Try the following GMAT data sufficiency question that tests your understanding of finding lengths of line segments in a circle.

Question 46:

In the semicircle shown below with center $O$, the length of $OA$ is $8$. What is the length of line segment $AB$ ?

1. (1) The area of the semicircle is $200 \pi$.
2. (2) $OC=16$ and $CD=12$.

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 applying distance, rate, and time relationships to problems tested on the GMAT.

Question 45:

Trains $A$ and $B$ left stations $R$ and $S$ simultaneously on two separate parallel rail tracks that are $350$ miles long. The trains passed each other at point $X$ after traveling for a certain amount of time. How many miles of the rail tracks had train $A$ traveled when the two trains passed each other?

1. (1) Up to point $X$, the average speed of train $B$ was $25\%$ less than the average speed of train $B$.
2. (2) Up to point $X$, the average speed of train $B$ was $60$ mph and it took two and a half hours for train $B$ to arrive at point $X$.

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 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. $\quad \textrm{I, II, and III}$