In a certain code language, ‘TOUGH’ is coded as ‘89251’ and ‘GHOST’ is coded as ‘93258’. What is the code for ‘S’ in the given code language?
- (a)3
- (b)1
- (c)9
- (d)8
Answer
Why
Correct — A. Compare the two words as sets rather than position by position.
TOUGH = 8 9 2 5 1
GHOST = 9 3 2 5 8
Rule: the letters both words share must be using the digits both codes share.
Shared letters: T, O, G, H. Shared digits: 8, 9, 2, 5.
TOUGH's unmatched letter is U and its unmatched digit is 1, so U = 1.
GHOST's unmatched letter is S and its unmatched digit is 3, so S = 3 -> option (a).
Why the others are wrong
- (b)1 — 1 is the digit that appears in TOUGH's code and not in GHOST's, so it belongs to U — the letter in TOUGH and not in GHOST. S appears in GHOST only.
- (c)9 — 9 appears in both codes, so it must belong to one of the four letters both words carry: T, O, G or H. S is in only one of the words and cannot own a shared digit.
- (d)8 — 8 also appears in both codes and is therefore spoken for by a shared letter. Any digit common to the two codes is unavailable to S.
Concept
When two coded words share most of their letters, you do not need the whole cipher — you need the parts that fail to overlap.
Set the two letter sets beside each other and the two digit sets beside each other. Whatever the internal pairing, the letters common to both words must be consuming the digits common to both codes.
That leaves exactly one letter and one digit unmatched on each side, and those two must belong together. It is the same move as cancelling common terms from both sides of an equation.
The code is not positional. O is the 2nd letter of TOUGH and the 3rd of GHOST, and the digits in those slots are 9 and 2, so lining letters up against digits gives contradictions.
Key facts
- TOUGH and GHOST share the letters T, O, G and H.
- Their codes 89251 and 93258 share the digits 8, 9, 2 and 5.
- The unmatched pairs give U = 1 and S = 3.
- The individual codes for T, O, G and H cannot be fixed from these two words alone.
Study next
Common traps
- Lining the codes up letter by letter, which makes G = 5 from TOUGH and G = 9 from GHOST.
- Assuming a repeated digit must stand for a repeated letter.
- Trying to pin down all five letters when the question asks for one.
The word pair is built so that exactly one letter and one digit are left unmatched on each side. Find them and the answer is forced, with none of the rest of the cipher decoded.
Letter-position arithmetic drives Reasoning Q.1 and Q.11 in this shift (19 Sep 2024, 09:00), which is a different idea from this set comparison.
Related PYQs
No directly related past PYQ was found.