Data Sufficiency

This is from Official Guide: DS Qn 89

If @ represents one of operations +.- and x, is k@(l+m) = (k@l) + (k@m) for all numbers k, l, m?

1. k@1 is not equal to 1@k for some numbers k.
2. @ represents subtraction.

The answer says D.

--- However i see that the above expression would hold good for multiplication and not subtraction or addition.

Can someone please explain if I am missing somthing here?

In statement 1, it states that k@1 does NOT equal 1@k, so that rules out addition and multiplication and is only true for addition.

In addition and multiplication operations, you can arrange the integers in an equationand still get the same answer. Only in division and subtration, this does not hold true.

Ex: if K=4, then in statement 1:
4*1 is equal to 1*4
4+1 is equal to 1+4
4-1 is NOT equal to 1-4.
So the statement is sufficient for subtraction only.

Hope this helps!

Ok.. but this solution is not complete.

It is asking whether it is true for k@(l+m) = (k@l) + (k@m) for all numbers k, l, m

and it is not true:

For eg: K= 3; l =2 and m= 1
then
3-(2+1) = (3-2) + (3 -1)
0 = 3
and that is not true so its answer should be E;

Can anyone please explain this?

priyankamishra11 wrote:This is from Official Guide: DS Qn 89

If @ represents one of operations +.- and x, is k@(l+m) = (k@l) + (k@m) for all numbers k, l, m?

1. k@1 is not equal to 1@k for some numbers k.
2. @ represents subtraction.

The answer says D.

--- However i see that the above expression would hold good for multiplication and not subtraction or addition.

Can someone please explain if I am missing somthing here?

The answer should be D.

This is a two part question. One part is value i.e. whether @ is -, + or X, the other part, is k@(l+m) = (k@l) + (k@m) for all numbers k, l, m?

You can easily figure out that in both statements the value is subtraction.

The second part of the question can be a bit tricky.

The second part is whether the expression will hold true for all numbers.

If subtraction is used the expression does not hold true for all numbers.
Therefore, answer is NO and both the statements are sufficient.

Thus, D is the answer.