In the following letter analogy, CD is related to PQ in a particular way. Using the same pattern, which pair of letters should complete the analogy CD : PQ :: GH : ?

Introduction / Context:
This letter analogy is based on a fixed shift forward in the alphabet. CD is related to PQ, and we must determine what GH will relate to under the same letter shift. The key is to find a consistent number of positions by which both letters in the first pair move forward to become the second pair. Then, we apply that same shift to the new pair GH. This kind of problem tests careful counting of letter positions and consistent application of a Caesar style transformation.

Given Data / Assumptions:
First pair: CD : PQ. Second pair: GH : ?. All letters are capital letters from A to Z. The same fixed shift is used for both letters in each pair.

Concept / Approach:
We convert the letters C, D, P, and Q into their numerical positions in the alphabet and calculate the difference between each pair. If the shift is the same for both letters, we have identified the coding rule. We then add that same number of positions to the letters G and H to obtain the corresponding pair. It is important to track the positions accurately and apply the shift consistently to both letters in GH.

Step-by-Step Solution:
Step 1: Determine positions for C, D, P, and Q. C = 3, D = 4. P = 16, Q = 17. Step 2: Compute the shifts. From C to P: 3 to 16 is +13. From D to Q: 4 to 17 is also +13. Thus, each letter is shifted forward by 13 positions in the alphabet. Step 3: Apply the same +13 shift to GH. G = 7, H = 8. G plus 13 is 7 + 13 = 20, which is T. H plus 13 is 8 + 13 = 21, which is U. Therefore, GH becomes TU under the same rule.

Verification / Alternative check:
We can confirm the reasoning by checking whether TU and GH maintain the same distance as PQ and CD. If we subtract 13 from T and U, we should obtain G and H. T is 20; 20 minus 13 is 7, which is G. U is 21; 21 minus 13 is 8, which is H. This backward check confirms that the +13 shift works perfectly for both pairs and that TU is the correct partner for GH in the analogy.

Why Other Options Are Wrong:
RS, UV, WX, and IJ do not result from adding 13 to G and H; their positions differ by other amounts. Any pair that does not reflect a uniform +13 shift from GH fails to match the pattern established between CD and PQ.

Common Pitfalls:
Candidates sometimes try to use smaller shifts such as +2 or +3 without checking carefully whether those shifts actually transform CD into PQ. Another common mistake is to forget that the same exact shift must apply to both letters in a pair. In Caesar style analogies, always calculate the numerical positions for each letter, compute the difference for the first pair, and then systematically apply that difference to each letter in the new pair.

Final Answer:
Using the same +13 shift that maps CD to PQ, GH should be mapped to TU.