WBCS Preliminary Examination 2023 — General Studies · Question 187 of 200

Answer: (D) 9

Write the two numbers around their mean, 8795: $8798\times8792=(8795+3)(8795-3)=8795^2-3^2=8795^2-9$. Adding 9 gives $8795^2$, a perfect square, and 9 is the least such number, because the product lies just below $8795^2$ and far above the previous square $8794^2$ (which is $2\times8795-1=17589$ less than $8795^2$). In general, for two numbers that differ by $2k$, the product falls short of the square of their mean by $k^2$.