Problem Solving

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

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

OA: D

Is it a good approach to use numbers here? I did try this in the timed test that I took and failed to find numbers that would satisfy both equations within the alloted time of 2 minutes. Can someone help? Please comment if picking number is a good approach here. Else, what other method is recommended?

Thanks!

In such cases, it is best to eliminate answers one by one.

You start with A and work down.

Since most equations are similar, the work done for this will still be very less and should fit into 2 mins.

Taking numbers is too tough an approach. To take numbers, you need to find out the value of t and u that satisfy the equation and that would have already taken u to the answer. Does not work.

jsasipriya wrote:If t/u = x/y and t/y = u/x and t, x, u, and y are non-zero integers, which of the following is true?

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

OA: D

Is it a good approach to use numbers here? I did try this in the timed test that I took and failed to find numbers that would satisfy both equations within the alloted time of 2 minutes. Can someone help? Please comment if picking number is a good approach here. Else, what other method is recommended?

Thanks!

In such cases, its best to first simplify the given information:
Given info: t/u=x/y & t/y=u/x, which can be written as; t/u=x/y & t/u=y/x
Now multiplying the two we get; (t/u)^2=1 ----> t/u=-+1 (-1 or +1) ---> t=-u or +u
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Now, considering the options, D is the answer. The question could have been made complicated by giving options such as 1) both A&D 2) only A etc..etc..here even y/x=-+1 (-1 or +1)

IMO- D

jsasipriya wrote:If t/u = x/y and t/y = u/x and t, x, u, and y are non-zero integers, which of the following is true?

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

OA: D

Is it a good approach to use numbers here? I did try this in the timed test that I took and failed to find numbers that would satisfy both equations within the alloted time of 2 minutes. Can someone help? Please comment if picking number is a good approach here. Else, what other method is recommended?

Thanks!

The answer choices are erroneous here, I see no difference in answer choices A and C, moreover the answer choice E None of the above is something that we rarely see in a GMAT PS.

Anyway, we have t/u = x/y and t/y = u/x to rewrite as t/u = x/y and t/u = y/x and multiply together to have (t/u) ^2 = 1 or t/u = ±1 or indubitably [spoiler]t = ±u.


D[/spoiler]

jsasipriya wrote:If t/u = x/y and t/y = u/x and t, x, u, and y are non-zero integers, which of the following is true?

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

OA: D


Is it a good approach to use numbers here? I did try this in the timed test that I took and failed to find numbers that would satisfy both equations within the alloted time of 2 minutes. Can someone help? Please comment if picking number is a good approach here. Else, what other method is recommended?

Thanks!

t/u=x/y;------1)
t/y=u/x; t/u=y/x-------2)
comparing 1 and 2 we have
x/y=y/x; x^2-y^2=0(x-y)(x+y)=0; x=y or x=-y;
t/u=x/y; when x=y; we have t/u=1 and when x=-y we have t/u=-1;
i.e. t= (+ or -)u; hence D

sanju09 wrote: The answer choices are erroneous here, I see no difference in answer choices A and C, moreover the answer choice E None of the above is something that we rarely see in a GMAT PS.

Hi,

if t=u=0, then (C) would be true and (A) would be false, so there's at least some difference between the options.

However, if two answer choices were exactly the same, and you noticed that fact, then you could quickly eliminate both choices (unless it's a roman numeral question); since only 1 answer can be correct, they'd both have to be wrong.