Try the following GMAT Problem Solving question on functions and algebraic manipulation.

Question 44:

The function $f$ is defined by $f(x)=1-x^2$ for all values of $x$. What is $-f(-f(-x))$ ?

1. $\quad 0$

2. $\quad x^2-2x$

3. $\quad x^2+2x$

4. $\quad x^4-2x^2$

5. $\quad x^4+2x^2$

 
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. $\quad 0.75$