What is x? (1) |x| < 2 (2) |x| = 3x – 2 GMAT Data Sufficiency

byRituparna Nath Content Writer at Study Abroad Exams

Question - What is x?
(1) |x| < 2
(2) |x| = 3x – 2

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are not sufficient.

‘What is x? (1) |x| < 2 (2) |x| = 3x – 2’ - is a topic that belongs to the GMAT Quantitative reasoning section of GMAT. The question is borrowed from the book “GMAT Quantitative Review”. The GMAT Quant section mainly comprises a set of 31 questions that need to be answered logically. GMAT Data Sufficiency questions include a problem statement that is heeded by two factual arguments. GMAT data sufficiency consists of 15 questions which are two-fifths of the entire sum of 31 GMAT quant questions.

Solution and Explanation

Approach Solution 1:

It is asked to find what is x
Statement 1 says |x| < 2
Since Only a feasible range of values for x are given by this expression.it is insufficient
Now let us see statement 2 which says |x| = 3x – 2
Since the expression contained within the absolute value bars can be either positive or negative even if its absolute value is always positive, absolute value issues frequently, but not always, have several solutions.
Eg-
When considering the equation |2 + x| = 3, we must take both the chance that 2 + x is negative and the possibility that it is already positive into account. The equation is the same as 2 + x = 3 and x = 1 if 2 + x is positive. However, since |-3| = 3 and 2 + x must equal -3 if it is negative, x must = -5 and 2 + x must = -3.
Therefore, in this instance, it is important to solve for x under both potential situations in order to identify the answers for x.
For the case where x > 0:
x = 3x – 2
-2x = -2
x = 1
Always verify that the solution is correct when dealing with absolute values that include variables. In the original equation, enter x = 1.
|1| = 3(1) – 2
1 = 3 – 2
The equation is true, so the statement is sufficient.
The answer is B which is statement 1 is insufficient but statement 2 is sufficient

Approach Solution 2:

Correct Answer: B
There is another approach to answering this question which is the variable approach, just remember that independent equations with an equal number of variables always have a solution.
There is only one variable, x, and a 0 variable equation in the initial condition. Therefore, just one equation is required.
Looking at statement 1
There is no equation because it is an inequality. As a result, we are unable to recognise the variable x, and this is insufficient.
Looking at statement 2
x≥0
|x|=3x−2 is equivalent to x=3x−2 or 2x−2=0
Therefore we have x=1
This is sufficient.
The answer is B which is statement 1 is insufficient but statement 2 is sufficient

Correct Answer: B

Approach Solution 3:
Case (1) |x| < 2
this implies x<2 x>-2
Invalid, x could be any number greater than 2 or less than 2.
INSUFFICIENT

Case (2) |x| = 3x – 2
this implies x>=0
this implies |x| = 3x – 2
implies x = 3x - 2
this implies -2x = -2
this implies x = 1 Valid OR x<0
this implies -x = 3x - 2
therefore -4x = -2 and x = (1/2) Invalid as 1/2 is not less than zero.
SUFFICIENT

Correct Answer: B

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What is x? (1) |x| < 2 (2) |x| = 3x – 2 GMAT Data Sufficiency

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