If c and d are integers, is c − 3d even?

Question

(1) c and d are odd.
(2) c − 2d is odd.

GMATWhizTeam · Answer

Step 1: Analyze Question Stem 
 • c and d are integers.
• We need to find if c – 3d = even or not.
• For c - 3d to be even, there can be two possibilities:
 o Case 1: Both c and d are even.
  c – 3d = Even – Odd * Even = Even 
o Case 2: Both c and d are odd.
  c – 3d = Odd – Odd * Odd = Even

Thus, only when both c and d are even or both are odd, then c – 3d is even. Keeping this in mind, let’s analyze the statements.

Step 2: Analyze individual statements

Statement 1:  c and d are odd.
 • We know that if both c and d are odd, then c – 3d is even. 
Hence, statement 1 is sufficient and we can eliminate answer options B, C, and E.

Statement 2:  c − 2d is odd.
 • c – even * d = odd
• c – even = odd
• c = odd + even = odd 
Thus, using this statement, we can find the even-odd nature of c. However, we don’t know the nature of d.

Hence, statement 2 is not sufficient and the correct answer is  Option A .

prescott · Answer

Hello  Bunuel  ,

Can we definitively say that A is the correct answer?

What if C=9 and D=3, then c-3d is 9-3(3) = Zero, thus not even nor odd.

Would E be the true correct answer for this problem?

Bunuel · Answer

0 is an even number. ZERO: 1. 0 is an integer. 2. 0 is an even integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even. 3. 0 is neither positive nor negative integer (the only one of this kind). 4. 0 is divisible by EVERY integer except 0 itself. Check more here: https://gmatclub.com/forum/number-proper ... 74996.html

If c and d are integers, is c − 3d even?

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