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# M13-01

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 00:48
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45% (medium)

Question Stats:

74% (00:30) correct 26% (00:58) wrong based on 125 sessions

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If $$m$$ and $$n$$ are positive numbers, what is the value of $$m*n$$?

(1) $$m^n = 1$$

(2) $$n^m = 1$$

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Joined: 02 Sep 2009
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16 Sep 2014, 00:48
Official Solution:

(1) $$m^n=1$$. If $$m=1$$ then $$n$$ can be any positive number. Not sufficient.

(2) $$n^m=1$$. If $$n=1$$ then $$m$$ can be any positive number. Not sufficient.

(1)+(2) From above we have that $$m=1$$ and $$n=1$$, hence $$mn=1$$. Sufficient.

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14 Mar 2015, 13:44
Math Expert
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14 Mar 2015, 20:12
samcialek wrote:

hi
since it is given m and n are positive, they cannot be 0..
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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06 Dec 2015, 12:49
Bunuel wrote:
Official Solution:

(1) $$m^n=1$$. If $$m=1$$ then $$n$$ can be any positive number. Not sufficient.

(2) $$n^m=1$$. If $$n=1$$ then $$m$$ can be any positive number. Not sufficient.

(1)+(2) From above we have that $$m=1$$ and $$n=1$$, hence $$mn=1$$. Sufficient.

But the Stem doesn't mention m and n to be positive integers.The stem says they are positive numbers > 0
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15 Jan 2016, 18:51
Question stem says: m & n are positive numbers. Note that 0 isn't a positive number, hence zero is ruled out
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10 Jun 2016, 04:51
HI ... why have we ruled out the fact that a number raised to 0 is also equal to 1 and that 0 raised to 0 is also equal to one. m and n could both be equal to 0
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10 Jun 2016, 06:17
sheetaldodani wrote:
HI ... why have we ruled out the fact that a number raised to 0 is also equal to 1 and that 0 raised to 0 is also equal to one. m and n could both be equal to 0

We are told that m and n are positive numbers, 0 is neither positive nor negative.
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Updated on: 07 Aug 2016, 05:09
I don't agree with the explanation. both the numbers m & n can be 0 . so it should be E.

* OOPS! My bad! Ignored vital point in question statement.

Originally posted by Lastlap2016 on 06 Aug 2016, 08:23.
Last edited by Lastlap2016 on 07 Aug 2016, 05:09, edited 1 time in total.
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06 Aug 2016, 11:08
Lastlap2016 wrote:
I think this is a poor-quality question and I don't agree with the explanation. both the numbers m & n can be 0 . so it should be E.

The question is correct. You should read questions more carefully: we are told that m and n are positive numbers, 0 is neither positive nor negative.
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10 Sep 2016, 09:42
1
Hey - can m or n be decimals which happen to equals to both m and n being raised to the power of each other =1 ?
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19 Sep 2016, 08:33
marshnaz wrote:
Hey - can m or n be decimals which happen to equals to both m and n being raised to the power of each other =1 ?

If m and n are positive numbers, what is the value of m∗nm∗n?

In GMAT positive number means integer greater than 0.
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19 Sep 2016, 15:07
0ld wrote:
marshnaz wrote:
Hey - can m or n be decimals which happen to equals to both m and n being raised to the power of each other =1 ?

If m and n are positive numbers, what is the value of m∗nm∗n?

In GMAT positive number means integer greater than 0.

Is this true? If we see x is a positive number, we know that x is a positive integer?

Thanks!
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20 Sep 2016, 04:25
ddb123 wrote:
0ld wrote:
marshnaz wrote:
Hey - can m or n be decimals which happen to equals to both m and n being raised to the power of each other =1 ?

If m and n are positive numbers, what is the value of m∗nm∗n?

In GMAT positive number means integer greater than 0.

Is this true? If we see x is a positive number, we know that x is a positive integer?

Thanks!

No, that's NOT true. Positive numbers are numbers greater than 0, not necessarily integers.
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14 Sep 2017, 06:04
Bunuel wrote:
If $$m$$ and $$n$$ are positive numbers, what is the value of $$m*n$$?

(1) $$m^n = 1$$

(2) $$n^m = 1$$

Hi Bunuel,

When we combine both statements, we get
m^n = n^m

2^4= 4^2 also satisfies this condition. Hence mn can be 8 as well as 1. So the answer should be E.

Is this incorrect?
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14 Sep 2017, 06:07
1
Yashodhan123 wrote:
Bunuel wrote:
If $$m$$ and $$n$$ are positive numbers, what is the value of $$m*n$$?

(1) $$m^n = 1$$

(2) $$n^m = 1$$

Hi Bunuel,

When we combine both statements, we get
m^n = n^m

2^4= 4^2 also satisfies this condition. Hence mn can be 8 as well as. So the answer should be E.

Is this incorrect?

No, because we now that $$m^n = 1$$ and $$n^m = 1$$, not 16...
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04 May 2018, 08:40
marshnaz wrote:
Hey - can m or n be decimals which happen to equals to both m and n being raised to the power of each other =1 ?

Is the above situation possible?
Re: M13-01   [#permalink] 04 May 2018, 08:40
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# M13-01

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