<p>**If x and y are positive odd integers and squareroot of x plus squareroot of y equal 10, what is one possible value of x + y ? **</p>
<p>Knowing that x and y are odd integers, possibilities for sq(x), sq(y) would be:</p>
<p>1, 9
3, 7
5, 5</p>
<p>(Obviously you can reverse them for y and x, but since you’re looking for the sum, those would be duplicates.)</p>
<p>Therefore, x+y:
1, 9 => 1 + 81 = 82
3, 7 => 9 + 49 = 58
5, 5 => 25 + 25 = 50</p>
<p>**In the figure above, the circle with center P has radius 6 and the circle with center Q has radius 1. The circles are tangent to each other. Segment QR is tangent to the larger circle and intersects the smaller circle at S. What is the length of segment RS ? **</p>
<p>First of all, since QR is tangent to the larger circle, therefore PRQ is a right triangle. We know:</p>
<p>PR = radius of larger circle = 6
PQ = radius of larger circle + radius of smaller circle = 7</p>
<p>Therefore, via Pythagorean theorem, RQ = sq(49-36) = sq(13)</p>
<p>Since RQ = RS + SQ
Therefore RS = RQ - SQ</p>
<p>Notice that SQ = radius of smaller circle
Therefore RS = sq(13) - 1</p>