UPSC CDS 2 2018 Math Paper

Since the HCF of given numbers is the highest common factor of numbers, therefore, numbers are 16a and 16b, where a and b are some natural numbers
16a×16b=7168⇒ab=28.
Here, a and b are co–prime to each other.
Also, 16a > 60, i.e., a > 3 and 16b > 60, i.e., b > 3.
Therefore, the only possible pair for (a, b) can be (4, 7).
Numbers are 16×4, i.e., 64 and 16×7, i.e., 112.
Sum of numbers =64+112=176