This is about hiring standards, not the award criterion. Even if hiring has been consistent for 15 years, the conclusion still depends on the award criterion 15 years ago. If 15 years ago the criterion was top half rather than top third, the math falls apart no matter how strict or lax hiring has been.

The number passed over equals total salespeople minus awarded. If the total has grown and the number awarded has shrunk, then the number passed-over has grown since 15 years ago, which is the opposite of what the president concludes.

This makes the argument valid. With the criterion locked at top third throughout the 15 years, the number passed over has always been exactly twice the number awarded. So if awarded declined, passed-over (which is just 2 × awarded) declined too. The conclusion now follows.

This is about absolute sales numbers, but the award criterion is relative. The criterion is about ranking within the sales force, not about hitting any particular sales target. Whether average sales went up or down over the 15 years doesn't change how the top third is determined. The top third is still 1/3 of whoever's on the sales force, regardless of what their actual sales figures look like. So (D) doesn't speak to the criterion's history, which is the gap in the argument.

This ensures sales figures are calculated consistently year to year, which sounds close to what we want. But measuring sales the same way is a different issue from awarding the same proportion of salespeople. Even with sales calculated identically the whole 15 years, the company could have moved from rewarding the top half to rewarding the top third. The argument's gap is about the cut-off for getting an award and whether it has changed, not about how sales are measured.