is 4t – (3/t) + 3 = 0?

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]

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

Regards