Merged similar topics.
achan wrote:
If m and n are both positive, what is the value of m*\sqrt{n}?
(1) \frac{m*n}{\sqrt{n}}=10
(2) \frac{m^2*n}{2}=50
The textbook answer says (D) but the Square root of choice (2) will give us +/- 10.
Should we ignore -10 and conclude that (2) also gives us the answer
Theory: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.
Back to the original question:If
m and n are both positive, what is the value of
m*\sqrt{n}?
(1)
\frac{m*n}{\sqrt{n}}=10 --> reduce by
\sqrt{n} -->
m*\sqrt{n}=10. Sufficient.
(2)
\frac{m^2*n}{2}=50 -->
(m*\sqrt{n})^2=100 -->
m*\sqrt{n}=10 or
m*\sqrt{n}=-10. BUT since m and n are both positive (given)
m*\sqrt{n} can not equal to -10. Hence only one solution is valid:
m*\sqrt{n}=10. Sufficient.
Answer: D.
Hope it helps.
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52% (02:01) correct
