Try the following GMAT Problem Solving question that tests your ability to find the sum of the terms of a sequence.

Question 43:

Let $a_1$, $a_2$, $a_3$, $\ldots$, $a_n$, be a sequence of numbers where $a_1=-2$, $a_2=4$, and for $n \geq 3$, $a_n = \left(\dfrac{a_{n-1}}{a_{n-2}}\right)$. What is the sum of the first $99$ terms?

1. $\quad -16$

2. $\quad -12$

3. $\quad -8$

4. $\quad -4$

5. $\quad 0$

 
Try the following GMAT Problem Solving question that tests your understanding of identifying patterns in sequences, and using that pattern to add the terms of the sequence.

Question 42:

The terms of a sequence follow the pattern: $-1$, $-2$, $3$, $4$, $-5$, $-6$, $7$, $8,$ $-9$, $-10$, $11$, $12, \ldots \ldots$. If $S$ is the sum of the first $n$ terms of this sequence, then for which of the following values of $n$ is $S=0$ ?

1. $59$
2. $75$
3. $97$

1. $\quad \textrm{II only}$
2. $\quad \textrm{I and II only}$
3. $\quad \textrm{I and III only}$
4. $\quad \textrm{II and III only}$
5. $\quad \textrm{I, II, and III}$

 
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. $\quad \dfrac{6}{7}$