and since 65​ and 63​ are each equal to about 8, the answer must be near 1/8. Specifically,
65​+63​>7.5+7.5=15, so 65​−63​<2/15≈.1333
Thus the answer is (A) or (B). To determine which, we must decide whether 65​+63​ is larger or smaller than 8+8, since 2/16=.125 exactly. In fact, it is smaller: this is the case n=64 and a=1 of the inequality
n+a​+n−a​<2n​
valid whenever 0<∣a∣≤n, which one may verify by squaring. (Alternately, the fact that the graph of y=x​ is concave down shows geometrically that 64​ is greater than the average of 63​ and 65​ - how?) Therefore, 65​−63​>2/16 and the answer is (B).
Note. 65​−63​≈.125004, as can be verified using the Binomial series or (after the test) a calculator.