GMAT Math : Changing variables

In this chapter, we will learn to tackle GMAT Math questions where a change in one variable is expected to bring a change in another. More often than not, such questions will not pop up in the Quant section but no harm in being prepared, no? 🙂

Let’s start with an illustrative example :

Q) If the dimensions of a rectangle are in the ration 7:5 and the total perimeter reduction achieved by shrinking length and width in their original ratio has been 30 cm. What is the difference between the old width and new width?

A. 6.25 cm

B. 7.25 cm

C. 8.00 cm

D. 5.75 cm

E. 10.20 cm

Readers! Please take some time to attempt the question 🙂

Solution :

The math hack here is :

if y = cp + sk where c, s are constants and p, y, k are variables

Change in y = c x Change in p + s x Change in k.

Notice how change follows a transitive relation. 

Change in perimeter = 30 cm

Change in[2(l+b)] = 30 cm

2 x Change in (l+b) = 30 cm

Change in (l+b) = 15 cm

Since the reduction in dimensions follow the original ratio, 7:5,

Change in width = 15 cm x 5/(5+7) = 15 x 5/12 = 6.25 cm which leads to option (A)

Now dear reader, you are well equipped to tackle any oddball change related GMAT problems 🙂