CAPF AC 2020 Q119: General Mental Ability – Logical Reasoning & Puzzles
The alphabets from A to J are numbered from 0 to 9 respectively. Which one of the following is the value of AGJ - CEG + EDB?
- (a) CFE
- (b) DGF
- (c) GFD
- (d) FCE
Answer: (a) CFE
Explanation
Letters as digits
Given: the alphabets from A to J are numbered from 0 to 9 respectively.
We need the value of AGJ − CEG + EDB.
How to think: turn each letter into its digit, do the sum, and turn the answer back into letters.
| Letters | Digits |
|---|---|
| A, B, C, D, E | 0, 1, 2, 3, 4 |
| F, G, H, I, J | 5, 6, 7, 8, 9 |
The three numbers:
| Word | Digits | Value |
|---|---|---|
| AGJ | 0, 6, 9 | 69 |
| CEG | 2, 4, 6 | 246 |
| EDB | 4, 3, 1 | 431 |
The sum: 69 − 246 + 431 = 500 − 246 = 254.
Back to letters: 2 is C, 5 is F, 4 is E.
So the value is CFE.
Answer: (a) CFE.
Why each option is right or wrong
- (a) CORRECT. 69 − 246 + 431 = 254, which is CFE.
- (b) Incorrect. DGF is 365; this comes from numbering A as 1.
- (c) Incorrect. GFD is 653, not 254.
- (d) Incorrect. FCE is 524; the first two digits are swapped.
Key point
A = 0, B = 1, ... J = 9. AGJ = 69, CEG = 246, EDB = 431. 69 − 246 + 431 = 254 = CFE.
Remember
A starts at 0 here, so J is 9.
Common mistakes
- Starting with A = 1 instead of A = 0.
- Doing 246 + 431 first and then subtracting from 69 with the wrong sign.
- Writing the answer digits in the wrong order.
Exam tip
Educated guess: add first: 69 + 431 = 500. Then 500 − 246 ends in 4, which is E. Only (a) and (d) end in E.
Sources
- NCERT Class VIII Mathematics — Playing with Numbers (letters for digits)
- R. S. Aggarwal — A Modern Approach to Verbal and Non-Verbal Reasoning (Puzzle Test)