## Exponents and roots

##### This topic has expert replies
Master | Next Rank: 500 Posts
Posts: 163
Joined: 13 Jan 2015
Thanked: 2 times

### Exponents and roots

by didieravoaka » Wed Mar 23, 2016 9:29 am
How can we know from the prompt that y=0 or y=1. I don't understand that.

Thanks to explain. Legendary Member
Posts: 2083
Joined: 03 Feb 2014
Location: New York City Metro Area and Worldwide Online
Thanked: 955 times
Followed by:140 members
GMAT Score:800
by [email protected] » Wed Mar 23, 2016 5:45 pm
didieravoaka wrote:If m and k are non zero integers and yáµ�â�ºáµ� = yáµ�, what is the value of y?

(1) k is odd.

(2) y is odd.
Given that m and k are non zero integers, m + k cannot equal m.

Most numbers generate different numbers when raised to different powers.

The only numbers that can generate the same numbers when raised to different powers are 0, 1 and -1.

So there are only three values of y that could work in the equation yáµ�â�ºáµ� = yáµ� , y = 0, y = 1 and y = -1.

0 and 1 raised to any power generate 0 and 1.

-1 raised to any even power generates 1. So if m is even and m + k is even, -1áµ�â�ºáµ� = -1áµ�.

-1 raised to any odd power generates -1. So if m is odd and m + k is odd, -1áµ�â�ºáµ� = -1áµ�.

Statement 1: k is odd.

This tells us that y â‰  -1.

If y = -1 and if m is even and k is odd, then m + k is odd. So yáµ� = 1 and yáµ�â�ºáµ� = -1.

If y = -1 and if m is odd and k is odd, then m + k is even. So yáµ� = -1 and yáµ�â�ºáµ� = 1.

So if k is odd, yáµ�â�ºáµ� cannot be equal to yáµ� if y = -1.

Still, y could be 0 or 1.

Insufficient.

Statement 2: y is odd.

This tells us that y cannot be 0, but y could be 1 or -1.

Insufficient.

Combined the statements tell us that y is not 0 or -1. So y must be 1.

Sufficient. 