A4. Of two whole numbers, the difference is 10. If you multiply the two numbers, the result is one of the following five numbers.

Which one is it?
A) 22398
B) 22420
C) 22442
D) 22453
E) 22475
A4. E) 22475 Let the average of the two numbers be $n$. In that case, one number is equal to $n-5$ and the other number is $n+5$. Their product is $(n-5)(n+5)=n^{2}-25$. Therefore, we add 25 to each of the five answers to see which one results in a perfect square. We find: $22423, 22445, 22467, 22478$, and 22500. It is clear that $22500=150^{2}$, so answer E is correct.

For verification, we calculate $149^{2}=(150-1)^{2}=22500-300+1=22201$. Since $149^{2}<22423$, answers A through D are indeed eliminated.