A number, being successively divided by 5, 7 and 11, leaves 3, 1 and 1 as remainders respectively. Find the remainder, if the same number is divided by 385.
A
35
B
55
C
77
D
78
Correct Option:
D
Explanation
The intended interpretation is N ≡ 3 (mod 5), N ≡ 1 (mod 7), and N ≡ 1 (mod 11). The number 78 satisfies all three conditions: 78 mod 5 = 3, 78 mod 7 = 1, and 78 mod 11 = 1. Since 5 × 7 × 11 = 385, the remainder on division by 385 is 78. The word “successively” is somewhat loose here.
