In this letter analogy, JK is related to TV by a specific position rule. Applying the same alphabet position rule, which pair of letters corresponds to OP?

Introduction / Context:
This question presents a two letter analogy based on positions of letters in the alphabet. The given pair JK : TV hides a mathematical relationship between the alphabet positions of J, K, T and V. Once we discover this rule, we must apply the same transformation to the pair OP in order to identify the correct coded pair from the options. Such questions are common in reasoning sections and reward a clear, numeric way of thinking about letters.

Given Data / Assumptions:

J and K form the first pair, which transforms to T and V as the second pair in the example.
We work with positions A = 1, B = 2, ..., Z = 26.
In the question part, OP must be changed under the same rule to find the answer.
The answer choices are DF, WV, ST and QR.
We assume that letters are not rearranged, only position values are transformed using a consistent rule.

Concept / Approach:
The key idea is to treat each letter as a number and look at how positions change. J is the 10th letter and K is the 11th. T is the 20th letter and V is the 22nd. Notice that the second set positions are approximately double the first set positions. Checking this more carefully, 10 multiplied by 2 gives 20, and 11 multiplied by 2 gives 22. So the coding rule appears to be: multiply the alphabet position of each letter by 2, then convert back to a letter, wrapping around if necessary. Once this is clear, we can apply the same multiplication rule to O and P.

Step-by-Step Solution:
Step 1: Write positions for J and K. J = 10, K = 11. Step 2: Write positions for T and V. T = 20, V = 22. Step 3: Observe that 10 * 2 = 20 and 11 * 2 = 22, confirming that each position is doubled to obtain the code. Step 4: Now consider O and P. The positions are O = 15 and P = 16. Step 5: Apply the same rule: 15 * 2 = 30 and 16 * 2 = 32. Since the alphabet only has 26 letters, we wrap around by subtracting 26 when the result exceeds 26. Step 6: For 30, 30 - 26 = 4, which corresponds to D. For 32, 32 - 26 = 6, which corresponds to F. Step 7: The resulting coded pair for OP is therefore DF.

Verification / Alternative check:
To verify, we can reverse the logic by halving the positions of T and V. T is 20, which when divided by 2 returns 10, the position of J. V is 22, which when divided by 2 returns 11, the position of K. This confirms that the original mapping uses doubling of positions. Applying the same check to DF, D is 4 and F is 6. Doubling the original positions 15 and 16 gave 30 and 32, and subtracting 26 gave 4 and 6, which matches D and F exactly. Thus DF is correctly derived from OP under the same rule.

Why Other Options Are Wrong:
WV corresponds to positions 23 and 22, which are not the doubled and wrapped values of 15 and 16. ST corresponds to 19 and 20, again not matching the required 4 and 6. QR corresponds to 17 and 18, which would imply some other pattern such as a fixed shift, not a multiplication rule. None of these pairs reflect the precise doubling and wrapping operation observed in the example JK : TV.

Common Pitfalls:
A common pitfall is to look only at simple addition or subtraction when comparing letters, ignoring possibilities like multiplication or division. Another mistake is to forget wrap around when results go beyond 26. In letter coding questions, whenever you multiply or add and exceed 26, you must loop back to the start of the alphabet. Maintaining this habit will help you handle more complex codes without error. Always check your discovered pattern in both directions on the example pair before applying it to the target pair.

Final Answer:
Using the rule “double each alphabet position and wrap around beyond 26”, the pair OP is coded as DF, so DF is the correct answer.