In a certain code language, 'DEMAND' is written as ‘410132144' and 'SUPPLY' is written as '194216161225'.How will 'PRODUCT' be written in that language?
- (a)161815421320
- (b)161830442320
- (c)323615821640
- (d)161542320
Answer
Why
Correct — B. Rule: replace each letter by its alphabet position, then double that value if the letter is a vowel.
DEMAND: D 4, E 5 → 10, M 13, A 1 → 2, N 14, D 4, strung together as 410132144.
SUPPLY: S 19, U 21 → 42, P 16, P 16, L 12, Y 25, strung together as 194216161225.
Now PRODUCT: P 16, R 18, O 15 → 30, D 4, U 21 → 42, C 3, T 20.
Strung together that is 16 18 30 4 42 3 20 = 161830442320, option (b).
Why the others are wrong
- (a)161815421320 — This is PRODUCT with no doubling at all — 16 18 15 4 21 3 20. It ignores the vowel rule that DEMAND's E → 10 and A → 2 establish.
- (c)323615821640 — The rule is applied backwards, doubling the consonants and leaving the vowels alone — 32 36 15 8 21 6 40. Under that rule DEMAND would read 8 5 26 1 28 8, not 410132144.
- (d)161542320 — Nine digits where twelve are needed. PRODUCT encodes as 16, 18, 30, 4, 42, 3, 20, which is twelve digits, so a nine-digit string cannot carry all seven letters.
Concept
Letter-to-number codes are built on the alphabet position, A = 1 to Z = 26, with one modifier laid on top. That modifier is usually a class rule — vowels treated differently from consonants, say, or the first half of the alphabet from the second.
Find the modifier by looking for a value too big to be a position. In SUPPLY the value 42 exceeds 26, and the only letter that could produce it is U at 21 doubled. That single observation names the rule, and DEMAND then confirms it on E and A.
Both given words have to be decoded before the answer word is encoded. One word can fit several rules — DEMAND alone would also fit 'double the second and fourth letters' — and SUPPLY is what kills that reading, because its fourth letter P stays at 16.
Key facts
- The code is alphabet position with every vowel's value doubled.
- DEMAND becomes 4, 10, 13, 2, 14, 4 and is written 410132144.
- SUPPLY becomes 19, 42, 16, 16, 12, 25 and is written 194216161225.
- PRODUCT becomes 16, 18, 30, 4, 42, 3, 20 and is written 161830442320.
Study next
Common traps
- Reading the code left to right without first splitting it into one- and two-digit values.
- Doubling every letter instead of only the vowels.
- Treating Y as a vowel, when SUPPLY codes Y as 25 and leaves it undoubled.
A positional code of the same family appears at 12 Sep 2024, 09:00, Reasoning Q.10 (FIVE → 12184410 and FOUR → 12304236, where every letter is doubled), and a letter-shift code at 10 Sep 2024, 12:30, Reasoning Q.4 (TIZZ → VKBB). Reasoning Q.8 of the same paper codes a whole word as a single number.
Related PYQs
No directly related past PYQ was found.