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07 Jan 2025, 22:56
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I did not quite understand the solution. The solution is fine. But how to get the 3 ranges and different versions of |x+5| and |x-5| For e.g. how do we readily identify that for -5 > x > 5 |x-5| = 5-x; is it through trial and error?
07 Jan 2025, 23:40
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sathiesh123
Absolute value properties:
When \(x \le 0\) then \(|x|=-x\), or more generally when \(\text{some expression} \le 0\) then \(|\text{some expression}| = -(\text{some expression})\). For example: \(|-5|=5=-(-5)\);
When \(x \ge 0\) then \(|x|=x\), or more generally when \(\text{some expression} \ge 0\) then \(|\text{some expression}| = \text{some expression}\). For example: \(|5|=5\).
When \(x \le 0\) then \(|x|=-x\), or more generally when \(\text{some expression} \le 0\) then \(|\text{some expression}| = -(\text{some expression})\). For example: \(|-5|=5=-(-5)\);
When \(x \ge 0\) then \(|x|=x\), or more generally when \(\text{some expression} \ge 0\) then \(|\text{some expression}| = \text{some expression}\). For example: \(|5|=5\).
Therefore, when -5 < x < 5, then x + 5 > 0 and x - 5 < 0, thus |x + 5| = x + 5 and |x - 5| = -(x - 5) = 5 - x.
Brush-up fundamentals:
Absolute Value
- Theory
- Math: Absolute value (Modulus)
Absolute Value: Tips and hints
Properties of Absolute Values on the GMAT
Absolute modulus : A better understanding
GMAT Question Patterns: Abolute Value
The Reason Behind Absolute Value Questions on the GMAT
For more check Ultimate GMAT Quantitative Megathread
20 Jan 2025, 23:47
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I like the solution - it’s helpful. And a very high-quality question
