A certain company consists of three divisions, A, B, and C. Of the emp

Question

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.

ID: 700289
DS87910.02

Kinshook · Accepted Answer

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

itspCv2 · Answer

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

MathRevolution · Answer

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.

PierTotti17 · Answer

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).

PhantomAY · Answer

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

Nipunh1991 · Answer

Statement 1 is insufficient because it gives the information about 2 divisions only. Division C could have a much higher average pulling the combined divisions average to more than 55k. It could also have an average of 46k which would result in the combined average of all 3 divisions to be less than 55k.

Statement 2 is enough to answer the question by itself because C division has the highest average which is 55k. Other divisions are lower than that, which will anyway pull the average below 55k (Can be calculated considering numbers in case the explanation is not clear).

ashishsamant2311 · Answer

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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binarytree · Answer

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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ashishsamant2311 · Answer

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.

CEdward · Answer

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

achloes · Answer

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!

avigutman · Answer

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.

1616 · 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?

Bunuel · Answer

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.

Tat000 · Answer

No need to think A=B=C=$55,000?
In this case C is also the highest.

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satish_sahoo · Answer

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

gmatftw777 · Answer

when the greatest average is given - the overall average immediately falls under the range above the overall average and below the greatest average value given.

A certain company consists of three divisions, A, B, and C. Of the emp

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GMAT Data Sufficiency (DS) Questions

A certain company consists of three divisions, A, B, and C. Of the emp

Prep Toolkit

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