Select the related group of letters to complete the analogy: ABDE : FGIJ :: IJLM : ?. Which option best represents the missing group so that the same alphabetic relationship holds on both sides?

Introduction / Context:
This question is an analogy based on alphabetic transformations. We are given ABDE : FGIJ :: IJLM : ?, and must determine the second group of letters that stands in the same relationship to IJLM as FGIJ stands to ABDE. Such analogies test the ability to detect uniform shifts in letter positions and apply them consistently in a comparative setting.

Given Data / Assumptions:

• First pair in the analogy: ABDE and FGIJ.
• Second pair: IJLM and an unknown group.
• We assume a fixed transformation, such as adding a constant number of positions to each letter.
• Options: NOQR, NOPQ, NMOP, NPQR.

Concept / Approach:
To solve the analogy, we first identify the exact transformation that converts ABDE into FGIJ by mapping each letter to its numerical position. Once we determine the step size, we apply the same transformation to each letter of IJLM. The correct option will be the group that matches the transformed letters exactly.

Step-by-Step Solution:
Step 1: Convert ABDE to positions: A(1), B(2), D(4), E(5).Step 2: Convert FGIJ to positions: F(6), G(7), I(9), J(10).Step 3: Determine the change for each corresponding letter: A(1) to F(6) is +5, B(2) to G(7) is +5, D(4) to I(9) is +5, and E(5) to J(10) is also +5.Step 4: The rule is therefore to add 5 to the position of each letter in the original group to get the new group.Step 5: Now convert IJLM into positions: I(9), J(10), L(12), M(13).Step 6: Add 5 to each position: 9 + 5 = 14 (N), 10 + 5 = 15 (O), 12 + 5 = 17 (Q), and 13 + 5 = 18 (R).Step 7: The resulting letters are N, O, Q, R, forming the group NOQR.

Verification / Alternative check:
We can quickly verify the mapping by rewriting both transformations: ABDE plus 5 positions gives FGIJ, and IJLM plus 5 positions gives NOQR. The transformation is uniform and consistent across all letters. Checking the options, only NOQR matches this exact sequence of letters, so it is the only valid choice.

Why Other Options Are Wrong:
Options NOPQ, NMOP, and NPQR contain letters that would require different step sizes from at least one of the letters in IJLM. Since the analogy is based on a strict +5 transformation, any sequence that breaks this rule cannot represent the correct related group.

Common Pitfalls:
Some test takers may try to evaluate the options by approximate visual closeness to IJLM instead of calculating exact positional changes. Others may check only the first letter and ignore the rest. A reliable method is to translate all letters to numbers, determine the transformation precisely, and apply that transformation consistently to each letter in the second group.

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