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The 7-digit numbers 7123A32, 2B25689 and 450ABC6 are divisible by 3. Find the sum of all possible values of C.

User Aishwarya
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1 Answer

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9514 1404 393

Answer:

15

Explanation:

For numbers to be divisible by 3, the sum of their digits must be divisible by 3.

This means we require ...

(7 + 1 + 2 + 3 + A + 3 + 2) mod 3 = 0 ⇒ A mod 3 = 0

(2 + B + 2 + 5 + 6 + 8 + 9) mod 3 = 0 ⇒ (2+B) mod 3 = 0 ⇒ B mod 3 = -2

(4 + 5 + 0 + A + B + C + 6) mod 3 = 0 ⇒ (C -2) mod 3 = 0

Possible values of C are 2, 5, 8. Their sum is 15.

_____

For example, let A=0, B=1, C=2. Then we have ...

7123032 = 2374344×3

2125689 = 708563×3

4500126 = 1500042×3

User Moamen Naanou
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