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5^9 or 25^4
[#permalink]
09 May 2022, 02:00
09 May 2022, 02:00
Expert Reply
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Question Stats:
100% (00:14) correct
0% (00:00) wrong based on 8 sessions
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Quantity A |
Quantity B |
\( 5^9\) |
\(25^4\) |
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
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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
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: 5^9 or 25^4
[#permalink]
09 May 2022, 05:58
09 May 2022, 05:58
1
Carcass wrote:
Quantity A |
Quantity B |
\( 5^9\) |
\(25^4\) |
Given:
QUANTITY A: \( 5^9\)
QUANTITY B: \(25^4\)
Strategy: It's much easier to compare powers when they have the same base.
So let's rewrite \(25\) as \(5^2\) and go from there:
QUANTITY A: \( 5^9\)
QUANTITY B: \((5^2)^4\)
Apply the power of a power law to Quantity B to get:
QUANTITY A: \( 5^9\)
QUANTITY B: \(5^8\)
At this point, it's clear that Quantity A is greater.
Answer: A
Intern
Joined: 19 Mar 2022
Posts: 43
Given Kudos: 114
GRE 1: Q163 V156
Re: 5^9 or 25^4
[#permalink]
10 May 2022, 02:52
10 May 2022, 02:52
1
thumb rule to compare indices is by bringing them to its prime factors.
B can be further reduced to (5^2)^4 which is equal to 5^8
A is given as 5^9.
Hence, A is greater and so A is the answer.
B can be further reduced to (5^2)^4 which is equal to 5^8
A is given as 5^9.
Hence, A is greater and so A is the answer.
