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

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

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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) \(\frac{m^2*n}{2}=50\)

[Reveal] Spoiler:
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.
[Reveal] Spoiler: OA
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Re: DS Problem - "unsquaring" vs taking a square root [#permalink]

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New post 27 Sep 2009, 21:35
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.
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Re: DS Problem - "unsquaring" vs taking a square root [#permalink]

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New post 31 Dec 2009, 04:37
for this problem:

m^2*n=100
m^2=100\n
m=sqrt(100\n)

since no number is -ve when sqrt the answer is d
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Tricky DS question [#permalink]

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New post 30 Apr 2010, 00:57
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.
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If m and n are both positive, what is the value of m*root(n) [#permalink]

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New post 30 Apr 2010, 01:34
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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.
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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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Re: If m and n are both positive, what is the value of m*root(n) [#permalink]

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New post 13 Jun 2015, 12:33
Hello from the GMAT Club BumpBot!

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

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New post 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 ??
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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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New post 14 Jun 2015, 07:28
adityadon wrote:
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 ??


Hi,
the answer in that case will not B..
statement two will give you two values for m one +ive and other -ive..
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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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New post 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
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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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New post 06 Jul 2016, 03:59
bhamini1 wrote:
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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Re: If m and n are both positive, what is the value of m*root(n) [#permalink]

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New post 06 Jul 2016, 11:42
gb82 wrote:
If m and n are both positive, what is the value of \(m*\sqrt{n}\)?

(1) \(\frac{m*n}{\sqrt{n}}=10\)
(2) \(\frac{m^2*n}{2}=50\)



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

Multiply both numerator and denominator by \sqrt{n}

we will get \(m*\sqrt{n}\)= 10

(2) \(\frac{m^2*n}{2}=50\)

\frac{m^2*n}{2}= 100
Squaring both sides \(m*\sqrt{n}\)= 10

D is the answer
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Re: If m and n are both positive, what is the value of m*root(n)   [#permalink] 06 Jul 2016, 11:42
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