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The operation* represents either addition, subtraction, or multiplication of integers, what is the value of 1*0? (1) 0*2=2 (2) 2*0=2

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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(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.

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.

(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.

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 -).

Bunuel, Thanks for you reply. However by subtraction, I meant 2-0=2 not 0-2=-2. i.e. the operation 0*2 can be construed as addition (like you said) i.e. 2+0=2 or subtraction i.e 2-0=0. Please note that for subtraction, I am considering the case: a*b=b-a (which is 2-0 = 2) and not a-b (which is 0-2=-2) . hope my query is clear to you ?

Bunuel, Thanks for you reply. However by subtraction, I meant 2-0=2 not 0-2=-2. i.e. the operation 0*2 can be construed as addition (like you said) i.e. 2+0=2 or subtraction i.e 2-0=0. Please note that for subtraction, I am considering the case: a*b=b-a (which is 2-0 = 2) and not a-b (which is 0-2=-2) . hope my query is clear to you ?

Notice that the first statement is 0*2 not 2*0.
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