Understanding the Letter Series Puzzle

The question presents a series of letter pairs: MR, TO, QV, XS. We need to identify the pattern governing this series to find the missing pair that logically follows XS.

Analyzing the Letter Series Pattern

To understand the pattern, let's convert each letter into its corresponding position in the English alphabet (A=1, B=2, ..., Z=26).

• MR: M is the 13^th letter, R is the 18^th letter. Pair: (13, 18)
• TO: T is the 20^th letter, O is the 15^th letter. Pair: (20, 15)
• QV: Q is the 17^th letter, V is the 22^nd letter. Pair: (17, 22)
• XS: X is the 24^th letter, S is the 19^th letter. Pair: (24, 19)

Identifying the Series Progression

Now, let's look at the differences between the positions of the letters in consecutive pairs:

From MR (13, 18) to TO (20, 15):

• Difference in first letters: $20 - 13 = +7$
• Difference in second letters: $15 - 18 = -3$

So, the transition is (+7, -3).

From TO (20, 15) to QV (17, 22):

• Difference in first letters: $17 - 20 = -3$
• Difference in second letters: $22 - 15 = +7$

The transition here is (-3, +7).

From QV (17, 22) to XS (24, 19):

• Difference in first letters: $24 - 17 = +7$
• Difference in second letters: $19 - 22 = -3$

The transition is (+7, -3).

We can observe an alternating pattern in the transitions: (+7, -3), (-3, +7), (+7, -3), ...

Determining the Missing Term

Following the alternating pattern, the next transition after (+7, -3) should be (-3, +7).

We need to apply this transition to the last pair, XS (24, 19):

• For the first letter: Apply -3 to the position of X (24). Calculation: $24 - 3 = 21$. The 21^st letter of the alphabet is U.
• For the second letter: Apply +7 to the position of S (19). Calculation: $19 + 7 = 26$. The 26^th letter of the alphabet is Z.

Therefore, the missing pair is UZ.