Data sufficiency qst! Help!

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Data sufficiency qst! Help!

by alwayslulu » Fri Apr 30, 2010 10:00 am
If 60 percent of the employees at Company X are female, does Company X have more than 100 female employees?

(1) Company X has more than 150 employees.

(2) Company X has 74 more female employees than male employees.

a. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
b. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
c. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
d. EITHER statement BY ITSELF is sufficient to answer the question.
e. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

answer: b

I know why stmt 1 is not sufficient. I need to know why stmt 2 is sufficient. Here is the explanation, but i don't get it where the 20% comes from.

Statement (2): SUFFICIENT

If there are 74 more female employees than male, and the percent difference between male and female is 20%, then we have sufficient information. Let x = total number of employees. Then 20% of x is 74. We could solve for the total number of employees, and then find the number female employees.
Source: — Data Sufficiency |

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by Brian@VeritasPrep » Fri Apr 30, 2010 10:36 am
Good question, alwayslulu.

Algebraically, we know that females + males = total employees, or f + m = total.

We also know that f = 6/10 (T) and that m = 4/10 (T), and that f - m > 74 (the information from statement 1).

So, we can use substitution for f and m to get everything in terms of the total:

6/10 (T) - 4/10 (T) > 74
2/10 (T) > 74
T > 5 (74)
T > 370

Since our job is to determine the number of female employees, we then take 60% (or 3/5) of >370, which will be greater than 100, so we know that the answer is "yes", and the statement is sufficient.
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by boazkhan » Fri Apr 30, 2010 10:37 am
The Question provides us the 20% difference....60%F, 40%M --> 60-40=20%

Statement 2 provides us the actual difference..74.

20% of T = 74 --- Where T is the total number of Male and Female.

I hope this makes sense.

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by alwayslulu » Fri Apr 30, 2010 10:42 am
Thank you so much Brian@VeritasPrep and Boazkhan!

I know where the 20% comes from now! Your response is totally make sense to me! :)

boazkhan wrote:The Question provides us the 20% difference....60%F, 40%M --> 60-40=20%

Statement 2 provides us the actual difference..74.

20% of T = 74 --- Where T is the total number of Male and Female.

I hope this makes sense.