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# Find an integer M. (1) M^M=M^3 (2) =1

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Manager
Joined: 25 May 2003
Posts: 54
Followers: 1

Kudos [?]: 3 [0], given: 0

bill gates trying to screw us on GMAT???

i have to burst my bubble tho

0^0 =1, but 0^3=0, so x=0 is not a possible solution from (1)

originally i was thinking 0^0=0, and therefore a possible solution
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Founder
Affiliations: AS - Gold, UA - Silver, HH-Diamond
Joined: 04 Dec 2002
Posts: 12821
Location: United States (WA)
GMAT 1: 750 Q49 V42
GPA: 3.5
WE: Information Technology (Hospitality and Tourism)
Followers: 2726

Kudos [?]: 13541 [0], given: 3865

Expert's post
I think Billy is right behind us

I tried multiplying 0 x 0 and such - as to the rules of powers (2^3 = 2x2x2) but it gives a 0. So far there are 3 choices for 0^0 (1, 0, and undefined, which I would claim makes it an undefined case, but we'll soon see. I am writing a short message to GMAC). It is obviously one of those made up things for the sake of sanity in the Universe.

-=-

Last edited by bb on 26 May 2003, 00:30, edited 1 time in total.
Manager
Joined: 25 May 2003
Posts: 54
Followers: 1

Kudos [?]: 3 [0], given: 0

here's my understanding:

0^x, where x>0, is always equal to 0

0^x, where x<0, is undefined

x^0, where x is ANY number (negative, positive, or zero) always equal to 1
SVP
Joined: 03 Feb 2003
Posts: 1607
Followers: 6

Kudos [?]: 84 [0], given: 0

Guys, 0^0 ≠ 0^3.
0^0 has no solution, at least for the GMAT program.
Thus, negate it, eliminate it, terminate it, kill it, forget about it
Intern
Joined: 25 May 2003
Posts: 17
Location: Thailand
Followers: 0

Kudos [?]: 0 [0], given: 0

COOL ! [#permalink]  01 Jun 2003, 22:41
The answer is E... I love this question.
SVP
Joined: 03 Feb 2003
Posts: 1607
Followers: 6

Kudos [?]: 84 [0], given: 0

X, Y, and Z are integers. Find (X*Y)^Z. (1) 1=|X*Y| (2) [#permalink]  02 Jun 2003, 00:11
X, Y, and Z are integers. Find (X*Y)^Z.

(1) 1=|X*Y|
(2) Z^2=Z^3
SVP
Joined: 03 Feb 2003
Posts: 1607
Followers: 6

Kudos [?]: 84 [0], given: 0

Who knows... Let us wait what other people say
Manager
Joined: 12 Mar 2003
Posts: 59
Followers: 1

Kudos [?]: 1 [0], given: 0

Ans : E

1) 1 or -1
2) 0 or 1

Combined : 1, 1, 1, or -1

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