Currently, y percent of the members on the finance committee

[LinaFahmi]

I have a tough time answering this question and understanding the answer for:

Question:
Currently, y percent of the members on the finance committee are women and next month, z percent of the men on the finance committee will resign. If no other personnel changes occur, then after the resignations next month, the men who remain on the finance committee will represent what percent of the total finance committee members?

Answers:
A) (100 - z)(100 - y)/100
B) (100 - z)(100 - y)/100
C) (100 - z)(100 - y)
D) zy/100 - z
E) z(100 - y)/100

The answer for this question is A and the explanation is that you would pick values for y, z and the total number of members. I've read this chapter before in the FDP book but I still don't understand why and how you could randomly pick numbers. Is it because it is a percentage question so the absolute value doesn't matter?

A similar question I have is that the FDP book mentions something about picking a Smart Number and that you should only pick one Smart Number. In this case, I am confused because in the question above, there appears to be 3 Smart Numbers being chosen.

Thank you!

[tim]

Your question seems to boil down to "why and how you could randomly pick numbers".

WHY - If you don't have a clear and easy algebraic solution in mind, and there are variables in the answer choices, picking numbers is a great strategy.

HOW - Just pick numbers! 2 for instance, or maybe 3. It's that easy! :) It's usually a good idea to pick easy numbers (not 7.2 or -pi) and to avoid 0 or 1

I do have to admit I'm at a loss to understand how this problem could involve picking 3 numbers, as you claim.

[LinaFahmi]

Thanks for your response Tim.

As to how the answer to the problem involves picking three numbers, below is the explanation from the FDP question bank, where the question came from.

Highlighted in red is where numbers are being chosen. Perhaps what's still bothering me is WHEN you decide to choose numbers - obviously this doesn't work for every single question with variables!

In order to make this problem less abstract, we can pick values for each of the unknown variables in the problem.

Let's assume there are 100 individuals originally on the committee.
Let y = 60.
Let z = 25.

The problem states that y percent of the original committee members are women. 60% of 100 = 60, so there are 60 original women members. This leaves 40 original members who are men.

The problem states that z percent of the men will resign next month. 25% of 40 = 10, so there are 30 men who will remain on the committee after the resignations.

No women resign, so 60 women remain on the committee, which, after the resignations, has a total of 30 + 60 = 90 members. The men who remain now constitute 30/90 or approximately 33.3 % of the committee.

Plug our assumed values for y (60) and z (25) into the answer choices to see which one yields 33.3 as a solution. Answer choice A is the only one that works:

(100)(100 - z)(100 - y)/ 100^2 - z(100 - y)
= (100)(75)(40)/100^2 - 25(40)
= (100)(75)(40)/100^2 - 25(40)
= 33 1/3

The correct answer is A.

[jnelson0612]

You should at least consider testing numbers in the following scenarios:

1) You see variables in the problem and answers and the algebra is not extremely simple. (similar to this problem)
2) You see all fractions in the problem and answers.
3) You see all percents in the problem and answers.

Picking numbers is one of the greatest techniques for the GMAT. It takes algebra problems and turns them into arithmetic problems, avoiding wasting time, stress, and common mistakes.

A great start would be to go through the Official Guide and look for problems that fit these criteria, then try picking numbers. You may be surprised at how much easier these problems are when you don't try to use algebra.