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Lynn counts numbers from 105 and adds 4 each time. So she counts 105, 109, 113, and continues. What is the largest three-digit whole number that Lynn counts?

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Think of any number divisible by 4. It can be 988, 984 or else. Add it to 105 then if you think it's the largest three-digit whole number on the sequence, then it's the answer to your question. 

105 + 988 = 1093 - It's already 4 - digit number.
105 + 904 = 1009 - still a 4 - digit number.
105 + 892 =   997 - it's a 3-digit number. Just simply add 3 to it and it will become 4 - digit, so that, it's the largest three-digit number in the sequence.

Therefore, the answer to your question is 997.