If the symbol @ represents either addition or multiplication, which op

Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

in statement B.. Why dont we consider the case of 0 where both +, x will work there by yielding E as answer? Is it because the Question says a,b,c are Numbers and hence we dont consider the case of 0? Which implies to consider 0 only when the it is mentioned to consider all integers/ or just integers. Therefore, if question mentions numbers it will be false to assume integers?

Bunuel please verify. Thanks.

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 the symbol @ represents either addition or multiplication, which operation does it represent?

(1) a@b=b@a for all numbers a and b
(2) a@(b–c)=(a@b)–(a@c) for all numbers a, b, and c

There is one variable (@) and 2 equations are given by the 2 conditions, so there is high chance (D) will be our answer.
For condition 1, @=*,+ , so this is insufficient.
For condition 2, @=*. This is sufficient, so the answer becomes (B).

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

The symbol \(\triangle\) can be + or *

1) a \(\triangle\) b = b \(\triangle\) a for all numbers a and b

If a=1 and b=1
1+1 = 1+1 = 2
1*1 = 1*1 = 1

If a=2 and b=1
2+1 = 1+2 = 3
2*1 = 1*2 = 2

These give us 2 different answers + or *
INSUFFICIENT


2) a \(\triangle\) (b-c) = (a \(\triangle\) b) - (a \(\triangle\) c) for all numbers a, b, and c.

If a=1 b=1 c=1

1 + (1 - 1) = (1+1) - (1+1)
1 + 0 = 2 - 2
1=0
It can not be addition +

1 * (1 - 1) = (1*1) - (1*1)
1* 0 = 1 - 1
0 = 0
It has to be multiplication * Only one answer. SUFFICIENT

Answer B

Hope it helps!
Thanks, Alecita

If in statement 2 we consider number 0 , △ can be "+" or "*" . Can someone explain please? Bunuel

The statement (2) says that the equation must hold true for ALL numbers, not just specific ones. If \(\text{@}\) were addition, the equation wouldn't work for all numbers. However, with multiplication, it does work for ALL numbers, including 0.