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605-655 (Medium)|   Statistics and Sets Problems|   Word Problems|                  
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A certain company consists of three divisions, A, B, and C. Of the emp 28 Apr 2020, 04:47
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A certain company consists of three divisions, A, B, and C. Of the employees in the three divisions, the employees in Division C have the greatest average (arithmetic mean) annual salary. Is the average annual salary of the employees in the three divisions combined less than $55,000 ?

(1) The average annual salary of the employees in Divisions A and B combined is $45,000.
(2) The average annual salary of the employees in Division C is $55,000.


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DS87910.02­
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A certain company consists of three divisions, A, B, and C. Of the emp 28 Apr 2020, 04:53
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parkhydel
A certain company consists of three divisions, A, B, and C. Of the employees in the three divisions, the employees in Division C have the greatest average (arithmetic mean) annual salary. Is the average annual salary of the employees in the three divisions combined less than $55,000 ?

(1) The average annual salary of the employees in Divisions A and B combined is $45,000.
(2) The average annual salary of the employees in Division C is $55,000.


DS87910.02
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Given:
1. A certain company consists of three divisions, A, B, and C.
2. Of the employees in the three divisions, the employees in Division C have the greatest average (arithmetic mean) annual salary.

Asked: Is the average annual salary of the employees in the three divisions combined less than $55,000 ?

(1) The average annual salary of the employees in Divisions A and B combined is $45,000.
Since the average annual salary of the employees in Divisions C is unknown
NOT SUFFICIENT

(2) The average annual salary of the employees in Division C is $55,000.
Since, of the employees in the three divisions, the employees in Division C have the greatest average (arithmetic mean) annual salary.
The average annual salary of the employees in Divisions A and B combined is less than $55,000.
The average annual salary of the employees in the three divisions combined is less than $55,000.
SUFFICIENT

IMO B
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A certain company consists of three divisions, A, B, and C. Of the emp 12 May 2020, 06:05
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parkhydel
A certain company consists of three divisions, A, B, and C. Of the employees in the three divisions, the employees in Division C have the greatest average (arithmetic mean) annual salary. Is the average annual salary of the employees in the three divisions combined less than $55,000 ?

(1) The average annual salary of the employees in Divisions A and B combined is $45,000.
(2) The average annual salary of the employees in Division C is $55,000.


DS87910.02
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Straight to point:
Given C>A,B(average salaries)
Is (Aa+Bb+Cc)/a+b+c<55000?(a,b,c are number of people)

1) Aa+Bb/a+b=45k ; no info about C n c

2)C=55000; & we know C has highest average >>>> A,B has less than this>>>> Overall average will be less than 55000 :)

Therefore B is the answer

HOPE THIS HELPS

Thanks :thumbsup:
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A certain company consists of three divisions, A, B, and C. Of the emp 30 Apr 2020, 22:32
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parkhydel
A certain company consists of three divisions, A, B, and C. Of the employees in the three divisions, the employees in Division C have the greatest average (arithmetic mean) annual salary. Is the average annual salary of the employees in the three divisions combined less than $55,000 ?

(1) The average annual salary of the employees in Divisions A and B combined is $45,000.
(2) The average annual salary of the employees in Division C is $55,000.


DS87910.02
Show more

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

Since the division C has the greatest average annual salary, the combined average is less than that of division C.
Then the combined average is less than $55,000 and condition 2) is sufficient since C has the average $55,000 from condition 2).
Thus condition 2) is sufficient, since it yields a unique answer.

Condition 1)
Since we don’t know the annual salary of the division C and the numbers of employees in divisions A, B and C, condition 1) does not yield a unique solution, it is not sufficient.

Therefore, B is the answer.
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A certain company consists of three divisions, A, B, and C. Of the emp 12 May 2020, 17:28
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Not sure why 1) isn't sufficient. The question stem already gives us that employees in division C have the greatest average salary.

Divisions A and B have a combined salary of 45,000 and we don't care which division is greater. If we divide evenly, both groups have 22.5k as an average salary. If C were just 0.01 greater than 22.5k, we would still get "no" as an answer to the question (I.e. all groups having around 22.5k in average salaries).
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A certain company consists of three divisions, A, B, and C. Of the emp 23 May 2020, 19:00
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parkhydel
A certain company consists of three divisions, A, B, and C. Of the employees in the three divisions, the employees in Division C have the greatest average (arithmetic mean) annual salary. Is the average annual salary of the employees in the three divisions combined less than $55,000 ?

(1) The average annual salary of the employees in Divisions A and B combined is $45,000.
(2) The average annual salary of the employees in Division C is $55,000.


