Company M has two divisions X and Y. Both the divisions have exactly

Question

Company M has two divisions – X and Y. Both the divisions have exactly two types of employees – operators and executives. Is the total number of employees in Division X greater than that in division Y?
 
(1) The division X has 10% executives and division Y has 25% executives.
(2) The company M has 15% executives.

This is a  Data Sufficiency Butler Question

Check the links to other Butler Projects:

Problem Solving Butler  
  Data Sufficiency Butler  
  Critical Reasoning Butler  
  Reading Comprehension Butler  
  Data Insights Butler

Dereno · Answer

Company M has two types of divisions ; and in each divisions there are exactly 2 types of Employees - Operators and Executives.

Is the total number of employees in Division X greater than that in division Y ?

Statement 1:

The division X has 10% executives and division Y has 25% executives.

Since we don’t know the total values of Division X and Division Y.

We cannot find the any concrete from this statement.

Hence,  Insufficient

Statement 2:

The company M has 15% executives.

This explains the total % of executives in Company M.

Since, we don’t know the total value of Employees in M.

Hence,  Insufficient

Combining both statements, we can use alligations.

10% ————- 15% —————— 25%

Company X : Company Y

10 : 5

2 : 1.

we can clearly say population of Division X is greater than Population of Division Y.

Hence,  Sufficient

Option C

ExpertsGlobal5 · Answer

Explanation Video:

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

Apoorv0194 · Answer

Isn't the question asking  "Total number of employees in Division X greater than that in division Y?"

We are getting a ratio of executives, but what about operators?

MilanaK12 · Answer

It was my question as well, don't we have to know information about operators as well? It might be the case that division Y has significantly larger amount of operators making the total amount of employees bigger as well. Could someone clarify why E still is not the correct answer?

DeepGOO225 · Answer

Its just a guess that if 15% of company m are executives the the rest 85% (the percentage to total employee has to be 100%)are operators so in case of x its 90% operators (the total employee in x out of which 10% are executives) and i case of y its 75% operators so when we use alligation method 90 ------------ 85 ------------ 75 the ratio is still 10:5 that is 2:1. Even then the percent of operators in x is greater than y. (This is just my thinking process )

FrozenDragon · Answer

Yes, your intuition is right. Your allegation method is a perfectly valid

egmat · Answer

Hi MilanaK12,

I can see exactly where this is snagging. You're picturing operators as a separate, unknown pile that could tip the totals in Y's favor. But here's the key:  operators are already inside the totals , so you don't need a separate count for them.

When Statement ( 1 ) says Division X is  10%  executives, that automatically means the other  90%  are operators. Same for Y:  25%  executives, so  75%  operators. The percentages are taken out of the  whole  division - total employees, operators and executives combined. So the operator count isn't missing; it's built into X and Y already.

Now let X and Y be the  total  employees in each division. The executives must add up:

- Executives =  0.10 X +  0.25 Y
- Statement ( 2 ) says overall executives =  0.15 (X + Y)

Setting them equal:

0.10 X +  0.25 Y =  0.15 X +  0.15 Y -  0.10 Y =  0.05 X -  X = 2Y

That's a locked ratio, so X is always bigger. Operators never needed their own equation.

Your worry, tested directly  - can Y be the bigger division?

- Try  Y = 100, X = 200 : execs =  25  +  20  =  45 , out of  300  total =  15% . Works, and X > Y.
- Try to flip it,  Y = 200, X = 100 : execs =  50  +  10  =  60 , out of  300  =  20% . This breaks Statement ( 2 )'s  15% .

Any attempt to load Y up with more people pushes the overall executive rate off  15% , because Y is executive-heavy ( 25% ) and X is executive-light ( 10% ). The  15%  blend can only sit where X is twice Y.

So the two statements together pin the answer to a definite  yes  - that's why it's  C , not E.

Answer: C

Company M has two divisions X and Y. Both the divisions have exactly

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

GMAT Data Sufficiency (DS) Questions

Company M has two divisions X and Y. Both the divisions have exactly

Prep Toolkit

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