which of the foll is true?

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vittalgmat: Legendary Member; Posts: 621; Joined: Wed Apr 09, 2008 7:13 pm; Thanked: 33 times; Followed by:4 members

which of the foll is true?

by vittalgmat » Fri Jan 02, 2009 1:54 am

if t/u = x/y and t/y = u/x and t, u , x, y are non-zero integers which of the foll is true?

A. t/u = 1
B. y/x = -1
C. t=u
D. t=+or- u
E. None of the above.

[spoiler]OA is D but I am not sure. I did the following: Pls let me know where I went wrong.
from the two equations,
ty = ux and tx = uy.
Adding these two, t(x+y) = u(x+y)
--> t = u.
[/spoiler]

Quote

Source: Beat The GMAT — Problem Solving | Fri Jan 02, 2009 1:54 am

Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pm; Location: Toronto; Thanked: 1710 times; Followed by:614 members; GMAT Score:800

Re: which of the foll is true?

by Stuart@KaplanGMAT » Fri Jan 02, 2009 2:01 am

vittalgmat wrote:if t/u = x/y and t/y = u/x and t, u , x, y are non-zero integers which of the foll is true?

A. t/u = 1
B. y/x = -1
C. t=u
D. t=+or- u
E. None of the above.

I did the following: Pls let me know where I went wrong.
from the two equations,
ty = ux and tx = uy.
Adding these two, t(x+y) = u(x+y)
--> t = u.
[/spoiler]

The problem is that you simplified by dividing both sides by (x+y). In doing so, you ignored the possibility that x + y = 0, which can happen if x=-y. It's very dangerous to simplify equations by dividing out variables or variable expressions unless you're 100% sure that the variable or expression does NOT equal 0.

Going back one step:

t(x+y) = u(x+y)
t(x+y) - u(x+y) = 0
(t-u)(x+y) = 0

so, either:
t = u or x = -y

and if x = -y, then:

t/u = -y/y
t/u = -1
t = -u

so, either t = u OR t = -u... choose (D).