gmat1011 wrote:
If & represents one of the operations +, - and X
is (a & b) + (a & c) = a & (b + c) for all numbers a, b, and c ?
(1) & represents subtraction.
(2) m&2 is not equal to 2&m for some numbers m.
C/right Jeff Sackmann. Just posting it here for educational purposes.
Don't get how it can be D. Shouldn't it be E? in 2a-b-c = a-b-c, a can be 0 when there would in fact be a "Yes" answer, while it would also be possible to get "No" with other values?
The point here is that the question asks whether \((a@b)+(a@c)=a@(b+c)\) is true
FOR ALL NUMBERS a, b, and c?
(1) \(@\) represents subtraction --> the question becomes is \(2a-b-c=a-b-c\), or is \(a=0\)? So \((a@b)+(a@c)=a@(b+c)\) is NOT true for all numbers a, b, and c (so the answer to the question is NO), for this expression to be true \(a\) must equal to zero (so not for all values of \(a\)). Sufficient.
(2) \(m@2\neq{2@}\) --> \(@\) represents subtraction (as it can not be addition or multiplication), so we have the the same info as above. Sufficient.
Answer: D.
Alternately you can see that \((a@b)+(a@c)=a@(b+c)\) to be true
FOR ALL NUMBERS a, b, and c then \(@\) must represent multiplication as only for multiplication it's true for all numbers: \(ab+ac=ab+ac\). So the question basically ask whether \(@\) represents multiplication, both (1) and (2) give answer No toth is question.
Hope it's clear.