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m >1
[#permalink]
05 May 2022, 06:26
05 May 2022, 06:26
Expert Reply
00:00
Question Stats:
87% (00:36) correct
12% (00:17) wrong based on 24 sessions
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\(m >1\)
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 |
\(\sqrt{m^{12}} \) |
\( (m^2)^5\) |
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
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Posts: 6218
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Re: m >1
[#permalink]
05 May 2022, 07:20
05 May 2022, 07:20
1
Carcass wrote:
\(m >1\)
Quantity A |
Quantity B |
\(\sqrt{m^{12}} \) |
\( (m^2)^5\) |
Key concept: If \(x > 0\), then \(\sqrt{x} = x^{\frac{1}{2}}\)
So, we can rewrite Quantity A as follows:
QUANTITY A: \((m^{12})^{\frac{1}{2}}\)
QUANTITY B: \( (m^2)^5\)
Apply the power of a power law to both quantities to get:
QUANTITY A: \(m^{6}\)
QUANTITY B: \(m^{10}\)
Since \(m > 1\), we can be certain that Quantity B is greater.
Re: m >1
[#permalink]
05 May 2022, 11:38
05 May 2022, 11:38
2
Option A = sq m^12 = m ^ 12/2 = m^6
Option B = (m^2)^5 = m ^ 2*5 = m^ 10
Since m>1, option B > A, hence the correct ans
Option B = (m^2)^5 = m ^ 2*5 = m^ 10
Since m>1, option B > A, hence the correct ans
