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In a real estate office that employs n salespeople, f of them are fema

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In a real estate office that employs n salespeople, f of them are fema  [#permalink]

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New post 24 Jun 2018, 20:51
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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.



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In a real estate office that employs n salespeople, f of them are fema  [#permalink]

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New post 24 Jun 2018, 21:58
Bunuel 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.



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(DS03999)


As all we're given are variables, we'll pick simple numbers to help make things concrete.
This is an Alternative approach.

(1) Say that f = 10. Then there are 3/2 * 10 = 15 employees. Clearly, if there is a different number of females there will be a different number of employees.
Insufficient.

(2) Say, again, that f = 10. Then x = 10 * 1/2 = 5 are new employees. We have no way to calculate n so this cannot be sufficient.
Insufficient.

Combined:
Combining the statements doesn't help much: if we pick f = 10, then we get the same values as above and if we pick f = 20 we get values twice as large. As there are no additional constraints in the question we cannot determine the value of n.
Insufficient.

(E) is our answer.

Note that a shorter, Logical approach would be to notice that we are asked to give a specific number but not given any numbers to start with. That means we cannot answer.
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Re: In a real estate office that employs n salespeople, f of them are fema  [#permalink]

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New post 25 Jun 2018, 03:05

Solution



Given:
    • In a real estate office that employs n salespeople, f of them are females and x of the females are new employees

To find:
    • The value of n

Analysing Statement 1
    • As per the information given in statement 1, if an employee were randomly selected from the n employees, the probability of selecting a female would be \(\frac{2}{3}\)
      o This statement does not provide us any information about the male employees, and hence about the total number of employees

Hence, statement 1 is not sufficient to answer

Analysing Statement 2
    • As per the information given in statement 2, if an employee were randomly selected from the f female employees, the probability of selecting a new employee would be \(\frac{1}{2}\)
      o This statement says that half of the female employees are new, and again, does not provide us any information about the male employees, and the total number of employees

Hence, statement 2 is not sufficient to answer

Combining Both Statements
Even if we combine both the statements, we can’t find any information about the total number of employees

Hence, the correct answer is option E.

Answer: E
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In a real estate office that employs n salespeople, f of them are fema  [#permalink]

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New post 08 Sep 2018, 22:07
Bunuel 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.



NEW question from GMAT® Official Guide 2019


(DS03999)


n?

1)\(\frac{f}{n}\)= \(\frac{2}{3}\)

3f=2n
INSUFFICIENT

2) \(\frac{x}{f}\) = \(\frac{1}{2}\)

f=2x
INSUFFICIENT

Combining 1 and 2,
There are 3 variables and only 2 equation. So INSUFFICIENT
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In a real estate office that employs n salespeople, f of them are fema &nbs [#permalink] 08 Sep 2018, 22:07
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