A number when divided by 126, leaves remainder 43. If the same number is…
2023
A number when divided by 126, leaves remainder 43. If the same number is divided by 21, the remainder will be.
- A.
7
- B.
1
- C.
2
- D.
9
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Correct answer: B
Given: a number leaves remainder 43 when divided by 126.
Find: the remainder when the same number is divided by 21.
Let the number be N = 126k + 43 for some integer k.
When dividing by 21, 126k is divisible by 21 because 126 = 21 × 6, so 126k/21 = 6k with no remainder.
Compute the remainder of 43 divided by 21: 43 = 21 × 2 + 1, so the remainder is 1.
Therefore, when N = 126k + 43 is divided by 21, the remainder is 1.