GMAT Data Sufficiency Question 19: Equations with integer solutions

 
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.