Select the number-pair that is different from the rest in some respect.

Key insight: the first three pairs have both numbers divisible by 13, while the fourth pair does not. 26 : 78 → 26 = 2 × 13, 78 = 6 × 13 (both divisible by 13)

52 : 117 → 52 = 4 × 13, 117 = 9 × 13 (both divisible by 13)

39 : 104 → 39 = 3 × 13, 104 = 8 × 13 (both divisible by 13)

65 : 120 → 65 = 5 × 13, but 120 = 2³ × 3 × 5 (120 is not divisible by 13)

Conclusion: 65 : 120 is the different pair because it is the only pair where both numbers do not share 13 as a common factor.