Is the positive integer N a perfect square? (1) The number

Question

Are you sure you correctly transcribed the question? 
As it is currently worded, the answer to this question is E.
The answer WOULD be D, if we changed "distinct factors" to "POSITIVE distinct factors."

When asking questions about factors (aka divisors), the GMAT typically restricts the discussion to POSITIVE factors/divisors. If we don't specify such a restriction, then we must also consider negative factors.

From the Official Guide: 
 
So, for example, the  -2  is a factor of 6 since 6 = ( -2 )(-3)

Now onto the question....

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Target question :    Is the positive integer N a perfect square?

Statement 2 : The number of distinct factors of N is even  
There are infinitely many values of N that satisfy this condition. Here are two: 
Case a: N = 3. The distinct factors of N are {-3, -1, 1, 3}. As you can see, there is an even number of distinct factors of N. In this case  N is NOT a perfect square 
Case b: N = 4. The distinct factors of N are {-4, -2, -1, 1, 2, 4}. As you can see, there is an even number of distinct factors of N. In this case  N IS perfect square 
Since we cannot answer the  target question  with certainty, statement 1 is NOT SUFFICIENT

Statement 2 : The sum of all distinct factors of N is even 
There are infinitely many values of N that satisfy this condition. Here are two: 
Case a: N = 3. The distinct factors of N are {-3, -1, 1, 3}, so the sum = (-3) + (-1) + 1 + 3 = 0. The sum of the distinct factors = 0, which is EVEN. In this case  N is NOT a perfect square 
Case b: N = 4. The distinct factors of N are {-4, -2, -1, 1, 2, 4}, so the sum = (-4) + (-2) + (-1) + 1 + 2 + 4 = 0. The sum of the distinct factors = 0, which is EVEN. In this case  N IS a perfect square 
Since we cannot answer the  target question  with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined    
In  both  cases, I showed that N COULD equal 3 or 4. 
So, when we  combine  the statements, N COULD still equal 3 or 4. 
 3 is NOT a perfect square , and  4 IS a perfect square . 
Since we cannot answer the  target question  with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent

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Is the positive integer N a perfect square? (1) The number

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