Problem Solving

boomgoesthegmat wrote:There are 4 more women than men on Centerville's board of education. If there are 10 members on the board, how many are women?
A) 3
B) 4
C) 6
D) 7
E) 8

OA: D

One approach is to TEST each answer choice. I'll leave that to you to try.

Another option is to create and solve an equation.
Let W = # of women

There are 4 more women than men
In other words, there are 4 FEWER men than women.
So, W - 4 = # of men

There are 10 members on the board
So, (# of women) + (# of men) = 10
Or, W + (W - 4) = 10
Simplify: 2W - 4 = 10
So: 2W = 14
And: W = 7

Answer: D

Related Resources
The following videos cover the concepts/strategies that are useful for answering this question:
- Intro to GMAT word problems: https://www.gmatprepnow.com/module/gmat ... /video/900
- Testing the answer choices: https://www.gmatprepnow.com/module/gmat ... /video/901
- Assigning variables: https://www.gmatprepnow.com/module/gmat ... /video/902
- Writing equations: https://www.gmatprepnow.com/module/gmat ... /video/903
- How many variables to assign?: https://www.gmatprepnow.com/module/gmat ... /video/906

Cheers,
Brent

Hi boomgoesthegmat,

This question can be solved rather easily by TESTing THE ANSWERS.

We're told that there are 4 MORE women then men on the board and that there are 10 total board members. Since there are more women than men, women have to make up MORE than half of the 10 people.

Let's TEST Answer D: 7

IF.... there are 7 women...
There will be 7-4 = 3 men
7+3 = 10; this is an exact match for what we were told, so this MUST be the answer.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

boomgoesthegmat wrote:There are 4 more women than men on Centerville's board of education. If there are 10 members on the board, how many are women?
A) 3
B) 4
C) 6
D) 7
E) 8

OA: D

Solution:

We can solve the problem by setting up a few equations. First let's define some variables.

m = number of men on the board

w = number of women on the board

We are given that there are 4 more women than men on the board. Let's express this in an equation.

w = m + 4

We are also given that there are a total of 10 members on the board. Let's express this in an equation.

m + w = 10

Since w = m + 4, we can substitute m + 4 for w into the equation m + w = 10 and we have:

m + m + 4 = 10

2m = 6

m = 3

Since m + w = 10, we know that 3 + w = 10 or w = 7.

The answer is D