The greatest 4 digit number which when divided by 4, 6, 8, 10 leaves remainders 3, 5, 7, 9 respectively is ______.
Show answer & explanation
Correct answer: A
Explanation
Given:
When a number is divided by 4, 6, 8, and 10, the remainders are 3, 5, 7, and 9, respectively.
According to the formula:
If dividing N by (4, 6, 8, 10) yields remainders of (3, 5, 7, 9) ⇒
N + 1 will be completely divisible by all of these numbers.
LCM(4, 6, 8, 10) = 120
N + 1 = 120k
For the largest 4-digit number:
120k ≤ 10000 ⇒ k = 83
N + 1 = 120 × 83 = 9960
N = 9960 − 1 = 9959