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

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

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

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

thanks guys. tricky.

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

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

Regards,
Ashish

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.

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

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?

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.

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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