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If x > y and x < 0, then which of the following must be true

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If x > y and x < 0, then which of the following must be true [#permalink] New post   28 Mar 2019, 13:27
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If \(x > y\) and \(x < 0\), then which of the following must be true?

(I) \(\frac{1}{x} < \frac{1}{y}\)

(II) \(\frac{1}{x−1} < \frac{1}{y−1}\)

(III) \(\frac{1}{x+1} < \frac{1}{y+1}\)

(A) I only

(B) II only

(C) III only

(D) I and II only

(E) I and III only
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D
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rmarea7
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Re: If x > y and x < 0, then which of the following must be true [#permalink] New post   16 Jan 2020, 19:46
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Seems we can safely exclude (iii) from the answer, because,
- Given x < 0, x could be -1.
- In (iii), we 1/(x+1), which if x =-1, equals, 1/(-1+1) = 1/0 = undefined and breaks the inequality.

Meanwhile, we do not have the above problem with (ii) because since x is a negative, (x-1) will become more negative and respects the initial condition of the inequality whereby x < 0.
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Re: If x > y and x < 0, then which of the following must be true [#permalink] New post   07 Oct 2024, 12:40
Carcass wrote:
If \(x > y\) and \(x < 0\), then which of the following must be true?

(I) \(\frac{1}{x} < \frac{1}{y}\)

(II) \(\frac{1}{x−1} < \frac{1}{y−1}\)

(III) \(\frac{1}{x+1} < \frac{1}{y+1}\)

(A) I only

(B) II only

(C) III only

(D) I and II only

(E) I and III only

The question mentions which one of the following *must be* true but if in case we take x=-2 and y=-3 it invalidates the *must be* condition even though in case x =-1 could cause the third inequality to be true but again, it's conditional here, could you please explain how D is correct?
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Re: If x > y and x < 0, then which of the following must be true [#permalink] New post   07 Oct 2024, 22:28
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As you said if x=-2 and y=-3 then we do have \(-\frac{1}{2}<-\frac{1}{3}\) which is true on the number line on the LHS of zero

\(-\frac{1}{2}=-0.5\)

\(-\frac{1}{3}=-0.33\)

A is true always
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gmatclubot
Re: If x > y and x < 0, then which of the following must be true [#permalink]
07 Oct 2024, 22:28
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