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DS - LCM and root

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DS - LCM and root [#permalink] New post 08 May 2010, 11:58
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, 05:32, edited 1 time in total.
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Re: DS - LCM and root [#permalink] New post 09 May 2010, 02:21
bunuel or any other - comments please.
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Re: DS - LCM and root [#permalink] New post 09 May 2010, 02:59
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.

Answer: C.

I don't quite understand your question about "negative root"... Anyway:

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] New post 09 May 2010, 05:51
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] New post 09 May 2010, 06:49
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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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: DS - LCM and root [#permalink] New post 09 May 2010, 07:42
Ok - thanks for the notes.
Re: DS - LCM and root   [#permalink] 09 May 2010, 07:42
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