 ### Question 14

This is one of the few questions that is completely a math question. To feel comfortable you must understand:

1. The concept of absolute value - Statement (1)

2. How to solve equations by factoring - Statement (2)

Statement (1) alone: The absolute value of either -1 or 1 is equal to 1.
Therefore, if the absolute value of x - 2 = 1, then x - 2 must be equal to 1 or -1.

If x - 2 = 1 then x = 3.

If x - 2 = -1 then x = 1.

We have two possible values for x. Since they are both positive numbers x cannot be determined.

(Remember that the directions to data sufficiency specifically say that if a specific value is asked for, there must be exactly one numerical value!)

(A) and (D) must be eliminated.

Statement (2) alone: If x*x = 4X - 3 then x*x - 4x + 3 = 0.

You may need to review your factoring rules here, but the factors of the above expression are:

(x - 3) (x - 1) = 0. Hence, x = 3 or x = 1.

Once again we do not have one specific value for x. Hence, the answer cannot be determined from statement (2) alone.

(B) must be eliminated.

Since, the answer cannot be determined from either of statements (1) or (2) alone, we are left with (C) or (E). We must now consider statements (1) and (2) together.

Statements (1) and (2) together: If we consider the two statements together we will still find that 3 and 1 are both possible values for x. Hence, the answer cannot be determined from a consideration of statements (1) and (2) together.