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 ?

Notice that in each case the difference between divisor and remainder is the same: 3−1 = 2, 5−3 = 2, 6−4 = 2, 9−7 = 2. So N + 2 is divisible by LCM(3,5,6,9) = 90. The smallest 4-digit multiple of 90 is 1080 (since 90×12 = 1080). Therefore N = 1080 − 2 = 1078. Wait — checking 1078: 1078/3 gives remainder 1 ✓, 1078/5 remainder 3 ✓, 1078/6 remainder 4 ✓, 1078/9 remainder 7 ✓. So N = 1078, option (c). The official answer is 1078.