Can we generalize this approach to consider C is right

[utkalnayak]

There are quite a few questions I came across, where using option 1, the answer would come up with x = 2 or x = -2 hence insufficient. Using option 2, x = 2 or x = 5 hence insufficient. But the answer is explained as - if we add option 1 and 2 we see that the common value of x between the two is x = 2, hence option C is the right answer. Is this right approach ? I do not understand if the equations were simplified to come to 2 possible values of x, how can we simply ignore those just because we are considering both equations true.

Example -
What is the greatest common divisor of positive integers j and k ?

1) The greatest common divisor of 3j and 2k is 2
2) The greatest common divisor of 5j and k is 10

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Hi utkalnayak,

When dealing with an individual Fact in a DS question, if you determine that the answer to the given question changes, then that Fact is INSUFFICIENT.

When both Facts are individually insufficient, then you must combine the Facts and use them BOTH to try to answer the question. In your initial example, you provide the following:

Fact 1: X = 2 or X = -2
Fact 2: X = 2 or X = 5

At this point, you look for "overlap" - what answer (or answers) fit BOTH Facts? In this example, there is JUST ONE (X = 2). In this way, the Facts TOGETHER are SUFFICIENT to answer the question (so the final answer is C).

GMAT assassins aren't born, they're made,
Rich

[utkalnayak]

Thank you Rich for the clarification. That info is going to be very useful to me

[Matt@VeritasPrep]

Utkal, the key idea here is that both statements are true, so when we combine them, anything on which they disagree must be false. For instance, if S1 says x = 2 or x = -2, we know that one of those is the value of x, we just don't know which. Similarly, if S2 says x = 2 or x = 5, we know that one of those is the value of x, but we still don't know which.

Taking the two together, however, we can't have x = -2 or x = 5. If x = 5, then S1 is false ... but the statements can't be false! Same issue with x = -2: if x = -2, then S2 is false, but we can't have that either.