Question: Which of the following represents the range for all x which satisfy inequality |2-x| < 2?

1. -2 < x < 2
2. -2 < x < 4
3. 0 < x < 2
4. 0 < x < 4
5. 2 < x < 4

Answer:

Approach Solution (1):

We are given that: |2 – x| < 2

We will have two cases here:

(1) 2 – x < 2
-x < 2 – 2
-x < 0
x > 0

(2) – (2 – x) < 2
-2 + x < 2
x < 2 + 2
x < 4

So correct answer: 0 < x < 4

Correct option: D

Approach Solution (2):

We will break down this question as:
-2 < 2 – x < 2
-2 -2 < -x < 2 – 2
-4 <- x < 0
4 > x > 0
This can be re- written as:
0 < x < 4

Correct option: D

“Which of the following represents the range for all x which satisfy inequality |2-x| < 2?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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