# GMAT Sample Questions | GMAT Inequalities Q2

#### Algebraic Inequalities | GMAT Quant Questionbank

This GMAT quant practice question is a problem solving question from Inequalities. Concept: Finding solution set to an algebraic inequality. Level of difficulty: Easy to moderate. GMAT 650 level inequalities sample question.

Question 2: What range of values of 'x' will satisfy the inequality 15x - $$frac{2}{x}$ > 1? 1. x > 0.4 2. x < $\frac{1}{3}$ 3. -$\frac{1}{3}$ < x < 0.4, x > $\frac{15}{2}$ 4. -$\frac{1}{3}$ < x < 0, x > $\frac{2}{5}$ 5. x < -$\frac{1}{3}$and x > $\frac{2}{5}$ ## Get to Q51 in GMAT Quant #### Online GMAT Course @ INR 3500 ### Video Explanation ## GMAT Live Online Classes #### Starts Tue, Oct 12, 2021 ### Explanatory Answer | GMAT Algebraic Inequalities We can rewrite the above inequality as 15x - $\frac{2}{x}$ - 1 > 0 i.e., $\frac{15x^2 - 2 - x}{x}$ > 0 Split the middle term of the numerator as a precursor to factorizing it: $\frac{15x^2 - 6x + 5x - 2}{x}$ > 0 Factorize the quadratic expression: $\frac{$5x - 2$(3x + 1)}{x}) > 0
The above inequality will hold good if the numerator and denominator are both positive or are both negative.

Possibility 1: When (5x - 2)(3x + 1) > 0 and x > 0
Rule: (x - a)(x - b) > 0 when x does not lie between "a" and "b".
Applying the rule, the values of 'x' that will satisfy (5x - 2)(3x + 1) > 0 will not lie between -$$frac{1}{3}$ and $\frac{2}{5}$. Combining the above result with the second condition that x > 0, we get x > $\frac{2}{5}$ Possibility 2: When$5x - 2)(3x + 1) < 0 and x < 0.
Rule: (x - a)(x - b) < 0 when x lies between "a" and "b".
Applying the rule, the following values of 'x' will satisfy (5x - 2)(3x + 1) < 0: -$$frac{1}{3}$ < x < $\frac{2}{5}$. Combining the above range of values with the second condition that x < 0, we get -$\frac{1}{3}$ < x < 0. Therefore, the range of values of x that will satisfy the inequality is: -$\frac{1}{3}$ < x < 0 $\cup$ x > $\frac{2}{5}$. #### Choice D is the correct answer. #### GMAT Online CourseTry it free! Register in 2 easy steps and Start learning in 5 minutes! #### Already have an Account? #### GMAT Live Online Classes Next Batch Oct 12, 2021 #### GMAT Coaching in Chennai Next Batch after Lockdown #### GMAT Coaching in Chennai Sign up for a Free Demo of our GMAT Classes in Chennai ##### Where is Wizako located? Wizako - GMAT, GRE, SAT Prep An Ascent Education Initiative 14B/1 Dr Thirumurthy Nagar 1st Street Nungambakkam Chennai 600 034. India ##### How to reach Wizako? Phone:$91) 44 4500 8484
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