gmat club DS

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bblast: Legendary Member; Posts: 1077; Joined: Mon Dec 13, 2010 1:44 amFollowed by: 33 members; Thanked: 118 times; GMAT Score:710

by bblast » Mon May 23, 2011 11:58 pm

What is the value of integer J ?

1. |J| = J^-1
2. J^J = 1

D

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Source: Beat The GMAT — Data Sufficiency | Mon May 23, 2011 11:58 pm

smackmartine: Legendary Member; Posts: 516; Joined: Fri Jul 31, 2009 3:22 pmFollowed by: 13 members; Thanked: 112 times

by smackmartine » Tue May 24, 2011 12:18 am

IMO D

Asked : Whats the value of J?

1) |J| = J^-1 = 1/J

if J>0 , J=1/J => j^2 = 1 => J=1
if J<0 , J= - 1/J => j^2 = -1 (Square of any number can never be negative so we cannot consider this case)

So , J=1 Sufficient.

2) J^J =1

Because any number raise to power 0 is 1 , j=0 ,in fact 0^0 is 1
So, Sufficient.

So D

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VivianKerr: GMAT Instructor; Posts: 1035; Joined: Fri Dec 17, 2010 11:13 amFollowed by: 365 members; Location: Los Angeles, CA; Thanked: 474 times

by VivianKerr » Tue May 24, 2011 6:44 am

The key here is to recognize that |J| will always be positive.

J^-1 = 1/J

So J = 1/J. It has to be +1. SUFF.

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sourabh33: Master | Next Rank: 500 Posts; Posts: 135; Joined: Tue Mar 22, 2011 12:01 pmFollowed by: 3 members; Thanked: 21 times; GMAT Score:720

by sourabh33 » Tue May 24, 2011 7:23 am

I have a small doubt here.

In Equation 2

J^J = 1

J could be either 1 or 0 because both 0^0 and 1^1 will be equal to 1, and therefore statement 2 should be insufficient

Shouldn't the answer be A for this?

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sourabh33: Master | Next Rank: 500 Posts; Posts: 135; Joined: Tue Mar 22, 2011 12:01 pmFollowed by: 3 members; Thanked: 21 times; GMAT Score:720

by sourabh33 » Tue May 24, 2011 7:27 am

The answer could be D only if we consider 0^0 as undefined.

https://www.math.utah.edu/~pa/math/0to0.html
https://www.math.hmc.edu/funfacts/ffiles/10005.3-5.shtml

but google says 0^0 is 1
https://www.google.co.in/search?aq=1&oq= ... he+power+0

Last edited by sourabh33 on Tue May 24, 2011 7:30 am, edited 1 time in total.

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VivianKerr: GMAT Instructor; Posts: 1035; Joined: Fri Dec 17, 2010 11:13 amFollowed by: 365 members; Location: Los Angeles, CA; Thanked: 474 times

by VivianKerr » Tue May 24, 2011 7:29 am

Good question!

Any nonzero number raised to the power 0 is 1. 0^0 = indeterminate.

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