In a certain code language, ‘PANTHER’ is written as ‘0146283’ and ‘ANOTHER’ is written as ‘2864109’. How will ‘O’ be written in that language?
- (a)3
- (b)8
- (c)0
- (d)9
Answer
Why
Correct — D.
Rule: the digits are not aligned letter by letter — compare the two words as sets and cancel what they share.
PANTHER and ANOTHER share A, N, T, H, E and R. The letter found only in PANTHER is P, and the letter found only in ANOTHER is O.
Their codes 0146283 and 2864109 share the digits 0, 1, 2, 4, 6 and 8. The digit found only in the first is 3, and the digit found only in the second is 9.
So P = 3 and O = 9, which is option (d).
Why the others are wrong
- (a)3 — 3 is the digit unique to PANTHER's code, so it belongs to P — the letter ANOTHER does not contain. Answering 3 cancels in the right way but the wrong direction.
- (b)8 — 8 appears in both code strings, so it must code one of the six letters both words share. A digit common to both cannot belong to O, which sits in only one word.
- (c)0 — 0 is also in both strings, so it too codes a shared letter. Being the first digit of PANTHER's code tempts you to read it as P, but position carries no meaning in this code.
Concept
Letter-to-digit codes come in two families, and telling them apart is the whole difficulty. In the first, the nth letter takes the nth digit. In the second, which is this one, the digits are the right set of codes but shuffled, so position tells you nothing.
Test the family before you work. If PANTHER's digits mapped in order, P = 0 and A = 1, but ANOTHER would then need A = 2. That contradiction settles it.
Once you know the codes are unordered, the tool is set difference: whatever is unique to one word must match whatever is unique to its code.
The two words are chosen to overlap in six of seven letters, which is what makes the cancellation clean. With two or three letters differing you would need a third word to pin any single value.
Key facts
- PANTHER and ANOTHER differ by exactly one letter each, P against O.
- Their codes differ by exactly one digit each, 3 against 9.
- Both words contain A, N, T, H, E and R, so those six letters take the six digits common to both codes.
Study next
Common traps
- Matching the first digit to the first letter, which forces A to be both 1 and 2.
- Answering 3 by taking the digit unique to the wrong word.
- Assuming a seven-digit code must map one digit per letter in order simply because the counts agree.
Only one letter is wanted, not the whole word, so the cancellation is enough and no full key needs building. The same intersect-rather-than-align idea runs the coded-sentence item at 19 Sep 2024, 12:30, Reasoning Q.1.
Related PYQs
No directly related past PYQ was found.