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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