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# If x and y are non-zero numbers such that x>y, which of the following

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Manager
Joined: 11 Dec 2013
Posts: 107
Location: India
GMAT Date: 03-15-2015
WE: Education (Education)
If x and y are non-zero numbers such that x>y, which of the following  [#permalink]

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27 Jan 2019, 23:36
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85% (hard)

Question Stats:

33% (01:48) correct 67% (01:46) wrong based on 73 sessions

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If x and y are non-zero numbers such that x > y, which of the following is always true?

A) $$\frac{1}{x} < \frac{1}{y}$$

B) $$\frac{x}{y} > 1$$

C) $$|x| > |y|$$

D) $$\frac{1}{xy^2} < \frac{1}{x^2y}$$

E) $$\frac{x}{y} < \frac{y}{x}$$

_________________

Director
Joined: 09 Mar 2018
Posts: 909
Location: India
If x and y are non-zero numbers such that x>y, which of the following  [#permalink]

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28 Jan 2019, 08:59
4d wrote:
If x and y are non-zero numbers such that x > y, which of the following is always true?

A) $$\frac{1}{x} < \frac{1}{y}$$

B) $$\frac{x}{y} > 1$$

C) $$|x| > |y|$$

D) $$\frac{1}{xy^2} < \frac{1}{x^2y}$$

E) $$\frac{x}{y} < \frac{y}{x}$$

IMO D

Just test values, Given x > y
If x and y are non-zero numbers
Test values : 2> 1 or -1 > -2

A) $$\frac{1}{x} < \frac{1}{y}$$, To avoid any confusion, always do this.

$$\frac{1}{y} > \frac{1}{x}$$, this works for me

C1: 1 > 0.5, Yes
C2: -1 > -0.5 No

B) $$\frac{x}{y} > 1$$

C1: 2 > 1 Yes
C2: 0.5 > 1 No

C) $$|x| > |y|$$
This will give multiple values

D) $$\frac{1}{xy^2} < \frac{1}{x^2y}$$, same here as well

$$\frac{1}{x^2y} > \frac{1}{xy^2}$$

For any set of values, Here i am always getting a No.

E) $$\frac{x}{y} < \frac{y}{x}$$[/quote], same here as well

$$\frac{y}{x} > \frac{x}{y}$$[/quote]

Here you can get a Yes and a No
_________________

If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.

Intern
Joined: 01 Jan 2017
Posts: 13
Re: If x and y are non-zero numbers such that x>y, which of the following  [#permalink]

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30 Jan 2019, 02:55
4d wrote:
If x and y are non-zero numbers such that x > y, which of the following is always true?

A) $$\frac{1}{x} < \frac{1}{y}$$

B) $$\frac{x}{y} > 1$$

C) $$|x| > |y|$$

D) $$\frac{1}{xy^2} < \frac{1}{x^2y}$$

E) $$\frac{x}{y} < \frac{y}{x}$$

Can someone tell me why C is wrong
Director
Joined: 18 Jul 2018
Posts: 670
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Re: If x and y are non-zero numbers such that x>y, which of the following  [#permalink]

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30 Jan 2019, 03:04
AlN wrote:
4d wrote:
If x and y are non-zero numbers such that x > y, which of the following is always true?

A) $$\frac{1}{x} < \frac{1}{y}$$

B) $$\frac{x}{y} > 1$$

C) $$|x| > |y|$$

D) $$\frac{1}{xy^2} < \frac{1}{x^2y}$$

E) $$\frac{x}{y} < \frac{y}{x}$$

Can someone tell me why C is wrong

If you take x as -2 and y as -3. We can see that x > y as -2 > -3. But |x| = 2 and |y| = 3. And |x| is not greater than |y|.

Hence C is wrong

Posted from my mobile device
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Intern
Joined: 24 Nov 2018
Posts: 2
Re: If x and y are non-zero numbers such that x>y, which of the following  [#permalink]

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30 Jan 2019, 07:19
KanishkM wrote:
4d wrote:
If x and y are non-zero numbers such that x > y, which of the following is always true?

