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Manager  G
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GMAT Date: 03-15-2015
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If x and y are non-zero numbers such that x>y, which of the following  [#permalink]

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Question Stats: 34% (01:43) correct 66% (01:51) 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) $$\frac{x}{y} < \frac{y}{x}$$

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

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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
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Manager  B
Joined: 02 Jan 2017
Posts: 59
Location: India
Schools: Oxford "21
Re: If x and y are non-zero numbers such that x>y, which of the following  [#permalink]

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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
NUS School Moderator V
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Re: If x and y are non-zero numbers such that x>y, which of the following  [#permalink]

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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  B
Joined: 25 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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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  G
Joined: 09 Mar 2018
Posts: 994
Location: India
Re: If x and y are non-zero numbers such that x>y, which of the following  [#permalink]

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

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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

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

D cannot be the answer.

Take X=100
Y=1

how can D be the Answer?
Intern  B
Joined: 01 Nov 2018
Posts: 30
Re: If x and y are non-zero numbers such that x>y, which of the following  [#permalink]

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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
NUS School Moderator V
Joined: 18 Jul 2018
Posts: 1020
Location: India
Concentration: Finance, Marketing
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Re: If x and y are non-zero numbers such that x>y, which of the following  [#permalink]

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None of the options is correct. All give Yes or No as answers.
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Manager  B
Joined: 02 Jan 2017
Posts: 59
Location: India
Schools: Oxford "21
Re: If x and y are non-zero numbers such that x>y, which of the following  [#permalink]

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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!
SVP  P
Joined: 03 Jun 2019
Posts: 1756
Location: India
If x and y are non-zero numbers such that x>y, which of the following  [#permalink]

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

Given: x and y are non-zero numbers such that x > y

Asked: Which of the following is always true?

A) $$\frac{1}{x} < \frac{1}{y}$$
If xy>0 ; $$\frac{1}{x} < \frac{1}{y}$$
If xy<0 ; $$\frac{1}{x} > \frac{1}{y}$$
3>2 => 1/3<1/2 YES
-2>-3 => -1/2<-1/3 YES
3>-2 => 1/3<-1/2 NO
NOT NECESSARILY TRUE

B) $$\frac{x}{y} > 1$$
If y>0 x/y >1 ; 3>2 => 3/2 > 1 YES
If y<0 x/y <1 ; 3>-2 => -3/2>1 NO
NOT NECESSARILY TRUE

C) $$|x| > |y|$$
3>2 => |3|>|2| YES
-2>-3 => |-2| > |-3| => 2>3 NO
NOT NECESSARILY TRUE

D) $$\frac{1}{xy^2} < \frac{1}{x^2y}$$
$$\frac{1}{xy^2} < \frac{1}{x^2y}$$
Multiplying both sides by$$x^2y^2$$
x>y TRUE
MUST BE TRUE

E) $$\frac{x}{y} < \frac{y}{x}$$
3>2 => 3/2 < 2/3 NO
NOT NECESSARILY TRUE

IMO D
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Re: If x and y are non-zero numbers such that x>y, which of the following  [#permalink]

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

This is a flawed question. None of the options is always true.

D cannot be the answer because it's never true if x > y. Check x = 2 and y = 1.

TOPIC IS LOCKED.
_________________ Re: If x and y are non-zero numbers such that x>y, which of the following   [#permalink] 18 Aug 2019, 23:58
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