The following GMAT data sufficiency question tests your understanding of how to deal with linear equations with two unknowns where the variables are constrained to be integer values.

Question 19:

A bag contains $\$2.90$ with a mix of quarters ($25$ cents) and dimes ($10$ cents). How many dimes are in the bag?

1. (1) There are fewer dimes than quarters in the bag.
2. (2) There are $6$ more quarters than dimes in the bag.

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 simplify expressions using algebraic identities that are commonly tested on the GMAT.

Question 18:

$\dfrac{(18x^2-8y^2)(3x-2y)}{9x^2+4y^2-12xy}=$

1. $\quad 3x+2y$
2. $\quad 6x-4y$
3. $\quad 6x+4y$
4. $\quad 18x-8y$
5. $\quad 18x+8y$

 
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. $\quad 3^{89}$