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Intern  Joined: 04 May 2009
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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) $$\frac{m^2*n}{2}=50$$

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.
Math Expert V
Joined: 02 Sep 2009
Posts: 58427
If m and n are both positive, what is the value of m*root(n)  [#permalink]

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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 $$\sqrt{x}$$, 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, $$\sqrt{125} =5$$ and $$\sqrt{-64} =-4$$.

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.

Hope it helps.
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Re: DS Problem - "unsquaring" vs taking a square root  [#permalink]

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

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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
Manager  Joined: 30 Apr 2010
Posts: 53
Tricky DS question  [#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) $$\frac{m^2*n}{2}=50$$

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

Originally posted by achan on 30 Apr 2010, 00:57.
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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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 $$\sqrt{x}$$, 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, $$\sqrt{125} =5$$ and $$\sqrt{-64} =-4$$.

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.

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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Joined: 02 Aug 2009
Posts: 8006
Re: If m and n are both positive, what is the value of m*root(n)  [#permalink]

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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 $$\sqrt{x}$$, 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, $$\sqrt{125} =5$$ and $$\sqrt{-64} =-4$$.

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.

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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GMAT 1: 580 Q37 V33 GMAT 2: 580 Q39 V31 GMAT 3: 560 Q40 V28 GMAT 4: 580 Q37 V32 GMAT 5: 680 Q45 V37 GMAT 6: 690 Q47 V37 Re: If m and n are both positive, what is the value of m*root(n)  [#permalink]

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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
Math Expert V
Joined: 02 Sep 2009
Posts: 58427
Re: If m and n are both positive, what is the value of m*root(n)  [#permalink]

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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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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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GMAT 1: 700 Q50 V34 Re: If m and n are both positive, what is the value of m*root(n)  [#permalink]

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1) msqrt(n) = 10
2) m2n = 100
square root on both sides
msqrt(n) = 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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_________________ Re: If m and n are both positive, what is the value of m*root(n)   [#permalink] 20 Dec 2018, 00:28
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