Infinite Solutions

by | Brain Teasers

­Select for a and for b values such that the equation x/a=x-b has more than one solution for x. Make only two selections, one in each column.



Answer:
A=1 and B=0. This is a GMAT question from the Data Insights section and is technically not a brain teaser, but it is very brain-teaser-like in the sense that clever reasoning is the order of the day, not brute force Math (and this can be said of many GMAT questions!). There is an algebraic way to do this question, but that is definitely NOT the best way to approach this. One just needs to step back and realize that in order for there to be more than one solution for x, the equation must end up as x = x. So one simply needs to think about what values of an and b will create that equation. If you look at the answer choices and think about how to get the left and right sides of the equation to equal x, you will probably quickly see that if a = 1, the left side of the equation will equal x, and if b = 0, then the right side will equal x. That’s all there is to it!