3-digit number minimizing ratio to its digit sum
Question
D is a 3-digit number such that the ratio of the number to the sum of its digits is least. What is the difference between the digit at the hundred's place and the digit at the unit's place of D?
Options
0
7
8
9
Explanation
Let D = 100h + 10t + u. We want to minimize the ratio: R = 100h + 10t + u/h + t + u
To minimize this fraction, we must make the numerator as small as possible while making the denominator as large as possible.
This isolates the target number as ⟨MATH⟩D = 199⟨/MATH⟩, where the ratio is 199 / 19 ≈ 10.47 (which is strictly smaller than alternate combinations like 109 / 10 = 10.9).
Finally, calculate the difference between the hundreds digit (1) and the units digit (9): Difference = 9 - 1 = 8.
Answer: (c).
Question details
Year
2023
Paper
CSAT
Question
Q10
Section
Numerical Ability
Sub-topic
Number Properties
Type
Number theory
Difficulty
Hard
Source hint
Number theory
Same sub-topic — other years
Number Properties has appeared in multiple CSAT papers:
See all questions on Number Properties
Browse every tagged question across all years