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Posts: 6,486
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Difficulty:
45%
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Question Stats:
67% (01:54) correct
33%
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wrong
based on 471
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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.
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
_________________
(1) The division X has 10% executives and division Y has 25% executives.
(2) The company M has 15% executives.
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
_________________
ExpertsGlobal5
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
Posts: 6,486
ExpertsGlobal5
Explanation Video:
_________________
Apoorv0194
Joined: 15 Jul 2025
Last visit: 03 Sep 2026
Posts: 139
Location: India
Schools: NUS '26 (WL) Jones '26 (A$$)
GMAT Focus 1: 655 Q85 V82 DI81 
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?
We are getting a ratio of executives, but what about operators?
ExpertsGlobal5
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?
Apoorv0194
DeepGOO225
Joined: 10 Nov 2025
Last visit: 14 Sep 2026
Posts: 32
Location: India
Schools: ESSEC MiM '27 ISB HEC MiM '27
GPA: 3.22
Schools: ESSEC MiM '27 ISB HEC MiM '27
Posts: 32
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 )
MilanaK12
GMAT Focus 1: 615 Q83 V81 DI78 
Posts: 409
DeepGOO225
Yes, your intuition is right. Your allegation method is a perfectly valid
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 = 0.10X + 0.25Y
- Statement (2) says overall executives = 0.15(X + Y)
Setting them equal:
0.10X + 0.25Y = 0.15X + 0.15Y - 0.10Y = 0.05X - 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
_________________
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 = 0.10X + 0.25Y
- Statement (2) says overall executives = 0.15(X + Y)
Setting them equal:
0.10X + 0.25Y = 0.15X + 0.15Y - 0.10Y = 0.05X - 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
MilanaK12
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