The following GMAT Problem Solving question tests your understanding of how to simplify arithmetic expressions that use factorials.

Question 4:

$$\dfrac{(48!)(22!)(10!)(8!)}{(50!)(20!)(12!)(6!)}=$$

1. $\quad \dfrac{2}{25}$
2. $\quad \dfrac{3}{20}$
3. $\quad \dfrac{5}{18}$
4. $\quad \dfrac{6}{17}$
5. $\quad \dfrac{7}{15}$

 
The following GMAT Problem Solving question tests your understanding of how to deal with distance/rate/time questions.

Question 3:

Train $A$ and $B$, $455$ miles apart, are traveling towards each other on parallel tracks at constant rates and in the same time zone. If train $A$ left at $4$ pm traveling at a speed of $60$ miles per hour, and train $B$ left at $5:45$ pm traveling at $45$ miles per hour, then at what time would they pass each other?

1. $\quad 7:20 \; \textrm{pm}$
2. $\quad 8:55 \; \textrm{pm}$
3. $\quad 9:05 \; \textrm{pm}$
4. $\quad 9:20 \; \textrm{pm}$
5. $\quad 9:25 \; \textrm{pm}$

 
The following GMAT Problem Solving question tests your understanding of identifying identities and then applying them to simplify the computational effort.

Question 2:

$\dfrac{0.1001}{(-1.002)^2 – 1}=$

1. $\quad 0.025$
2. $\quad 0.25$
3. $\quad 2.5$
4. $\quad 25$
5. $\quad 250$

 
The following GMAT Problem Solving question tests your understanding of how to find the sum of an arithmetic sequence and also about observing patterns.

Question 1: If the sum of the first $100$ positive even integers is $10,100$, then what is the sum of the first $200$ positive even integers?

1. $\quad 20,100$
2. $\quad 20,200$
3. $\quad 25,100$
4. $\quad 40,100$
5. $\quad 40,200$

 
The following GMAT Problem Solving question tests your understanding of how to find the sum of an arithmetico-geometric series. This is a difficult question and you should expect something along these lines if you are scoring Q49+ on the GMAT quantitative section.

The limiting sum of the infinite series
$$ \dfrac{1}{2} + \dfrac{3}{4} + \dfrac{5}{8} + \dfrac{7}{16} + \dfrac{9}{32} + \ldots $$
whose $n$-th term is $\dfrac{2n-1}{2^n}$ is:

1. $\quad \dfrac{5}{2}$
2. $\quad 3$
3. $\quad \dfrac{7}{2}$
4. $\quad \dfrac{15}{4}$
5. $\quad 4$