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by bkw » Mon Jul 11, 2011 9:07 am
( x+1 / x-1 )^2
If x != 0,1, and if x is replaced by 1/x everywhere in the expression above, then the resulting expression is equivalent to:

a) ( x+1 / x-1 )^2
b) ( x-1 / x+1 )^2
c) x^2+1 / 1-x^2
d) x^2-1 / x^2+1
e) -( x-1 / x+1 )^2

Is it possible to solve this problem by using plugging-in?
I tried to replace x=2, 1/x=1/2 and insert, but did not really know what my target was.
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by winniethepooh » Mon Jul 11, 2011 9:17 am
There is no need to plug in.
The answer is the question.
Just plug in 1/x instead of x in the question, you'll get a. as the answer.
Gmat questions are very very precise, don't try to use plugins when the answer is just so straight forward:
(x+1 / x-1)^2
=(1/x+1 / 1/x-1)^2
=(x+1/x / x-1/x)^2
=(x+1 / x-1)^2
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by bkw » Mon Jul 11, 2011 10:01 am
winniethepooh wrote: =(1/x+1 / 1/x-1)^2
=(x+1/x / x-1/x)^2
I don't follow you between these two steps, could you please clarify?
Looks to me that 1/x -> x (given in the statement), but +1->1/x, or what happens here? :roll:
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by sumit88 » Mon Jul 11, 2011 10:08 am
Yes, there is indeed no need to use plug-ins if q's can be solved otherwise..

Anyways if you want to try using plug-in technique you can proceed like:

put x = 2 in (x+1/x-1)^2

=> (2+1/2-1)^2
=> (3/1)^2
= 9

According to question X needs to be replaced by 1/x

Now key in x as 1/2

((1/2+1)/(1/2-1))^2
((3/2)/(-1/2))^2
(-3)^2
=9

This replacing x by 1/x leads to same result 9. Thus look for the equation which is same as the original. Only a is correct.
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by GMATGuruNY » Mon Jul 11, 2011 10:09 am
bkw wrote:( x+1 / x-1 )^2
If x != 0,1, and if x is replaced by 1/x everywhere in the expression above, then the resulting expression is equivalent to:

a) ( x+1 / x-1 )^2
b) ( x-1 / x+1 )^2
c) x^2+1 / 1-x^2
d) x^2-1 / x^2+1
e) -( x-1 / x+1 )^2

Is it possible to solve this problem by using plugging-in?
I tried to replace x=2, 1/x=1/2 and insert, but did not really know what my target was.
Let x=2.

Now insert 1/x = 1/2 into the expression and simplify:
[ (1/2 + 1) / (1/2 - 1) ] ²
= { (3/2) / -(1/2) }²
= (-3)²
= 9. This is our target.

Now plug x=2 into the answers to see which yields our target of 9.
Only answer choice A works:
( x+1 / x-1 )^2
= [ (2+1) / (2-1) ]²
= 3²
= 9.

The correct answer is A.
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by winniethepooh » Mon Jul 11, 2011 11:50 am
Its just the LCM that I have taken in that step.
You can put it down on a piece of paper, it'll be easier to solve.
Well, but if you want to necessarily take plug-ins then, mind you its a time killing task in such questions!
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by MBA.Aspirant » Tue Jul 12, 2011 1:53 am
bkw wrote:( x+1 / x-1 )^2
If x != 0,1, and if x is replaced by 1/x everywhere in the expression above, then the resulting expression is equivalent to:

a) ( x+1 / x-1 )^2
b) ( x-1 / x+1 )^2
c) x^2+1 / 1-x^2
d) x^2-1 / x^2+1
e) -( x-1 / x+1 )^2

Is it possible to solve this problem by using plugging-in?
I tried to replace x=2, 1/x=1/2 and insert, but did not really know what my target was.
( x+1 / x-1 )^2

if x = 2, replace with 1/2

(1/2 + 1 / 1/2 -1)^2

(3/2 / -1/2)^2

(-3)^2 = 9

plugin 2 in choices

A)( x+1 / x-1 )^2

(3/1)^2 = 9

Alegbra:

( x+1 / x-1 )^2

= x^2+2x+1/ x^2 -2x+1

with x = 1/x

(1/x +1 / 1/x -1)^2

(1+x/x / 1-x/x)^2

( x+1/1-x)^2

= x^2 +2x+1/ x^2 -2x +1
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by artistocrat » Wed Jul 13, 2011 10:38 pm
You can do this mentally and shave off valuable seconds. Just choose x=2, so 1/x=1/2. Get the target (9), and find the equation (mentally) that equals 9. GMAT is going to be tougher than this...sorry!
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