A) $$\frac{1}{x} < \frac{1}{y}$$

B) $$\frac{x}{y} > 1$$

C) $$|x| > |y|$$

D) $$\frac{1}{xy^2} < \frac{1}{x^2y}$$

E) $$\frac{x}{y} < \frac{y}{x}$$

IMO D

Just test values, Given x > y
If x and y are non-zero numbers
Test values : 2> 1 or -1 > -2

A) $$\frac{1}{x} < \frac{1}{y}$$, To avoid any confusion, always do this.

$$\frac{1}{y} > \frac{1}{x}$$, this works for me

C1: 1 > 0.5, Yes
C2: -1 > -0.5 No

B) $$\frac{x}{y} > 1$$

C1: 2 > 1 Yes
C2: 0.5 > 1 No

C) $$|x| > |y|$$
This will give multiple values

D) $$\frac{1}{xy^2} < \frac{1}{x^2y}$$, same here as well

$$\frac{1}{x^2y} > \frac{1}{xy^2}$$

For any set of values, Here i am always getting a No.

E) $$\frac{x}{y} < \frac{y}{x}$$
, same here as well

$$\frac{y}{x} > \frac{x}{y}$$[/quote]

Here you can get a Yes and a No[/quote]

If D is giving a NO with every set of values of x and y. How come is D the right answer?
Isnt te question stem asking for an option which is always true??
Director
Joined: 09 Mar 2018
Posts: 909
Location: India
Re: If x and y are non-zero numbers such that x>y, which of the following  [#permalink]

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30 Jan 2019, 11:24
hannan4644 wrote:
KanishkM wrote:
4d wrote:
If x and y are non-zero numbers such that x > y, which of the following is always true?

A) $$\frac{1}{x} < \frac{1}{y}$$

B) $$\frac{x}{y} > 1$$

C) $$|x| > |y|$$

D) $$\frac{1}{xy^2} < \frac{1}{x^2y}$$

E) $$\frac{x}{y} < \frac{y}{x}$$

IMO D

Just test values, Given x > y
If x and y are non-zero numbers
Test values : 2> 1 or -1 > -2

A) $$\frac{1}{x} < \frac{1}{y}$$, To avoid any confusion, always do this.

$$\frac{1}{y} > \frac{1}{x}$$, this works for me

C1: 1 > 0.5, Yes
C2: -1 > -0.5 No

B) $$\frac{x}{y} > 1$$

C1: 2 > 1 Yes
C2: 0.5 > 1 No

C) $$|x| > |y|$$
This will give multiple values

D) $$\frac{1}{xy^2} < \frac{1}{x^2y}$$, same here as well

$$\frac{1}{x^2y} > \frac{1}{xy^2}$$

For any set of values, Here i am always getting a No.

E) $$\frac{x}{y} < \frac{y}{x}$$
, same here as well

$$\frac{y}{x} > \frac{x}{y}$$

Here you can get a Yes and a No[/quote]

If D is giving a NO with every set of values of x and y. How come is D the right answer?
Isnt te question stem asking for an option which is always true??[/quote]

Though i am not an expert, but i believe if we look at the rest of the options, we are able to negate this option completely with the same test cases.

What one can try is to look for other options which will satisfy D, for different test cases.

But i doubt that will happen, under the stipulated time limit of trying to solve a question in 2-3 minutes.

Let me know if this helps you in anyway

Posted from my mobile device
_________________

If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.

Intern
Status: when you say,"I can or I can't", Both times you are right!
Joined: 26 Nov 2018
Posts: 9
If x and y are non-zero numbers such that x>y, which of the following  [#permalink]

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03 Feb 2019, 06:15
hannan4644 wrote:
KanishkM wrote:
4d wrote:
If x and y are non-zero numbers such that x > y, which of the following is always true?

