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…

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?

1. A. 1068
2. B. 1072
3. C. 1078 (Correct answer)
4. D. 1082

Correct Answer

Option C — 1078

Detailed Solution & Explanation

The correct answer is 1078.

Key Points

• In each division, the remainder is 2 less than the divisor: 3−1=2 short, wait: 1=3−2, 3=5−2, 4=6−2, 7=9−2. So N ≡ −2 (mod 3), N ≡ −2 (mod 5), N ≡ −2 (mod 6), N ≡ −2 (mod 9).
• N+2 divisible by LCM(3,5,6,9) = 90. N = 90k − 2. Smallest 4-digit: 90×12−2 = 1080−2 = 1078. Answer: 1078.