Difficulty: Medium
Correct Answer: QSO
Explanation:
Introduction / Context:
This question uses a mirror or complementary coding of letters in the alphabet. The pair CAE : XZV is constructed so that each letter in CAE is replaced with its complementary letter measured from opposite ends of the alphabet. You must apply the same principle to JHL and find the correct option. This type of analogy is common in high level letter coding problems.
Given Data / Assumptions:
- Alphabet positions are A = 1, B = 2, ..., Z = 26.
- XZV corresponds to CAE through a consistent rule applied to every letter.
- The same rule must be applied to JHL to get the answer group.
- Only one of QSO, IGK, PRU, or GEI uses that exact correspondence.
Concept / Approach:
In mirror or complementary coding, each letter is replaced by the one that stands at the same distance from the other end of the alphabet. Concretely, for a letter with position n, the complementary letter has position 27 - n. For example, A (1) pairs with Z (26) because 1 + 26 = 27. Using this idea, we can verify whether CAE to XZV follows the same pattern and then apply it to JHL.
Step-by-Step Solution:
Step 1: Convert CAE to positions. C = 3, A = 1, E = 5.
Step 2: Convert XZV to positions. X = 24, Z = 26, V = 22.
Step 3: Apply the complementary rule. For C (3), 27 - 3 = 24, which is X. For A (1), 27 - 1 = 26, which is Z. For E (5), 27 - 5 = 22, which is V. This confirms that each letter is replaced with its 27 - n counterpart.
Step 4: Convert JHL to positions. J = 10, H = 8, L = 12.
Step 5: Apply the same complementary rule. For J (10), 27 - 10 = 17, which is Q. For H (8), 27 - 8 = 19, which is S. For L (12), 27 - 12 = 15, which is O.
Step 6: This yields the group QSO, which matches option A.
Verification / Alternative check:
To verify, we can reverse the process by applying the complementary rule again to QSO. Q (17) maps back to J (10) because 27 - 17 = 10. S (19) maps to H (8) because 27 - 19 = 8. O (15) maps to L (12) because 27 - 15 = 12. So the mapping is perfectly symmetric, confirming that QSO is indeed the mirror code of JHL under the same rule used for CAE and XZV.
Why Other Options Are Wrong:
Option B "IGK" does not match the positions obtained using the 27 - n rule and would require a different transformation pattern.
Option C "PRU" and option D "GEI" also fail to correspond to the complementary positions of J, H, and L. None of them produce symmetric mappings back to JHL via the same formula.
Common Pitfalls:
Students sometimes confuse simple shifts such as +3 with complementation around the middle of the alphabet. Another common mistake is to check only one or two letters and ignore the rest. For mirror coding, all letters must be replaced using the 27 - n rule, and reversing the process should bring you back to the original word. This double check is very helpful in exam situations.
Final Answer:
The correct related group of letters is QSO.
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