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

Question
Which of the following inequalities have a finite range of values of "x" satisfying them?

A. x² + 5x + 6 > 0
B. |x + 2| > 4
C. 9x - 7 < 3x + 14
D. x² - 4x + 3 < 0
E. (B) and (D)

The correct choice is (D) and the correct answer is x² - 4x + 3 < 0.

Explanatory Answer
We have to find out the values of "x" that will satisfy the four inequalities given in the answer choices and check out the choice in which the range of values satisfying is finite.

Choice A
Factorizing the given equation, we get (x + 2)(x + 3) > 0.
This inequality will hold good when both x + 2 and x + 3 are simultaneously positive or simultaneously negative.

Evaluating both the options, we get the range of values of "x" that satisfy this inequality to be x < -2 or x > -3. i.e., "x" does not lie between -2 and -3 or an infinite range of values.

Choice B
|x + 2| > 4 is a modulus function and therefore, has two options

Option 1: x + 2 > 4 or
Option 2: (x + 2) < -4.

Evaluating the two options we get the values of "x" satisfying the inequality as x > 2 and x < -6. i.e., "x" does not lie between -6 and 2 or an infinite range of values.

Choice C
9x - 7 < 3x + 14
Simplifying, we get 6x < 21 or x < 3.5. Again an infinite range of values.

Choice D
x² - 4x + 3 < 0
Factorizing we get, (x - 3)(x - 1) < 0.

This inequality will hold good when one of the terms (x - 3) and (x - 1) is positive and the other is negative.
Evaluating both the options, we get 1 < x < 3. i.e., a finite range of values for "x".

Hence, choice D is the correct answer.

This eBook covers all the topics in Number Theory and Inequalities related to GMAT. Explanation of topics provide in-depth knowledge of concepts such as LCM, HCF, remainder theorem in number theory and the rules governing inequalities.

The book contains over 50 solved examples and illustrative examples. In addition, the eBook contains 44 exercise questions covering a wide variety of questions from these two topics for you to practise.
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