In a real estate office that employs n salespeople, f of the

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In a real estate office that employs n salespeople, f of them are females and x of the females are new employees. What is the value of n ?

(1) If an employee were randomly selected from the n employees, the probability of selecting a female would be 2/3.
(2) If an employee were randomly selected from the f female employees, the probability of selecting a new employee would be 1/2.

OA E

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by Jay@ManhattanReview » Sun Sep 01, 2019 9:01 pm

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BTGmoderatorDC wrote:In a real estate office that employs n salespeople, f of them are females and x of the females are new employees. What is the value of n ?

(1) If an employee were randomly selected from the n employees, the probability of selecting a female would be 2/3.
(2) If an employee were randomly selected from the f female employees, the probability of selecting a new employee would be 1/2.

OA E

Source: Official Guide
The question asks for the unique value of n and not a relative value. Looking at the statements, we see that the values of probabilities are given, suggesting that we cannot get the unique value of n. Let's solve this questions.

Let's take each statement one by one.

(1) If an employee were randomly selected from the n employees, the probability of selecting a female would be 2/3.

=> f = 2n/3. Can't get the unique value of n. Insufficient.

(2) If an employee were randomly selected from the f female employees, the probability of selecting a new employee would be 1/2.

x = f/2. Can't get the unique value of n. Insufficient.

(1) and (2) together

Even after combining both statements, we can't get the unique value of n. Insufficient.

The correct answer: E

Hope this helps!

-Jay
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BTGmoderatorDC wrote:
Sun Sep 01, 2019 6:11 pm
In a real estate office that employs n salespeople, f of them are females and x of the females are new employees. What is the value of n ?

(1) If an employee were randomly selected from the n employees, the probability of selecting a female would be 2/3.
(2) If an employee were randomly selected from the f female employees, the probability of selecting a new employee would be 1/2.

OA E

Source: Official Guide
Solution:

Question Stem Analysis:

We need to determine the value of n, the number of salespeople in a certain real estate office.

Statement One Alone:

From statement one, we see that f/n = 2/3. However, since we don’t know the value of f, we can’t determine the value of n. Statement one alone is not sufficient.

Statement Two Alone:

From statement one, we see that x/f = 1/2. However, since we know neither the value of x nor the value of f, we can’t determine the value of n. Statement two alone is not sufficient.

Statements One and Two Together:

With the two statements, we still can’t determine the value of x or f; thus, we can’t determine the value of n. Both statements together are not sufficient.

Answer: E

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