Inferring the primary cause of modern geopolitical tensions from the text

Let P's age be 10a + b and Q's age be 10b + a. The positive difference between their ages is always a multiple of 9: |P - Q| = |(10a + b) - (10b + a)| = 9|a - b|. Their sum is P + Q = 11(a + b).

Statement I indicates P > Q, meaning a > b. This merely establishes the sign of the difference but yields no numerical metrics. Insufficient .

Statement II states that the sum is 11/6 times their difference: 11(a + b) = 11/6 × 9|a - b| Divide both sides by 11: a + b = 9/6|a - b| \implies a + b = 3/2|a - b|.

Notice that this equation relies entirely on the digits ⟨MATH⟩a⟨/MATH⟩ and ⟨MATH⟩b⟨/MATH⟩. If a > b, it reduces to 2(a + b) = 3(a - b) \implies 2a + 2b = 3a - 3b \implies a = 5b. Since a and b are single digits, the only possible solution is b = 1 and a = 5, making the ages 51 and 15, and their difference 51 - 15 = 36. If b > a, the ratio symmetrically yields b = 5a, leading to ages 15 and 51, and their difference remains exactly 36.

Because Statement II independently computes the exact age difference (36) without needing to know which person is older, it is sufficient on its own.

Answer: (a).