This GMAT Problem Solving practice question tests basic concepts in solving algebraic expressions comprising absolute values and elementary concepts in number properties.

Question 12: If x and y are integers and |x - y| = 12, what is the minimum possible value of xy?

- -12
- -18
- -24
- -36
- -48

@ INR

x and y are integers and |x - y| = 12

Squaring both sides, we get (x - y)^{2} = 144

x^{2} + y^{2} - 2xy = 144

Add, 4xy to both sides of the equation.

x^{2} + y^{2} - 2xy + 4xy = 144 + 4xy

x^{2} + y^{2} + 2xy = 144 + 4xy

Or (x + y)^{2} = 144 + 4xy

(x + y)^{2} will NOT be negative for real values of x and y.

i.e., (x + y)^{2} ≥ 0

∴ 144 + 4xy ≥ 0

Or 4xy ≥ -144

So, xy ≥ -36

The least value that xy can take is -36.

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