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x/y>1
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02 Sep 2024, 08:05
02 Sep 2024, 08:05
Expert Reply
00:00
Question Stats:
66% (01:49) correct
33% (00:40) wrong based on 3 sessions
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\(\frac{x}{y}>1\)
Quantity A |
Quantity B |
\( \frac{x}{y} + \frac{y}{x}\) |
\( 2\) |
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Re: x/y>1
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02 Sep 2024, 10:05
02 Sep 2024, 10:05
1
Since \(\frac{x}{y}>1\), let us write: \(\frac{x}{y}=1+k\), where \(k\) is a positive quantity.
\(\frac{x}{y}+\frac{y}{x} = 1+k + \frac{1}{1+k}\)
\(= \frac{(1+k)^2 +1}{1+k}\)
\(= \frac{(2+2k)+k^2 }{1+k}\)
\(=2 + \frac{k^2 }{1+k} > 2 \) because k is positive.
Hence, A is correct.
\(\frac{x}{y}+\frac{y}{x} = 1+k + \frac{1}{1+k}\)
\(= \frac{(1+k)^2 +1}{1+k}\)
\(= \frac{(2+2k)+k^2 }{1+k}\)
\(=2 + \frac{k^2 }{1+k} > 2 \) because k is positive.
Hence, A is correct.
gmatclubot
Re: x/y>1 [#permalink]
02 Sep 2024, 10:05
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