<|system|>
The difference when the product of 4 and a number is subtracted from 16 is greater than 10. How many positive integers satisfy the given conditions?</s>.
<|user|>
Can you answer based on context?
<|assistant|>
I want to find all the positive integers that make the difference between 16 and 4 times the number greater than 10. I can write this as an inequality: 16 - 4n > 10, where n is the positive integer I'm looking for. To solve for n, I can add 4n to both sides and subtract 10 from both sides: 6 > 4n. Then I can divide both sides by 4 to get: 1.5 > n. This means that n has to be less than 1.5, but also a positive integer. The only positive integer that satisfies this condition is 1. So there is only one positive integer that makes the difference greater than 10. 