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# If M and N are positive, what is M*N ?

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If M and N are positive, what is M*N ? [#permalink]

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21 Nov 2009, 10:05
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If M and N are positive, what is M*N ?

(1) M^N=1
(2) N^M=1

[Reveal] Spoiler:
C
. But I picked
[Reveal] Spoiler:
E
. M, N could be 0, or 1, because whatever to the power of zero is 1. Or is it different in GMATland?

Thanks guys
[Reveal] Spoiler: OA

Last edited by Bunuel on 04 Jul 2013, 23:48, edited 1 time in total.
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Re: GMAT Club Test...needs clarification. Thanks [#permalink]

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21 Nov 2009, 10:28
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wolver123 wrote:
If M and N are positive, what is M*N ?

1.M^N=1
2.N^M=1

Answer is C. But I picked E. M, N could be 0, or 1, because whatever to the power of zero is 1. Or is it different in GMATland?

Thanks guys

m and n are positive.

(1) m^n=1 --> m=1 and n is any value (satisfying the condition that they are both positive). mn unknown. Not sufficient;

(2) n^m=1 --> n=1 and m is any value (satisfying the condition that they are both positive). mn unknown. Not sufficient;

(1)+(2) m=1 and n=1, mn=1. Sufficient.

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Re: GMAT Club Test...needs clarification. Thanks [#permalink]

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21 Nov 2009, 20:27
agree. gmat club teaches you to really be careful in reading the question
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Re: GMAT Club Test...needs clarification. Thanks [#permalink]

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21 Nov 2009, 23:18
thanks guys. tricky.
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Re: GMAT Club Test...needs clarification. Thanks [#permalink]

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22 Nov 2009, 05:32
St1: M^N=1 => M =1 & N=any number or M= any number & N=0; So M*N could be 0 or any number; Insuff
St2: N^M=1 => M =any number & N=1 or M= 0 & N=any number; So M*N could be 0 or any number; Insuff

Combined M=1 and N=1. Hence M*N=1

Hence C
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Re: If M and N are positive, what is M*N ? [#permalink]

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26 Dec 2013, 04:05
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wolver123 wrote:
If M and N are positive, what is M*N ?

(1) M^N=1
(2) N^M=1

[Reveal] Spoiler:
C
. But I picked
[Reveal] Spoiler:
E
. M, N could be 0, or 1, because whatever to the power of zero is 1. Or is it different in GMATland?

Thanks guys

IMO C.

M and N are positive , hence M or N cannot be 0.

1) M = 1 and N can be 1,2,3.. .. hene M*N can be 1,2,3....Not Sufficient.

2) N=1 and M can be anything 1,2,3 ... Not sufficient ....

Combined .. we have M=1 and N=1 .. Sufficient....
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Re: If M and N are positive, what is M*N ? [#permalink]

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27 Jun 2014, 02:07
Bunuel wrote:
wolver123 wrote:
If M and N are positive, what is M*N ?

1.M^N=1
2.N^M=1

Answer is C. But I picked E. M, N could be 0, or 1, because whatever to the power of zero is 1. Or is it different in GMATland?

Thanks guys

m and n are positive.

(1) m^n=1 --> m=1 and n is any value (satisfying the condition that they are both positive). mn unknown. Not sufficient;

(2) n^m=1 --> n=1 and m is any value (satisfying the condition that they are both positive). mn unknown. Not sufficient;

(1)+(2) m=1 and n=1, mn=1. Sufficient.

Thanks. In GC math book I read that 0 should be treated as positive. Please correct me if I am wrong here.

Regards,
Ashish
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Re: If M and N are positive, what is M*N ? [#permalink]

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27 Jun 2014, 02:17
Expert's post
1
This post was
BOOKMARKED
asagraw wrote:
Bunuel wrote:
wolver123 wrote:
If M and N are positive, what is M*N ?

1.M^N=1
2.N^M=1

Answer is C. But I picked E. M, N could be 0, or 1, because whatever to the power of zero is 1. Or is it different in GMATland?

Thanks guys

m and n are positive.

(1) m^n=1 --> m=1 and n is any value (satisfying the condition that they are both positive). mn unknown. Not sufficient;

(2) n^m=1 --> n=1 and m is any value (satisfying the condition that they are both positive). mn unknown. Not sufficient;

(1)+(2) m=1 and n=1, mn=1. Sufficient.

