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: p^{2} = 9

p^{2} = 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?

Statement 1:

(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.

Statement 2:

(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.

Answer: (A)

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