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]
The mind is everything. What you think you become. -Lord Buddha
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
