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If 1 < x < y, which of the following must be true?

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Carcass
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If 1 < x < y, which of the following must be true? [#permalink] New post   29 Nov 2021, 05:53
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If \(1 < x < y\), which of the following must be true?

(A) \(−x^2 < −y^2\)

(B) \(\frac{x}{y} < \frac{y}{x}\)

(C) \(\frac{y}{x} < \frac{x}{y}\)

(D) \(\frac{−x}{y} < −\frac{y}{x}\)

(E) \(x^2 > y^2\)
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Re: If 1 < x < y, which of the following must be true? [#permalink] New post   29 Nov 2021, 06:28
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Carcass wrote:
If \(1 < x < y\), which of the following must be true?

(A) \(−x^2 < −y^2\)

(B) \(\frac{x}{y} < \frac{y}{x}\)

(C) \(\frac{y}{x} < \frac{x}{y}\)

(D) \(\frac{−x}{y} < −\frac{y}{x}\)

(E) \(x^2 > y^2\)

When I scan the answer choices, I see that B and C are saying the opposite thing. This leads me to believe that the correct answer is either B or C. Let's find out....

If x and y are both POSITIVE, and x is less than y, we know that y/x is greater than 1, and x/y is less than 1.
In other words we can write: x/y < 1 < y/x, which means we can conclude that x/y < y/x

Answer: B
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gmatclubot
Re: If 1 < x < y, which of the following must be true? [#permalink]
29 Nov 2021, 06:28
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