# Question: Does the Power Equal 1?

## Comment on Does the Power Equal 1?

### Hi, Just another addition to

Hi, Just another addition to info.
For the second statement if we take x=-1 and y= 2 then x+y=1 holds sufficient too. ### Yes, x=-1 and y= 2 then x+y=1

Yes, x=-1 and y= 2 then x+y=1 satisfies the equation in statement 2. However, we might want to use a word different from "sufficient," because statement 2 is not sufficient.

When we use your values (x=-1 and y= 2), the answer to the target is YES, x^y = 1
When we use other values, like x=0 and y=1, the answer to the target is NO, x^y does NOT equal 1
So, statement 2 is not sufficient.

### This looks like one of those

This looks like one of those scenarios you warned test takers about where Statement 1 and 2 are essentially the same...is that right? ### Not quite.

Not quite.

In this question, we can use the same x- and y-values to show that each statement is not sufficient. However, this doesn't mean that the two statements are essentially the same.

Here are a couple of examples, where the two statements are virtually identical:

Statement 1: The radius of circle Q is 5
Statement 2: The circumference of circle Q is 10pi
These statements provide the exact same information. So, the correct answer will be either D or E (depending on the target question).

Statement 1: Integer K has exactly 2 positive divisors
Statement 2: Integer K is prime
These statements provide the exact same information. So, the correct answer will be either D or E (depending on the target question).

For more on this, start watching the following video at 3:20: https://www.gmatprepnow.com/module/gmat-data-sufficiency/video/1109 ### Hi Brent,

Hi Brent,

Can we further simplify this equation to "does x^y = x^0 so does y = 0?

So using logic

1) y can be negative, zero or positive (not sufficient)
2) y can be negative, zero or positive (not sufficient)

1 and 2)
Y can be negative, zero or positive ### Unfortunately, we cannot

Unfortunately, we cannot rephrase the target question as "Does y = 0?"

Here's why:

If x^y = x^0, it COULD be the case that x = 1 and y = 3, since these values satisfy the equation x^y = x^0

Since it's entirely possible for y to equal a number other than 0, we cannot rephrase the target question as "Does y = 0?"

Cheers,
Brent

### Hi Brent,

Hi Brent,
When we look at both the statements together, I am using the following approach and I am concluding that the answer is C (i.e. both statements together are sufficient), please can you advise why this is not correct?
Statement 2 says, x+y =1 , we can re-write it as x = 1-y or y = 1-x. Replacing these values on to statement one:
Xy=0 replacing x with (1-y)*y = 0 or y-y^2=0 or y = y^2. Here I am concluding that this is only possible if y =1.
Similarly, xy=0, replacing y with (1-x)*x=0 or x-x^2=0 or x=x^2. Here also I am concluding x=1. Now we can answer the target question with certainty, hence answer is C. Please can you advise where I am going wrong? ### The only problem with your

The only problem with your solution is when you take the equation y = y^2, there are actually two solutions: y = 1 and y = 0
Likewise, the equation x = x^2 also has two solutions: x = 0 and x = 1

If x = 1 and y = 1, then x^y = 1^1 = 1
If x = 0 and y = 1, then x^y = 0^1 = 0

So the combined statements are not sufficient.