Final answer:
To prove the divisibility of 257+513 by 30, we find their sum (770) and check divisibility by 3 and 10. Since the sum of the digits of 770 is not divisible by 3, 770 is not divisible by 30, leading to 10 as the correct answer.
Step-by-step explanation:
We are tasked to prove the divisibility of the sum of 257 and 513 by 30. To do this, we can first add the two numbers together:
Sum = 257 + 513 = 770.
Next, we determine if the sum is divisible by 30. A number is divisible by 30 if it is divisible by both 3 and 10 since 30 is the product of 3 and 10. A number is divisible by 3 if the sum of its digits is divisible by 3, and it is divisible by 10 if its last digit is zero.
Looking at the sum, 770, the sum of the digits (7 + 7 + 0) equals 14, which is not divisible by 3. Therefore, the sum, 770, is not divisible by 3 and hence not divisible by 30. This leads us to the choice of B) 10, as it is the only multiple of 10 that is less than 30 and can be a divisor of 770.