In a certain code language, ‘BREAK’ is coded as ‘57123’ and ‘BROKE’ is coded as ‘91753’. What is the code for ‘A’ in that language?
- (a)2
- (b)9
- (c)3
- (d)5
Answer
Why
Correct — A. The digits are not positional — match the two words by what they do not share.
Rule: letters common to both words take the digits common to both codes, so the one leftover letter takes the one leftover digit.
BREAK and BROKE share B, R, E and K. BREAK alone has A, BROKE alone has O.
The codes 57123 and 91753 share 5, 7, 1 and 3. BREAK alone has 2, BROKE alone has 9.
One unmatched letter against one unmatched digit gives A = 2, option (a). The same step hands you O = 9 for free.
Why the others are wrong
- (b)9 — 9 belongs to BROKE, not BREAK. Option (b) is the code for O, the letter BROKE has and BREAK lacks — the right method run in the wrong direction.
- (c)3 — 3 appears in both codes. Option (c) must therefore belong to one of the four shared letters B, R, E or K, and cannot code A, which appears in only one of the words.
- (d)5 — 5 appears in both codes. Like option (c) it is a shared digit and so codes a shared letter, while A is unique to BREAK and must take the digit unique to its code.
Concept
This coding type looks as though it needs letter-by-letter matching, and does not. The digits are deliberately scrambled against the letters, so aligning first letter with first digit fails.
The method is set difference. List the letters of each word and the digits of each code, strike out everything the two words share, and whatever is left on each side must correspond.
It works because the two words are chosen to differ by exactly one letter. That guarantees exactly one leftover digit, so the pairing is forced rather than guessed.
The item asks only for A, but the same step also yields O = 9. Deriving both is a cheap check that you have read the two words correctly.
Key facts
- BREAK and BROKE share the four letters B, R, E and K.
- The codes 57123 and 91753 share the four digits 5, 7, 1 and 3.
- A is unique to BREAK and 2 is unique to its code, so A = 2.
- O is unique to BROKE and 9 is unique to its code, so O = 9.
Study next
Common traps
- Assuming the digits line up with the letters position by position, which the second word immediately contradicts — B would have to be both 5 and 9.
- Striking out the shared letters but forgetting to strike out the shared digits.
- Answering with the digit unique to the other word, 9, which codes O.
The stem is fixed and only the word pair changes — 17 Sep 2024, 12:30, Reasoning Q.8 codes TIDE and DENT and asks for N, 18 Sep 2024, 09:00, Reasoning Q.9 codes DRIVE and RIDES and asks for V, and 25 Sep 2024, 12:30, Reasoning Q.25 codes DRAPE and TAPED and asks for R.
Each of those pairs, like this one, overlaps in every letter but one.
Related PYQs
No directly related past PYQ was found.