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# If x > y, then which of the following could be true?

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If x > y, then which of the following could be true? [#permalink]  19 Oct 2019, 02:16
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Question Stats:

55% (00:54) correct 44% (01:50) wrong based on 9 sessions
If $$x > y$$, then which of the following could be true?

I. $$|x||y|x<|xy|y$$
II. $$|x||y|x>|xy|y$$
III. $$|x||y|x=−|xy|y$$

(a) I only
(b) II only
(c) III only
(d) I and II only
(e) I, II, and III

Last edited by Carcass on 20 Oct 2019, 00:08, edited 3 times in total.
Edited by Carcass
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WE: Engineering (Energy and Utilities)
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Re: If x > y, then which of the following could be true? [#permalink]  21 Oct 2019, 23:07
1
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sanna14 wrote:
If $$x > y$$, then which of the following could be true?

I. $$|x||y|x<|xy|y$$
II. $$|x||y|x>|xy|y$$
III. $$|x||y|x=−|xy|y$$

(a) I only
(b) II only
(c) III only
(d) I and II only
(e) I, II, and III

*** Kindly mention the source in your present and future post. Plz don't forget to mention the Official answer
Here,
since, we don't what is x and y , so we have two take all possible values:

Let x and y be positive integer, such that x = 2 and y = 1

Put the values in |x||y|x and |xy|y

|x||y|x = 2 * 1 * 2 = 4

and |xy|y = 2*1 * 1 = 2

SO, |x||y|x > |xy|y

Let x and y be negative integer, such that x = -1 and y = -2

Put the values in |x||y|x and |xy|y

|x||y|x = 1 * 2 * -1 = -2

and |xy|y = 2*1 * -2 = -4

SO, |x||y|x>|xy|y

Let x and y be fraction, such that x = 0.5 and y = -0.1

Put the values in |x||y|x and |xy|y

|x||y|x = 0.5 * 0.1 * 0.5 = 0.025

and |xy|y = 0.5*0.1 * -0.1 = -0.005

SO, |x||y|x>|xy|y

Hence, we have tried out different possibilities and only option II is feasible.
Option B
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Re: If x > y, then which of the following could be true? [#permalink]  16 Sep 2020, 00:36
2
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I think the options are wrong. Both 2 and 3 are possible. Since the question asks for could be true, means we need to find one case where it is true.

As we know, by property,

|x||y| = |xy|

Therefore,

1. Can never be true.
2. Is true always
3. Is true when y = -x. In this case, x > y and |x||y|x = -|x||y|y, therefore 3 holds too.

Therefore, both option 2 and 3 are correct.
Re: If x > y, then which of the following could be true?   [#permalink] 16 Sep 2020, 00:36
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