Each employee who works in company X works in exactly one of

Question

Each employee who works in company X works in exactly one of departments A, B, and C. What fraction of all the employees who work in company X work in department A?

(1) The ratio of the total number of employees who work in departments A and C to the number of employees who work in department B is 7 to 3.

(2) The average (arithmetic mean) of the numbers of employees who work in departments A, B, and C is times the number of employees who work in department A.

sujoykrdatta · Answer

Assuming the number of employees in A, B and C as a, b, c respectively:

We have:

Statement 1: (a + c) : b = 7 : 3 - Clearly this is insufficient since we have no information about the value of 'a'

Statement 2: The average (arithmetic mean) of the numbers of employees who work in departments A, B, and C is  ??  times the number of employees who work in department A --- I am assuming that the value for the  ??  was given - I am assuming it to be  k

=> The average (arithmetic mean) of the numbers of employees who work in departments A, B, and C is k times the number of employees who work in department A

=> (a+b+c)/3 = k*a

=> a/(a+b+c) = 1/3k (Note: the value of k is known) --- Sufficient

Answer B

Bunuel · Answer

__________________________
Please edit the post. Thank you.

SaquibHGMATWhiz · Answer

Solution:      
  Pre Analysis:  
  Each employee in company X works in exactly one of departments A, B and C  
 Let the number of employees working in these departments be a, b and c respectively  
 We are asked the value of  \frac{a}{a+b+c}

Statement 1:   The ratio of the total number of employees who work in departments A and C to the number of employees who work in department B is 7 to 3 
  Accordign to this statement,  \frac{a+c}{b}=\frac{7}{3}  
 From this we can assume  a+c=7x  and  b=3x  and we can get  a+b+c=7x+3x=10x  
 This will not help us get the value of  \frac{a}{a+b+c}=\frac{a}{10x}   
 Thus,  statement 1 alone is not sufficient and we can eliminate options A and D

Statement 2:   The average (arithmetic mean) of the numbers of employees who work in departments A, B, and C is times the number of employees who work in department A 
  According to this statement,  \frac{a+b+c}{3}=3a  or  \frac{a}{a+b+c}=\frac{1}{9}

Hence the right answer is    Option B

Each employee who works in company X works in exactly one of

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards