ardz24 wrote:Is x divisible by 3?
(1) x + y is divisible by 3.
(2) x - y is divisible by 3.
What's the best way to determine which statement is sufficient? Can any experts help?
This question can be dealt with an ease by choosing smart numbers for x and y.
(1) x + y is divisible by 3.
Case 1: Say x = 3 and y =0, then x + y = 3 + 0 = 3. We see that x + y and x are divisible by 3. The answer is Yes.
Case 2: Say x = 4 and y = 2, then x + y = 5 + 2 = 6. We see that though x + y is divisible by 3, x is NOT. The answer is No.
No unique answer. Not sufficient.
(2) x - y is divisible by 3.
Case 1: Say x = 3 and y =0, then x - y = 3 - 0 = 3. We see that x - y and x are divisible by 3. The answer is Yes.
Case 2: Say x = 5 and y = 2, then x - y = 5 - 2 = 3. We see that though x - y is divisible by 3, x is NOT. The answer is No.
No unique answer. Not sufficient.
(1) and (2) together
You cannot find a pair of integers such that x + y and x - y are each divisible by 3, and x is not. Thus, x is divisible by 3. The answer is Yes. Sufficient.
Let's take an algebraic route to understand this.
Say x + y = 3k, and x - y = 3q, where k and q are any integers
Thus, x =
3[(k + q)/2]; and y = 3[(k - q)/2]
We see that x is a multiple of 3. Sufficient.
The correct answer:
C
Hope this helps!
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