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

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

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New post 26 Mar 2018, 23:17
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Re: If x and y are both positive numbers, is x/y > y/x?  [#permalink]

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New post 27 Mar 2018, 00:30
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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New post 27 Mar 2018, 00:31
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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Re: If x and y are both positive numbers, is x/y > y/x?  [#permalink]

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New post 27 Mar 2018, 00:33
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Re: If x and y are both positive numbers, is x/y > y/x?  [#permalink]

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New post 27 Mar 2018, 00:35
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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Re: If x and y are both positive numbers, is x/y > y/x?  [#permalink]

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New post 27 Mar 2018, 00:37
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Re: If x and y are both positive numbers, is x/y > y/x?  [#permalink]

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New post 27 Mar 2018, 00:47
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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If x and y are both positive numbers, is x/y > y/x?  [#permalink]

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New post Updated on: 26 May 2019, 00:05
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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Originally posted by AkshdeepS on 27 Mar 2018, 09:40.
Last edited by AkshdeepS on 26 May 2019, 00:05, edited 1 time in total.
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Re: If x and y are both positive numbers, is x/y > y/x?  [#permalink]

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New post 28 Mar 2018, 01:01
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

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

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New post 28 Mar 2018, 15:02
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

Answer: D
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Re: If x and y are both positive numbers, is x/y > y/x?   [#permalink] 28 Mar 2018, 15:02
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