The following GMAT Problem Solving question tests your ability to apply concepts of divisibility and prime factorization.

Question 7:

What is the least value of $n$ for which the product of the first $n$ positive integers is divisible by $8505$ ?

1. $\quad 9$
2. $\quad 12$
3. $\quad 15$
4. $\quad 18$
5. $\quad 21$

 
The following GMAT data sufficiency question tests your understanding of the relationship between average (arithmetic mean) and median when given additional constraints.

Question 6:

Given $a \gt b \gt c \gt 0$, is the average of $a$, $b$, and $c$ equal to their median ?

1. (1) $\dfrac{a}{b} – 1 = 1 – \dfrac{c}{b} $
2. (2) $b$ is equal to the average of $a$ and $c$.

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are NOT sufficient.

 
The following GMAT data sufficiency question tests your understanding of average (arithmetic mean) in the context of being able to manipulate algebraic expressions and observe patterns.

Question 5:

What is the average (arithmetic mean) of $x$, $y$, and $z$ ?

1. (1) The average of $2x-5$, $2y-5$, $2z-5$ is $25$.
2. (2) The average of $2x-y$, $4y+3z$, and $x+9$ is $48$.

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are NOT sufficient.

 
The following GMAT Problem Solving question tests your understanding of how to simplify arithmetic expressions that use factorials.

Question 4:

$$\dfrac{(48!)(22!)(10!)(8!)}{(50!)(20!)(12!)(6!)}=$$

1. $\quad \dfrac{2}{25}$
2. $\quad \dfrac{3}{20}$
3. $\quad \dfrac{5}{18}$
4. $\quad \dfrac{6}{17}$
5. $\quad \dfrac{7}{15}$

 
The following GMAT Problem Solving question tests your understanding of how to deal with distance/rate/time questions.

Question 3:

Train $A$ and $B$, $455$ miles apart, are traveling towards each other on parallel tracks at constant rates and in the same time zone. If train $A$ left at $4$ pm traveling at a speed of $60$ miles per hour, and train $B$ left at $5:45$ pm traveling at $45$ miles per hour, then at what time would they pass each other?

1. $\quad 7:20 \; \textrm{pm}$
2. $\quad 8:55 \; \textrm{pm}$
3. $\quad 9:05 \; \textrm{pm}$
4. $\quad 9:20 \; \textrm{pm}$
5. $\quad 9:25 \; \textrm{pm}$