ABC Consulting

[kris610]

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?

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

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
(C) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
(D) EACH statement ALONE is sufficient to answer the question asked
(E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed

A

[Mike@Magoosh]

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

[dhiren8182]

I solved in some other way.
Is my approach correct?

Total fees=14000 man hrs=??
st1)100/man hr for 100 man hrs and 80/man hr for additional man hrs or fratcion of hr.
therefore 100*100=10000
so 14000-10000=4000
4000/80=50
so total man hrs=150
statement 1 is SUFFICIENT

ST 2)
gives information only about rate/man hr and not for additional.
So ST 2 is INSUFFICIENT
AND is A