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if x not equal to 0, and if x is replaced by 1/x everywhere

This topic has 4 expert replies and 9 member replies
mitzwillrockgmat Master | Next Rank: 500 Posts
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if x not equal to 0, and if x is replaced by 1/x everywhere

Mon Jun 21, 2010 3:05 am
Pls help me out with this question!!

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

If x not equal to 0, and if x is replaced by 1/x everywhere in the expression above, then the resulting expression is equivalent to?

[answer choices are in the image, sorry will take too long to type them all out! lol ]

This is what I've done so far, dunno how to simplify beyond a point....

(x+1/x -1)^2 become [(1/x + 1)/(1/x -1)]^2 => [(1+x/x) / (1-x/x) ] ^2

=> [1+x / x * x/1-x ] ^2 => [(1 +x)/(1-x)]^2 => NOW WHAT?

How do i manipulate [(1+x)/(1-x)]^2 to become one of the answer choices????? HELP!

krusta80 Master | Next Rank: 500 Posts
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Sat Mar 03, 2012 9:27 am
kwhite wrote:
krusta80 wrote:
kwhite wrote:
is it possible to solve this by picking numbers?
Let's give it a shot! Let's keep it simple with x = 2

From the original equation, we get 9

When replacing 2 with 1/2, we get

[(3/2)/(-1/2)]^2 = 9

Obviously A works

B is the recipcrocal of A -> 1/9

C gives (5/4)/(3/4) = 5/3

D gives (-3/4)/(5/4) = -3/5

E is just the negative of B -> -1/9

A is the answer...no algebra needed
Thank you for your quick reply, but I guess my confusion comes in because I don't understand how we can decipher from the question that we are to plug 1/x into the solution part. I understand switching X --> 1/x in the example equation but shouldn't we use X for the answer choices when picking numbers? because we are trying to match the original equation with "1/x" to an answer with "x"? so confused because i don't see where it says to match sub 1/x into the answer solutions.
You're right! I think I was looking at this problem in a weird way when I did it before. Of course, the easiest thing to do would be to substitute x = 2 into the choices. As you can see, A gives you 9 when doing so.

Sorry for any confusion...I should have substituted x into the choices as you said.

kwhite Junior | Next Rank: 30 Posts
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Sat Mar 03, 2012 9:21 am
krusta80 wrote:
kwhite wrote:
is it possible to solve this by picking numbers?
Let's give it a shot! Let's keep it simple with x = 2

From the original equation, we get 9

When replacing 2 with 1/2, we get

[(3/2)/(-1/2)]^2 = 9

Obviously A works

B is the recipcrocal of A -> 1/9

C gives (5/4)/(3/4) = 5/3

D gives (-3/4)/(5/4) = -3/5

E is just the negative of B -> -1/9

A is the answer...no algebra needed
Thank you for your quick reply, but I guess my confusion comes in because I don't understand how we can decipher from the question that we are to plug 1/x into the solution part. I understand switching X --> 1/x in the example equation but shouldn't we use X for the answer choices when picking numbers? because we are trying to match the original equation with "1/x" to an answer with "x"? so confused because i don't see where it says to match sub 1/x into the answer solutions.

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Rahul@gurome GMAT Instructor
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Mon Jun 21, 2010 3:19 am
You got [(1 +x)/(1-x)]^2
Then we can write (1-x)^2 = (x-1)^2, since we are squaring so both (1-x)^2 and (x-1)^2 will give same values.
Hence, [(1+x)/(1-x)]^2 = [(x+1)/(x-1)]^2

Hope this helps?

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mitzwillrockgmat Master | Next Rank: 500 Posts
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Mon Jun 21, 2010 3:25 am
Rahul@gurome wrote:
You got [(1 +x)/(1-x)]^2
Then we can write (1-x)^2 = (x-1)^2, since we are squaring so both (1-x)^2 and (x-1)^2 will give same values.
Hence, [(1+x)/(1-x)]^2 = [(x+1)/(x-1)]^2

Hope this helps?
Hey, that works!! cool that's something i didn't notice before that (1-x)^2 & (x-1)^2 give the same values! tried it on the numerator too...will def come in handy! thanks!!!

