In this letter analogy, find the pair of letters that correctly completes the relation ? : GA :: QR : JI.

Introduction / Context:
This question tests your understanding of letter analogy and positional relationships in the English alphabet. Instead of simple alphabetical order, you must recognize a hidden numerical pattern that links each pair of letters. Such questions are common in reasoning and aptitude tests, where the goal is to check your ability to observe patterns and apply them consistently to find the missing term in an analogy.

Given Data / Assumptions:

• The analogy is ? : GA :: QR : JI.
• We use the English alphabet positions A = 1, B = 2, …, Z = 26.
• GA and JI are the second elements in each pair, while ? and QR are the first elements.
• The same pattern that connects QR to JI must connect ? to GA.

Concept / Approach:
The key idea is to convert letters into their numerical positions and look for a consistent relationship. One useful technique is to check whether the sum or difference of letter positions is constant across corresponding letters. In this analogy, the first letters of each pair are related to the second letters through a constant sum. Once you find this relationship in the known pair (QR : JI), you can apply it in reverse to find the missing pair corresponding to GA.

Step-by-Step Solution:
Step 1: Write positions of letters in QR and JI. Q = 17, R = 18, J = 10, I = 9.Step 2: Check sums for corresponding letters: Q + J = 17 + 10 = 27, R + I = 18 + 9 = 27.Step 3: This shows that in the pair QR : JI, the positions of corresponding letters add up to 27.Step 4: Now apply the same rule to the pair ? : GA. Positions: G = 7, A = 1.Step 5: Let the unknown pair be XY. Then X + G must equal 27, and Y + A must equal 27.Step 6: So X = 27 - 7 = 20 and Y = 27 - 1 = 26.Step 7: The 20th letter is T and the 26th letter is Z, so the missing pair is TZ.

Verification / Alternative check:
We can quickly verify the pattern. If we take the found pair TZ and the given GA, we must maintain the same constant sum of 27. T is the 20th letter and Z is the 26th. Now 20 + 7 = 27 and 26 + 1 = 27, which confirms that the same rule holds. This confirms that TZ : GA follows the same positional relationship as QR : JI, so the analogy is consistent.

Why Other Options Are Wrong:
KN: K is 11 and N is 14, so 11 + 7 = 18 and 14 + 1 = 15, which does not give a constant sum of 27.
RS: R is 18 and S is 19, giving 18 + 7 = 25 and 19 + 1 = 20, again not 27.
NQ: N is 14 and Q is 17, giving 14 + 7 = 21 and 17 + 1 = 18, which fails the pattern. Only TZ maintains the constant sum of 27 for both letter pairs.

Common Pitfalls:
Candidates may focus only on forward or backward shifts in the alphabet and miss the constant sum pattern. Another common mistake is to compare non corresponding letters, such as Q with I or R with J, instead of aligning first letters with first letters and second letters with second letters. Some test takers also guess based on partial similarity instead of fully verifying the pattern numerically.

Final Answer:
The pair of letters that completes the analogy is TZ.