A) $$\frac{1}{x} < \frac{1}{y}$$

B) $$\frac{x}{y} > 1$$

C) $$|x| > |y|$$

D) $$\frac{1}{xy^2} < \frac{1}{x^2y}$$

E) $$\frac{x}{y} < \frac{y}{x}$$

IMO D

Just test values, Given x > y
If x and y are non-zero numbers
Test values : 2> 1 or -1 > -2

A) $$\frac{1}{x} < \frac{1}{y}$$, To avoid any confusion, always do this.

$$\frac{1}{y} > \frac{1}{x}$$, this works for me

C1: 1 > 0.5, Yes
C2: -1 > -0.5 No

B) $$\frac{x}{y} > 1$$

C1: 2 > 1 Yes
C2: 0.5 > 1 No

C) $$|x| > |y|$$
This will give multiple values

D) $$\frac{1}{xy^2} < \frac{1}{x^2y}$$, same here as well

$$\frac{1}{x^2y} > \frac{1}{xy^2}$$

For any set of values, Here I am always getting a No.

E) $$\frac{x}{y} < \frac{y}{x}$$
, same here as well

$$\frac{y}{x} > \frac{x}{y}$$

Take X=100
Y=1

how can D be the Answer?
Intern
Joined: 01 Nov 2018
Posts: 15
Re: If x and y are non-zero numbers such that x>y, which of the following  [#permalink]

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03 Feb 2019, 07:56
KanishkM wrote:
4d wrote:
If x and y are non-zero numbers such that x > y, which of the following is always true?

A) $$\frac{1}{x} < \frac{1}{y}$$

B) $$\frac{x}{y} > 1$$

C) $$|x| > |y|$$

D) $$\frac{1}{xy^2} < \frac{1}{x^2y}$$

E) $$\frac{x}{y} < \frac{y}{x}$$

IMO D

Just test values, Given x > y
If x and y are non-zero numbers
Test values : 2> 1 or -1 > -2

A) $$\frac{1}{x} < \frac{1}{y}$$, To avoid any confusion, always do this.

$$\frac{1}{y} > \frac{1}{x}$$, this works for me

C1: 1 > 0.5, Yes
C2: -1 > -0.5 No

B) $$\frac{x}{y} > 1$$

C1: 2 > 1 Yes
C2: 0.5 > 1 No

C) $$|x| > |y|$$
This will give multiple values

D) $$\frac{1}{xy^2} < \frac{1}{x^2y}$$, same here as well

$$\frac{1}{x^2y} > \frac{1}{xy^2}$$

For any set of values, Here i am always getting a No.

E) $$\frac{x}{y} < \frac{y}{x}$$
, same here as well

$$\frac{y}{x} > \frac{x}{y}$$[/quote]

Here you can get a Yes and a No[/quote]

In A you haven't done it correct. It should be -0.5>-1 after reciprocal which is a yes.

Also in D, it can be proven wrong if we take 5 & -5
Director
Joined: 18 Jul 2018
Posts: 670
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Re: If x and y are non-zero numbers such that x>y, which of the following  [#permalink]

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03 Feb 2019, 07:59
None of the options is correct. All give Yes or No as answers.
_________________

Press +1 Kudo If my post helps!

Intern
Joined: 01 Jan 2017
Posts: 13
Re: If x and y are non-zero numbers such that x>y, which of the following  [#permalink]

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03 Feb 2019, 08:01
1
Afc0892 wrote:
AlN wrote:
4d wrote:
If x and y are non-zero numbers such that x > y, which of the following is always true?

A) $$\frac{1}{x} < \frac{1}{y}$$

B) $$\frac{x}{y} > 1$$

C) $$|x| > |y|$$

D) $$\frac{1}{xy^2} < \frac{1}{x^2y}$$

E) $$\frac{x}{y} < \frac{y}{x}$$

Can someone tell me why C is wrong

If you take x as -2 and y as -3. We can see that x > y as -2 > -3. But |x| = 2 and |y| = 3. And |x| is not greater than |y|.

Hence C is wrong

Posted from my mobile device

Thank you Got it!
Re: If x and y are non-zero numbers such that x>y, which of the following   [#permalink] 03 Feb 2019, 08:01
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