The following GMAT Problem Solving question tests your understanding of how to approach counting and probability questions that are tested on the GMAT.

Question 17:

A basket contains $5$ red balls and $3$ green balls. If $3$ balls are selected from the basket simultaneously, what is the probability that at least one of the $3$ balls selected will be green?

1. $\quad \dfrac{5}{7}$
2. $\quad \dfrac{3}{4}$
3. $\quad \dfrac{11}{14}$
4. $\quad \dfrac{23}{28}$
5. $\quad \dfrac{7}{8}$

 
The following GMAT Problem Solving question tests your understanding of how to recognize algebraic identities and to manipulate exponent terms.

Question 16:

If $8^{2x}+8^{x}=0.75$, then $x=$

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

 
The following GMAT Problem Solving question tests your understanding of how to apply exponent rules.

Question 15:

If $x=27^{27}$ and $x^{x}=3^{y}$, then $y=$?

1. $\quad 3^{81}$
2. $\quad 3^{83}$
3. $\quad 3^{85}$
4. $\quad 3^{87}$
5. $\quad 3^{89}$

 
The following GMAT data sufficiency question tests your understanding of how to deal with remainder questions in the context of GMAT data sufficiency.

Question 14:

What is the remainder when the positive integer $n$ is divided by $30?$

1. (1) The remainder when $n$ is divided by $15$ is $7$.
2. (2) The remainder when $n$ is divided by $12$ is $4$.

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 Problem Solving question tests your understanding of how to add up a finite set of terms that form a geometric sequence.

Question 13:

$\dfrac{3(4^5 + 4^6+4^7+4^8+4^9+4^{10})}{2^5+2^6+2^7+2^8+2^9+2^{10}}=$

1. $\quad 2^{10}+2^{5}$
2. $\quad 2^{10}+2^6$
3. $\quad 2^{11}+2^{5}$
4. $\quad 2^{11}+2^{6}$
5. $\quad 2^{16}$