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If n >2 and (2/n) is substituted for all instances of n in t

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If n >2 and (2/n) is substituted for all instances of n in t [#permalink] New post 04 Feb 2014, 05:06
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(n – 2)^-1 (2 + n)
If n >2 and 2/n is substituted for all instances of n in the above expression, then the new expression will be equivalent to which of the following:

A. (n + 1)(n – 1)^(-1)
B. –(n + 1)(n – 1)^(-1)
C. –(n – 1)(n + 1)^(-1)
D. (2 + n)^(-1)*(n – 2)
E. (n – 2)^(-1)*(2 + n)
[Reveal] Spoiler: OA

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Re: If n >2 and (2/n) is substituted for all instances of n in t [#permalink] New post 04 Feb 2014, 05:17
Expert's post
Bunuel wrote:
(n – 2)^-1 (2 + n)
If n >2 and 2/n is substituted for all instances of n in the above expression, then the new expression will be equivalent to which of the following:

A. (n + 1)(n – 1)^(-1)
B. –(n + 1)(n – 1)^(-1)
C. –(n – 1)(n + 1)^(-1)
D. (2 + n)^(-1)*(n – 2)
E. (n – 2)^(-1)*(2 + n)


Number plugging:

Say \(n=3\), then substitute \(\frac{2}{n}=\frac{2}{3}\) into \((n - 2)^{-1} (2 + n)=-2\).

Now, substitute \(n=3\) into the answer choices and see which of them gives -2. Only B fits.

Answer: B.

Note that for plug-in method it might happen that for some particular number(s) more than one option may give "correct" answer. In this case just pick some other numbers and check again these "correct" options only.

Alebra:

Substitute \(\frac{2}{n}\) into \((n - 2)^{-1} (2 + n)\):

\((\frac{2}{n} - 2)^{-1} (2 + \frac{2}{n})=(\frac{2-2n}{n})^{-1}(\frac{2n+2}{n})=(\frac{n}{2-2n})(\frac{2n+2}{n})=\frac{n+1}{1-n}=-\frac{n+1}{n-1}=-(n+1)(n-1)^{-1}\).

Answer: B.
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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. Tricky questions from previous years.

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If n >2 and (2/n) is substituted for all instances of n in t [#permalink] New post 17 Mar 2015, 19:45
\(\frac{(n+1)}{(1-n)}=-\frac{(n+1)}{(n-1)}\)

How do you do this kind of operation? Can you share any study materials on this topic? Thanks
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Re: If n >2 and (2/n) is substituted for all instances of n in t [#permalink] New post 17 Mar 2015, 21:08
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evdo wrote:
\(\frac{(n+1)}{(1-n)}=-\frac{(n+1)}{(n-1)}\)

How do you do this kind of operation? Can you share any study materials on this topic? Thanks


This is basic algebra and fraction.

You take our "-" common from the denominator to get

\(\frac{(n+1)}{(1-n)}=\frac{(n+1)}{-(n-1)}\)

And from theory of fractions, you know that

\(\frac{(n+1)}{-(n-1)}=-\frac{(n+1)}{(n-1)} = \frac{-(n+1)}{(n-1)}\)

For these basics, check purplemath.com or khanacademy.org
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Re: If n >2 and (2/n) is substituted for all instances of n in t [#permalink] New post 12 Jun 2015, 14:37
Moderators please move this question into PS section.This is not DS question!
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Re: If n >2 and (2/n) is substituted for all instances of n in t   [#permalink] 12 Jun 2015, 14:37
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