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Number Properties - m, n

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by hulahooporiginal » Tue Oct 16, 2012 3:50 am
If m and n are nonzero integers, is m^n an integer?

1. n^m is positive
2. n^m is an integer

Manhattan has rephrased this question as

Is n a positive integer, or is m equal to 1?

I do not get the drift! Could someone explain, please?

Thanks!
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by anuprajan5 » Tue Oct 16, 2012 4:03 am
Hi,

The answer is E

Statement 1 - n^m is positive. This could be the case if n is negative and m is even or if n is positive and m is any number. Example

(-1)^2 = 1
1^3 = 1

But if you flip it to m^n, then the same examples become 1/2 and 3. Insufficient

Statement 2 - n^m is an integer. Same 2 examples as above.

Combined, it does not tell you anything. In general, if you have a statement that can be proved using the examples from the previous one, then you should go for E as combined, they say nothing new.

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by hulahooporiginal » Tue Oct 16, 2012 4:46 am
Thanks Anup. Basically, if we look for whether n is positive in each statement, it could be either positive or negative. Even on combining the two statements, it doesn't matter whether n is positive or negative as long as m is positive.

great, what level of difficulty do you think this might be?
anuprajan5 wrote:Hi,

The answer is E

Statement 1 - n^m is positive. This could be the case if n is negative and m is even or if n is positive and m is any number. Example

(-1)^2 = 1
1^3 = 1

But if you flip it to m^n, then the same examples become 1/2 and 3. Insufficient

Statement 2 - n^m is an integer. Same 2 examples as above.

Combined, it does not tell you anything. In general, if you have a statement that can be proved using the examples from the previous one, then you should go for E as combined, they say nothing new.

REgards
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by anuprajan5 » Tue Oct 16, 2012 4:56 am
Well it need not be positive for statement 2 - it just needs to be an integer. but since our example in statement 1 is a subset of the solution for statement 2 and it already proves that statement 2 is insufficient, i wouldnt work on statement 2 further.

I am no expert, but this is maybe a 500-600 range question. Don't quuote me on it though :)

Regards
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by hulahooporiginal » Tue Oct 16, 2012 5:23 am
Hang on a second! Statement 2 is NOT a subset of Statement 1.

In statement 1, n^m is positive.

this will happen under 2 conditions:
a. n is negative, but m is even
b. n is positive, m is positive OR NEGATIVE. if if m is negative, all you get is a fraction. So, you can't just ignore Statement 2 as a subset of Statement 1.

yea?

anuprajan5 wrote:Well it need not be positive for statement 2 - it just needs to be an integer. but since our example in statement 1 is a subset of the solution for statement 2 and it already proves that statement 2 is insufficient, i wouldnt work on statement 2 further.

I am no expert, but this is maybe a 500-600 range question. Don't quuote me on it though :)

Regards
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by anuprajan5 » Tue Oct 16, 2012 6:17 am
hulahooporiginal wrote:Hang on a second! Statement 2 is NOT a subset of Statement 1.

In statement 1, n^m is positive.

this will happen under 2 conditions:
a. n is negative, but m is even
b. n is positive, m is positive OR NEGATIVE. if if m is negative, all you get is a fraction. So, you can't just ignore Statement 2 as a subset of Statement 1.

yea?

anuprajan5 wrote:Well it need not be positive for statement 2 - it just needs to be an integer. but since our example in statement 1 is a subset of the solution for statement 2 and it already proves that statement 2 is insufficient, i wouldnt work on statement 2 further.

I am no expert, but this is maybe a 500-600 range question. Don't quuote me on it though :)

Regards
Anup

Hi,

I think you misunderstood. I mentioned that the example in statement 1 is a subset of the examples we could take for statement 2.

Statement 1 says that n^m is positive.
Statement 2 says that n^m is an integer which could mean that n^m is a positive or negative integer. If the example I used in statement 1 is insufficient - it is a subset of the examples we could use for statement 2 meaning that statement 2 is also insufficient.

I hope that clears things.

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by Brent@GMATPrepNow » Tue Oct 16, 2012 6:56 am
hulahooporiginal wrote:If m and n are nonzero integers, is m^n an integer?

1. n^m is positive
2. n^m is an integer

Manhattan has rephrased this question as

Is n a positive integer, or is m equal to 1?
This is a great rephrasing of the target question. However, I think it needs one more condition.
It should be: Is n a positive integer, or is m equal to 1 or -1?

For this question, if m = -1, then m^n is guaranteed to be an integer

Cheers,
Brent
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by hulahooporiginal » Thu Oct 18, 2012 2:32 am
Cheers Brent! I am having severe trouble with Data Sufficiency questions. I mean, yesterday i did 35 questions, out of which i got 10 wrong. and these are not high difficulty level questions. Any general advice to get DS right?

My Problem Solving strike rate on the other hand is way stronger.

Brent@GMATPrepNow wrote:
hulahooporiginal wrote:If m and n are nonzero integers, is m^n an integer?

1. n^m is positive
2. n^m is an integer

Manhattan has rephrased this question as

Is n a positive integer, or is m equal to 1?
This is a great rephrasing of the target question. However, I think it needs one more condition.
It should be: Is n a positive integer, or is m equal to 1 or -1?

For this question, if m = -1, then m^n is guaranteed to be an integer

Cheers,
Brent
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by Brent@GMATPrepNow » Thu Oct 18, 2012 5:55 am
hulahooporiginal wrote:Cheers Brent! I am having severe trouble with Data Sufficiency questions. I mean, yesterday i did 35 questions, out of which i got 10 wrong. and these are not high difficulty level questions. Any general advice to get DS right?

My Problem Solving strike rate on the other hand is way stronger.
Hi hulahooporiginal,

Don't worry. Practically everyone struggles with Data Sufficiency questions at first. It's a question type that's totally unique to the GMAT, so it's foreign territory.

If you're interested, our company has a free set of videos that cover every aspect of Data Sufficiency: https://www.gmatprepnow.com/module/gmat-data-sufficiency

Also be sure to review tons of posts in this forum, and watch how the experts tackle DS questions.

Cheers,
Brent


Cheers,
Brent
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by hulahooporiginal » Thu Oct 18, 2012 3:04 pm
thank you so much Brent. Some of the strategies are very useful. The simplest of them being hiding statement 1 while evaluating statement 2. I make the mistake of carrying information forward very often.

Also, in value questions, i do end up solving. So even though i know i don't need to, it is useful to have all the rules and common mistakes laid out in one place. i have actually written these rules/common errors down to remind myself not to repeat them.

Thanks once again :)

Brent@GMATPrepNow wrote:
hulahooporiginal wrote:Cheers Brent! I am having severe trouble with Data Sufficiency questions. I mean, yesterday i did 35 questions, out of which i got 10 wrong. and these are not high difficulty level questions. Any general advice to get DS right?

My Problem Solving strike rate on the other hand is way stronger.
Hi hulahooporiginal,

Don't worry. Practically everyone struggles with Data Sufficiency questions at first. It's a question type that's totally unique to the GMAT, so it's foreign territory.

If you're interested, our company has a free set of videos that cover every aspect of Data Sufficiency: https://www.gmatprepnow.com/module/gmat-data-sufficiency

Also be sure to review tons of posts in this forum, and watch how the experts tackle DS questions.

Cheers,
Brent


Cheers,
Brent
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