The question states that the

ratio must always be greater than 3:80, not the number of students (or burgers). So when you calculate the ratio \(\frac{5}{x}>\frac{3}{80}\), increasing the value of \(x\) will

decrease the ratio \(\frac{5}{x}\), and decreasing the value of \(x\) will

increase the ratio \(\frac{5}{x}\).

If you calculate the number of burgers to be 133.3, then decide whether to round up or down, understand what will happen to the ratio of \(\frac{5}{x}\).

If \(\frac{5}{133.33}=\frac{3}{80}\), and that is the minimum (because \(\frac{5}{x}\) must always be greater than \(\frac{3}{80}\)), what happens if you round \(x\) up to 134? Is \(\frac{5}{134}\) > or < \(\frac{3}{80}\)?

As explained above, if you increase \(x\) to 134, then the ratio \(\frac{5}{x}\) is

decreased, and it will be less than the minimum of \(\frac{3}{80}\). If you round \(x\) down to 133, then the ratio \(\frac{5}{x}\) will increase, and you will not violate the condition that it must always be greater than \(\frac{3}{80}\).

Looking at it another way, if we know that the ratio of assistants to students must always be greater than 3:80, then we know that for any given number of assistants, there is a maximum number of students allowed. For every assistant, a maximum of 26.66 students are allowed (80/3). So if there is 1 assistant and 27 students, that is too many. 26 is the maximum number of students allowed if there is only 1 assistant in order to keep the

ratio greater than 3:80. Using the same logic, if there are 5 assistants, then the maximum number of students allowed is 133.33. If there were 134 students that would be more than the maximum, therefore the maximum number of students allowed is 133.

Does that help?

Cheers

_________________

Dave de Koos

GMAT aficionado