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If u and –3v are greater than 0, and [#permalink]
Expert's post 00:00

Question Stats: 40% (01:45) correct 60% (01:28) wrong based on 75 sessions
If u and –3v are greater than 0, and $$\sqrt{u} < \sqrt{-3v}$$ , which of the following cannot be true ?

A. $$\frac{u}{3} < -v$$

B. $$\frac{u}{v} > -3$$

C. $$\sqrt{\frac{u}{-v}} < \sqrt{3}$$

D. $$u + 3v > 0$$

E. $$u < -3v$$
[Reveal] Spoiler: OA

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Re: If u and –3v are greater than 0, and [#permalink]
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Carcass wrote:
If u and –3v are greater than 0, and $$\sqrt{u} < \sqrt{-3v}$$ , which of the following cannot be true ?

A. $$\frac{u}{3} < -v$$

B. $$\frac{u}{v} > -3$$

C. $$\sqrt{\frac{u}{-v}} < \sqrt{3}$$

D. $$u + 3v > 0$$

E. $$u < -3v$$

A quick glance through all the option, we will see that

option D which is $$u + 3v > 0$$ is not possible, so might be the answer, however lets look at the remaing option

option A :: $$\frac{u}{3} < -v$$ - This is possible if we divide by 3 on both sides

Option B:: $$\frac{u}{v} > -3$$ - This is possible, since -3v > 0 so v < 0

Option C:: $$\sqrt{\frac{u}{-v}} < \sqrt{3}$$ - It is possible by dividing $$\sqrt{-v}$$ on both sides

Option E:: $$u < -3v$$ - It is also possible by squaring on both sides.

** When the GRE writes a root sign, they are indicating a nonnegative root only**
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Manager Joined: 08 Dec 2018
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Re: If u and –3v are greater than 0, and [#permalink]
here, u>0, and -3v>0
So, u+(-3v)>0
U-3v >0
But, option D is not as above . So, D. GRE Instructor Joined: 10 Apr 2015
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Re: If u and –3v are greater than 0, and [#permalink]
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Expert's post
Carcass wrote:
If u and –3v are greater than 0, and $$\sqrt{u} < \sqrt{-3v}$$ , which of the following cannot be true ?

A. $$\frac{u}{3} < -v$$

B. $$\frac{u}{v} > -3$$

C. $$\sqrt{\frac{u}{-v}} < \sqrt{3}$$

D. $$u + 3v > 0$$

E. $$u < -3v$$

If $$\sqrt{u} < \sqrt{-3v}$$, then it must also be true that u < -3v

Hmmm, D says that u + 3v > 0
However, if we take u < -3v and add 3v to both sides, we get: u + 3v < 0, which is the OPPOSITE of what answer choice D is saying.

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com
If you enjoy my solutions, you'll like my GRE prep course. Intern Joined: 10 Apr 2020
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Re: If u and –3v are greater than 0, and [#permalink]
** When the GRE writes a root sign, they are indicating a nonnegative root only**

Can someone explain what is the exact meaning of this with an example? GRE Instructor Joined: 10 Apr 2015
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Re: If u and –3v are greater than 0, and [#permalink]
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Expert's post
ZIONGRE wrote:
** When the GRE writes a root sign, they are indicating a nonnegative root only**

Can someone explain what is the exact meaning of this with an example?

Every positive number has two square roots.
For example, the square root of 25 is 5, since 5² = 25 AND -5, since (-5)² = 25

However, the square root NOTATION tells us to indicate the non-negative root only.

So, for example:
$$\sqrt{25}=5$$
$$\sqrt{49}=7$$
$$\sqrt{0.25}=0.5$$
$$\sqrt{0}=0$$
etc

Does that help?

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com
If you enjoy my solutions, you'll like my GRE prep course.  Re: If u and –3v are greater than 0, and   [#permalink] 21 Apr 2020, 09:44
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