<|system|>
What is the greatest possible sum of two consecutive integers whose product is less than 400?</s>.
<|user|>
Can you answer based on context?
<|assistant|>
To find the greatest possible sum of two consecutive integers, I want to find the largest pair of consecutive integers that multiply to less than 400. Let x be the smaller integer and x + 1 be the larger one. Then their product is x(x + 1), which is less than 400. I can try to estimate the value of x by finding the square root of 400, which is 20. If x is 20, then x(x + 1) is 20(21), which is 420. That's too big. So I need to reduce x by one and try again. If x is 19, then x(x + 1) is 19(20), which is 380. That's less than 400, so this is a possible pair. So x = 19 is the largest value of x that satisfies the condition. The sum of x and x + 1 is 19 + 20, which is 39. This is the greatest possible sum of two consecutive integers whose product is less than 400. 