What is the value of the greatest common divisor of integers *a* and *b*?
>(1) $$a$$ is divisible by 15.
>(2) $$b=2a$$

Correct.
[[snippet]]
Stat. (1) doesn't tell us anything about $$b$$. **Stat.(1) → IS → BCE**
According to Stat. (2), $$b$$ is an even number and a multiple of $$a$$. Thus, $$a$$ is the GCD of $$a$$ and $$b$$, but we don't know the value of $$a$$. For example:
>If $$a=20$$ and $$b=40$$, then the GCD of $$a$$ and $$b$$ is 20.
>If $$a=10$$ and $$b=20$$, then the GCD of $$a$$ and $$b$$ is 10.
**Stat.(2) → IS → CE**
According to Stat. (1+2), even if $$a$$ is a multiple of 15 and $$b$$ is $$2a$$, it can be
that $$a=15$$ and $$b=30$$, which will make their GCD 15, or it can be that $$a=30$$ and $$b=60$$, which will make their GCD 30. Therefore, **Stat.(1+2) → IS → E**

No, it doesn't. In "what is the value of…" type DS questions (such as this one), a statement must lead to a single **numerical** value in order to be considered sufficient. As long as we can't derive **the value of $$a$$**, the statements are insufficient.

Incorrect.
[[snippet]]
Stat. (1) doesn't tell us anything about $$b$$. **Stat.(1) → IS → BCE**
According to Stat. (2), $$b$$ is an even number and a multiple of $$a$$. Thus, $$a$$ is the GCD of $$a$$ and $$b$$, but we don't know the value of $$a$$. For example:
>If $$a=20$$ and $$b=40$$, then the GCD of $$a$$ and $$b$$ is 20.
>If $$a=10$$ and $$b=20$$, then the GCD of $$a$$ and $$b$$ is 10.
**Stat.(2) → IS → CE**
According to Stat. (1+2), even if $$a$$ is a multiple of 15 and $$b$$ is $$2a$$, it can be
that $$a=15$$ and $$b=30$$, which will make their GCD 15, or it can be that $$a=30$$ and $$b=60$$, which will make their GCD 30. All we know from the combination is
that the GCD of $$a$$ and $$b$$ is **$$a$$** itself, which doesn't really answer the question. Remember—if a statement doesn't lead to a single **numerical** value, it isn't sufficient. **Stat.(1+2) → IS → E**

Incorrect.
[[snippet]]
According to Stat. (2), $$b$$ is an even number and a multiple of $$a$$. Thus, $$a$$ is the GCD of $$a$$ and $$b$$, but we don't know the value of $$a$$. For example:
>If $$a=20$$ and $$b=40$$, then the GCD of $$a$$ and $$b$$ is 20.
>If $$a=10$$ and $$b=20$$, then the GCD of $$a$$ and $$b$$ is 10.
**Stat.(2) → IS → ACE**

Incorrect.
[[snippet]]
Stat. (1) doesn't tell us anything about $$b$$. **Stat.(1) → IS → BCE**

Okay, let's move on.

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.

When using both statements, the GCD is always $$a$$. Doesn't that mean that Stat. (1+2) are sufficient?

Got it!