In a certain code language, ‘BLEACHERS’ is coded as ‘63’ and ‘ABACAS’ is coded as ‘42’. How will ‘FIZZY’ be coded in the same language?

Correct — D. The letters themselves do nothing here. Count them.

Rule: code = (number of letters) x 7.

BLEACHERS has 9 letters, and 9 x 7 = 63
ABACAS has 6 letters, and 6 x 7 = 42
FIZZY has 5 letters, and 5 x 7 = 35 → option (d)

Why the others are wrong

• (a)
  52 — 52 is not a multiple of 7. Both given codes are (63 = 9 x 7, 42 = 6 x 7), so the answer has to be one too.
• (b)
  45 — 45 is not a multiple of 7 either — 7 x 6 = 42 and 7 x 7 = 49, so no whole number of letters lands on 45.
• (c)
  44 — 44 fails the same test and sits close to the 42 of ABACAS, which catches anyone who reuses a given code instead of recomputing.

Letter-to-number codes come in a few families, and the whole job is telling them apart.

Some add the alphabetical positions of the letters. Some shift each letter by a fixed step and give back letters. And some, like this one, ignore the letters entirely and use only how many there are.

Test the cheapest family first. Divide each given code by its word length: 63 / 9 = 7 and 42 / 6 = 7. The same multiplier holds for both words, so the rule is fixed and can be applied to FIZZY.

Key facts

• BLEACHERS has 9 letters and is coded 63, which is 9 x 7.
• ABACAS has 6 letters and is coded 42, which is 6 x 7.
• FIZZY has 5 letters, so the same rule gives 5 x 7 = 35.
• Repeated letters are counted every time they appear, so the two Zs of FIZZY count as two.

Common traps

• Adding the letter positions before testing the far cheaper letter-count rule
• Miscounting a word with a doubled letter, which turns 35 into 28

No directly related past PYQ was found.