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

Question

(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

Bunuel · Accepted Answer

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.

flgators519 · Answer

agree. gmat club teaches you to really be careful in reading the question

wolver123 · Answer

thanks guys. tricky.

jade3 · Answer

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

seabhi · Answer

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....

asagraw · Answer

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

Regards,
Ashish

Bunuel · Answer

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

MathRevolution · Answer

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.

law258 · Answer

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

ajwithlove · Answer

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

Bunuel · Answer

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

ajwithlove · Answer

Thanks. Its neutral. But it is always counted as an even number right?

Bunuel · Answer

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.

daboo343 · Answer

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
so C is our answer

KrishnakumarKA1 · Answer

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

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

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