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

Question

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.

(DS03999)

satheshshiva · Accepted Answer

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

DavidTutorexamPAL · Answer

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.

EgmatQuantExpert · Answer

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

GMATinsight · Answer

Answer: Option E

Video solution by  GMATinsight

https://www.youtube.com/watch?v=HX0FGg8JLu4

ScottTargetTestPrep · Answer

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

anirchat · Answer

I think that having n in terms of  f  would actually be sufficient. How to understand when they are explicitly asking for a value and when in terms of f ?

Bunuel · Answer

1. YES/NO DS Questions:
In Yes/No Data Sufficiency questions, a statement is sufficient if the answer is always "yes" or always "no", whereas a statement is insufficient if the answer can be "sometimes yes" and "sometimes no".

2. VALUE DS QUESTIONS:
When a DS question asks about the value of some variable, then the statement is sufficient ONLY if you can obtain a single numerical value for this variable.

So, in this question, when it asks what is the value of n, it means we need to find a single numerical value of n for a statement to be sufficient.

anirchat · Answer

Thanks Bunuel. Now it makes all sense ...

SwethaReddyL · Answer

Here i understood, that both the statements aren't sufficient to answer the question. But while solving the question, I also thought that - since the question doesn't say that the total employees are only female. I found that additional reason to pick e. Is my thinking straight?  Bunuel  
Same for some set theory Ds questions, the question/statements never talked about (A n B)', can i explicitly pick not sufficient?

Regards,
Swetha Reddy

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

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GMAT Data Sufficiency (DS) Questions

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

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