In the following letter analogy based on position shifts, YONEX is related to DUUMG. Using the same pattern of transformation, JASPO is related to which of the following letter groups?

Introduction / Context:
This letter analogy involves a systematic but increasing shift in alphabet positions. The transformation from YONEX to DUUMG changes each letter by a different amount, following a clear numeric pattern. Our job is to extract this pattern and apply it to JASPO in order to determine the correct related group from the options. Questions of this type test careful observation of step wise changes across several letters.

Given Data / Assumptions:

• First pair: YONEX : DUUMG
• Second first term: JASPO
• Options: OGZXX, OXXZF, OZTYY, OZXXG.
• We map letters A to Z as positions 1 to 26, using modular arithmetic for wraparound if needed.

Concept / Approach:
We first convert YONEX and DUUMG into their numeric positions and compare each corresponding letter. If the increments form a pattern such as plus 5, plus 6, plus 7, plus 8, plus 9, we can then apply the same incremental shifts to the letters of JASPO. The presence of several letters and a non constant step makes this problem more challenging than a simple constant shift analogy.

Step-by-Step Solution:
Step 1: Convert YONEX into positions. Y is 25, O is 15, N is 14, E is 5, X is 24. Step 2: Convert DUUMG into positions. D is 4, U is 21, U is 21, M is 13, G is 7. Step 3: Compute the forward shifts using modular arithmetic. From Y (25) to D (4) we add 5 positions, because 25 plus 5 equals 30 and 30 minus 26 equals 4. From O (15) to U (21) we add 6. From N (14) to U (21) we add 7. From E (5) to M (13) we add 8. From X (24) to G (7) we add 9 after wrapping around. Step 4: Conclude that the pattern of shifts is plus 5, plus 6, plus 7, plus 8, and plus 9 applied respectively to the first, second, third, fourth, and fifth letters. Step 5: Apply the same pattern to JASPO. Positions: J is 10, A is 1, S is 19, P is 16, O is 15. Step 6: Add 5 to J: 10 plus 5 equals 15, which is O. Add 6 to A: 1 plus 6 equals 7, which is G. Add 7 to S: 19 plus 7 equals 26, which is Z. Add 8 to P: 16 plus 8 equals 24, which is X. Add 9 to O: 15 plus 9 equals 24, which is also X. Step 7: Combine these transformed letters to obtain OGZXX.

Verification / Alternative check:
Check OGZXX against the options and see that it appears exactly as one of the choices. For completeness, if we attempted to apply any different fixed shift such as plus three to JASPO, we would not match DUUMG when applied to YONEX, so that would be inconsistent. The increasing sequence of increments plus 5 through plus 9 is the only one that turns YONEX into DUUMG neatly and then turns JASPO into OGZXX. Thus the analogy is satisfied uniquely by this option.

Why Other Options Are Wrong:
Options OXXZF, OZTYY, and OZXXG differ in one or more positions from OGZXX. If we trace back from those groups to JASPO, the required shifts would no longer follow the plus 5 to plus 9 pattern in order, which contradicts the transformation discovered from the original pair. Since the mapping must be identical for both strings, any change to even one shift value invalidates the option.

Common Pitfalls:
One common mistake is to look only for a constant shift and to abandon the problem when such a shift is not found. Another pitfall is to overlook the modular nature of the alphabet, especially for letters near the end where shifting forward requires wraparound to A. Additionally, some learners may detect the plus 5 and plus 6 shifts but fail to notice that the increments continue as plus 7, plus 8, and plus 9. Careful column wise calculation prevents these errors.

Final Answer:
The letter group that completes the analogy YONEX : DUUMG :: JASPO : ? is OGZXX.