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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) \(\frac{m*n}{\sqrt{n}}=10\)

(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

Last edited by Bunuel on 30 Apr 2010, 01:15, edited 3 times in total.

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.

Re: If m and n are both positive, what is the value of m*root(n) [#permalink]

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24 Dec 2013, 15:44

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Re: If m and n are both positive, what is the value of m*root(n) [#permalink]

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13 Jun 2015, 12:33

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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If m and n are both positive, what is the value of m*root(n) [#permalink]

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14 Jun 2015, 07:22

Bunuel wrote:

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.

Bunuel , If they had not provided that m and n both are positive then also statement B alone would be sufficient right ?? I mean when question stem itself provides sqaure root sign , we should consider only POSITIVE root right ?? _________________

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.

Bunuel , If they had not provided that m and n both are positive then also statement B alone would be sufficient right ?? I mean when question stem itself provides sqaure root sign , we should consider only POSITIVE root right ??

Hi, the answer in that case will not B.. statement two will give you two values for m one +ive and other -ive..
_________________

Re: If m and n are both positive, what is the value of m*root(n) [#permalink]

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06 Jul 2016, 03:38

Please help clarify my doubt for statement 2.it says that m^2n=2*50 So basically,m^2*n=100,wherein there can be three possibilities 10^2 *1=100 5^2 *4=100,or 2^2 *25=100 Then how can we determine that it is the first scenario only??? please correct my concept if I am wrong

Please help clarify my doubt for statement 2.it says that m^2n=2*50 So basically,m^2*n=100,wherein there can be three possibilities 10^2 *1=100 5^2 *4=100,or 2^2 *25=100 Then how can we determine that it is the first scenario only??? please correct my concept if I am wrong

The question asks to find the value of \(m*\sqrt{n}\). In all cases you consider there the value of \(m*\sqrt{n}\) is the same: 10.
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