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If xy = 64 and x and y are positive integers, which of the f

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GMAT Club Legend
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Joined: 07 Jun 2014
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If xy = 64 and x and y are positive integers, which of the f [#permalink] New post 12 Aug 2018, 16:06
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Question Stats:

66% (01:11) correct 33% (00:07) wrong based on 6 sessions
If \(x^y = 64\) and x and y are positive integers, which of the following could be the value of x + y?

Indicate all such values.

A. 2
B. 6
C. 7
D. 8
E. 10
F. 12
[Reveal] Spoiler: OA

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GMAT Club Legend
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Joined: 07 Jun 2014
Posts: 4710
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Kudos [?]: 1612 [0], given: 375

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Re: If xy = 64 and x and y are positive integers, which of the f [#permalink] New post 15 Aug 2018, 05:26
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Explanation

If x y = 64 and x and y are positive integers, perhaps the most obvious possibility is that x = 8 and y = 2. However, “all such values” implies that other solutions are
possible. One shortcut is noting that only an even base, when raised to a power, could equal 64. So you only have to worry about even possibilities for x. Here are all the possibilities:

\(2^6 = 64\) → \(x + y = 8\)

\(4^3 = 64\) → \(x + y = 7\)

\(8^2 = 64\) → \(x + y = 10\)

\(64^1 = 64\) → \(x + y = 65\)

The only possible values of x + y listed among the choices are 7, 8, and 10.
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Re: If xy = 64 and x and y are positive integers, which of the f [#permalink] New post 15 Aug 2018, 17:06
Just list the factors of 64 in 2s and combine them to get different x and y values.
Re: If xy = 64 and x and y are positive integers, which of the f   [#permalink] 15 Aug 2018, 17:06
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If xy = 64 and x and y are positive integers, which of the f

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