# Integers: Rule of Divisibility by 3

Is the tens digit of a three-digit positive integer \$\$p\$\$ divisible by 3? >(1) \$\$p-7\$\$ is a multiple of 3. >(2) \$\$p-13\$\$ is a multiple of 3.
Incorrect. [[snippet]]
Correct. [[snippet]] Stat. (1): Plug in for \$\$p-7\$\$. If you plug in 123, which is a multiple of 3, then \$\$p=130\$\$. Now answer the question: the tens digit of \$\$p\$\$ is 3. Hence, 3 is divisible by 3, and the answer is "Yes." But is it always "Yes" for _any_ number? If you plug in 333 for \$\$p-7\$\$, then \$\$p=340\$\$. Now the answer is "No." Therefore, **Stat.(1) → Maybe → IS → BCE**. Stat. (2): Try using the same numbers; it's easier and it will save you time. If you plug in 123 for \$\$p-13\$\$, then \$\$p=136\$\$. The tens digit is 3, so the answer is "Yes." But is it "Yes" for _any_ number? If you plug in 333 for f \$\$p-13\$\$, then \$\$p=346\$\$, and the answer is now "No." Therefore, **Stat.(2) → Maybe → IS → CE**. Stat. (1+2): Use the same numbers to save time and effort. For instance, if \$\$p=136\$\$, then the answer is "Yes". But if you plug in \$\$p=346\$\$, then the answer is "No". Therefore, **Stat.(1+2) → Maybe → IS → E**.
Incorrect. [[snippet]]
Incorrect. [[snippet]]
Incorrect. [[snippet]]
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.
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.