What information guarantees a ranking in the 90th percentile is greater than a ranking in the 70th percentile?

Consider the following facts:

• Person A's salary is in the 90th percentile in Company A.
• Person B's salary is in the 70th percentile in Company B.

The question is: What piece of information is enough to ensure that Person A's salary is greater than person B's salary? Check all that apply:

• The mean salary in Company A is greater than the mean salary in Company B
• The median salary in Company A is equal to the median salary in Company B
• The 80th percentile of Company A is greater than the 70th percentile of Company B

At least one of the above options, but possibly more than one, must be true. To me, the question seems faulty because I don't think any of them is enough to ensure Person A's salary is greater than Person B's. It seems to me that just because Person B is in the 70th percentile (which means his salary is greater than 70% of other salaries) in his company doesn't mean he can't be in the 99th percentile as well; after all, 99>70 so it seems to meet the definition of being in the 70th percentile. If that were the case, and if Person A's salary lay somewhere in the 90%-99% range, none of the above conditions would prevent Person B's salary from being greater than Person A's. So it seems like none of the conditions ensure that Person A's salary is greater than Person B's. However, at least one of the above must be true, possibly more than one.

• The third bullet gives you $B_{SAL}<80_A<A_{SAL}$ Aug 11, 2020 at 14:21

• I would read "8th decile of A" $>$ "7th decile of B" as saying that 80th percentile of A $>$ 79th percentile of B (not in the sense of averages, but in the sense of intervals), in which case Person A $>$ 90th percentile of A $>$ 80th-percentile of A $>$ 79th percentile of B $>$ Person B, which in that reading makes 3 the correct answer, so I think it works. Nov 11, 2014 at 3:26