The operation* represents either addition, subtraction, or multiplicat

We know that * is a plus sign, a minus sign, or a multiplication sign. If Statement 1 is true, the '*' symbol must be a plus sign, since the equation in Statement 1 won't be true if '*' is subtraction or multiplication. Since * represents addition, 1*0 = 1+0 = 1, and Statement 1 is sufficient.

For Statement 2, we know 2*0 = 2. This would be true if * is either addition or subtraction; * cannot be multiplication. So we know that 1*0 is either equal to 1+0 = 1, or is equal to 1-0 = 1. Either way its value is 1, so Statement 2 is also sufficient.

The answer is D (the OA given above is not right).

Given: The operation * represents either addition, subtraction, or multiplication

Target question: What is the value of 1*0?

Statement 1: 0*2 = 2
Let's test all 3 possible operations:
0 + 2 = 2
0 - 2 = -2
0 x 2 = 0
We can see that * represents addition, which means the answer to the target question is 1*0 = 1+0 = 0
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: 2*0 = 2
Let's test all 3 possible operations:
2 + 0 = 2
2 - 0 = 2
2 x 0 = 0
We can see that * represents EITHER addition OR substitution.
Does this mean statement 2 is insufficient?
We don't know yet, since we haven't tried answering the target question yet.

Let's consider both possible cases:
Case a: * represents addition. In this case, the answer to the target question is 1*0 = 1+0 = 1
Case b: * represents subtraction. In this case, the answer to the target question is 1*0 = 1-0 = 1
So, even though we don't know which operation * represents, we can still answer the target question with certainty (1*0 definitely equals 1)
So, statement 2 is SUFFICIENT

Answer: D

It depends what reasoning you've used to reach that conclusion. It's true here, because we know the operation is addition, subtraction, or multiplication. So if 2*0 = 2, the operation isn't multiplication, and so it's addition or subtraction, and if that's the operation, k*0 = k no matter what (adding zero or subtracting zero won't change k).

But if * could be some other kind of operation, then you certainly can't conclude from "2*0 = 2" that "1*0 = 1" -- that might or might not be true. For example if a question defined a new operation where

\(\\
x * y = 2(x^y)\\
\)

or where

\(\\
x * y = \frac{x^2 + y^2}{2}\\
\)

(with the requisite restrictions on x and y to make sure the operations are defined) then 2*0 = 2 in each case, but 1*0 is not equal to 1 in either case.

Hi Bunuel,

Operation from statement 1: You assumed 0*2 is an "addition" operation i.e. a*b = a +b. But couldn't it be assumed that a*b could also be = b-a (subtraction) ?. And hence 0*2 = 2-0 = 2. Isn't this statement insufficient because of 2 scenarios?

Where as in statement 2: 2*0 could be 2-0 = 2 or 2+0= 2. In either case, this statement alone is sufficient. Hence answer is B.

Am I missing something ?

Best
Rohan

IanStewart for statement (2) can we say that since 2*0 is in the same "format" as 1*0 (i.e. integer --> then * ---> then 0), 2*0 gives a 2 then 1*0 will give a 1. Irrespective of the sign?

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