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

I wonder why OA should consider the possibility of negative root. I think OA should be

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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