Try the following GMAT Problem Solving question on conditions under which algebraic expressions are undefined.

Question 51:

For what real values of $x$ is the expression $\dfrac{3(x+3)}{(x-1)(x+2)}$ not defined ?

1. $\quad x=-3 \; \textrm{only}$

2. $\quad x=-2 \; \textrm{only}$

3. $\quad x=1 \; \textrm{only}$

4. $\quad x=-2 \; \textrm{or} \; 1 \; \textrm{only}$

5. $\quad x=-3, -2, \textrm{or} \; 1 $

 
Try the following GMAT Problem Solving question on plane geometry and finding area of a rectangular picture frame.

Question 50:

The figure below shows a picture frame that consists of a rectangular photograph(white region) surrounded by a border of uniform width of $x$ inches. The perimeter of the photograph is $27$ inches, and the area of the border(grey region) is $70$ square inches. What is the perimeter in inches of the entire picture frame including the border?

1. $\quad 37$

2. $\quad 43$

3. $\quad 48$

4. $\quad 51$

5. $\quad 56$

 
Try the following GMAT data sufficiency question that tests your understanding of dealing with algebraic inequalities.

Question 49:

If $x$ and $y$ are positive, is $x>y$ ?

1. (1) $x^2-xy > x$
2. (2) $y^2-y < xy$

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.

 
Try the following GMAT Problem Solving question on finding terms of a general sequence.

Question 48:

In a sequence each term after the first term is one less than twice the previous term. If the third term of the sequence is $t$, then what is the first term expressed in terms of $t$ ?

1. $\quad 2t-1$

2. $\quad \dfrac{t+1}{2}$

3. $\quad \dfrac{t+1}{4}$

4. $\quad \dfrac{t-3}{4}$

5. $\quad \dfrac{t+3}{4}$

 
Try the following GMAT Problem Solving question on the properties of right triangles that are commonly tested on the GMAT.

Question 47:

In the figure below, the perimeter of triangle $BDC$ exceeds the perimeter of triangle $ABD$ by how much?

1. $\quad 2\sqrt{3}$

2. $\quad 4$

3. $\quad 3\sqrt{3}$

4. $\quad 6$

5. $\quad 4\sqrt{3}$