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?

- x > 0.4
- x < \\frac{1}{3})
- -\\frac{1}{3}) < x < 0.4, x > \\frac{15}{2})
- -\\frac{1}{3}) < x < 0, x > \\frac{2}{5})
- x < -\\frac{1}{3})and x > \\frac{2}{5})

@ INR

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}).

Copyrights © 2016 - 21 All Rights Reserved by Wizako.com - An Ascent Education Initiative.

Privacy Policy | Terms & Conditions

GMAT^{®} is a registered trademark of the Graduate Management Admission Council (GMAC). This website is not endorsed or approved by GMAC.

GRE^{®} is a registered trademarks of Educational Testing Service (ETS). This website is not endorsed or approved by ETS.

SAT^{®} is a registered trademark of the College Board, which was not involved in the production of, and does not endorse this product.

Wizako - GMAT, GRE, SAT Prep

An Ascent Education Initiative

14B/1 Dr Thirumurthy Nagar 1st Street

Nungambakkam

Chennai 600 034. India

**Phone:** (91) 44 4500 8484

**Mobile:** (91) 95000 48484

**WhatsApp:** WhatsApp Now

**Email:** learn@wizako.com

Leave A Message