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## Comment on

Equivalent Powers## x^n= y^n. Can we not do this:

## No, we can't do that for a

No, we can't do that for a few reasons.

First, if n = 0, then x^n = y^n for all values of x and y.

For example, although 2^0 = 1^0, we cannot conclude that 2 = 1

Second, if n is an even integer, then x^n = y^n does not necessarily mean that x = y.

For example, although 3^2 = (-3)^2, we cannot conclude that 3 = -3

## This question by far is one

## Thanks Lee!

Thanks Lee!

## Brent, is it possible to have

## That's a great rule!

That's a great rule!

We can even prove it.

(-a)^n = [(-1)(a)]^n = [(-1)^n][a^n]

= (1)[a^n] since -1 raised to an even power equals 1

= a^n

## Brent,

I did not get how case 3 make statement 1 sufficient.

Our rephrased question states n should be 0, in case 3. How did you determine x/y ^ n , and n=0?

## We are told that x^n = y^n

We are told that x^n = y^n

There are 3 possible ways in which this equation can hold true.

In other words, at least one of the possible cases MUST be true:

case i) x/y = 1 (that is x = y)

case ii) x/y = -1 AND n is even

case iii) n = 0

Statement 1 allows us to rule out cases i and ii

This means case iii MUST be true (i.e., n MUST equal 0)

## hey that was a great

I came up with another way to solve it.

statement 1 says: x/y=2

lets suppose values for x and y

let x=4 , y=2

this satisfies statement one as 4/2=2

now put these values in given x^n=y^n

which makes 4^n=2^n

there is only one possible condition which can make this statement true,i.e when n=0

as 4^0=2^0=1

hence sufficient.

Statement 2 goes same as yours

please tell me if I am going wrong somewhere.

## That's a valid solution.

That's a valid solution.

## I must say that rephrasing DS

Thanks a lot!

## I'm glad you like the tip.

I'm glad you like the tip.

Some people fail to recognize that, by devoting some time to rephrasing the target question, we can actually analyze the statements faster.

## How did we know that case iii

Could anyone explain this part to me?

## I'm not 100% sure what you're

I'm not 100% sure what you're asking, but I have a feeling that you're wondering how we can be certain that n = 0 (in statement 1). If so, here's my response:

We're told that x^n = y^n

There are EXACTLY 3 possible ways in which this equation can hold true.

In other words, if x^n = y^n, then at least one of the following cases MUST be true:

case i) x/y = 1 (that is x = y)

case ii) x/y = -1 AND n is even

case iii) n = 0

Statement 1 allows us to rule out cases i and ii, leaving us with case iii (n = 0). So, it MUST be the case that n = 0

In statement 2, we're able to test some values to show that we cannot answer the target question with certainty.

Does that help?

## Brent, great question. Made

While I understood this one off question, I have a feeling that without further practice of the same kind of question, it is likely going to fade away. For some reinforcement, where can I find similar type questions I.e. Deducing the question stem type

## Yes, rephrasing the target

Yes, rephrasing the target question can be a huge time-saver for many Data Sufficiency questions.

If you want to see more instance where I've rephrased the target question, go to the Beat The GMAT forum or GMAT Club forum, and perform a search for "This is a good candidate for rephrasing the target question" (a preset phrase I often type when answering Data Sufficiency questions), you'll find all of the instances in which I've rephrased the target question.

I hope that helps.

Cheers,

Brent

## Is 0 considered as an Integer

## Yes, according to the GMAT

Yes, according to the GMAT test-makers, zero is an integer.

Zero is also considered an integer by mathematicians, teachers and everyone else :-)

Cheers,

Brent

## Is this the maximum level of

Honestly my answer was wrong

## I'd say this question falls

I'd say this question falls in the 700-750 range of difficulty.

Cheers,

Brent

## Hi Brent,

Can you please explain on the approach for solving this problem? There are some answers on gmatclub, but they skip steps making it hard to follow. Would appreciate it if you could give an overall tip on how to solve these questions and explain the logic behind the solution:

https://gmatclub.com/forum/what-is-the-rightmost-non-zero-digit-of-305422.html#p2359731

Thanks, much appreciated!

## Tricky question!!

Tricky question!!

Here's my full solution: https://gmatclub.com/forum/what-is-the-rightmost-non-zero-digit-of-30542...

## OK, somehow I just don't

## That's correct.

How did you conclude that x = y?

## is x not equal to y here?

## How did you conclude that x =

How did you conclude that x = y?