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

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

76% (01:08) correct 23% (00:39) wrong based on 26 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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Retired Moderator
Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 171

Kudos [?]: 2915 [0], given: 394

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