Below-C Rector

Our department was discussing whether or not to accept graduate students whose undergraduate average grade is below the current cutoff point C.

The chairman said: "If we do that, we will lose more than half of our good ('above-C') students!"

The rector (provost) overruled him, and decided that the department should accept 1% 'below-C' students.

At the end of the year, the rector said: "What was all the fuss about? The department accepted 1% below-C students at the beginning of the year, and by the end of the year the percentage of the above-C students dropped slightly from 99% to 98%.

What did the chairman say?

The chairman said: "I told you so! We lost more than half of our above-C students!"

Indeed:

• Assume that at the beginning of the year 100 students were accepted, out of which 1 was below-C (1%) and 99 were above-C (99%).
• At the end of the year the percentage of above-C students dropped to 98%, so their number must have dropped from 99 to 49 (the one below-C student is now 2% of the class, which thus totals only 50).
• So the "slight percentage drop" from 99% to 98% is in fact a big drop of more than half, from 99 to 49 students!
And the rector gets a failing, below-C, grade ... But that is probably just wishful thinking :-)

P.S. This riddle appears in David Gale, Tracking the Automatic Ant, Springer (1998), page 81

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