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If x > y and 1/x < 1/y, which of the following could be true:
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Bunuel
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If x > y and 1/x < 1/y, which of the following could be true: [#permalink] New post  01 Nov 2019, 05:26
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If \(x > y\) and \(\frac{1}{x} < \frac{1}{y}\), which of the following could be true:

I. \(0 < x < 1\) and \(0 < y < 1\)
II. \(xy < 0\)
III. \(-1 < x < 0\) and \(-1 < y < 0\)

A. I only
B. I only II only
C. II only III only
D. I only III only
E. I, II, and III


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chetan2u
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If x > y and 1/x < 1/y, which of the following could be true: [#permalink] New post  01 Nov 2019, 07:54
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Bunuel wrote:
If \(x > y\) and \(\frac{1}{x} < \frac{1}{y}\), which of the following could be true:

I. \(0 < x < 1\) and \(0 < y < 1\)
II. \(xy < 0\)
III. \(-1 < x < 0\) and \(-1 < y < 0\)

A. I only
B. I only II only
C. II only III only
D. I only III only
E. I, II, and III


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A very straight forward answer will be
\(x > y\) and \(\frac{1}{x} < \frac{1}{y}\), that is cross-multiplication is NOT changing the sign. MEANS both x and y have SAME sign or xy>0.
I. \(0 < x < 1\) and \(0 < y < 1\)...xy>0..YES
II. \(xy < 0\)...NO
III. \(-1 < x < 0\) and \(-1 < y < 0\)...xy>0..YES

I and III

D

OR



Choose values...
I. \(0 < x < 1\) and \(0 < y < 1\)..........x=0.9 and y=0.3...0.9>0.3 and \(\frac{1}{0.3}>\frac{1}{0.9}\)..\(\frac{10}{3}>\frac{10}{9}\)...YES
II. \(xy < 0\)....x=2 and y=-1...2>-1 but 1/2>1/-1...Eliminate
III. \(-1 < x < 0\) and \(-1 < y < 0\)....x=-0.3 and y=-0.9...-0.3>-0.9 and \(-\frac{1}{0.3}>-\frac{1}{0.9}\)..\(\frac{10}{3}>\frac{10}{9}\)...YES
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Archit3110
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Re: If x > y and 1/x < 1/y, which of the following could be true: [#permalink] New post  02 Nov 2019, 02:15
for given condition
\(x > y\) and \(\frac{1}{x} < \frac{1}{y}\)

we can test with integers and fractions ; ( 2,3) ( 1/2,1/3) & ( -1/2,-1/3)
\(0 < x < 1\) and \(0 < y < 1\)
\(-1 < x < 0\) and \(-1 < y < 0\)
true
IMO D;

Bunuel wrote:
If \(x > y\) and \(\frac{1}{x} < \frac{1}{y}\), which of the following could be true:

I. \(0 < x < 1\) and \(0 < y < 1\)
II. \(xy < 0\)
III. \(-1 < x < 0\) and \(-1 < y < 0\)

A. I only
B. I only II only
C. II only III only
D. I only III only
E. I, II, and III


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metalhead2593
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Joined: 14 Jul 2019
Posts: 34
Re: If x > y and 1/x < 1/y, which of the following could be true: [#permalink] New post  29 Feb 2020, 09:09
Bunuel wrote:
If \(x > y\) and \(\frac{1}{x} < \frac{1}{y}\), which of the following could be true:

I. \(0 < x < 1\) and \(0 < y < 1\)
II. \(xy < 0\)
III. \(-1 < x < 0\) and \(-1 < y < 0\)

A. I only
B. I only II only
C. II only III only
D. I only III only
E. I, II, and III



1/x<1/y
So (y-x)/xy <0

We know that x>y, so y-x <0. xy must be positive (>0).
So, either x,y >0 or x,y <0

I. Yes
II. NO
III. Yes

IMO D.
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Kinshook
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Re: If x > y and 1/x < 1/y, which of the following could be true: [#permalink] New post  28 Mar 2020, 03:04
Bunuel wrote:
If \(x > y\) and \(\frac{1}{x} < \frac{1}{y}\), which of the following could be true:

I. \(0 < x < 1\) and \(0 < y < 1\)
II. \(xy < 0\)
III. \(-1 < x < 0\) and \(-1 < y < 0\)

A. I only
B. I only II only
C. II only III only
D. I only III only
E. I, II, and III


Are You Up For the Challenge: 700 Level Questions


If \(x > y\) and \(\frac{1}{x} < \frac{1}{y}\), which of the following could be true:
x>y
1/y -1/x > 0
(x-y)/xy>0
Since x-y>0
xy>0

I. \(0 < x < 1\) and \(0 < y < 1\)
xy>0; COULD BE TRUE
II. \(xy < 0\)
MUST NOT BE TRUE
III. \(-1 < x < 0\) and \(-1 < y < 0\)
xy>0; COULD BE TRUE

IMO D
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Biplob12345
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Re: If x > y and 1/x < 1/y, which of the following could be true: [#permalink] New post  27 Nov 2020, 06:25
Given that xy>0 and x>y, which of the followingmust be true?
A.x+y>0
B.x^2+y^2>xy
C.x^2-y^2>0
seeking Detail solution Thank you

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Re: If x > y and 1/x < 1/y, which of the following could be true: [#permalink]
27 Nov 2020, 06:25
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