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rohit_gmat: Master | Next Rank: 500 Posts; Posts: 158; Joined: Wed Jun 16, 2010 8:21 amFollowed by: 1 member; Thanked: 13 times

by rohit_gmat » Sun Sep 18, 2011 6:18 am

If Z^(n) = 1 , what is the value of Z?

1.) n is a nonzero integer
2.) z > 0

IMO A
Need explanations...
OA C

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Source: Beat The GMAT — Data Sufficiency | Sun Sep 18, 2011 6:18 am

hitmoss: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Mon May 04, 2009 11:38 am; Location: India

by hitmoss » Sun Sep 18, 2011 7:47 am

z^n = 1.

from 1. n is not zero.
from 2. z>0; z=1,2,3,4,5......

if, z = 2,3,4,5.. in this case z^n can't be 1. as the value comes up more than or less than 1.

As it is mentioned in the question Z^n = 1. in that case z =1. Hence, by using both the equations we can find out the value of z.

Hitmoss:)

"Dreams are not what you see in sleep, Dreams is the thing does not let you sleep."

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

by knight247 » Sun Sep 18, 2011 8:08 am

Z^n = 1

Before we get to the statements. Understand that Z^n = 1 means z has a magnitude of 1 but we don't know its sign. Could be positive or negative.

example (-1)^2=1 or (1)^2=1 or (-1)^10=1 etc. So we basically have different possible values of 1. If n=0 then whatever the value of z, z^n=1

(1)If n is non zero, this doesn't really help us. It only repeats a part of what I've mentioned above. z could be +1 or -1. INSUFFICIENT.

(2)About this statement. I'm sure u remember one important funda, Any number raised to zero equals 1

z could be 1,9,42,10^7 and if n=0 then z^n=1
Also, it could also be that 1^1=1 In which case z=1. Since we get conflicting answers this statement is INSUFFICIENT.

Combining both we get n is non zero and z is +ve . The only possible value for z in this case is 1. Coz 1 raised to the power of a +ve or -ve number is going to equal 1. Hence C

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rohit_gmat: Master | Next Rank: 500 Posts; Posts: 158; Joined: Wed Jun 16, 2010 8:21 amFollowed by: 1 member; Thanked: 13 times

by rohit_gmat » Sun Sep 18, 2011 8:18 am

thanks Knight247 !!
I missed the part where z cud be (-1) and n = even and still z^n = 1

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