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# If x > y and 1/x < 1/y, which of the following could be true:

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Math Expert
Joined: 02 Sep 2009
Posts: 64134
If x > y and 1/x < 1/y, which of the following could be true:  [#permalink]

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01 Nov 2019, 05:26
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Difficulty:

75% (hard)

Question Stats:

56% (02:03) correct 44% (02:05) wrong based on 137 sessions

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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

Are You Up For the Challenge: 700 Level Questions

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 8589
If x > y and 1/x < 1/y, which of the following could be true:  [#permalink]

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01 Nov 2019, 07:54
2
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

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

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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

Are You Up For the Challenge: 700 Level Questions
Intern
Joined: 14 Jul 2019
Posts: 34
Re: If x > y and 1/x < 1/y, which of the following could be true:  [#permalink]

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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.
CEO
Joined: 03 Jun 2019
Posts: 2890
Location: India
GMAT 1: 690 Q50 V34
WE: Engineering (Transportation)
Re: If x > y and 1/x < 1/y, which of the following could be true:  [#permalink]

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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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Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com
Re: If x > y and 1/x < 1/y, which of the following could be true:   [#permalink] 28 Mar 2020, 03:04