Try the following GMAT Problem Solving question that tests your understanding of how to set up problems best solved using triple Venn diagrams.

Question 30:

Of $28$ students taking at least one subject, the number taking Mathematics and English only equals the number taking Mathematics only. No student takes English only or History only, and six students take Mathematics and History, but no English. The number taking English and History only is five times the number taking all three subjects. If the number taking all three subjects is even and non-zero, the number taking English and Mathematics only is:

1. $\quad 5$
2. $\quad 6$
3. $\quad 7$
4. $\quad 8$
5. $\quad 9$

 
Try the following GMAT Problem Solving question that tests your understanding of percent changes and ratios.

Question 29:

If $a$ is $40\%$ less than $b$ and $b$ is $25\%$ more than $c$, then what is the ratio of $c$ to $a$?

1. $\quad 3 \; \textrm{to} \; 4$
2. $\quad 3 \; \textrm{to} \; 5$
3. $\quad 4 \; \textrm{to} \; 3$
4. $\quad 5 \; \textrm{to} \; 3$
5. $\quad 2 \; \textrm{to} \; 1$

 
The following GMAT Problem Solving question tests your understanding of functions and how to manipulate algebraic expressions.

Question 28:

The function $f(x) = \dfrac{\left(x-\dfrac{1}{x}\right)}{\left(x+\dfrac{1}{x}\right)}$ is defined for all values of $x \neq 0$. Which of the following is equal to $f\left(-\dfrac{1}{x}\right)$?

1. $\quad -f(x)$
2. $\quad -f(-x)$
3. $\quad f(x)$
4. $\quad -f\left(\dfrac{1}{x}\right)$
5. $\quad f\left(\dfrac{1}{x}\right)$

 
The following GMAT data sufficiency question tests your understanding of dealing with remainder questions and their formulation in the context of data sufficiency.

Question 27:

Is the positive integer $n$ divisible by $15$ ?

1. (1) When $n$ is divided by $10$ the remainder is $5$.
2. (2) When $n$ is divided by $6$ the remainder is $3$.

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 straight lines and intercepts in the $xy-$coordinate plane.

Question 26:

In the $xy$-plane, what is the slope of the line $y=mx+c$, where $mc \neq 0$ ?

1. (1) The $x$ and $y$-intercepts of the line are equal.
2. (2) The product of the $x$ and $y$-intercepts is equal to $1$.

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.