UPSC Prelims 2009 Q97: Science & Technology – Logical Reasoning & Puzzles
How many letters of the English alphabet (capitals) appear same when looked at in a mirror?
- (a) 9
- (b) 10
- (c) 11
- (d) 12
Answer: (c) 11
Explanation
Capital letters that look the same in a mirror
A letter appears unchanged in a mirror reflection only if it has a specific kind of symmetry.
| Point | Reasoning |
|---|---|
| Vertical-axis symmetry needed | A letter looks the same in a (vertical) mirror only if it is symmetric about a vertical line through its centre |
| Qualifying letters | A, H, I, M, O, T, U, V, W, X, Y — each has this vertical symmetry |
| Count | These add up to 11 letters |
Why these specific letters qualify:
| Point | Detail |
|---|---|
| Example | 'A' looks identical whether viewed directly or mirrored, since its left and right halves match |
| Non-qualifying examples | Letters like B, C, D, E are NOT symmetric this way and would appear reversed |
Answer: (c) 11.
Why each option is right or wrong
- (a) Incorrect. 9 undercounts the actual number of mirror-symmetric capital letters.
- (b) Incorrect. 10 also undercounts the correct total.
- (c) CORRECT. There are 11 capital letters (A, H, I, M, O, T, U, V, W, X, Y) with vertical mirror symmetry.
- (d) Incorrect. 12 overstates the actual count.
Key point
11 capital English letters — A, H, I, M, O, T, U, V, W, X, Y — appear the same in a mirror, since each is symmetric about a vertical axis.
Remember
11 capital letters of the English alphabet look the same in a mirror: A, H, I, M, O, T, U, V, W, X, Y.
Common mistakes
- Missing one or more of the 11 qualifying letters when listing them out.
- Including letters that only have horizontal symmetry (which would look upside-down, not mirror-same, in a vertical mirror).
- Not systematically checking each of the 26 letters for vertical-axis symmetry.
Exam tip
Mirror-symmetric capital letters: A, H, I, M, O, T, U, V, W, X, Y — 11 letters total. A classic reasoning-puzzle fact worth memorising.
Sources
- R. S. Aggarwal — A Modern Approach to Verbal and Non-Verbal Reasoning (Mirror Images)
- Arun Sharma — How to Prepare for Logical Reasoning for the CAT (mirror images and alphabet problems)