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

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mitzwillrockgmat Master | Next Rank: 500 Posts Default Avatar
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if x not equal to 0, and if x is replaced by 1/x everywhere

Post 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 Wink ]

ttp://www.postimage.org/image.php?v=Pqdyc79" target="_blank">

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!

btw answer is A.

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kwhite Junior | Next Rank: 30 Posts Default Avatar
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Post 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 Smile

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

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kwhite Junior | Next Rank: 30 Posts Default Avatar
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Post 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 Smile

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

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Matt@VeritasPrep GMAT Instructor
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Post 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 Wink ]

ttp://www.postimage.org/image.php?v=Pqdyc79" target="_blank">

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!

btw answer is A.
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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Boredguy1543 Newbie | Next Rank: 10 Posts Default Avatar
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Post 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 Wink ]

ttp://www.postimage.org/image.php?v=Pqdyc79" target="_blank">

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!

btw answer is A.
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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mcdesty Master | Next Rank: 500 Posts
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Post Wed Jul 09, 2014 11:50 am
See Img
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krusta80 Master | Next Rank: 500 Posts
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Post 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 Smile

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 Smile
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. Smile

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

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krusta80 Master | Next Rank: 500 Posts
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Post 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 Smile

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 Smile

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

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

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mitzwillrockgmat Master | Next Rank: 500 Posts Default Avatar
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Post 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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Post 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
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