In a certain code language, ‘TRIED’ is coded as ‘54123' and ‘TREAD’ is coded as ‘12365’. What is the code for ‘I’ in the given code language?
- (a)5
- (b)1
- (c)6
- (d)4
Answer
Why
Correct — D. The digits are not printed in the order of the letters, so work from what the two words share.
TRIED and TREAD share T, R, E and D — four letters. The odd ones out are I in the first word and A in the second.
TRIED's digits: 5, 4, 1, 2, 3
TREAD's digits: 1, 2, 3, 6, 5
Shared digits: 1, 2, 3 and 5 — four of them.
Four shared letters take the four shared digits, in whatever order. That leaves exactly one digit spare in each word: 4 in TRIED and 6 in TREAD.
The unshared letter of TRIED is I, so I is coded 4 — option (d).
Why the others are wrong
- (a)5 — 5 appears in both code strings, so it belongs to one of the shared letters T, R, E or D. Whichever of those it stands for, it cannot also stand for I.
- (b)1 — 1 is likewise in both strings and so belongs to a shared letter. It is the first digit of TREAD's code, which tempts a positional reading the data will not support.
- (c)6 — 6 is the digit unique to TREAD, and the letter unique to TREAD is A. So 6 codes A, and I is left with 4.
Concept
When a code item gives no positional key, the method is set arithmetic. Intersect the letters, intersect the digits, and the two intersections have to match in size, letter for digit.
Here both intersections are four wide, so the leftovers pair off one to one: the letter found only in the first word takes the digit found only in the first code, and the same holds for the second.
Nothing beyond that can be extracted. You cannot say which shared letter is 1 or 2 or 3 or 5, and the question never asks — it asks about the letter standing outside the overlap.
The digits are deliberately shuffled against the letters. Reading TRIED position by position gives T = 5 and I = 1, which is offered as option (b), but the same reading of TREAD gives T = 1. T cannot be both, which is how you know the shuffle is real.
Key facts
- TRIED and TREAD share the letters T, R, E and D.
- Their codes share the digits 1, 2, 3 and 5.
- The letter unique to TRIED is I and the digit unique to its code is 4, so I is 4.
- A positional reading fails, because it would make T both 5 and 1.
Study next
Common traps
- Pairing digits to letters by position, which returns 1 for I.
- Assuming the shared letters can also be identified one by one.
- Skipping the count check, since the shared letters and shared digits must come to the same number.
The two-word overlap is the standard build for this item. 10 Sep 2024, 12:30, Reasoning Q.16 asks the code for O from COWS = 7935 and OILY = 2568, and 10 Sep 2024, 16:00, Reasoning Q.3 asks the code for A from VERY = 6314 and VARY = 1438.
Related PYQs
No directly related past PYQ was found.