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

Question

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

KanishkM · Answer

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

AlN · Answer

Can someone tell me why C is wrong

Chethan92 · Answer

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

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hannan4644 · Answer

, same here as well

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

Here you can get a Yes and a No

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??

KanishkM · Answer

Here you can get a Yes and a No 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?? 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

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Rupesh1Nonly · Answer

D cannot be the answer.

Take X=100
 Y=1

how can D be the Answer?

surbhi1991 · Answer

, same here as well

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

Here you can get a Yes and a No

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

Chethan92 · Answer

None of the options is correct. All give Yes or No as answers.

AlN · Answer

Thank you

Got it!

Kinshook · Answer

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

Bunuel · Answer

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.

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

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