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is 4t – (3/t) + 3 = 0?

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is 4t – (3/t) + 3 = 0?

by sanju09 » Fri Apr 25, 2014 10:16 pm
If x ≠ 0, y ≠ 0, and x/y = t, is 4t - (3/t) + 3 = 0?
(1) (y - 3x)/(x - y) = (2y + x)/(x + y).
(2) y^2 = x(4x + 3y)/3.

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by Brent@GMATPrepNow » Sun Apr 27, 2014 9:28 am
sanju09 wrote:If x ≠ 0, y ≠ 0, and x/y = t, is 4t - (3/t) + 3 = 0?
(1) (y - 3x)/(x - y) = (2y + x)/(x + y).
(2) y^2 = x(4x + 3y)/3.
Hey Sanjeev,

Seems like a pretty complex question (unless I'm missing something :-))

Are you sure the equation 4t - (3/t) + 3 = 0 is correct?
I can't help but think that you want it to be 4t - (1/t) + 3 = 0
Or perhaps 4t - (3/t) + 1 = 0

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by sanju09 » Mon Apr 28, 2014 11:36 pm
Brent@GMATPrepNow wrote:
sanju09 wrote:If x ≠ 0, y ≠ 0, and x/y = t, is 4t - (3/t) + 3 = 0?
(1) (y - 3x)/(x - y) = (2y + x)/(x + y).
(2) y^2 = x(4x + 3y)/3.
Hey Sanjeev,

Seems like a pretty complex question (unless I'm missing something :-))

Are you sure the equation 4t - (3/t) + 3 = 0 is correct?
I can't help but think that you want it to be 4t - (1/t) + 3 = 0
Or perhaps 4t - (3/t) + 1 = 0

Cheers,
Brent
Hi Brent,

I've rechecked the question and found it correct like as under:

If x ≠ 0, y ≠ 0, and x/y = t, is 4t - (3/t) + 3 = 0?
(1) (y - 3x)/(x - y) = (2y + x)/(x + y).
(2) y^2 = x(4x + 3y)/3.

"Is 4t - (3/t) + 3 = 0?" would mean "Is 4x/y - (3y/x) + 3 = 0?"

or "Is 4x^2 - 3y^2 + 3xy = 0?"

(1) (y - 3x)/(x - y) = (2y + x)/(x + y) solves in to

(y - 3x)(x + y) = (2y + x)(x - y)

or xy + y^2 - 3x^2 - 3xy = 2xy - 2y^2 + x^2 - xy

or 4x^2 - 3y^2 + 3xy = 0. Hence, [spoiler]YES! Sufficient[/spoiler].

(2) y^2 = x(4x + 3y)/3 opens to

3y^2 = 4x^2 + 3xy

or 4x^2 - 3y^2 + 3xy = 0. Hence, [spoiler]YES! Sufficient.


Answer is D[/spoiler]
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by Brent@GMATPrepNow » Tue Apr 29, 2014 10:47 am
Ah....

I incorrectly assumed that you wanted us to take 4t - (3/t) + 3 = 0 and rewrite it as 4t² + 3t - 3 = 0.
At that point, we can't factor (nicely) the left side. I assumed that you wanted us to factor the quadratic and, to do so, we'd need to change either the 2nd or 3rd term. My bad.

Nice question

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Brent
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by sanju09 » Wed Apr 30, 2014 9:53 pm
Brent@GMATPrepNow wrote:Ah....

I incorrectly assumed that you wanted us to take 4t - (3/t) + 3 = 0 and rewrite it as 4t² + 3t - 3 = 0.
At that point, we can't factor (nicely) the left side. I assumed that you wanted us to factor the quadratic and, to do so, we'd need to change either the 2nd or 3rd term. My bad.

Nice question

Cheers,
Brent
Thank you, Brent! More questions are waiting, perhaps for your attention only...

https://www.beatthegmat.com/a-rectangula ... tml#717065

https://www.beatthegmat.com/a-solo-tie-b ... tml#716913

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The mind is everything. What you think you become. -Lord Buddha



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The Princeton Review - Manya Abroad
Lucknow-226001

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