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5^3 - 5^2

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GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4720
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1622 [0], given: 385

CAT Tests
5^3 - 5^2 [#permalink] New post 19 May 2018, 12:00
Expert's post
00:00

Question Stats:

92% (00:08) correct 7% (00:16) wrong based on 14 sessions
Quantity A
Quantity B
\(5^3 - 5^2\)
\(5\)


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Sandy
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GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4720
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1622 [0], given: 385

CAT Tests
Re: 5^3 - 5^2 [#permalink] New post 28 May 2018, 13:07
Expert's post
Explanation

Do not make the mistake of thinking that \(5^3 - 5^2 = 5^1\).

You cannot just subtract the exponents when you are subtracting two terms with the same base! Instead, compute the exponents and subtract:

\(5^3 - 5^2 = 125 - 25 = 100\)

Quantity A is greater. Alternatively, you could factor out 52 (this is an important technique for large numbers and exponents where pure arithmetic would be impractical):

\(53 - 52 = 52(5^1 - 1) = 5^2(4) = 100\)

Hence option A is correct!
_________________

Sandy
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Re: 5^3 - 5^2   [#permalink] 28 May 2018, 13:07
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5^3 - 5^2

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