If $$K$$ is a sequence of $$n$$ consecutive integers, then what is the value of $$n$$?
>(1) The sum of all terms in $$K$$ is 21.
>(2) The average (arithmetic mean) of all terms in $$K$$ is less than 9.

Correct.
[[Snippet]]
For stat. (1), there can be more than one set of consecutive integers whose sum is
21. For example, the sum of 1, 2, 3, 4, 5, and 6 is 21, and the sum of 6, 7, and 8 is also 21. **Stat. (1) → IS → BCE**.
For stat. (2), the average of all terms in $$K$$ is less than 9. This average can be any number less than 9 (i.e., from 0 to 8 or even negative numbers). No single set satisfies stat. (2), and thus there is no single value for $$n$$. **Stat. (2) → IS → CE**.
For stat. (1+2), there is still more than one choice. The average
(arithmetic mean) of 1, 2, 3, 4, 5, and 6 is 3.5, while the average of 6, 7, and 8 is 7. Both
averages are less than 9, but the value of $$n$$ is different. **Stat. (1+2) → IS → E**.

Incorrect.
[[Snippet]]
For stat. (1), there can be more than one set of consecutive integers whose sum is
21. For example, the sum of 1, 2, 3, 4, 5, and 6 is 21, and the sum of 6, 7, and 8 is also 21. **Stat. (1) → IS → BCE**.

Incorrect.
[[Snippet]]
For stat. (2), the average of all terms in $$K$$ is less than 9. This average can be any number less than 9 (i.e., from 0 to 8 or even negative numbers). No single set satisfies stat. (2), and thus there is no single value for $$n$$. **Stat. (2) → IS → ACE**.

Incorrect.
[[Snippet]]
For stat. (1+2), there is still more than one choice. The average
(arithmetic mean) of 1, 2, 3, 4, 5, and 6 is 3.5, while the average of 6, 7, and 8 is 7. Both
averages are less than 9, but the value of $$n$$ is different. **Stat. (1+2) → IS → E**.

Incorrect.
[[Snippet]]
For stat. (1), there can be more than one set of consecutive integers whose sum is
21. For example, the sum of 1, 2, 3, 4, 5, and 6 is 21, and the sum of 6, 7, and 8 is also 21. **Stat. (1) → IS → BCE**.
For stat. (2), the average of all terms in $$K$$ is less than 9. This average can be any number less than 9 (i.e., from 0 to 8 or even negative numbers). No single set satisfies stat. (2), and thus there is no single value for $$n$$. **Stat. (2) → IS → CE**.

Statement (1) ALONE is sufficient, but Statement (2) alone is not sufficient to answer the question asked.

Statement (2) ALONE is sufficient, but Statement (1) alone is not sufficient to answer the question asked.

BOTH Statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

EACH statement ALONE is sufficient to answer the question asked.

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.