The following GMAT data sufficiency question tests your understanding of how to deal with overlapping sets using Venn diagrams or other approaches.

Question 8:

At a certain company with 90 employees, 70 have cell phones and 60 have laptops. How many employees do not have either a cell phone or a laptop?

1. (1) The number of employees that have cell phones only is twice the number of employees that have laptops only.
2. (2) 80 employees have either a cell phone or a laptop.

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 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. $\quad \dfrac{7}{15}$