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) \(m*\sqrt{n}\) cannot equal to -10. Hence only one solution is valid: \(m*\sqrt{n}=10\). Sufficient.
Answer: D.
Hope it helps.
If they had not provided that m and n both are positive then also statement B alone would be sufficient right ??