Source: Official Guide for the GMAT 13th Ed. Problem Solving; #14 Official Guide for the GMAT 2015 14th Ed. Problem Solving; #14


If |y-1/2|<11/2, which of the following could

If |y-1/2|<11/2, which of the following could be a value of y?

4 Explanations


Mohammad Aasim

I do not know how you guys got the right answer. It must be a nice method but here is how i made it to the right answer;

Looking at the inequality makes one thing prominent that value of y must keep the LHS (left hand side) smaller than the RHS (right hand side). Secondly, LHS, after simplication, would yield an absolute value with POSITIVE sign.

Ignore the intergers (whether positive or negative) in the options at your first sight because they would only make the numerator bigger. (You may notice that the denominator on both sides are going to be the same i.e. 2, after simplification)

Left with option B and C that bear fractions, you can configure that option B would again make the numerator equal to +12 (absolute value), resultantly making the LHS bigger than RHS. So, option B is out.

We are left with the 'OPTION C' only. (The explanation may seem lengthy, but is probably less vulnerable to time consumption, at least that is what i thought.)

Aug 10, 2017 • Comment

Sam Kinsman

Hi Mohammad, that's correct! Thanks for sharing your approach :)

Aug 26, 2017 • Reply


Ajosh John

|y-1/2| < 11/2

convert into decimals

|y-0.5| < 5.5

now subsitute

a) |-11-0.5| = |-11.5| = 11.5, hence 11.5>5.5

b) |-11/2-0.5| = |-5.5-0.5| = |-6| = 6, hence 6> 5.5

c) |5.5-0.5| = |5| = 5, hence 5 < 5.5 which is the answer.

Dec 18, 2015 • Comment

Sam Kinsman

Yes, that works as well - good job! :D

Dec 23, 2015 • Reply


Robert M Oliver

Is there a more simple way to come up with this answer?

Nov 16, 2015 • Comment

Sam Kinsman

Hi Robert! Another way you could this is to test each answer choice by plugging in for y (into the inequality). It's probably faster to use Mike's method, but you can use whichever way your more comfortable with!

Nov 19, 2015 • Reply


Gravatar Mike McGarry, Magoosh Tutor

Dec 26, 2013 • Comment

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