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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?
Archived Topic
Hi there,
Archived GMAT Club Tests question - no more replies possible.
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?
Because you can not tell from \(x(u-t)=y(t-u)\) that \(x=-y\) is necessarily true: \(x(u-t)=y(t-u)\) --> \(x(u-t)+y(u-t)=(x+y)(t-u)\) --> either \(x=-y\) or \(t=u\).
Complete solution: Given that: \(\frac{t}{u} = \frac{x}{y}\) and \(\frac{t}{y} = \frac{u}{x}\).
So, \(\frac{t}{u} = \frac{x}{y}\) and \(\frac{t}{u} = \frac{y}{x}\) (from 2), which means that \(\frac{t}{u}\) and \(\frac{x}{y}\) equal to their reciprocals: \(\frac{t}{u}=\frac{u}{t}\) and \(\frac{x}{y}=\frac{y}{x}\) --> \(t^2=u^2\) and \(t^2=u^2\) --> \(|t|=|u|\) (or which is the same \(t = \pm u\)) and \(|x|=|y|\) (or which is the same \(x = \pm y\)).
Answer: D.
One more thing: notice that answer choices A and C are the same, since we can not have two correct answers than both are wrong (there are some types of questions for which more than one answer can be correct but this is not that type).
This is confusing. I solved this question and immediately got A as the write answer. Thanks for pointing that A and C are the same. But how do we find that A or C is wrong even after getting this answer?
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?
Multiply both the given equalities, we get t/u*t/y = x/y*u/x--> t^2 =u^2--> D.
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!
Archived Topic
Hi there,
Archived GMAT Club Tests question - no more replies possible.