In a certain code language, ‘BIRTHDAY’ is written as ‘ADHTRIBY’ and ‘CONGRESS’ is written as ‘SERGNOCS’. How will ‘DIVISION’ be written in that language?

Correct — C. Line each code up under its word and see which letter has not moved.

BIRTHDAY to ADHTRIBY: the final Y stays put, and BIRTHDA reversed is ADHTRIB.
CONGRESS to SERGNOCS: the final S stays put, and CONGRES reversed is SERGNOC.

Rule: hold the last letter, reverse the first seven.

For DIVISION the held letter is N, and DIVISIO reversed is OISIVID.
OISIVID followed by N gives OISIVIDN, option (c).

Why the others are wrong

• (a)
  NDOISIVI — NDOISIVI ends in I. The rule pins the word's last letter in place, so whatever happens to the first seven, the code has to end in N.
• (b)
  DNOISIVI — DNOISIVI reverses the last seven letters and keeps the first — the opposite anchoring. Applied to BIRTHDAY it would give BYADHTRI, not ADHTRIBY.
• (d)
  NOISIVID — NOISIVID is DIVISION spelled backwards in full. A full reversal of BIRTHDAY would be YADHTRIB, whereas the given code ADHTRIBY keeps Y at the end.

Letter-shuffle codes are solved by alignment, not by intuition. Write the word above the code and mark the letters that have not moved.

In both worked pairs one letter stays where it was: the last one. Y is eighth in BIRTHDAY and eighth in ADHTRIBY. S is eighth in CONGRESS and eighth in SERGNOCS.

Once the anchor is fixed, the remaining seven letters are simply written backwards. Nothing here changes a letter into another letter, so no alphabet arithmetic is involved.

Key facts

• BIRTHDAY becomes ADHTRIBY because BIRTHDA reversed is ADHTRIB and Y is held.
• CONGRESS becomes SERGNOCS because CONGRES reversed is SERGNOC and the final S is held.
• DIVISIO reversed is OISIVID, and the held letter is N.

Common traps

• Reversing the whole word, which gives NOISIVID.
• Holding the first letter instead of the last, which gives DNOISIVI.
• Dropping one of the three I's while writing DIVISIO backwards.

No directly related past PYQ was found.