Inequality

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jayanti: Senior | Next Rank: 100 Posts; Posts: 72; Joined: Tue Apr 19, 2011 6:58 amFollowed by: 6 members

by jayanti » Fri Aug 05, 2011 4:16 am

If x â‰ 0, then (x + 1/x)^2 - (x - 1/x)^2

A. 1/x
B. x
C. 1
D. 2
E. 4

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Source: Beat The GMAT — Problem Solving | Fri Aug 05, 2011 4:16 am

knight247: Legendary Member; Posts: 504; Joined: Tue Apr 19, 2011 1:40 pmFollowed by: 11 members; Thanked: 114 times

by knight247 » Fri Aug 05, 2011 4:57 am

(x+1/x)^2-(x-1/x)^2
=(x^2+1)^2/x^2-(x^2-1)^2/x^2
={(x^2+1)^2-(x^2-1)^2}/x^2

Using the formula (x+y)^2=x^2+2xy+y^2 and (x-y)=x^2-2xy+y^2 we get

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

2x^2/x^2=2

Hence D

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Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Fri Aug 05, 2011 5:00 am

knight247 wrote:(x+1/x)^2-(x-1/x)^2
=(x^2+1)^2/x^2-(x^2-1)^2/x^2
={(x^2+1)^2-(x^2-1)^2}/x^2

Using the formula (x+y)^2=x^2+2xy+y^2 and (x-y)=x^2-2xy+y^2 we get

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

2x^2/x^2=2

Hence D

Hi,
(2x^2+2x^2)/x^2 = 4

Hence, E

Cheers!

Things are not what they appear to be... nor are they otherwise

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sushbis: Junior | Next Rank: 30 Posts; Posts: 23; Joined: Wed Feb 27, 2008 6:01 pmFollowed by: 1 member; Thanked: 1 times

by sushbis » Fri Aug 05, 2011 5:30 am

No need for any calculations..by looking at the prob itself you can eliminate all x's

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MBA.Aspirant: Master | Next Rank: 500 Posts; Posts: 401; Joined: Tue May 24, 2011 1:14 amFollowed by: 5 members; Thanked: 37 times

by MBA.Aspirant » Fri Aug 05, 2011 7:03 am

jayanti wrote:If x â‰ 0, then (x + 1/x)^2 - (x - 1/x)^2

A. 1/x
B. x
C. 1
D. 2
E. 4

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

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

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

= 4

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Fri Aug 05, 2011 8:10 am

jayanti wrote:If x â‰ 0, then (x + 1/x)^2 - (x - 1/x)^2

A. 1/x
B. x
C. 1
D. 2
E. 4

Let x=1.

(x + 1/x)Â² - (x - 1/x)Â²
= (1 + 1/1)Â² - (1 - 1/1)Â²
= 2Â² - 0Â²
= 4.

The correct answer is E.

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