PREVIOUSLY ASKED IN:
CTET 2026
Answer
\( A=5, B=1 \)
Explanation
Since \( A \times A \) ends with the digit \( A \), A can be 1, 5, or 6. If we take \( A = 5 \), then \( 25 \times 5 = 125 \), which matches the \( B2A \) format perfectly (with \( B = 1 \) and the tens digit being 2). If \( A = 6 \), then \( 26 \times 6 = 156 \), but the tens digit is 5, not 2. Therefore, \( A=5, B=1 \) is the correct answer.
Key Points
- > In such alphametic puzzles, begin by analyzing the units digit logic.
- > Digits whose squares end in themselves are 0, 1, 5, and 6.
- > If \( A = 1 \), \( 21 \times 1 = 21 \), which does not yield a 3-digit number like B2A.
- > For \( A = 5 \), the tens digit of its square is always 2 (e.g., 25, 225).
- > These puzzles are highly effective for improving logical reasoning and number sense.
- > Option testing is a very quick method to solve these in an exam setup.
- > This is a frequent pattern in CTET and other competitive exams.
Additional Information
Cryptarithmetic Puzzle Analysis
| Digit (A) | Equation | Result | Remark |
|---|---|---|---|
| 1 | 21 × 1 | 21 | Not a 3-digit number |
| 5 | 25 × 5 | 125 | B=1, Tens digit 2 (Correct) |
| 6 | 26 × 6 | 156 | Tens digit is 5 (Wrong) |
| 9 | 29 × 9 | 261 | Ends in 1, not A |
Memory Tips
- Square Property: The squares of numbers ending in 5 or 6 always end with the same digit.
- Option Test Approach: Instead of creating complex equations, simply plug in the given options to find the correct match.