GMAT prep Math - symbol

[romoe]

If @ denotes one of two arithmetic operations, addition or multiplication, and if k is an integer, what is the value of 3@k?

(1) 2@k = 3

(2) 1@0 = k



(source GPrep)

[yamini]

1) 2@k = 3 Here @ is + and K is 1

(2) 1@0 = k Here @ can be + or *

correct me if wrong

[RonPurewal]

Choice 1: Here, the @ sign must stand for addition. This is so because, were @ to stand for multiplication, then 'k' wolud have to be 1.5, violating the condition requiring it to be an integer. Therefore, k must be 1, and so we know the value of 3@k.

Choice 2: There are two possibilities. Since there are only two, you should go ahead and work them all the way through, just to make sure you get different answers for the final expression 3@k.
- Possibility 1: @ is addition. In this case k has to be 1+0, or 1. Therefore, 3@k is 3+1, or 4.
- Possibility 2: @ is multiplication. In this case k has to be 1x0, or 0. Therefore, 3@k is 3x0, or 0.
- 0 and 4 are different, so this choice is insufficient by itself.

HTH

[Guest]

Well I solved equation one and figured out that the operation for 2@k =3 must be addition and that the value of k =1

But plugging back into 3@k, we just know the value of k, how can we assume that @ is again addition

Dont we have to consider @ as addition or multiplication

3+1 or 3*1 ??

Confusing

[RonPurewal]

Well I solved equation one and figured out that the operation for 2@k =3 must be addition and that the value of k =1

But plugging back into 3@k, we just know the value of k, how can we assume that @ is again addition

Dont we have to consider @ as addition or multiplication

3+1 or 3*1 ??

Confusing

well, just think about how the process works.
if you take statement (1) to be true, then ... statement (1) is true!
in other words, if you deduce from statement (1) that @ stands for addition, then the WHOLE POINT is to transfer that knowledge into the question prompt.
so...
if you assume statement (1) to be true, then yes, you should transfer that knowledge (i.e., that @ stands for addition) into the question prompt.