interesting and challenging ds

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rohit.reddy: Newbie | Next Rank: 10 Posts; Posts: 5; Joined: Fri Jul 17, 2009 9:39 am

by rohit.reddy » Mon Dec 28, 2009 7:04 am

if z^n=1 then what's the value of z?

(1) n is a non zero integer
(2) z>0

Official answer after some discussion....expalin ur stand ...

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Source: Beat The GMAT — Data Sufficiency | Mon Dec 28, 2009 7:04 am

papgust: Community Manager; Posts: 1537; Joined: Mon Aug 10, 2009 6:10 pmFollowed by: 252 members; Thanked: 653 times

by papgust » Mon Dec 28, 2009 7:52 am

IMO A

We know that z^n = 1. We are asked for the value of z.

(I) n is a non-zero integer.

Here n could take positive or negative integers. In any case, z will always be 1 to satisfy z^n = 1. z cannot take 0 or -1 or any number other than 1. Hence, only 1 value. Sufficient.

(II) z>0

Here z can take any positive integer. n could only be 0. But we are not bothered about n.
1^0 = 1
2^0 = 1
.
.
You get multiple z values. Insufficient.

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rohan_vus: Master | Next Rank: 500 Posts; Posts: 189; Joined: Thu Apr 03, 2008 2:03 pm; Location: USA; Thanked: 21 times

by rohan_vus » Mon Dec 28, 2009 7:57 am

stmnt (1) is not suffcient .. when n is a even integer u can have z = -1 or 1 ,as Z^even =1
z = 1 only when n is odd integer

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papgust: Community Manager; Posts: 1537; Joined: Mon Aug 10, 2009 6:10 pmFollowed by: 252 members; Thanked: 653 times

by papgust » Mon Dec 28, 2009 8:14 am

Oh yes! Forgot to consider that case. Thanks for the catch

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deepakdewani: Junior | Next Rank: 30 Posts; Posts: 24; Joined: Sun Nov 29, 2009 3:00 am; GMAT Score:770

by deepakdewani » Mon Dec 28, 2009 10:30 am

IMO C

Clearly Statements 1 and 2 are not enough on their own.

But when when you combine both, you can conclude that the only way z^n = 1 when z>0 and n is not 0, is when z=1.

Hence we can find the value of z by combining both statements and therefore IMO C

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linkinpark: Master | Next Rank: 500 Posts; Posts: 124; Joined: Tue Dec 22, 2009 8:32 am; Location: Karjat; Thanked: 3 times

by linkinpark » Tue Dec 29, 2009 8:11 am

shouldn't it be (B), we're told z^n = 1 from stmt II z>0, z^n = 1 only if z = 1 coz 1^anything is 1

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deepakdewani: Junior | Next Rank: 30 Posts; Posts: 24; Joined: Sun Nov 29, 2009 3:00 am; GMAT Score:770

by deepakdewani » Tue Dec 29, 2009 8:36 am

shouldn't it be (B), we're told z^n = 1 from stmt II z>0, z^n = 1 only if z = 1 coz 1^anything is 1

Nopes. Even if z>o, z can take multiple values if you take n as 0 (which you can because Statement 2 alone does not put any conditions on the value of n). So if n=0, even 1^0 = 1, 2^0 = 1, 3^0 = 1.....and so on. Hence z can take on multiple values if you take only Statement 2 into account.

It's only when you combine Statement 2 with the first one, that you can conclude that the only possible value that z can take is 1.

Hence C

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