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If x and y are positive integers, and 4x^2=3y, then which of the follo

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If x and y are positive integers, and 4x^2=3y, then which of the follo  [#permalink]

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New post 01 Nov 2019, 05:39
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A
B
C
D
E

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Question Stats:

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Re: If x and y are positive integers, and 4x^2=3y, then which of the follo  [#permalink]

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New post 01 Nov 2019, 06:28
1
Since x and y are positive integers therefore,

y = 12*n^2
And
x = 3n
Where n is a positive integer.

This implies that x^2,y^2 and xy are multiple of 9 for sure.

Therefore, answer is (E).

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Re: If x and y are positive integers, and 4x^2=3y, then which of the follo  [#permalink]

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New post 01 Nov 2019, 07:04
1
Bunuel wrote:
If x and y are positive integers, and \(4x^2=3y\), then which of the following must be a multiple of 9?

I. \(x^2\)
II. \(y^2\)
III. \(xy\)

A. I only
B. II only
C. III only
D. I and II only
E. I, II and III


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\(4x^2=3y\)
--> \(x^2 = 3y/4\)
--> \(x\) is a multiple of 3 & \(y\) is also a multiple of 3 (only then \(x\) will be a positive integer)
--> \(x = 3p\), \(y = 3q\), for any positive integers \(p\) & \(q\)
--> \(x^2 = 9*p^2\) --> I is true
\(y^2 = 9*q^2\) --> II is true
\(x*y = 3p*3q = 9*p*q\) --> III is also true

IMO Option E
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Re: If x and y are positive integers, and 4x^2=3y, then which of the follo  [#permalink]

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New post 01 Nov 2019, 08:02
1
Bunuel wrote:
If x and y are positive integers, and \(4x^2=3y\), then which of the following must be a multiple of 9?

I. \(x^2\)
II. \(y^2\)
III. \(xy\)

A. I only
B. II only
C. III only
D. I and II only
E. I, II and III


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Let, \(4x^2=3y = 36\)

So, \(x^2 = 9\) Or, \(x = +3 , -3\)

And, \(y = 12\)

(I) \(\frac{x^2}{9}\) = \(\frac{9}{9} = 1\)
(II) \(\frac{y^2}{9} = 12*12/9 = 16\)
(III) \(xy/9 = 12*3/9 = 4\)

Thus, Answer must be (E) I, II and III
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Abhishek....

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Re: If x and y are positive integers, and 4x^2=3y, then which of the follo  [#permalink]

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New post 01 Nov 2019, 08:08
given
4*x^2/3y =1
x^2 has to be 3 ; and y = 12
4*3^2/3*12 = 1
in that case all given conditions are valid

I. \(x^2\)
II. \(y^2\)
III. \(xy\)

IMO E

Bunuel wrote:
If x and y are positive integers, and \(4x^2=3y\), then which of the following must be a multiple of 9?

I. \(x^2\)
II. \(y^2\)
III. \(xy\)

A. I only
B. II only
C. III only
D. I and II only
E. I, II and III


Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
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Re: If x and y are positive integers, and 4x^2=3y, then which of the follo   [#permalink] 01 Nov 2019, 08:08
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