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# DS - LCM and root

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Manager
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DS - LCM and root [#permalink]

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08 May 2010, 12:58
If m is a positive integer, is m^1/2 > 25 ?

a. m is divisible by 50
b. m is divisible by 52

[Reveal] Spoiler:
OA : C

I wonder why OA should not consider the possibility of negative root. I think OA should be
[Reveal] Spoiler:
E

Last edited by msand on 09 May 2010, 06:32, edited 1 time in total.
Manager
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Re: DS - LCM and root [#permalink]

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09 May 2010, 03:21
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Re: DS - LCM and root [#permalink]

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09 May 2010, 03:59
Expert's post
msand wrote:
If m is a positive integer, is m^1/2 > 25 ?

a. m is divisible by 50
b. m is divisible by 52

[Reveal] Spoiler:
OA : C

I wonder why OA should consider the possibility of negative root. I think OA should be
[Reveal] Spoiler:
E

Is $$\sqrt{m}>25$$? Or is $$m>625$$?

(1) m is divisible by 50 --> m=50p --> the least value of m is 50 (as m is positive). Max value not limited. Not sufficient.
(2) m is divisible by 52 --> m=52q --> the least value of m is 52 (as m is positive). Max value not limited. Not sufficient.

(1)+(2) The least value of m would be LCM of the least values from (1) and (2) --> $$50=2*5^2$$ and $$52=2^2*13$$ --> $$m_{min}=LCM(50,52)=2^2*5^2*13=1300>625$$. Sufficient.

GMAT is dealing only with Real Numbers: Integers, Fractions and Irrational Numbers.

When the GMAT provides the square root sign for an even root, such as $$\sqrt{x}$$ or $$\sqrt[4]{x}$$, then the only accepted answer is the positive root.

That is, $$\sqrt{25}=5$$, NOT +5 or -5. In contrast, the equation $$x^2=25$$ has TWO solutions, +5 and -5. Even roots have only a positive value on the GMAT.

Odd roots will have the same sign as the base of the root. For example, $$\sqrt[3]{125} =5$$ and $$\sqrt[3]{-64} =-4$$.
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Re: DS - LCM and root [#permalink]

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09 May 2010, 06:51
Hi Bunuel,
Thanks for the explanation. It was clear to me that m(minimum) is 1300>625.
As you mentioned that root(1300) can only have positive values in GMAT world. Again , if X^2 = 1300, root of X can have two values. That is the point I am confused. Didn't really understand and appreciate the apparent paradox. Any further clarification?
It seems for variables(such as X in algebra) , the roots can have two values, either positive or negative. Whereas for a positive number , only positive root should be considered. Am I correct ?
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Re: DS - LCM and root [#permalink]

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09 May 2010, 07:49
Expert's post
msand wrote:
Hi Bunuel,
Thanks for the explanation. It was clear to me that m(minimum) is 1300>625.
As you mentioned that root(1300) can only have positive values in GMAT world. Again , if X^2 = 1300, root of X can have two values. That is the point I am confused. Didn't really understand and appreciate the apparent paradox. Any further clarification?
It seems for variables(such as X in algebra) , the roots can have two values, either positive or negative. Whereas for a positive number , only positive root should be considered. Am I correct ?

Some notes:
$$\sqrt[{even}]{positive}=positive$$ - $$\sqrt{25}=5$$. Even roots have only a positive value on the GMAT.

$$\sqrt[{even}]{negative}=undefined$$ - $$\sqrt{-25}=undefined$$. Even roots from negative number is undefined on the GMAT.

$$\sqrt[{odd}]{positive}=positive$$ and $$\sqrt[{odd}]{negative}=negative$$ - $$\sqrt[3]{125} =5$$ and $$\sqrt[3]{-64} =-4$$. Odd roots will have the same sign as the base of the root.

For our question we have: $$m_{min}=1300$$, question is $$\sqrt{m}>25$$? As $$\sqrt{1300}$$ has only positive value, then $$\sqrt{m_{min}}=\sqrt{1300}\approx{36}>25$$.

Hope it helps.
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Re: DS - LCM and root [#permalink]

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09 May 2010, 08:42
Ok - thanks for the notes.
Re: DS - LCM and root   [#permalink] 09 May 2010, 08:42
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# DS - LCM and root

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