Question 9

Let $$N$$ be the smallest positive integer whose digits add up to 2026. What is the leading digit of $$N + 1$$?

Correct Answer: 2

Solution

A number with 225 digits has digit sum at most $$225 \times 9 = 2025$$, so $$N$$ needs at least 226 digits. The smallest such number has leading digit 1 followed by 225 nines, because $$1 + 225 \times 9 = 2026$$. Adding 1 carries through all the nines, giving $$N + 1 = 2 \times 10^{225}$$, whose leading digit is 2.

Get AI Help

Video Solution

Other Cracku’s Useful Resources:

JEE Questions JEE Question Bank JEE Mains Previous Papers JEE Advanced Previous Papers JEE Study Material PDF JEE Mains Mock Test JEE Advanced Mock Test JEE Daily Target

Free JEE Questions

JEE Physics Questions JEE Maths Questions JEE Chemistry Questions

Book Free CAT Mentorship

Get personalized CAT strategy from a 99%iler

500+ students mentored

Phone Number

Preferred Time