Thanks. In GC math book I read that 0 should be treated as positive. Please correct me if I am wrong here.

Regards,
Ashish

Where in math book is written this?

0 is neither positive nor negative integer (the only one of this kind).

Check tips on number properties here: tips-and-hints-for-specific-quant-topics-with-examples-172096.html#p1371030

Theory on Number Properties: math-number-theory-88376.html

DS Number Properties Problems to practice: search.php?search_id=tag&tag_id=38
PS Number Properties Problems to practice: search.php?search_id=tag&tag_id=59

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Re: If M and N are positive, what is M*N ? [#permalink]

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02 Feb 2016, 01:43
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Re: If M and N are positive, what is M*N ? [#permalink]

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03 Feb 2016, 01:15
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If M and N are positive, what is M*N ?

(1) M^N=1
(2) N^M=1

In the original condition, there are 2 variables(m,n), which should match with the number of equations. So you need 2 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make C the answer.
When 1) & 2), they become m=n=1.

-> For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
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Re: If M and N are positive, what is M*N ? [#permalink]

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18 Sep 2016, 09:45
C is correct. Here's why:

(1) M^N = 1

NOT SUFFICIENT (we don't know anything about M and N)

(2) N^M = 1

NOT SUFFICIENT (for the same reason as (1))

Together? (1) + (2) --> we know M=N=1
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Re: If M and N are positive, what is M*N ? [#permalink]

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14 Mar 2017, 17:30
Bunuel wrote:
wolver123 wrote:
If M and N are positive, what is M*N ?

1.M^N=1
2.N^M=1

Answer is C. But I picked E. M, N could be 0, or 1, because whatever to the power of zero is 1. Or is it different in GMATland?

Thanks guys

m and n are positive.

(1) m^n=1 --> m=1 and n is any value (satisfying the condition that they are both positive). mn unknown. Not sufficient;

(2) n^m=1 --> n=1 and m is any value (satisfying the condition that they are both positive). mn unknown. Not sufficient;

(1)+(2) m=1 and n=1, mn=1. Sufficient.

SO the catch here is that 1 is a positive number and 0 is not?
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Re: If M and N are positive, what is M*N ? [#permalink]

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14 Mar 2017, 21:24
ajwithlove wrote:
Bunuel wrote:
wolver123 wrote:
If M and N are positive, what is M*N ?

1.M^N=1
2.N^M=1

Answer is C. But I picked E. M, N could be 0, or 1, because whatever to the power of zero is 1. Or is it different in GMATland?

Thanks guys

m and n are positive.

(1) m^n=1 --> m=1 and n is any value (satisfying the condition that they are both positive). mn unknown. Not sufficient;

(2) n^m=1 --> n=1 and m is any value (satisfying the condition that they are both positive). mn unknown. Not sufficient;

(1)+(2) m=1 and n=1, mn=1. Sufficient.

SO the catch here is that 1 is a positive number and 0 is not?

0 is neither positive nor negative even integer. I would not call it a catch though, it's a math fact.
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Re: If M and N are positive, what is M*N ? [#permalink]

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14 Mar 2017, 21:48
Bunuel wrote:
ajwithlove wrote:
Bunuel wrote:

SO the catch here is that 1 is a positive number and 0 is not?

0 is neither positive nor negative even integer. I would not call it a catch though, it's a math fact.

Thanks. Its neutral. But it is always counted as an even number right?
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Re: If M and N are positive, what is M*N ? [#permalink]

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14 Mar 2017, 21:54
ajwithlove wrote:
Thanks. Its neutral. But it is always counted as an even number right?

An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder.

0/2 = 0 = integer, thus it's even.
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Re: If M and N are positive, what is M*N ? [#permalink]

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15 Mar 2017, 00:04
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from statement 1 m=1, because it is given m and n both are positive. so 1 to the power any number is always
1 only m= 1
Similarly statement 2 says n= 1
hence m*n =1
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Re: If M and N are positive, what is M*N ? [#permalink]

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15 Mar 2017, 01:57
St 1: M^N = 1. that means, either N=0 or M=1 or both. INSUFFICIENT
St 2: N^M = 1. that means, either M=0 or N=1 or both. INSUFFICIENT

St 1& St 2: can only be true if N=1 and M=1.hence, n*m = 1. ANSWER

Option C
Re: If M and N are positive, what is M*N ?   [#permalink] 15 Mar 2017, 01:57
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