well as 5,200, which is more than 625. Not sufficient.

(1)+(2) Since \(m\) is a multiple of both 50 and 52, it's a multiple of the least common multiple (LCM) of these two numbers, thus a multiple of 1,300. Given that \(m\) is a positive integer, the smallest value of \(m\) is 1,300, so \(m \gt 625\). Sufficient.


Answer: C
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padener
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Re: M06-26 [#permalink] New post  13 Mar 2016, 03:14
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Small question here just to clarify.
If in the question stem were written only m is an integer (without positive), could we pick as a value for m: m=0? Because in principle 0 is divisible by 50 and 52...so in this case the answer would be E. Is this right?

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Bunuel
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Re: M06-26 [#permalink] New post  13 Mar 2016, 08:12
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padener wrote:
Small question here just to clarify.
If in the question stem were written only m is an integer (without positive), could we pick as a value for m: m=0? Because in principle 0 is divisible by 50 and 52...so in this case the answer would be E. Is this right?

Thanks


Yes, 0 is divisible by every integer except 0 itself and yes, if m were non-negative instead of positive the answer would be E.
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TheNightKing
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Re: M06-26 [#permalink] New post  20 Oct 2019, 08:51
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Bunuel wrote:
If \(m\) is a positive integer, is \(\sqrt{m} \gt 25\)?


(1) \(m\) is divisible by 50

(2) \(m\) is divisible by 52


Since m is a positive integer we need to check if value of m is greater than 625.

Statement 1: m is divisible by 50. So m can be 50 or 5000. Not Sufficient.

Statement 2 : m is divisible by 52. So m can be 52 or 5200. Not sufficient.

Combined:
m is divisible by both 50=25*2 and 52=4*13. So we have at least 25*13*2 as the value of m. That is 650. Which means the square root of m is surely greater than 25.

Hence C.
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RenanBragion
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Re: M06-26 [#permalink] New post  11 Jun 2020, 06:27
I think this is a high-quality question and I agree with explanation.
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Bunuel
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Re: M06-26 [#permalink] New post  08 Jun 2023, 01:38
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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: M06-26 [#permalink]
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