# The Holistic Approach to Mods on the GMAT – Solutions

First, we would like to refer you back to a post we put up quite a while ago: The Holistic Approach to Mods

In this post, we discussed how to use graphing techniques to easily solve very high level questions on nested absolute values. We don’t think you will see such high level questions on actual GMAT. The aim of putting up the post was to illustrate the use of graphing technique and how it can be used to solve simple as well as complicated questions with equal ease. It was aimed at encouraging you to equip yourself with more visual approaches.

We gave you two questions at the end of that post to try on your own. We have seen quite a bit of interest in them and hence will discuss their solutions today.

The solutions involve a number of graphs and hence we have made pdf files for them.

Question 1: Given that y = |||x – 5| – 10| -5|, for how many values of x is y = 2?

Solution 1

Question 2: Given that y = |||x| – 3| – x|, for what range of x is y = 3?

Solution 2

Karishma, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America. She teaches the GMAT for Veritas Prep and regularly participates in content development projects such as this blog!