‘When is |x - 4| = 4 - x?’ is the topic from GMAT Quantitative problem set. GMAT quantitative reasoning section tests the candidate's ability to solve mathematical problems, interpret graph data, and mathematical reasoning. The quantitative section of the GMAT exam consists of 31 questions which needs to be answered. This topic from the GMAT Quant section has five options to answer from. The candidate has to choose the correct option from the given options. GMAT quant section has mainly two sections:
- Problem-solving: This question type in GMAT Quantitative analyses candidates' logical and analytical reasoning skills. In this section, candidates indicate the best five answer choices.
- Data sufficiency: This question type in GMAT Quantitative analyses candidates’ quantitative problems and identifies relevance with the data given.
Topic: When is |x - 4| = 4 - x?
- x = 4
- x = 0
- x > 4
- x <= 4
- x < 0
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Answer: D
Model Answer 1:
Explanation:
We will find the solution using the Absolute value properties:
The absolute value (or modulus) |x| of a real number x is x's numerical value without regard to its sign.
When x≤0 then |x|=−x,
More generally we can say that, when some expression ≤0 then,
|We get: |some expression|=−(some expression).
For example:
|−5|=5=−(−5)
When x≥0 then |x|=x,More generally we can say that, when some expression≥0 then,
|some expression|=some expression.
For example:
|5|=5
So, as per the given problem statement
|x−4|=4−x=−(x−4) to be true should be that
x−4≤0 --> x≤4
Hence, the correct answer is option D.
Model Answer 2:
Explanation:
Now, we will follow Critical Values method for the second process:
The Critical Value here is x=4 (we make the absolute value term equal to zero), so we have this conditions to check:
1) x<4: -(x-4)=4-x ---> x-4=x-4 ---> true for all values of x, but only when x<4 the initial condition is satisfied ---> true always that x<4
2) x=4: 0=0 ---> this is true always that x=4
3) x>4: x-4=4-x ---> 2x=8 ---> x=4 ---> initial condition of x>4 is not met
Therefore, there is a solution only when: x<=4
Hence, D is the correct answer.
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