mourinhogmat1 wrote:

If \(\frac{t}{u} = \frac{x}{y}\) and \(\frac{t}{y} = \frac{u}{x}\) and \(t\) , \(u\) , \(x\) , and \(y\) are non-zero integers, which of the following is true?

A. \(\frac{t}{u}=1\)

B. \(\frac{y}{x}=-1\)

C. \(t = u\)

D. \(t = \pm u\)

E. None of the above

A question to Bunuel or someone who actually wrote the test:

From the given equation we get ux=ty (1) and xt=uy (2)

subtracting 2 from 1 this we get x(u-t)= y (t-u) --> this gives us x=-y. This is option B.

So, why is option B wrong?

This is how I arrived at D:

1 step: we know that t/u = x/y. This could be converted into: t*y = u*x.

2 step: we know that: t/y = u/x.

At the same time: t*y = u*x

From these equations, based on common logic,

we understand that: |t| = |u| and |y| = |x|. For example,

2*3 = 2*3 and 2/3 = 2/3, or -2*3 = 2*-3 and -2/3 = 2/-3

Important to remember about possible negative values

3 step: now lets consider possible answers:

(A) t/u and (C) t =u could be eliminated at once, as they are the same -> impossible in gmat questions of this type

(B) y/x = -1 is possible, but could also be = 1

(D) correct, could be either + or -

As I'm a beginner in gmat, would be greatful if someone can challenge my approach!