CAT Quantitative Aptitude Questions | CAT Algebra - Inequalities questions

CAT Questions | Algebra | Modulus Inequalities

The question is about Modulus Inequalities. Our task is to identify the range of the given inequality. Inequalities are crucial to understand many topics that are tested in the CAT exam. Having a good foundation in this subject can help us tackle questions in Coordinate Geometry, Functions, and most importantly in Algebra. A range of CAT questions can be asked based on this simple concept.

Question 5: Find the range of x where ||x - 3| - 4| > 3?


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Explanatory Answer

Method of solving this CAT Question from Algebra - Inequalities : Similar to a previous question. When will the equation have an odd number of negative terms? When will it have an even number?

If we have an inequality |y| > 3, this will be satisfied if => y > 3 or y < -3.
So, the above inequality simplifies to two inequalities

Inequality I: |x - 3| - 4 > 3
|x - 3| - 4 > 3 => |x - 3| > 7
x - 3 > 7 or x - 3 < -7
Or, x > 10 or x < -4
Of, x lies outside of -4 and 10. Or, x can lie in the range (-∞, -4) or ( 10, ∞)

Inequality II: |x - 3| - 4 < -3
|x - 3| - 4 < - 3
=> |x - 3| < 1
=> -1 < x - 3 < 1 or x lies between 2 and 4
So, final solution is given by the range
( -∞, -4) or (2, 4) or ( 10, ∞)

The question is "Find the range of x where ||x - 3| - 4| > 3?"

Hence the answer is "( -∞, -4) or (2, 4) or ( 10, ∞)"

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