Before we get down to solving this question, let’s understand something fundamental about these data sufficiency questions. We can say that a statement is sufficient to find the value of a variable only if a unique, single value of the variable can be found.
Consider the following example:
What is the value of p?
Statement: p2 = 9
p2 = 9 means p can be +3 or −3. So even though we can “solve for” p, we cannot nail down a single, unique value of p. Therefore we will say the statement is not sufficient to answer the given question.
Given question: What is the value of x?
(x − 5)2 = 0 (x − 5) = 0 x = 5
As statement 1 gives us a unique value of x, it is sufficient to answer the given question.
(x − 3)2 = 4 x − 3 = =
x = 2 + 3 = 5 OR −2 + 3 = 1
Statement 2 does not give us a unique value of x (it may be 1 or 5). Therefore, statement 2 alone is not sufficient to answer the given question.
Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient.
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