# GMAT Question of the Day – Problem Solving – Exponents/Divisibility

[latexpage]If x and y are positive integers and $(2^{24})($$4^{12}) = x^y$ what is the value of x that produces the minimum value for x – y?

A. 2

B. 3

C. 4

D. 8

E. 16

[spoiler]**A.**[/spoiler]

## GMAT Question of the Day Solution

A significant portion of GMAT Quant questions require you to simplify expressions. So knowing all of the basic algebra rules is critical. You should not be hesitating with any of the basic rules. That will not only slow you down but cause doubt. Why? If you’re not sure about the basic rules how can you apply them to subtle GMAT questions? Master the basics!

In this question of the day you have to apply some exponent rules. It will certainly help to get the left side of the equation simplified so each term has the same base. This way you will be able to combine the terms and simplify the expression as whole. Why simplify? So that it is easier to make inferences. Whenever you have a chance to simplify a GMAT question go for it! Once you have simplified both sides consider what the possibilities are for x and y. x – y will be at a minimum when x is the least it can be and y is the greatest is can be. So x = 2 y = 48 will yield the minimum, -46.