GATE DA 2026 Set 1 — Question 9
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and are distinct single-digit whole numbers taking values from 0 to 9. is a two-digit number with being in the units place and in the tens place. Similarly, is a two-digit number.It is known that and are consecutive numbers and , with being a three-digit number.The value of is __________
Correct answer
(C) 6
Solution
Let . Then (or ). The equation is .
Since is a 3-digit number, . So is around 10-22.The last digit of the sum must be . Let's test consecutive pairs:
Since is a 3-digit number, . So is around 10-22.The last digit of the sum must be . Let's test consecutive pairs:
- 14, 15: . Here , last digit is 1. Matches. Digits: . and are not distinct (). Invalid.
- 15, 16: . , last digit 1. Matches. Digits: . and not distinct. Invalid.
- 19, 20: . Here . , last digit is 1. Matches.
- Distinct digits used: . All are distinct. Valid.
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