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You are here: Home CAT Questions Inequalities Domains and Ranges

Inequality - Math Questions & Answers - CAT 2016

Question 4 the day : April 01, 2005

The Math practice question for the day is an inequality question. Inequality is one of the easiest set of questions if the basic concepts are well understood.

Question
For what range of values of 'x' will the inequality 15x - CAT - Math Sample Question - Inequalities > 1?

(1) x > 0.4
(2) x < CAT - Math Sample Question - Inequalities
(3) -CAT - Math Sample Question - Inequalities < x < 0.4, x > CAT - Math Sample Question - Inequalities
(4) -CAT - Math Sample Question - Inequalities < x < 0, x > CAT - Math Sample Question - Inequalities

Correct choice (4). Correct Answer - (-CAT - Math Sample Question - Inequalities < x < 0, x > CAT - Math Sample Question - Inequalities)


Explanatory Answer

We can rewrite the above inequality as 15x - CAT - Math Sample Question - Inequalities - 1 > 0
i.e., CAT - Math Sample Question - Inequalities > 0
or CAT - Math Sample Question - Inequalities > 0.
Factorizing we get, CAT - Math Sample Question - Inequalities > 0
The above inequality will hold good if the numerator and denominator are both positive or are both negative.

Case 1: When (5x - 2)(3x + 1) > 0 and x > 0
This will hold true for values of 'x' that do not lie between CAT - Math Sample Question - Inequalities and CAT - Math Sample Question - Inequalities and for x > 0.
Combining all these conditions, we get x > CAT - Math Sample Question - Inequalities

Case 2: When (5x - 2)(3x + 1) < 0 and x < 0
This will hold true for the following values of 'x': CAT - Math Sample Question - Inequalities < x < CAT - Math Sample Question - Inequalities and x < 0.
Combining, we get CAT - Math Sample Question - Inequalities< x < 0.

Therefore, the final range for which the above inequality will hold true is given byCAT - Math Sample Question - Inequalities < x < 0 and x > CAT - Math Sample Question - Inequalities.


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