4-digit number with remainder conditions
Question
A 4-digit number N is such that when divided by 3, 5, 6, 9 leaves a remainder 1, 3, 4, 7 respectively. What is the smallest value of N?
Options
1068
1072
1078
1082
Explanation
The difference between each divisor and its corresponding remainder is constant: 3-1 = 2, 5-3 = 2, 6-4 = 2, and 9-7 = 2. When this difference (d) is uniform, the required number takes the form LCM(divisors) * k - d.
The LCM of 3, 5, 6, and 9 is 90. The number must be of the form 90k - 2. We need the smallest 4-digit number. The smallest 4-digit multiple of 90 is 90 * 12 = 1080. Subtracting the constant difference: 1080 - 2 = 1078.
Answer: (c).
Question details
Year
2025
Paper
CSAT
Question
Q8
Section
Numerical Ability
Sub-topic
Remainders & Divisibility
Type
Number theory
Difficulty
Hard
Source hint
Number theory
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