# Assume that the partners of the firm are ranked according to their salaries, from first (highest) to ninth (lowest), ...

caitlinmensah on May 28, 2020

Question 6

Hello, can someone explain why in this question, Glassen could not be ranked eighth? I approached the problem by writing out different scenarios (which I understand takes too much time) but when I did it that way and not by counting the letters/ranks before G, I was able to rank Glassen eighth.

shunhe on May 28, 2020

Hi @caitlinmensah,

Thanks for the question! So we know that there are nine total partners, and we rank them from highest salary to lowest salary. In this question, we also know that no two salaries are the same, so no ties for the same one. That means there are nine different salaries we get to order here.

Now, by the second-to-last rule, we know that G’s salary is greater than J’s, which means that G can’t be 9th (since J’s salary is always less than G’s). But we also know by the last rule that J’s salary is greater than H’s. That means that J can’t be 9th, since J is always greater than H. But that means J can be at latest 8th. But that means G can’t be 8th, since G is always greater than J. And so we can’t rank G as 8th, since both J and H have to follow G, and there are only 9 people.

Hope this helps! Feel free to ask any other questions that you might have.