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x>0
[#permalink]
09 May 2022, 02:00
09 May 2022, 02:00
Expert Reply
00:00
Question Stats:
85% (00:43) correct
14% (00:22) wrong based on 7 sessions
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\(x>0\)
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
Quantity A |
Quantity B |
\(7 \sqrt{x}\) |
\(\sqrt{ 3x}\) |
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
Part of the project: GRE Quantitative Comparison & Problem Solving Challenge
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
GRE - Math Book
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
GRE - Math Book
Intern
Joined: 19 Mar 2022
Posts: 43
Given Kudos: 114
GRE 1: Q163 V156
Re: x>0
[#permalink]
10 May 2022, 03:06
10 May 2022, 03:06
1
in A, take 7 inside the root sign. this makes it sq rt (49x)
B is sr rt (3x)
Hence, A is greater.
B is sr rt (3x)
Hence, A is greater.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
x>0
[#permalink]
10 May 2022, 05:49
10 May 2022, 05:49
1
Carcass wrote:
\(x>0\)
Quantity A |
Quantity B |
\(7 \sqrt{x}\) |
\(\sqrt{ 3x}\) |
Key property #1: \(\sqrt{a} < \sqrt{b}\) if and only if \(0 < a < b\)
Key property #2: \((\sqrt{x})(\sqrt{y}) = \sqrt{xy}\)
Quantity A: \(7 \sqrt{x} = (\sqrt{49})(\sqrt{x})= \sqrt{49x}\)
Quantity B: \(\sqrt{ 3x}\)
If x is positive (which it is), then \(49x > 3x\), which means \(\sqrt{49x} > \sqrt{3x}\)
Answer: A
