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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