SEAMO 2027 - Paper E - SET 01 - Self-study Question 6

Question 6

For $i=1,2,\ldots,100$, each $x_i$ can be either $\sqrt3-\sqrt2$ or $\sqrt3+\sqrt2$. Let $S=x_1x_2+x_3x_4+\cdots+x_{99}x_{100}$. How many different positive integer values can $S$ have?

$25$
$50$
$75$
$100$
None of the above