Company M has two divisions - X and Y. Each division

Question

Company M has two divisions - X and Y. Each division has exactly two types of employees - clerks and managers. Is the ratio of clerks to managers greater for division X than that for division Y?
 
(1) Division X has 20% managers.
(2) Company M has 15% managers.

Source: ExpertsGlobal

KarishmaB · Accepted Answer

Assuming equal number of employees in both divisions:

From stmnt 1

...................... X ....................Y................. Total M

Clerks ........... 80

Managers....... 20

Total ..............100.................100...................200

From stmnt 2

...................... X ....................Y................. Total M

Clerks ............................................................170

Managers.........................................................30

Total ..............100.................100...................200

Using both stmnts

....................... X ....................Y................. Total M

Clerks .............80....................90........................170

Managers.........20....................10.........................30

Total ..............100.................100.....................200

Ratio of clerks:managers for X = 4:1
Ratio of clerks" managers for Y = 9:1

....................... X ....................Y................. Total M

Clerks .............80....................175........................255

Managers.........20....................25........................45
Total ..............100.................200.....................300

Note that it doesn't matter how many employees Y has, the percent of managers will be less than 15% since X has 20% managers and total there are 15% managers. So to pull down the overall percentage to 15%, the percentage of managers in Y must be less than 15%. How much exactly will depend on how many employees X and Y have.

Sufficient.

Answer (C)

P.S. - The question is much better dealt using weighted averages.

chetan2u · Answer

Hi...

Q is... Is  \frac{c_x}{m_x}>\frac{c_y}{m_y}  ?
 Individually each statement is insufficient..

It may seem that combined also it is insufficient as details of y is not given.
But if M consists of only x and y, and the ratio of C:m is 20:80 in x or 1:4 AND overall it is 15:85..
Y will have even lower Ratio than overall to bring down ratio in x of 20/80 to 15/85..
Hence sufficient

C

pushpitkc · Answer

1. Division X has 20% managers to the 80% clerks, 
the ratio of managers to clerks in division X is  \frac{1}{4} 
Since we do not have any idea about the Division Y, this statement is not sufficient

2. It has been said the managers in the company are 15%, making the clerks 85%
The overall ratio of managers to clerks is  \frac{3}{17} . 
Again, without the information in both the divisions, 
we can't clearly tell which division has a higher ratio of managers to clerks.(Insufficient)

On combining the information we can clearly tell that,
Division Y has a lower ratio(Sufficient)  (Option C)

k1414 · Answer

My thought process was:

(1) Ok, we know the ratio of clerks/managers for division x, but know nothing about division y's ratio (NS)
(2) Now we know the company's ratio of clerks/managers, but know nothing about the proportion at each division (NS)

Together the statements tell us that the ratio of clerks/managers for division x is below the company's ratio, meaning that division y must have more clerks/managers

Answer: C

ShankSouljaBoi · Answer

How ? i used variables x and y , kept getting stuck. Can you please help with the algebraic approach?

Regards

Hanzel101 · Answer

Hi chetan2u VeritasKarishma Bunuel can you please explain this question using Sets table format? The above mentioned solution might not click in 2 mins under high pressure and the first instinct would be to draw the table. Thanks

Kinshook · Answer

Given:
1. Company M has two divisions - X and Y.
2. Each division has exactly two types of employees - clerks and managers.

Asked: Is the ratio of clerks to managers greater for division X than that for division Y?
 
(1) Division X has 20% managers.
Ratio of clerks to managers for Division X= 80/20= 4
No information is provided for Division Y
NOT SUFFICIENT

(2) Company M has 15% managers.
On information is provided for Division X & Division Y
NOT SUFFICIENT

Combining (1) & (2)
(1) Division X has 20% managers.
Ratio of clerks to managers for Division X=  \frac{80}{20}= 4 
(2) Company M has 15% managers.
Even if there is no information about ratio of clerks to managers for Division Y, it is certain that Division Y has <15% managers.
Ratio of clerks to managers for Division Y >  \frac{85}{15} = \frac{17}{3} = 5 \frac{2}{3} 
Ratio of clerks to managers for Division X < Ratio of clerks to managers for Division Y
SUFFICIENT

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Kritisood · Answer

Hi  VeritasKarishma  could you suggest how to do it with the weighted averages approach as well please?

AkashAvhad · Answer

Kritisood ,

I hope you don't mind if I respond to your query.

Kudos if it helps.

