An 8-digit number 4252746B leaves remainder 0 when divided by 3. How many values of B are possible?
- A2
- B3
- C4Correct
- D6
Explanation
A number is divisible by 3 if the sum of its digits is divisible by 3.
For the number 4252746B, the sum of its digits is: 4 + 2 + 5 + 2 + 7 + 4 + 6 + B = 30 + B
Since the number leaves remainder 0 when divided by 3, (30 + B) must be divisible by 3. As 30 is already divisible by 3, B must also be divisible by 3 for the entire sum to be divisible by 3.
B is a single digit, so its possible values range from 0 to 9. The values of B in this range that are divisible by 3 are: 0 (30+0 = 30, divisible by 3) 3 (30+3 = 33, divisible by 3) 6 (30+6 = 36, divisible by 3) 9 (30+9 = 39, divisible by 3)
There are 4 possible values for B.
The final answer is C) 4.
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