At a certain school, the ratio of the number of second graders to the number of fourth graders is 8 to 5, and the ratio of the number of first graders to the number of second graders is 3 to 4. if the ratio of the number of third graders to the number of fourth graders is 3 to 2, what is the ratio of the number of first graders to the number of third graders?

A. 16 to 15
B. 9 to 5
C. 5 to 16
D. 5 to 4
E. 4 to 5

A very fast approach:

1st/3rd = 1st/2nd * 2nd/4th * 4th/3rd.

In the equation above, all of the values in red cancel out.
Thus:
1st/3rd = 3/4 * 8/5 * 2/3 = 4/5.

The correct answer is E.

The OP doesn't need help with this particular problem. The OP needs help with mathematical reasoning. GMAT doesn't test math. It tests reasoning.

ISME -

Identify the problem. In this case it's a ratio and proportion problem.

Set up the solution - write what the problem tells you and what you know. The problem specifies rations. You know two things about ratios - they can cancel, and when two ratios are equal it's a proportion. In this problem writing the ratios and proportion, rather than thinking about the problem, leads to the solution. You may now know where you're going when you start writing, but it becomes clear.

Make Sure - Make sure you've written the correct info, and know what question the problem asks.

Execute - Complete the math. Solve the problem.