In the following letter pair analogy, PIR is related to OHQ in a particular way. Using the same pattern, which of the following letter pairs correctly completes the analogy?

Introduction / Context:
This question presents a relationship between two three letter groups, PIR and OHQ, and asks you to select another pair of three letter groups that follows the same rule. Letter analogies usually involve operations on positions in the English alphabet such as shifting letters forward or backward by a fixed number, or applying different shifts to different positions. Here we must carefully examine how each letter in PIR transforms into each letter in OHQ.

Given Data / Assumptions:
- First group: PIR is transformed into second group: OHQ.
- Each position may undergo the same or a different shift in the alphabet.
- The alphabet positions are A = 1, B = 2, and so on up to Z = 26.
- We must find the option whose first three letter group transforms into the second three letter group in exactly the same way that PIR transforms into OHQ.

Concept / Approach:
We convert letters to their alphabet positions and then compare. P is the 16th letter, O is the 15th letter, I is the 9th letter, H is the 8th letter, R is the 18th letter, and Q is the 17th letter. In each case, the second letter in the pair is one position earlier in the alphabet than the first letter. Therefore the rule is shift each letter back by one position. We must now find an option where the second group is formed by shifting every letter of the first group back by exactly one position, taking Z to mean a shift back to Y and so on, including wrap around if needed.

Step-by-Step Solution:
Step 1: Calculate shifts in the given pair. P to O is minus one, I to H is minus one, and R to Q is minus one in alphabet order. Step 2: Apply this rule to option C, FAX : EZW, as a candidate. Step 3: F is the 6th letter and E is the 5th, so this is a backward shift of one position. Step 4: A is the 1st letter and Z is the 26th. Moving from A back by one position wraps around to Z, again a backward shift of one. Step 5: X is the 24th letter and W is the 23rd, again a backward shift of one position. Step 6: Since each letter in FAX moves back by exactly one position to produce EZW, this pair follows the same pattern as PIR : OHQ.

Verification / Alternative check:
Check the other options to ensure they do not follow the same rule. In option A, KLO : MOR, K to M is plus two, not minus one. In option B, the shifts are inconsistent across letters, and in option D, KMN : LNO, again the first letters increase instead of decrease. Therefore, only option C obeys the consistent rule of each letter moving one step backward in the alphabet. This mirrors exactly how PIR transforms into OHQ.

Why Other Options Are Wrong:
Option A shows a forward shift rather than a backward one, which does not match the original pattern. Option B contains unequal shifts across letters, meaning there is no single step change from the first group to the second. Option D likewise fails to maintain a constant shift of minus one for each letter. Since the original analogy clearly uses a fixed backward shift of one step for each character, those options cannot be correct.

Common Pitfalls:
A frequent error is checking only one or two letters and ignoring the rest, which can make an inconsistent pattern appear valid. Another mistake is miscounting alphabet positions or forgetting to handle wrap around at A and Z. To avoid these issues, always verify the transformation for every letter in the group and confirm that the same operation is applied consistently. When you do this carefully, FAX : EZW stands out as the only pair that matches PIR : OHQ.

Final Answer:
Because each letter in FAX is shifted back by one position to form EZW, just as each letter in PIR is shifted back by one to form OHQ, the correct pair is FAX : EZW, so option C is correct.