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If a, b, x, and y are positive integers,
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26 Aug 2021, 05:28
26 Aug 2021, 05:28
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If a, b, x, and y are positive integers, and \(13^a\) x \(13^b\)=\({13^x}^y\)=\(13^{13}\), what is the average (arithmetic mean) of a, b, x, and y?
Give your answer as a decimal.
Give your answer as a decimal.
Show: ::
6.75
Re: If a, b, x, and y are positive integers,
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26 Aug 2021, 07:55
26 Aug 2021, 07:55
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\(a, b, x,\) and \(y\) are positive integers
\(13^a\) x \(13^b\)=\({13^x}^y\)=\(13^{13}\)
\(13^{a+b} = 13^{xy} = 13^{13}\)
\(a + b = 13\) & \(xy = 13\)
The only possibility for \(x\) & \(y\) is \(13\) & \(1\) (All are integers)
Average = \(\frac{a + y + x + b}{4}\)
= \(\frac{13 + 13 + 1}{4} = \frac{27}{4} = 6.75\)
Answer 6.75
\(13^a\) x \(13^b\)=\({13^x}^y\)=\(13^{13}\)
\(13^{a+b} = 13^{xy} = 13^{13}\)
\(a + b = 13\) & \(xy = 13\)
The only possibility for \(x\) & \(y\) is \(13\) & \(1\) (All are integers)
Average = \(\frac{a + y + x + b}{4}\)
= \(\frac{13 + 13 + 1}{4} = \frac{27}{4} = 6.75\)
Answer 6.75
Re: If a, b, x, and y are positive integers,
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27 Aug 2024, 10:20
27 Aug 2024, 10:20
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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