Question 15

The range of the integers in set K is 8.

The inequality |p - 17| < 4 indicates that p must be within 4 units of 17. This translates to the range of integers being from 13 to 21, which includes a total of 8 integers: 13, 14, 15, 16, 17, 18, 19, and 20.

A) 6

This option is incorrect because the range of integers from the inequality does not include the value 6. The smallest integer satisfying the inequality is 13, which is much larger than 6.

B) 8

This option is correct as the range of integers that satisfy the inequality |p - 17| < 4 is indeed 8, consisting of the integers from 13 to 20 inclusive.

C) 13

While 13 is one of the integers included in the set K, it does not represent the total count of integers within the specified range. Thus, this option is incorrect as it does not answer the question regarding the range.

D) 16

This option, like C, refers to one of the integers within the range but fails to reflect the total quantity of integers that meet the condition. Therefore, it is incorrect in the context of the question.

E) 19

Although 19 is part of the integers satisfying the inequality, it does not represent the total range of integers. Hence, this option is not correct when determining the range of set K.

Conclusion

The correct answer, B, accurately identifies the range of integers in set K as 8, encompassing the values from 13 to 20. All other options fail to address the question's requirement of finding the total number of integers within the specified range.