DS87910.02
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This question basically asks about the relationship between average of total set and average of subsets. 2 things to keep in mind

  • the average of total <> the average of averages of subsets
  • if the one of the subsets have the greatest subset average x, then the average of total <= x

Now approach the conditions

1) we know the average of subset (A + B), but we don't know about division C (which has the greatest divisional average, could be $100,000 or $50,000), insufficient - BCE
2) BINGO, the greatest divisional average is given, and based on rule#2 the average of total <=$55,000, sufficient - correct answer is B
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A certain company consists of three divisions, A, B, and C. Of the emp 18 Dec 2020, 00:42
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PierTotti17
Not sure why 1) isn't sufficient. The question stem already gives us that employees in division C have the greatest average salary.

Divisions A and B have a combined salary of 45,000 and we don't care which division is greater. If we divide evenly, both groups have 22.5k as an average salary. If C were just 0.01 greater than 22.5k, we would still get "no" as an answer to the question (I.e. all groups having around 22.5k in average salaries).
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1 is not enough because the question stem tells us simply that the average of 3rd group is higher. It doesn't tell us the amount. For an instance, if the average of third group is 1mil, then average of all 3 will be greater than 55k. If however, the average of the 3rd group is 55k (the highest) then the net average should be less than 55k.

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A certain company consists of three divisions, A, B, and C. Of the emp 28 Dec 2020, 23:41
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Why can't we consider the fact that if Average of A=Average of B=Average of C ,still we can call the average of C to be the greatest among the three.

In that case shouldn't C be the answer?

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A certain company consists of three divisions, A, B, and C. Of the emp 29 Dec 2020, 00:49
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binarytree
Why can't we consider the fact that if Average of A=Average of B=Average of C ,still we can call the average of C to be the greatest among the three.

In that case shouldn't C be the answer?

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Let's assume that your assumption is correct (it isn't, the question doesn't say that avg a= avg b= avgc. the question stem says average of A and B together is 45). The question stem tells you that C is the highest. Which implies A and B are atleast 1 less than avergae of C. B now tells you just the average of C (the highest average). And asks if average of 3 numbers, of which 2 are less than $55k(let's assume 54999 and 54999) and $55k is greater than 55k. This will never be possible, irrespective of the number of people in either of the groups. Please drop me a message if you still don't get it and Kudos if you did.
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A certain company consists of three divisions, A, B, and C. Of the emp 02 May 2021, 10:04
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Nice trap and I fell for it.

A certain company consists of three divisions, A, B, and C. Of the employees in the three divisions, the employees in Division C have the greatest average (arithmetic mean) annual salary. Is the average annual salary of the employees in the three divisions combined less than $55,000 ?

Sa = average annual salary of division A
Sb = average annual salary of division B
Sc = average annual salary of division C
A = # of employees in A
B = # of employees in B
C = # of employees in C

SaA + SbB + ScC / A + B + C

(1) The average annual salary of the employees in Divisions A and B combined is $45,000.
Sa + Sb / 2 = 45000
Insufficient...still lots of unknowns

(2) The average annual salary of the employees in Division C is $55,000.
The weighted average of all the salaries is necessarily < 55,000

B
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A certain company consists of three divisions, A, B, and C. Of the emp 28 Jan 2023, 06:58
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avigutman

I'd love to see your reasoning-based approach for this question.

I picked E because I felt that we needed more info such as the total sum and total quantities of the three sets. I think I understand the logic for how to deal with averages of sets after reading the responses but I'd appreciate your input so I can solidify my understanding.

Thanks in advance! :please:
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A certain company consists of three divisions, A, B, and C. Of the emp 28 Jan 2023, 09:01
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achloes
avigutman

I'd love to see your reasoning-based approach for this question.

I picked E because I felt that we needed more info such as the total sum and total quantities of the three sets. I think I understand the logic for how to deal with averages of sets after reading the responses but I'd appreciate your input so I can solidify my understanding.

Thanks in advance! :please:
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This question is asking about the average of three averages, achloes.
Logically, the answer must lie somewhere within the range of those three averages (below the greatest and above the smallest of the three).
We are told in the free info that C is the greatest, so the answer must be lower than that.
Since the question is a YES/NO inequality question, we can rephrase the question to: is C lower than $55k (keeping in mind that if C isn't lower than $55k we'd need more info)?
Then I start with statement (2) obviously, because it provides a definitive YES.
Statement (1) must allow for the possibility of a YES (since statement (2) gave a definitive YES - see here for further explanation) so I just have to show that statement (1) also allows for the possibility of a NO. Well, if C is $1,000,000,000,000 (for example), that would be a NO.
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A certain company consists of three divisions, A, B, and C. Of the emp 20 Jul 2024, 22:15
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MathRevolution

parkhydel
A certain company consists of three divisions, A, B, and C. Of the employees in the three divisions, the employees in Division C have the greatest average (arithmetic mean) annual salary. Is the average annual salary of the employees in the three divisions combined less than $55,000 ?

(1) The average annual salary of the employees in Divisions A and B combined is $45,000.
(2) The average annual salary of the employees in Division C is $55,000.


DS87910.02
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

Since the division C has the greatest average annual salary, the combined average is less than that of division C.
Then the combined average is less than $55,000 and condition 2) is sufficient since C has the average $55,000 from condition 2).
Thus condition 2) is sufficient, since it yields a unique answer.

