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# If x and y are both positive numbers, is x/y > y/x?

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Math Expert
Joined: 02 Sep 2009
Posts: 52161
If x and y are both positive numbers, is x/y > y/x?  [#permalink]

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26 Mar 2018, 22:17
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Difficulty:

35% (medium)

Question Stats:

74% (01:12) correct 26% (01:57) wrong based on 31 sessions

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If x and y are both positive numbers, is x/y > y/x?

(1) 4y/x = 5
(2) x +4 = y

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Joined: 20 Sep 2016
Posts: 554
Re: If x and y are both positive numbers, is x/y > y/x?  [#permalink]

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26 Mar 2018, 23:30
D.

A. Sufficient . y/X= 5/4 X/y= 4/5... So answer is X/y< y/X ...

B. Sufficient.

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Re: If x and y are both positive numbers, is x/y > y/x?  [#permalink]

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26 Mar 2018, 23:31
Bunuel wrote:
If x and y are both positive numbers, is x/y > y/x?

(1) 4y/x = 5
(2) x +4 = y

Do you know some link or something for ps and ds problems on number properties and absolute value ?

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Math Expert
Joined: 02 Sep 2009
Posts: 52161
Re: If x and y are both positive numbers, is x/y > y/x?  [#permalink]

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26 Mar 2018, 23:33
Bunuel wrote:
If x and y are both positive numbers, is x/y > y/x?

(1) 4y/x = 5
(2) x +4 = y

Do you know some link or something for ps and ds problems on number properties and absolute value ?

Sent from my XT1562 using GMAT Club Forum mobile app

Check the links below:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread

Hope it helps.
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Director
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Re: If x and y are both positive numbers, is x/y > y/x?  [#permalink]

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26 Mar 2018, 23:35
Bunuel wrote:
If x and y are both positive numbers, is x/y > y/x?

(1) 4y/x = 5
(2) x +4 = y

What is the OA?

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Math Expert
Joined: 02 Sep 2009
Posts: 52161
Re: If x and y are both positive numbers, is x/y > y/x?  [#permalink]

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26 Mar 2018, 23:37
Bunuel wrote:
If x and y are both positive numbers, is x/y > y/x?

(1) 4y/x = 5
(2) x +4 = y

What is the OA?

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Check the original post:

The OA will be automatically revealed on Monday 2nd of April 2018 11:17:42 PM Pacific Time Zone
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Re: If x and y are both positive numbers, is x/y > y/x?  [#permalink]

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26 Mar 2018, 23:47
Bunuel wrote:
If x and y are both positive numbers, is x/y > y/x?

(1) 4y/x = 5
(2) x +4 = y

since x and y are both positive... we can cross-multiply without fear of sign.
The question is...x/y > y/x ?
or,

$$x^2 > y^2$$ ?

or,

$$x^2/y^2 > 1$$ ?

(1) 4y/x = 5 implies y/x = 5/4 (divide by 4)

Squaring both sides...

$$y^2/x^2 = 25/16 >1$$ Sufficient as the original question is reciprocal of this, so answer is "No".

(2) This is the tricky part. x + 4 = y

Since we know x>0 and y>0 ... hence min value of y is now 4.

since y is always 4 more than x, y^2 will always be larger than x^2. Sufficient

Hence Option (D) is correct.
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Re: If x and y are both positive numbers, is x/y > y/x?  [#permalink]

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27 Mar 2018, 08:40
Bunuel wrote:
If x and y are both positive numbers, is x/y > y/x?

(1) 4y/x = 5
(2) x +4 = y

Question: x/y > y/x ? (Given : x and y > 0)

Or x^2 > y^2 ?

Or x^2 - y^2 > 0 ?

Or (x + y)(x - y) > 0 ?

St 1: 4y/x = 5

Or x/y = 4/5

x = 4, y = 5

As x - y = 4 - 5 = -1, Answer to the question is NO. Sufficient

St 2 : x + 4 = y

means x < y

Or (x - y) < 0 or -ve

Therefore, Answer to the question is NO Sufficient

(D)
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Joined: 01 Feb 2018
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Re: If x and y are both positive numbers, is x/y > y/x?  [#permalink]

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28 Mar 2018, 00:01
Bunuel wrote:
If x and y are both positive numbers, is x/y > y/x?

(1) 4y/x = 5
(2) x +4 = y

(1) 4y/x=5 therefore y/x =5/4 and x/y =4/5 Sufficient
(2) x+4 = y therefore x/y = 1-4/y (x/y <1) and y/x= 1 + 4/x (y/x > 1) Also Sufficient

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Joined: 26 Mar 2013
Posts: 1998
Re: If x and y are both positive numbers, is x/y > y/x?  [#permalink]

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28 Mar 2018, 14:02
Bunuel wrote:
If x and y are both positive numbers, is x/y > y/x?

(1) 4y/x = 5
(2) x +4 = y

(1) 4y/x = 5

$$\frac{y}{x}$$ = $$\frac{5}{4}$$

$$\frac{x}{y}$$ = $$\frac{4}{5}$$

Answer is Always NO

Sufficient

(2) x+4 = y

As both are positive, y is always greater than x

$$\frac{x}{y}$$ > $$\frac{y}{x}$$..........Answer is Always NO

Sufficient

Re: If x and y are both positive numbers, is x/y > y/x? &nbs [#permalink] 28 Mar 2018, 14:02
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# If x and y are both positive numbers, is x/y > y/x?

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