Hi, there. I'm happy to help with this.

Prompt:
ABC Consulting charges more for the first 100 man-hours of a project than for additional hours beyond the first 100. If Acme's fees for using ABC Consulting's services were $14,000, how many man-hours were charged?

If A is the rate for the first hundred man-hours, and B is the rate thereafter, then we have

14000 = A*100 + B*(T-100)

where T is the total number of man-hours, the quantity sought in the prompt. Notice we have three unknowns and only a single equation relating them.

Statement #1: ABC Consulting charges $100 per man-hour for the first 100 man-hours and $80 per man-hour for each additional hour or fraction of an hour.

This tell us: A = 100, and B = 80. Going back to our equation, we have:


14000 = 100*100 + 80*(T-100)

Only one variable left, which means we could solve for T, thus answering the prompt question. Statement #1, by itself, is sufficient.

Statement #2: If the charges for the first 100 hours had been $120/man-hour, Acme's total consulting charges would have been $16,000.

This implies a second equation:

16000 = 120*100 + B*(T-100) ---> 16000 - 12000 = 4000 = B*(T-100)

Now, we can go back to the first equation, and plug that value in for the term B*(T-100)

14000 = A*100 + B*(T-100)

14000 = A*100 + 4000 ---> 10000 = A*100 ---> A = 100

Statement #2 leads us to a value for A. Unfortunately, we are still left with

4000 = B*(T-100)

one equation with two unknowns. In the absence of further information, we cannot solve one equation with two unknowns. Therefore, Statement #2, by itself, is insufficient.

Answer = A

For free, here's a challenging DS question with some similar ideas.

https://gmat.magoosh.com/questions/934

The question at that link should be followed, when you submit an answer, but a complete video explanation.

Does all this make sense? Please let me know if you have any further questions.

Mike