i have a follow up question for a previous post

How do you know 2B is (20 "+" B) and not (2 "x" B)
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to me this question does not make sense... it comes from a review packet for the SAT
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Q: If 299 is divisible by 2B, and B represents a positive digit, what is the value of B?

a.) 2
b.) 3
c.) 4
d.) 6
e.) 9

2B is not 20 + B, in general. They can only be equal if B=20.

299 is evenly divisible by the integers 13 and 23 only. If 2B is 13 or 23, B cannot be an integer. None of the multiple choices are correct.

From the original question (not posted here) it was clear that 2B means 20 + B here, because B was referred to aa a digit. Also, as drwls pointed out, the question doesn't make sense if 2B is interpreted as 2*B

As I replied below, from the fact that 23 is a divisor, you can read off that B = 3.

got it!

To solve this problem, we can use the divisibility rule for the number 299. According to the divisibility rule for 299, a number is divisible by 299 if and only if it is divisible by both 13 and 23.

Now, let's consider the possible values of B. Since B represents a positive digit, it can take on the values 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9.

Let's go through each option and see if it satisfies the divisibility rule:

a.) If B = 2, then 2B = 4. However, 299 is not divisible by 4.
b.) If B = 3, then 2B = 6. Again, 299 is not divisible by 6.
c.) If B = 4, then 2B = 8. 299 is not divisible by 8.
d.) If B = 6, then 2B = 12. This time, 299 is divisible by 12 since 12 x 24 = 288, which is close to 299.
e.) If B = 9, then 2B = 18. Once again, 299 is not divisible by 18.

From our analysis, we found that only option d (B = 6) satisfies the divisibility rule for 299. Therefore, the value of B that makes 299 divisible by 2B is 6.