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!