In the following analogy question, choose the pair of letters that bears the same relationship to each other as JK does to QR: JK : QR :: ____ : ____?

Introduction / Context:
This is a letter analogy question commonly found in reasoning sections of competitive exams. You are given a pair of letters JK and QR and asked to find another pair that shows the same pattern. To solve such questions, you must examine the alphabetical positions of the letters and identify the transformation that converts the first letter of the pair into the second. Then you must apply the same transformation to a new pair from the options.

Given Data / Assumptions:

The given pair is JK : QR.

We consider J and Q, K and R, and note their positions in the English alphabet.

Alphabet positions are: A 1, B 2, C 3, ..., J 10, K 11, Q 17, R 18.

We assume that the same operation is applied to both letters in each pair.

Exactly one of the options should follow this pattern.

Concept / Approach:

The strategy is to convert letters to numbers using their positions in the alphabet and then compute the difference between each pair. For JK : QR, we check how far Q is from J and how far R is from K. If both differences are the same, that difference becomes the rule. Then we search among the options for a pair of letters where the second letter is formed by adding or subtracting the same number to the first letter's position. This systematic approach avoids guesswork.

Step-by-Step Solution:
Step 1: Assign numerical positions to the letters: J is 10, K is 11, Q is 17, and R is 18. Step 2: Compute the differences: from J (10) to Q (17) the difference is +7, and from K (11) to R (18) the difference is also +7. Step 3: Conclude that the pattern for the given pair is: second letter equals first letter plus 7 positions in the alphabet, applied to both letters in the pair. Step 4: Now test each option to see which follows the same +7 pattern for both letters. Step 5: Option a: ST. S is 19, T is 20; UV: U is 21, V is 22. From S to U is +2, from T to V is +2. This is +2, not +7, so it does not match. Step 6: Option b: WX : ZY. W is 23, X is 24, Z is 26, Y is 25. From W to Z is +3, from X to Y is +1; the differences are not equal, so the pattern is inconsistent. Step 7: Option c: BC : IJ. B is 2, C is 3, I is 9, J is 10. From B to I is +7 and from C to J is also +7. This matches the pattern of adding 7. Step 8: Option d: MN : OR. M is 13, N is 14, O is 15, R is 18. From M to O is +2, from N to R is +4; these differences do not match each other and do not equal 7. Step 9: Option e: AB : CD. From A to C is +2 and from B to D is +2, so this is also +2, not +7. Step 10: Conclude that only BC : IJ matches the +7 pattern.

Verification / Alternative check:

To verify, we can write out the alphabet and manually count: After B (2) come C (3), D (4), E (5), F (6), G (7), H (8), and I (9), so I is 7 steps ahead of B. Similarly, after C (3) we count up seven positions to reach J (10). This confirms that BC : IJ uses the same transformation as JK : QR, where each second letter is seven positions ahead of the first.

Why Other Options Are Wrong:

Option a has a consistent pattern but with a difference of +2 instead of +7.

Option b does not even maintain a consistent difference between letters in the pair.

Option d also shows inconsistent differences between letters.

Option e again uses a +2 pattern, not +7.

Common Pitfalls:

Some students may pick an option simply because letters look similar or because they notice that both pairs are in alphabetical order. However, analogy questions demand that you identify the exact numerical relationship, not just a vague similarity. Failing to convert letters to numbers often leads to careless mistakes. Always calculate the differences carefully for both letters of the pair to ensure that the pattern truly matches.

Final Answer:

The pair of letters that follows the same pattern as JK : QR is BC : IJ.