Try the following GMAT Problem Solving question that tests your ability to find areas of intersections of circles.

Question 41:

Three semicircles of radius $1$ are constructed on diameter $\overline{AB}$ of a semicircle of radius $2$. The centers of the small semicircles divide $\overline{AB}$ into four line segments of equal length, as shown below. What is the area of the shaded region that lies within the large semicircle but outside the smaller semicircles?

1. $\quad \pi-\sqrt{3}$

2. $\quad \pi-\sqrt{2}$

3. $\quad \dfrac{\pi+\sqrt{2}}{2}$

4. $\quad \dfrac{\pi+\sqrt{3}}{2}$

5. $\quad \dfrac{7}{6}\pi \; – \; \dfrac{\sqrt{3}}{2}$

 
Try the following GMAT Problem Solving question that tests your ability to simplify arithmetic terms.

Question 40:

$\dfrac{(0.037^2 – 0.012^2)^{\frac{1}{2}}}{0.07}=$

1. $\quad 0.4$

2. $\quad 0.5$

3. $\quad 0.6$

4. $\quad 0.7$

5. $\quad 0.75$

 
Try the following GMAT Problem Solving question that tests your ability to solve word problems based on distance-rate-time relationship.

Question 39:

Yan is somewhere between his home and the stadium. To get to the stadium he can walk directly to the stadium, or else he can walk home and then ride his bicycle to the stadium. He rides $7$ times as fast as he walks, and both choices require the same amount of time. What is the ratio of Yan’s distance from his home to his distance from the stadium?

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

2. $\quad \dfrac{3}{4}$

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

4. $\quad \dfrac{5}{6}$

5. $\quad \dfrac{6}{7}$

 
Try the following GMAT Problem Solving question that tests your understanding of the averages (arithmetic mean).

Question 38:

The Dunbar family consists of a mother, a father, and some children. The average age of the members of the family is $20$, the father is $48$ years old, and the average age of the mother and children is $16$. How many children are in the family?

1. $\quad 2$

2. $\quad 3$

3. $\quad 4$

4. $\quad 5$

5. $\quad 6$

 
The following GMAT data sufficiency question tests your understanding of properties of parabolas in the coordinate plane that are commonly tested on the GMAT.

Question 37:

Given $mn \neq 0$, does the parabola $y=x^2+2mx+n$ intersect the $x-$axis at two distinct points ?

1. (1) $n \lt 0$
2. (2) $m^2 \gt n$

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.