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If xy = 64 and x and y are positive integers, which of the f
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12 Aug 2018, 16:06
12 Aug 2018, 16:06
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65% (01:05) correct
34% (00:47) wrong based on 70 sessions
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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
Indicate all such values.
A. 2
B. 6
C. 7
D. 8
E. 10
F. 12
Re: If xy = 64 and x and y are positive integers, which of the f
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15 Aug 2018, 05:26
15 Aug 2018, 05:26
Expert Reply
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.
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
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15 Aug 2018, 17:06
15 Aug 2018, 17:06
Just list the factors of 64 in 2s and combine them to get different x and y values.
