GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
x>0, y>0, z>0
[#permalink]
Updated on: 07 Oct 2020, 03:34
Updated on: 07 Oct 2020, 03:34
1
2
Bookmarks
00:00
Question Stats:
62% (00:48) correct
37% (00:50) wrong based on 98 sessions
Hide Show timer Statistics
\(x>0 \)
\(y>0\)
\(z>0\)
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
\(y>0\)
\(z>0\)
Quantity A |
Quantity B |
\(\frac{\sqrt{yx} \sqrt{x} }{\sqrt{y}}\) |
\(\frac{\sqrt{z}}{\sqrt{x^{-2}z}}\) |
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
x>0, y>0, z>0
[#permalink]
07 Oct 2020, 05:39
07 Oct 2020, 05:39
1
1
Bookmarks
Farina wrote:
\(x>0 \)
\(y>0\)
\(z>0\)
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
\(y>0\)
\(z>0\)
Quantity A |
Quantity B |
\(\frac{\sqrt{yx} \sqrt{x} }{\sqrt{y}}\) |
\(\frac{\sqrt{z}}{\sqrt{x^{-2}z}}\) |
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
We can solve this question using matching operations (my favorite Quantitative Comparison strategy)
Key property: \((\sqrt{x})(\sqrt{y}) = \sqrt{xy}\)
Given:
Quantity A: \(\frac{\sqrt{yx} \sqrt{x} }{\sqrt{y}}\)
Quantity B: \(\frac{\sqrt{z}}{\sqrt{x^{-2}z}}\)
Multiply both quantities by \(\sqrt{y}\) to get:
Quantity A: \((\sqrt{yx})(\sqrt{x})\)
Quantity B: \(\frac{(\sqrt{z})(\sqrt{y})}{\sqrt{x^{-2}z}}\)
Multiply both quantities by \(\sqrt{x^{-2}z}\) to get:
Quantity A: \((\sqrt{yx})(\sqrt{x})(\sqrt{x^{-2}z})\)
Quantity B: \((\sqrt{z})(\sqrt{y})\)
Apply the above property to get:
Quantity A: \(\sqrt{(yx)(x)(x^{-2}z)}\)
Quantity B: \(\sqrt{yz}\)
Simplify:
Quantity A: \(\sqrt{yz}\)
Quantity B: \(\sqrt{yz}\)
Answer: C
RELATED VIDEO
General Discussion
Re: x>0, y>0, z>0
[#permalink]
07 Oct 2020, 04:06
07 Oct 2020, 04:06
Thanks @Carcass for editing. I was confused in this question but while typing the confusion I got my answer 
