HOLN is related to XGBF in a certain way based on the English alphabetical order. In the same way, TIXH is related to JANZ. To which of the given options is PKTJ related, following the same logic?
Decoding the Alphabetical Relationship: PKTJ
This question requires us to find a specific logical connection between pairs of letter groups based on their order in the English alphabet. We first analyze the given examples, HOLN → XGBF and TIXH → JANZ, to identify the underlying pattern. Once the pattern is confirmed, we apply it to the group PKTJ to determine its corresponding group.
Step 1: Analyzing the HOLN → XGBF Relationship
Let's determine the numerical positions of the letters in the English alphabet (A=1, B=2, ..., Z=26).
| Letter in HOLN | H | O | L | N |
| Position | 8 | 15 | 12 | 14 |
| Letter in XGBF | X | G | B | F |
| Position | 24 | 7 | 2 | 6 |
Now, we calculate the difference in positions for each letter pair. We use modulo 26 arithmetic to handle wrap-around cases (where the result goes beyond Z).
- H (position 8) → X (position 24): The shift is calculated as $(24 - 8 + 26) \pmod{26} = 16$.
- O (position 15) → G (position 7): The shift is calculated as $(7 - 15 + 26) \pmod{26} = 18$.
- L (position 12) → B (position 2): The shift is calculated as $(2 - 12 + 26) \pmod{26} = 16$.
- N (position 14) → F (position 6): The shift is calculated as $(6 - 14 + 26) \pmod{26} = 18$.
The pattern observed for HOLN → XGBF is an alternating sequence of shifts: +16, +18, +16, +18.
Step 2: Verifying the Pattern with TIXH → JANZ
To ensure the identified pattern is correct, let's apply it to the second example.
Alphabetical positions:
| Letter in TIXH | T | I | X | H |
| Position | 20 | 9 | 24 | 8 |
| Letter in JANZ | J | A | N | Z |
| Position | 10 | 1 | 14 | 26 |
Calculating the shifts:
- T (position 20) → J (position 10): Shift = $(10 - 20 + 26) \pmod{26} = 16$.
- I (position 9) → A (position 1): Shift = $(1 - 9 + 26) \pmod{26} = 18$.
- X (position 24) → N (position 14): Shift = $(14 - 24 + 26) \pmod{26} = 16$.
- H (position 8) → Z (position 26): Shift = $(26 - 8 + 26) \pmod{26} = 18$.
The shifts (+16, +18, +16, +18) match the pattern derived from the first pair. This confirms our understanding of the logic.
Step 3: Applying the Pattern to PKTJ
We now use the confirmed pattern (+16, +18, +16, +18) to find the related group for PKTJ.
First, find the positions of the letters in PKTJ:
| Letter in PKTJ | P | K | T | J |
| Position | 16 | 11 | 20 | 10 |
Apply the alternating shifts:
- P (position 16): Apply the first shift, +16. The new position is $(16 + 16) \pmod{26} = 32 \pmod{26} = 6$. The 6th letter is F.
- K (position 11): Apply the second shift, +18. The new position is $(11 + 18) \pmod{26} = 29 \pmod{26} = 3$. The 3rd letter is C.
- T (position 20): Apply the third shift, +16. The new position is $(20 + 16) \pmod{26} = 36 \pmod{26} = 10$. The 10th letter is J.
- J (position 10): Apply the fourth shift, +18. The new position is $(10 + 18) \pmod{26} = 28 \pmod{26} = 2$. The 2nd letter is B.
Step 4: Final Result
Combining the calculated letters F, C, J, and B gives us the resulting group FCJB. This matches one of the provided options.
Important Questions from Coding and Decoding By Letter Shifting
WPKD is related to TNHB in a certain way based on the English alphabetical order. In the same way, KHYV is related to HFVT. To which of the given options is BBPP related, following the same logic?
- Replace the question mark with an option that follows the same logic applied in the first pair.
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- In a certain code language, if ALLOW is coded as DOORZ, then how is DELAY coded in that language?
- In a certain code language, if GRANT is coded as TIZMG, then how is ROUGH coded in that language?
