In a certain code language, ‘DRAPE’ is coded as ‘65432’ and ‘TAPED’ is coded as ‘24596’. What is the code for ‘R’ in that language?
- (a)9
- (b)6
- (c)2
- (d)3
Answer
Why
Correct — D. The digits are not assigned letter by letter in position, so compare the two words as sets.
DRAPE and TAPED share D, A, P and E. R belongs to DRAPE alone, and T to TAPED alone.
Their codes 65432 and 24596 share 6, 4, 5 and 2. 3 appears only in DRAPE's code, and 9 only in TAPED's.
The letter unique to DRAPE must take the digit unique to DRAPE's code, so R = 3 -> option (d).
Why the others are wrong
- (a)9 — 9 is the digit found only in TAPED's code, so it belongs to T, the letter found only in TAPED.
- (b)6 — 6 appears in both codes, so it must stand for one of the four shared letters. R appears in DRAPE only.
- (c)2 — 2 likewise appears in both codes, which rules it out for R on exactly the same test.
Concept
When two coded words overlap, solve them by elimination on the sets, not by lining the digits up under the letters.
A positional reading collapses here immediately: DRAPE would make P = 3 and E = 2, while TAPED would make P = 5 and E = 9. The digits have been scrambled deliberately.
What survives scrambling is membership. A letter present in only one of the two words must be coded by a digit present in only that word's code, and that single pairing is all the question asks for.
The four shared letters cannot be pinned from this data at all - D, A, P and E hold the digits 6, 4, 5 and 2 in an order the question never fixes. Only R and T are decidable.
Key facts
- DRAPE and TAPED are the same five letters except that one has R and the other T.
- Their codes 65432 and 24596 differ by exactly one digit each, 3 and 9.
- The letter unique to a word takes the digit unique to that word's code, so R = 3 and T = 9.
Study next
Common traps
- Lining the digits up positionally, which hands P two different codes
- Answering 9, the digit that belongs to T
- Trying to fix D, A, P and E individually when the data cannot settle them
This intersection item recurs with different word pairs - TIDE and DENT for N at 17 Sep 2024, 12:30, Reasoning Q.8 (keyed 3), DRIVE and RIDES for V at 18 Sep 2024, 09:00, Reasoning Q.9 (keyed 9), and BREAK and BROKE for A at 25 Sep 2024, 16:00, Reasoning Q.23 (keyed 2).
Related PYQs
No directly related past PYQ was found.