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

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

Answer is
[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.
Added the OA.
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Re: GMAT Club Test...needs clarification. Thanks [#permalink]

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New post 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.

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

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

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New post 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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wolver123 wrote:
If M and N are positive, what is M*N ?

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

Answer is
[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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New post 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.

Answer: C.


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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New post 27 Jun 2014, 02:17
Expert's post
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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.

Answer: C.


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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

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

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New post 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.
Therefore, the answer is C.


-> 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] 03 Feb 2016, 01:15
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