If a,b, and c are positive integers with at least one of

At least one of the three = 7.

(1) a < 7
So at least one integer = 7, and one integer < 7.
If third integer = 7, then since two integers = 7, median of these three = 7
If third integer < 7, then since two integers < 7, median of these three < 7
If third integer > 7, then the median of these three = 7

So the median will either be = 7 or < 7, but never > 7. So this gives NO as an answer to the question asked. Sufficient.

(2) c > 7
So at least one integer = 7, and one integer > 7
If third integer = 7, then since two integers = 7, median of these three = 7
If third integer > 7, then since two integers > 7, median of these three > 7

So the median might be = 7 or greater than 7 also. This doesnt give a definite YES or NO to the question asked. Not Sufficient.

Hence A answer