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

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Joined: 02 Sep 2009
Posts: 60480
If x and y are positive integers, and 4x^2=3y, then which of the follo  [#permalink]

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01 Nov 2019, 05:39
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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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Joined: 21 Sep 2016
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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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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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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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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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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

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

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