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Patrick_GMATFix GMAT Instructor
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Mon Jun 21, 2010 5:05 am
This is #208 from the OG 12th edition. The official answer is A. Solution attached. If you can't see the attachment, see it here.

-Patrick
Attachments

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mitzwillrockgmat Master | Next Rank: 500 Posts
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Mon Jun 21, 2010 5:10 am
Patrick_GMATFix wrote:
This is #208 from the OG 12th edition. The official answer is A. Solution attached. If you can't see the attachment, see it here.

-Patrick
thanks! i have the og companion i'm a BIG fan of it but this one is not explained in much detail or at least I didn't get it! thanks though!

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Patrick_GMATFix GMAT Instructor
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Mon Jun 21, 2010 5:15 am
Thx for the feedback

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kwhite Junior | Next Rank: 30 Posts
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Thu Mar 01, 2012 5:20 pm
is it possible to solve this by picking numbers?

krusta80 Master | Next Rank: 500 Posts
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Thu Mar 01, 2012 7:24 pm
kwhite wrote:
is it possible to solve this by picking numbers?
Let's give it a shot! Let's keep it simple with x = 2

From the original equation, we get 9

When replacing 2 with 1/2, we get

[(3/2)/(-1/2)]^2 = 9

Obviously A works

B is the recipcrocal of A -> 1/9

C gives (5/4)/(3/4) = 5/3

D gives (-3/4)/(5/4) = -3/5

E is just the negative of B -> -1/9

A is the answer...no algebra needed

krusta80 Master | Next Rank: 500 Posts
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Thu Mar 01, 2012 7:34 pm
Never mind.

mcdesty Master | Next Rank: 500 Posts
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Wed Jul 09, 2014 11:50 am
See Img
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Boredguy1543 Newbie | Next Rank: 10 Posts
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Wed Oct 14, 2015 9:04 am
mitzwillrockgmat wrote:
Pls help me out with this question!!

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

If x not equal to 0, and if x is replaced by 1/x everywhere in the expression above, then the resulting expression is equivalent to?

[answer choices are in the image, sorry will take too long to type them all out! lol ]

This is what I've done so far, dunno how to simplify beyond a point....

(x+1/x -1)^2 become [(1/x + 1)/(1/x -1)]^2 => [(1+x/x) / (1-x/x) ] ^2

=> [1+x / x * x/1-x ] ^2 => [(1 +x)/(1-x)]^2 => NOW WHAT?

How do i manipulate [(1+x)/(1-x)]^2 to become one of the answer choices????? HELP!

I found this question very odd and confusing. Because the equation that is given and the answer choice A is completely identical. I somehow talked myself out of selecting that answer, because that seems too easy. I don't know why GMAT would ask this question. Can anyone shed some light on this.

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Matt@VeritasPrep GMAT Instructor
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Wed Oct 14, 2015 10:49 pm
Boredguy1543 wrote:
mitzwillrockgmat wrote:
Pls help me out with this question!!

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

If x not equal to 0, and if x is replaced by 1/x everywhere in the expression above, then the resulting expression is equivalent to?

[answer choices are in the image, sorry will take too long to type them all out! lol ]

This is what I've done so far, dunno how to simplify beyond a point....

(x+1/x -1)^2 become [(1/x + 1)/(1/x -1)]^2 => [(1+x/x) / (1-x/x) ] ^2

=> [1+x / x * x/1-x ] ^2 => [(1 +x)/(1-x)]^2 => NOW WHAT?

How do i manipulate [(1+x)/(1-x)]^2 to become one of the answer choices????? HELP!

I found this question very odd and confusing. Because the equation that is given and the answer choice A is completely identical. I somehow talked myself out of selecting that answer, because that seems too easy. I don't know why GMAT would ask this question. Can anyone shed some light on this.
Probably just to see if you could catch that and had the confidence to realize that the equation might be unchanged. (It does require you to do a bit of a double take, doesn't it?)

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