If z^n = 1, what is the value of z?

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nwalker001: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Sun May 02, 2010 11:10 am; Thanked: 1 times

by nwalker001 » Wed May 19, 2010 1:16 pm

I didn't get a response yet on the MGMAT forum so I thought I'd post this here:

If z^n = 1, what is the value of z?

1. n is a non zero integer.

2. z > 0.

An expert, Ron Purewal, agreed that the answer is C. I think that it's E, since we don't know that z is an integer.

z = (1^(1/2)) and n = 2 works

and so does:

z = 1 and n = 1

Link to original post:

https://www.manhattangmat.com/forums/if- ... t2264.html

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Source: Beat The GMAT — Data Sufficiency | Wed May 19, 2010 1:16 pm

bharatishiv: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Thu May 13, 2010 12:13 pm

by bharatishiv » Wed May 19, 2010 1:56 pm

nwalker001 wrote:I didn't get a response yet on the MGMAT forum so I thought I'd post this here:

If z^n = 1, what is the value of z?

1. n is a non zero integer.

2. z > 0.

An expert, Ron Purewal, agreed that the answer is C. I think that it's E, since we don't know that z is an integer.

z = (1^(1/2)) and n = 2 works

and so does:

z = 1 and n = 1

Link to original post:

https://www.manhattangmat.com/forums/if- ... t2264.html

You aren't concerned whether Z is an integer or not. The Q asks for the value of Z.

Z^n = 1

As per Stmt 1: n is a non-zero integer. To satisfy the above eqn. Z can be either -1 or 1 for the Z^n to be = 1.

If n = -2 then it would 1/Z^2 = 1, in which case Z has to be an integer for Z^n = 1.

{
Say, If u consider Z = 1/4 and n =3 then (1/4)^3 is not equal to 1 as per the Q.
and if Z=1/4 and n = -2, then too (1/4)^-2 = 1/(1/4)^2 = 1/(1/16)= 16 which again is not equal to 1.

So Z has to be 1 or an integer.
}

So, this is insufficient.

As per Stmt 2: Z>0, it could be any no. greater than 0. So, insufficient.

Combining 2 statements, we get that Z= 1.

So, the Ans is "C"

Hope this clarifies your doubt!!!
Do let me know if am going wrong somewhere.

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nwalker001: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Sun May 02, 2010 11:10 am; Thanked: 1 times

by nwalker001 » Wed May 19, 2010 5:45 pm

Here's why I still think the answer is E

If z^n = 1, what is the value of z?

1. n is a non zero integer.

2. z > 0.

Evaluate Just Statement 1 (n is a non zero integer)

This means that n is not 0 and that n is an integer

This leaves a lot of possibilities for both z and n:

z = 1, n = 1
z = -1, n = 2
z = 1, n = 2
z = 1^(1/2), n = 2
z = 1^(1/4), n = 4
etc.

Statement 1 is insufficient

Evaluate Just Statement 2 (z > 0)

This means that z is positive, which is the same thing as saying that z is not negative or equal to zero

This leave a lot of possibilities for both z and n:

z = 1, n = any number
z = 1^(1/2), n = 2
z = 1^(1/4), n = 4
z = any positive number, n = 0
etc.

Statement 2 is insufficient

Evaluate Statements 1 & 2 Together

If z^n = 1, what is the value of z?

1. n is a non zero integer.

2. z > 0.

Both statements can still be satisfied with many possibilities for z:

z = 1, n = 1
z = 1^(1/2), n = 2
z = 1^(1/4), n = 4
z = 1^(1/6), n = 6
etc.

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krazy800: Master | Next Rank: 500 Posts; Posts: 136; Joined: Sun Sep 28, 2008 8:20 pm; Location: fssf; Thanked: 17 times

by krazy800 » Wed May 19, 2010 6:59 pm

nwalker001 wrote:Here's why I still think the answer is E

If z^n = 1, what is the value of z?

1. n is a non zero integer.

2. z > 0.

Evaluate Just Statement 1 (n is a non zero integer)

This means that n is not 0 and that n is an integer

This leaves a lot of possibilities for both z and n:

z = 1, n = 1
z = -1, n = 2
z = 1, n = 2
z = 1^(1/2), n = 2
z = 1^(1/4), n = 4
etc.

Statement 1 is insufficient

Evaluate Just Statement 2 (z > 0)

This means that z is positive, which is the same thing as saying that z is not negative or equal to zero

This leave a lot of possibilities for both z and n:

z = 1, n = any number
z = 1^(1/2), n = 2
z = 1^(1/4), n = 4
z = any positive number, n = 0
etc.

Statement 2 is insufficient

Evaluate Statements 1 & 2 Together

If z^n = 1, what is the value of z?

1. n is a non zero integer.

2. z > 0.

Both statements can still be satisfied with many possibilities for z:

z = 1, n = 1
z = 1^(1/2), n = 2
z = 1^(1/4), n = 4
z = 1^(1/6), n = 6
etc.

In your example:

1^(1/2) = 1^(1/4)=1^(1/6) =1 (1 to the power any number is 1 itself)

so we end up with Z=1 (i.e. unique value, Considering Statements I & II)

I believe, despite considering any decimal value for Z, if Z^n =1, Z should be 1 if n is non zero integer

OA - C

HTH!!

Aiming High

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Patrick_GMATFix: GMAT Instructor; Posts: 1052; Joined: Fri May 21, 2010 1:30 amFollowed by: 98 members; Thanked: 335 times

by Patrick_GMATFix » Fri May 21, 2010 10:36 am

Because there are only a few distinct ways to get an exponential expression to equal 1, it makes sense to list out the possibilities:

1) n = 0 and z is anything
2) z =1 and n is anything
3) z = -1 and n is even.

Alone, neither statement limits us to a unique value of z, but together they guarantee that z will be 1.

This is QID 1225

-Patrick

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