In this letter analogy, “NPR is to GHI as TVX is to ______”. Choose the group of letters that completes the analogy by following the same alphabet position halving pattern.

Introduction / Context:
This question presents a letter analogy where each letter in one group corresponds to a letter in another group by a positional rule in the alphabet. The pair NPR : GHI is given, and we must detect the exact relationship between these two sequences. After discovering the pattern, we apply it to TVX to find its corresponding group from the options. This tests knowledge of alphabet positions and the ability to observe number based patterns hidden inside letters.

Given Data / Assumptions:

• First letter group: NPR. • Second letter group: GHI. • Third group: TVX with an unknown partner. • Options: JKL, KLM, IJK, IKL. • Alphabet positions: A = 1, B = 2, ..., Z = 26.

Concept / Approach:
Instead of looking for simple additions or subtractions, we examine whether the positions of the letters in the second group are related to the positions in the first group through halving. If the position of each letter in GHI is equal to half of the position of the corresponding letter in NPR, we have a consistent rule. We then apply the same halving rule to TVX and choose the option that matches the resulting letters.

Step-by-Step Solution:
Step 1: Convert NPR to numeric positions. N = 14, P = 16, R = 18. Step 2: Convert GHI to numeric positions. G = 7, H = 8, I = 9. Step 3: Compare positions in each pair. 14 / 2 = 7, which gives G. 16 / 2 = 8, which gives H. 18 / 2 = 9, which gives I. Thus, each letter in the second group has a position equal to half of the corresponding letter in the first group. Step 4: Apply the same rule to TVX. T = 20, V = 22, X = 24. Half of 20 is 10 → J. Half of 22 is 11 → K. Half of 24 is 12 → L. So the resulting letter group is JKL.

Verification / Alternative check:
To verify, we can reverse the rule by doubling the positions of GHI and JKL. Doubling 7, 8, and 9 gives 14, 16, and 18, which correspond to N, P, and R, so NPR is recovered. Doubling 10, 11, and 12 gives 20, 22, and 24, which correspond to T, V, and X, so TVX is recovered. This confirms that the relationship is stable and symmetric: first group positions are exactly twice the second group positions.

Why Other Options Are Wrong:
• KLM and IJK: These groups do not arise from halving 20, 22, and 24; their letter positions do not match the halved values. • IKL: Also does not correspond to exact halves of T, V, and X when converted to numeric positions.

Common Pitfalls:
Many candidates first look for constant addition or subtraction, such as shifting letters by a fixed number of positions. When this fails, they may guess based on partial similarities instead of considering division patterns. In analogies that use letters with relatively large positions, checking for halving or doubling is often very productive. Always translate letters to numbers and explore both multiplication and division when simple addition does not fit.

Final Answer:
The group of letters that correctly completes the analogy is JKL.