Basics of Average: 
The average of two distinct numbers is always a value between the two numbers.
The average of two identical numbers is always equal to both the numbers.
 In no case , can the average of two numbers be smaller or larger than both the numbers
 Corollary  to above: If one number is greater than the average, then the other number has to be smaller than the average.

We clearly see that both statements individually are insufficient to answer the question.

Let us apply the weighted average logic after combining the two statements:

Since, division X and division Y are the only two divisions in company M, we can say that the % of managers in M is the weighted average of the % of managers in X and that in Y.

Now we know, % of managers in X (20%) is greater than the weighted average (15%).
Using the corollary mentioned above, % of managers in Y should definitely be less than 15%.

Hence, using both statements, we definitely know that ratio of clerks to managers in Y will be greater than that in X.

SUFFICIENT.

Hence C.

P.S.: You notice than only the basic conceptual understanding of averages was required here, to answer the question. No solving was required.

Hope this helped.

KarishmaB · Answer

The note I have given in my solution above is the weighted average approach. You don't need to do anything if you understand weighted averages.

"Note that it doesn't matter how many employees Y has, the percent of managers will be less than 15% since X has 20% managers and total there are 15% managers. So to pull down the overall percentage to 15%, the percentage of managers in Y must be less than 15%. How much exactly will depend on how many employees X and Y have. "

X has 20% managers and overall there are 15% managers so in any case, Y will have less than 15% managers (to make the average 15%). So in any case, ratio of clerks to managers will be higher for Y. 
Answer (C)

weakatstudies · Answer

Approach Using Weighted Average Basics:-

- Suppose there are  X1  employees in division X and  Y1  employees in division Y

- X has 20% managers and whole company has 15% managers(weighted average of two departments(Aw))

- Let M2 be ratio of managers in department Y and M1 be the ratio of managers in department X

then  \frac{X1}{X2}  =  \frac{(M1-Aw)}{(Aw-M2)}

=  \frac{X1}{X2}  =  \frac{(20-15)}{(15-M2)}

since (15-M2) has to be positive, M2 has to be less than 15.

Hence, Aw(weighted average) will always be between lower average and greater average

ProfChaos · Answer

Statements 1 and 2 are INSUFFICIENT alone

Combining S1 and S2 we can plug some values
We know 
- 15% employees in M are Managers
- 20% employees in X are Managers

Lets assume number of employees in M to be 300 
Lets assume number of employees in X are 100   (We can also assume this to be 200)

Thus, C:M division for M is 255:45 and C:M division for X is 80:20 = 4   (160:40 = 4)  
Now even if we dont know any info about employee division in Y we can subtract the above values and find out.
So, C:M for Y would be 175:25 = 7   (95:5 = 19)

Thus the ratio is greater for Y than X

Hence, option C is correct

Pujju13 · Answer

Bumping it up after a long time.
Why did we assume that X and Y have equally distributed employees, it isn't mentioned in the question?

The equation changes if we consider they are not equally distributed.
Let's assume total employees in company M are 100

Let's assume there are 10 employees in division X & 90 employees in division Y

Statement 1:
C_x = 8
M_x = 2

Statement 2:
C_m = 85
M_m = 15

So the ratio for division X would be: C/M = 4
& the Ratio for division Y would be: C/M = 77/13 ~ 6

So according to this scenario, ratio of X < Y

Whereas, when we divide them equally, as described by you, X > Y

So, we cannot answer the question until we know the distribution of employees between X and Y.

Where did I go wrong? Please help!!

sarthak1701 · Answer

You don't even need to jump into calculations, just straight logic (it is a data-sufficiency question after all)

X's ratio is 4:1 (C:M)

Overall company's ratio is 17:3

What would cause the ratio of the overall company to rise more than the ratio of the X department? Only if the ratio of Y (C:M) is higher than X. Ans. C

Vaishbab · Answer

For both scenarios, Y has a higher ratio than X.

Assumption: The company has 100 employees.
For equal distribution, with 50 employees in each division,

Based on statement (1):
Number of managers in division X = 20% of 50 = 10
Number of clerks in division X = 50-10 = 40

Hence, clerk:manager ratio for division X would be 40/10 = 4.

Based on statement (2):
15% of the company's workforce are managers. This means the total number of managers in the company is 15 (considering our 100 employee assumption)

Combining this info from that of statement (1), we can find out the number of managers in division Y = 15-10 = 5.
Therefore, the number of clerks in division Y = 50-5 = 45.

And therefore, the ratio in division Y = 45/5 = 9

As you can see, the ratio of Y is still greater than that of X

Company M has two divisions - X and Y. Each division

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