Condition 1)
Since we don’t know the annual salary of the division C and the numbers of employees in divisions A, B and C, condition 1) does not yield a unique solution, it is not sufficient.

Therefore, B is the answer.
Show more
­Hello MathRevolution, Bunuel

For the statement number 2, I am still confused, How just on the information that C has avg of 55000 dollar and C is the greatest(highlighted above), How are we concluding that we Combined average will be less than C? Can you please explain?
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A certain company consists of three divisions, A, B, and C. Of the emp 21 Jul 2024, 02:42
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MathRevolution

parkhydel
A certain company consists of three divisions, A, B, and C. Of the employees in the three divisions, the employees in Division C have the greatest average (arithmetic mean) annual salary. Is the average annual salary of the employees in the three divisions combined less than $55,000 ?

(1) The average annual salary of the employees in Divisions A and B combined is $45,000.
(2) The average annual salary of the employees in Division C is $55,000.


DS87910.02
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

Since the division C has the greatest average annual salary, the combined average is less than that of division C.
Then the combined average is less than $55,000 and condition 2) is sufficient since C has the average $55,000 from condition 2).
Thus condition 2) is sufficient, since it yields a unique answer.

Condition 1)
Since we don’t know the annual salary of the division C and the numbers of employees in divisions A, B and C, condition 1) does not yield a unique solution, it is not sufficient.

Therefore, B is the answer.
­Hello MathRevolution, Bunuel

For the statement number 2, I am still confused, How just on the information that C has avg of 55000 dollar and C is the greatest(highlighted above), How are we concluding that we Combined average will be less than C? Can you please explain?
Show more
­
The average salary of the combined group will always be somewhere between the lowest and highest averages. For example, if the average salaries of groups are $10,000, $20,000, and $55,000, then the average salary of the combined group will be somewhere between $10,000 and $55,000. Since, according to the stem, the average salaries in divisions A and B are less than that in division C, the overall average when combined will be less than $55,000 because the divisions with lower average salaries will drag the combined average down.

Hope it's clear.
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A certain company consists of three divisions, A, B, and C. Of the emp 23 Oct 2024, 23:21
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It is very easy to fall in the C-Trap here, if we don't think this logically.

Avg will always lie between the set of elements and shift towards a more heavier weight, if there is one.

Since, C is greatest, it means A & B are smaller, so avg will lie between (something less than 55k) to (55k) and cannot surpass 55k mark.

Hence, B
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A certain company consists of three divisions, A, B, and C. Of the emp Updated on: 21 May 2026, 10:55
Originally posted by KevinMercurio on 21 May 2026, 10:38.
Last edited by Bunuel on 21 May 2026, 10:55, edited 1 time in total.
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What I'm confused on is what if they are all 3 equal? In that case C is the correct answer, what if they are all the greatest? Thus, all 3 are equal to $55K.
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A certain company consists of three divisions, A, B, and C. Of the emp 21 May 2026, 10:57
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What I'm confused on is what if they are all 3 equal? In that case C is the correct answer, what if they are all the greatest? Thus, all 3 are equal to $55K.
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“Greatest” means C is higher than A and higher than B. If all three averages were equal, then C would not have the greatest average.

So with statement (2), if C’s average is $55,000, then A and B must each be less than $55,000, and the combined average must be less than $55,000.
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A certain company consists of three divisions, A, B, and C. Of the emp 02 Jun 2026, 03:50
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I don't understand why the answer isnt D, as A alone and B alone satisfy the equation. A tells us that the sum of the two A+B is 45000, so if they were even half, it would be 22.5k so even the value of all three as 22.5k, 22.5k and 22501 would be greater than 55k.
parkhydel
A certain company consists of three divisions, A, B, and C. Of the employees in the three divisions, the employees in Division C have the greatest average (arithmetic mean) annual salary. Is the average annual salary of the employees in the three divisions combined less than $55,000 ?

(1) The average annual salary of the employees in Divisions A and B combined is $45,000.
(2) The average annual salary of the employees in Division C is $55,000.


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A certain company consists of three divisions, A, B, and C. Of the emp 02 Jun 2026, 16:44
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curatelycurious
I don't understand why the answer isnt D, as A alone and B alone satisfy the equation. A tells us that the sum of the two A+B is 45000, so if they were even half, it would be 22.5k so even the value of all three as 22.5k, 22.5k and 22501 would be greater than 55k.

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Statement (1) is not sufficient.

Suppose each division has 1 employee.

Case 1: A = $44,000, B = $46,000, and C = $50,000. Then A and B combined average $45,000, C has the greatest average, and the overall average is less than $55,000.

Case 2: A = $44,000, B = $46,000, and C = $1,000,000. Then A and B combined still average $45,000, C still has the greatest average, but the overall average is greater than $55,000.

So statement (1) is not sufficient.
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