There is a set of beads, each of which is painted either red or blue.

Interesting setup. If we just care whether we had more red than blue beads to start with, the 'merged' beads don't really matter, because half of them were originally red, and half were originally blue, so they even out. Algebraically, if we end up with r red beads, b blue beads, and p merged beads, then we originally had r + (p/2) red beads, and b + (p/2) blue beads, and we will have started with more red than blue if

r + (p/2) > b + (p/2)

is true, and subtracting p/2 from both sides, we just need to know if r > b, or if we ended up with more pure red than pure blue beads.

Statement 1 tells us r < p + b. That's not sufficient; maybe p = 0, and r < b, but maybe b=0 and p is large, and r > b.

Statement 2 tells us b > p + r. But p + r > r, so b > r, which means we started with more blue than red beads, which is sufficient (we know the answer to the question is 'no'). So the answer is B.