In a certain code language, 'ESTATE' is written as '80', 'FAMOUS' is written as '85', how will 'FOREST' be written in that language?
- (a)88
- (b)90
- (c)93
- (d)83
Answer
Why
Correct — C. Add the alphabetical positions of the letters, then compare that sum with the code given.
E S T A T E = 5 + 19 + 20 + 1 + 20 + 5 = 70, and the code is 80.
F A M O U S = 6 + 1 + 13 + 15 + 21 + 19 = 75, and the code is 85.
Rule: code = sum of letter positions + 10.
F O R E S T = 6 + 15 + 18 + 5 + 19 + 20 = 83
83 + 10 = 93 → option (c)
Why the others are wrong
- (a)88 — 88 implies a letter total of 78. F O R E S T totals 83, so 88 falls five short of the code.
- (b)90 — 90 implies a letter total of 80. The six letters come to 83, not 80 — recheck R = 18 and T = 20.
- (d)83 — 83 is the raw letter sum with the + 10 dropped. That step is exactly what turns 70 into 80 and 75 into 85 in the two coded words.
Concept
Letter-sum coding turns a word into a number by adding the alphabetical positions of its letters. The raw sum often does not match the printed code, so the next move is to set sum against code and look for a constant.
Here 70 against 80 and 75 against 85 both show a gap of exactly 10, and a constant confirmed on two words can be carried to the third.
Positions worth holding in memory for speed: E = 5, J = 10, O = 15, T = 20, Y = 25. Every other letter is then at most two steps from a landmark.
Two coded words are given so the constant can be confirmed rather than guessed. From ESTATE alone, adding 10 and multiplying by 8/7 both fit — 70 × 8/7 is also 80 — and only the second word kills the multiplier, since 75 × 8/7 is not 85.
Key facts
- A = 1 through Z = 26, so E = 5, O = 15, R = 18, S = 19 and T = 20.
- ESTATE sums to 70 and is coded 80, while FAMOUS sums to 75 and is coded 85.
- FOREST sums to 83, so its code is 93.
Study next
Common traps
- Answering with the raw sum and forgetting the constant.
- Miscounting R as 17 or S as 18, which shifts the total by one or two.
- Fixing the rule on one coded word, where a multiplier fits just as well.
Two worked words are given, and the second exists to kill the rules the first cannot. Codes built by stringing letter positions together rather than adding them are set at 13 Sep 2024, 12:30, Reasoning Q.1 and at 25 Sep 2024, 09:00, Reasoning Q.20.
Related PYQs
No directly related past PYQ was found.