Question

Deshawn is given the following conjecture. How can he determine whether the conjecture is true? The first and third digits of a three-digit number are the same. If the second digit is equal to the sum of the first and third digits, then the number must be divisible by 11. Select the correct choice below and fill in the answer box(es) to complete your choice. (Use a comma to separate answers as needed.) OA. The only number(s) whose digits fit the given pattern is/are OB. The only number(s) whose digits fit the given pattern is/are OC. The only number(s) whose digits fit the given pattern is/are D. There are too many numbers whose digits fit the given pattern for testing each to be practical. The four smallest such numbers are least one counterexample, and so the conjecture is false. Of these, only is/are divisible by 11. This means there is at least one counterexample, and so the conjecture is false. Each of these is divisible by 11, so the conjecture is true. None of these is divisible by 11. This means there is at least one counterexample, and so the conjecture is false. OE. There are too many numbers whose digits fit the given pattern for testing each to be practical. The four smallest such numbers are pattern continues, so the conjecture is true. Sep 15 9:40 ar OF. There are too many numbers whose digits fit the given pattern for testing each to be practical. The four smallest such numbers are is at least one counterexample, and so the conjecture is false. None of these is divisible by 11. This means there is at Each of these is divisible by 11. It can be assumed the Of these, only is/are divisible by 11. This means there​

Answer 1

See below.

Explanation:

Wow, a lot of words here! But I'm gonna try to work it out, then I may let you "select the correct choice below" because that's a lot to digest all strung together like that.

What are the rules for Deshawn's conjecture?

• 3 digits
• 1st & 3rd digits the same
• IF: 2nd = 1st plus 3rd,
• THEN: the number is divisible by 11

Let's noodle on that. A three-digit number has 3 places of course:

1st & 3rd digits equal each other:

x x

Now add the bit about the middle number. It's the sum of (x + x), which can be simplified to 2x:

x 2x x

Now we know what the number has to look like. Let's start trying some combinations. (You might already see that there will only be 4.)

121

242

363

484

(Can we use 5 in the 1st and last places? No, because that would put a 10 in the middle place, and we can't have that.)

So now you only have to test these 4 numbers for divisibility by 11. And they all are. 121 is 11², 242 is twice that, etc.

So there's your answer. I'll leave it to you how to write or input it.

Cool question, thanks for asking it!