The following GMAT Problem Solving question tests your understanding of counting principles.

Question 22:

How many three-digit numbers have at least one $2$ and at least one $3$ ?

1. $\quad 52$
2. $\quad 54$
3. $\quad 56$
4. $\quad 58$
5. $\quad 60$

 
The following GMAT data sufficiency question tests your understanding of algebraic inequalities with two unknowns.

Question 21:

Is $ab+2>a+2b$ ?

1. (1) $a>2$
2. (2) $b<-1$

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 prime factorization and divisibility concepts that are tested on the GMAT.

Question 20:

If $252$ and $1176$ are factors of $n$, then which of the following could be the value of $n$ ?

1. $2^{3} \cdot 3^{2} \cdot 7^{2}$
2. $2^{6} \cdot 3^{1} \cdot 7^{2}$
3. $2^{5} \cdot 3^{3} \cdot 7^{3}$

1. $\quad \textrm{I only}$
2. $\quad \textrm{III only}$
3. $\quad \textrm{I and III only}$
4. $\quad \textrm{II and III only}$
5. $\quad \textrm{I, II, and III}$

 
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. $\quad 18x+8y$