The operation* represents either addition, subtraction, or multiplication of integers, what is the value of 1*0?

(1) 0*2=2 --> operation * represents addition --> 1*0=1+0=1. Sufficient.

(2) 2*0=2 --> operation * represents either addition or subtraction --> 1*0=1+0=1 and 1*0=1-0=1, the same answer. Sufficient.

Answer: D.

OA must be wrong.
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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).
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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

In (1) the operation cannot be subtraction, since \(0-2=-2\) and not 2, as stated. But even if you were right, so suppose the operation can be addition or subtraction (as in the second statement), still (1) would be sufficient because we need to find the value of 1*0 which is the same for either of these two operations (+ or -).

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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
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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?

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.
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