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16 May 2009, 12:26
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
68% (01:10) correct
32%
(01:30)
wrong
based on 1047
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If m and n are both positive, what is the value of \(m*\sqrt{n}\)?
(1) \(\frac{m*n}{\sqrt{n}}=10\)
(2) \(\frac{m^2*n}{2}=50\)
(1) \(\frac{m*n}{\sqrt{n}}=10\)
(2) \(\frac{m^2*n}{2}=50\)
I thought I was doing well understanding the difference between taking a square root and unsquaring a variable. Then I ran into the following DS problem:
If m and n are both positive, what is the value of \(m\sqrt{n}\) ?
1.\(\frac{m*n} {\sqrt{n}}\)= 10 (this is sufficient, no problem there)
2. \(m^2*n = 100\)
For statement 2, the explanation in the book says that we take the positive square root of both sides to obtain m√n = 10. If -10 is not a solution here, then (2) would indeed be suffcient.
But how is that different from saying we are unsquaring (m√n)^2, which would yield m√n = 10, -10 ?
As an example, the number properties guide in mgmt claims that x^2 = 4 has two solutions, x=2 and x=-2. That makes sense and I'm just not seeing what's different here.
If m and n are both positive, what is the value of \(m\sqrt{n}\) ?
1.\(\frac{m*n} {\sqrt{n}}\)= 10 (this is sufficient, no problem there)
2. \(m^2*n = 100\)
For statement 2, the explanation in the book says that we take the positive square root of both sides to obtain m√n = 10. If -10 is not a solution here, then (2) would indeed be suffcient.
But how is that different from saying we are unsquaring (m√n)^2, which would yield m√n = 10, -10 ?
As an example, the number properties guide in mgmt claims that x^2 = 4 has two solutions, x=2 and x=-2. That makes sense and I'm just not seeing what's different here.
30 Apr 2010, 01:34
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Merged similar topics.
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.
achan
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.
General Discussion
27 Sep 2009, 21:35
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This is a specific concept about GMAT.
If you know that the sign of the variable inside the square root is positive then ALWAYS ignore the negative value.
If you know that the sign of the variable inside the square root is positive then ALWAYS ignore the negative value.
