Find the missing letters in the series given below: Y, T, O, ____, ____

CONCEPT

In a letter series, assign each letter its alphabet position (A = 1 through Z = 26) and compare the change between consecutive positions.

When the same difference repeats, continue that invariant to determine each missing letter.

APPLICATION

1. Y is at position 25 and T is at position 20, so the change is 20 - 25 = -5.

2. T is at position 20 and O is at position 15, so the change is again 15 - 20 = -5.

3. Continuing the constant step, 15 - 5 = 10; position 10 is J.

4. Applying the step once more, 10 - 5 = 5; position 5 is E.

The governing assumption is the simplest repeated constant-step pattern; scanning the series takes O(n) time.

CROSS-CHECK AND CONTRAST

The completed position sequence is 25, 20, 15, 10, 5, whose consecutive differences are all -5.

• J, D gives positions 10 and 4, so its consecutive changes after O are -5 and -6.

• K, F gives positions 11 and 6, so its consecutive changes after O are -4 and -5.

• The completed invariant identifies one listed pair, so the set-level alternatives do not describe the result.

Therefore, the missing letters are J, E.