We cover every section of the GMAT with in-depth lessons, 5000+ practice questions and realistic practice tests.

## Up to 90+ points GMAT score improvement guarantee

### The best guarantee you’ll find

Our Premium and Ultimate plans guarantee up to 90+ points score increase or your money back.

## Master each section of the test

### Comprehensive GMAT prep

We cover every section of the GMAT with in-depth lessons, 5000+ practice questions and realistic practice tests.

## Schedule-free studying

### Learn on the go

Study whenever and wherever you want with our iOS and Android mobile apps.

# Integers: Remainder Problems

If \$\$m\$\$ and \$\$n\$\$ are prime numbers, is the remainder when \$\$7m\$\$ is divided by \$\$n\$\$ smaller than 3? >(1) \$\$m \lt 5\$\$ >(2) \$\$n \lt 11\$\$
According to Stat. (2), \$\$n \lt 11\$\$, so \$\$n\$\$ can be 2, 3, 5, and 7, and \$\$m\$\$ can be any prime number. * If \$\$m = 2\$\$ and \$\$n = 5\$\$, then the remainder is 4, which is _greater_ than 3. * If \$\$m = 7\$\$ and \$\$n = 7\$\$, then the remainder is zero, which is _less_ than 3. Thus, there is no definite answer, so **Stat.(2) → No → IS → CE**. According to Stat. (1+2), \$\$m \lt 5\$\$, so \$\$m\$\$ can be 2 or 3, and \$\$n \lt 11\$\$, so \$\$n\$\$ can be 2, 3, 5, and 7. * If \$\$m = 2\$\$ and \$\$n = 5\$\$, then the remainder is 4, which is _greater_ than 3. * If \$\$m = 2\$\$ and \$\$n = 7\$\$, then the remainder is zero, which is _less_ than 3. Thus, there is no definite answer, so **Stat.(1+2) → No → IS → E**.
Incorrect. [[snippet]] According to Stat. (1), \$\$m \lt 5\$\$, so \$\$m\$\$ can be 2 or 3, and \$\$n\$\$ can be any prime number. * If \$\$m = 2\$\$ and \$\$n = 17\$\$, then the remainder when \$\$7m\$\$ is divided by \$\$n\$\$ is 14, which is _greater_ than 3. * If \$\$m = 3\$\$ and \$\$n = 3\$\$, then the remainder is zero, which is _less_ than 3. Thus, there is no definite answer, so **Stat.(1) → No → IS → BCE**.
Incorrect. [[snippet]] According to Stat. (2), \$\$n \lt 11\$\$, so \$\$n\$\$ can be 2, 3, 5, and 7, and \$\$m\$\$ can be any prime number. * If \$\$m = 2\$\$ and \$\$n = 5\$\$, then the remainder when \$\$7m\$\$ is divided by \$\$n\$\$ is 4, which is _greater_ than 3. * If \$\$m = 7\$\$ and \$\$n = 7\$\$, then the remainder is zero, which is _less_ than 3. Thus, there is no definite answer, so **Stat.(2) → No → IS → ACE**.
Incorrect. [[snippet]] According to Stat. (1+2), \$\$m \lt 5\$\$, so \$\$m\$\$ can be 2 or 3, and \$\$n \lt 11\$\$, so \$\$n\$\$ can be 2, 3, 5, and 7. * If \$\$m = 2\$\$ and \$\$n = 5\$\$, then the remainder when \$\$7m\$\$ is divided by \$\$n\$\$ is 4, which is _greater_ than 3. * If \$\$m = 2\$\$ and \$\$n = 7\$\$, then the remainder is zero, which is _less_ than 3. Thus, there is no definite answer, so **Stat.(1+2) → No → IS → E**.
Incorrect. [[snippet]] According to Stat. (1), \$\$m \lt 5\$\$, so \$\$m\$\$ can be 2 or 3, and \$\$n\$\$ can be any prime number. * If \$\$m = 2\$\$ and \$\$n = 17\$\$, then the remainder when \$\$7m\$\$ is divided by \$\$n\$\$ is 14, which is _greater_ than 3. * If \$\$m = 3\$\$ and \$\$n = 3\$\$, then the remainder is zero, which is _less_ than 3. Thus, there is no definite answer, so **Stat.(1) → No → IS → BCE**. According to Stat. (2), \$\$n \lt 11\$\$, so \$\$n\$\$ can be 2, 3, 5, and 7, and \$\$m\$\$ can be any prime number. * If \$\$m = 2\$\$ and \$\$n = 5\$\$, then the remainder is 4, which is _greater_ than 3. * If \$\$m = 7\$\$ and \$\$n = 7\$\$, then the remainder is zero, which is _less_ than 3. Thus, there is no definite answer, so **Stat.(2) → No → IS → CE**.
Correct. [[snippet]] According to Stat. (1), \$\$m \lt 5\$\$, so \$\$m\$\$ can be 2 or 3, and \$\$n\$\$ can be any prime number. * If \$\$m = 2\$\$ and \$\$n = 17\$\$, then the remainder when \$\$7m\$\$ is divided by \$\$n\$\$ is 14, which is _greater_ than 3. * If \$\$m = 3\$\$ and \$\$n = 3\$\$, then the remainder is zero, which is _less_ than 3. Thus, there is no definite answer, so **Stat.(1) → No → IS → BCE**.
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.