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# M06 #16

Author Message
Senior Manager
Joined: 08 Jun 2010
Posts: 397
Location: United States
Concentration: General Management, Finance
GMAT 1: 680 Q50 V32
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Kudos [?]: 88 [0], given: 13

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04 Feb 2012, 00:17
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?
Math Expert
Joined: 02 Sep 2009
Posts: 36618
Followers: 7100

Kudos [?]: 93585 [2] , given: 10578

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04 Feb 2012, 07:52
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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?

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 $$x = \pm y$$).

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).

Hope it's clear.
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Kudos [?]: -20 [0], given: 0

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25 Mar 2013, 23:06
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?
Intern
Joined: 29 Jul 2012
Posts: 29
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15 Apr 2013, 16:14
I'm stumped on this one too. Not clear at all.
Math Expert
Joined: 02 Sep 2009
Posts: 36618
Followers: 7100

Kudos [?]: 93585 [0], given: 10578

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16 Apr 2013, 01:46
youngkacha wrote:
I'm stumped on this one too. Not clear at all.

Can you please tell me which part(s) of the solution didn't you understand?
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16 Apr 2013, 19:32
Bunuel wrote:
youngkacha wrote:
I'm stumped on this one too. Not clear at all.

Can you please tell me which part(s) of the solution didn't you understand?

I'm lost when you take the absolute value of t and u, yet u is +/- and t isn't.

Why is t = +/- u instead of being +/- t = +/- u?
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18 Apr 2013, 15:11
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?

Multiply both the given equalities, we get t/u*t/y = x/y*u/x--> t^2 =u^2-->
D.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 36618
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Kudos [?]: 93585 [0], given: 10578

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19 Apr 2013, 02:42
youngkacha wrote:
Bunuel wrote:
youngkacha wrote:
I'm stumped on this one too. Not clear at all.

Can you please tell me which part(s) of the solution didn't you understand?

I'm lost when you take the absolute value of t and u, yet u is +/- and t isn't.

Why is t = +/- u instead of being +/- t = +/- u?

|t|=|u| means that t=u (which is the same as -t=-u) or t=-u (which is the same as -t=u), so only two cases.
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02 Jul 2014, 00:24
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!
Re: M06 #16   [#permalink] 02 Jul 2014, 00:24
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# M06 #16

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