At Happywell, Inc., last year the average annual salary for dieticians

Question

At Happywell, Inc., last year the average annual salary for dieticians was $50,000, while the average annual salary for physical therapists was $42,000. The average annual salary for all Happywell employees last year was $40,000.

If the information above is correct, which one of the following conclusions can properly be drawn on the basis of it?

(A) There were more physical therapists than dieticians at Happywell last year.

(B) There was no dietician at Happy well last year who earned less than the average for a physical therapist.

(C) At least one Happywell employee earned less than the average for a physical therapist last year.

(D) At least one physical therapist earned less than the lowest-paid Happywell dietician last year.

(E) At least one dietician earned more than the highest-paid Happywell physical therapist last year.

Source: LSAT

Lucky2783 · Accepted Answer

This is a weighted average question .

we can have D a set in which salary starts from 1,2,3,4,5,6,7,8,9.... 50000*N  ,
at the same time we can have set P which start with 2,3,4,5,6,7,8,9..... 42000*K  
now we can see there is no element in set P which is lower than the lowest element in set D .

As for answer choice C , why is this correct ? it is correct because if there is no employee who earned less than the average of P group then the average should go above 42000 K . 
it is a weighted avg . question

(50000*D + 42000*K)/(N+K) = 40000
now if none of the member in K earned less than 42000 then this average would never be less than 42000.

aditya8062 · Answer

C it is:   At least one Happywell employee earned less than the average for a physical therapist last year.
 -------->to pull the average down to 40,000, there must be some one who is earning less than the average of 42,000

Ivan91 · Answer

What about D ) ???
Surely, at least one physician needs to earn less than the lowest paid dietitian in ordar to bring the average income of physicians (42 000) to be less than the one of dietitians (50,000) ?

Ivan91 · Answer

What about D ) ???
Surely, at least one physician needs to earn less than the lowest paid dietitian in ordar to bring the average income of physicians (42 000) to be less than the one of dietitians (50,000) ?

TARGET730 · Answer

Ivan91,

Imagine the below situation.
Let's say D is the set of the salary of dieticians D = {Lowest, ----, --- etc} Avg = 50K
Let's say PT is the set of the salary of physical trainers PT = {Lowest, ----, --- etc} Avg = 42K

D says "At least one physical therapist earned less than the lowest-paid Happywell dietician last year."

Dis not necessarily true always. Imagine the lowest pay of PT is 39K. You can still have the lowest paid dietician to earn less than 39K and still average 50K.

hsbinfy · Answer

m happy to answer for the above doubt

C is the correct choice..coz one employee must be earning less than the total average to bring the average package pf the company down.

D and E both are contnders, but my friend there is an equal possibility they can be false.

In MUST BE TRUE/INFERENCE questions the answer should follow from the premises and it should be the only possibility not any possibilty.

C is true in any sense u cant say no to choice C. 
For D ,E u can.So there 's a doubt.

hope it hepls

-h

Lucky2783 · Answer

for E 
atleast 1 dietician earned more than highest paid therapist . 
here is the set of dietician in which none has earned more than highest paid Therapist. 
D=  {50000,50000,50000, 50000, 50000}  Average =50000
PR =  {1,2,3,4,209990}  Average=42000

Kurtosis · Answer

(A) There were more physical therapists than dieticians at Happywell last year. - Incorrect - We cannot infer this

(B) There was no dietician at Happy well last year who earned less than the average for a physical therapist. - Incorrect - We cannot infer this

(C) At least one Happywell employee earned less than the average for a physical therapist last year. - Correct - If the average of Happywell employees is 40k, atleast one employee must earn less than the physical therapist

(D) At least one physical therapist earned less than the lowest-paid Happywell dietician last year. - Incorrect - We cannot infer this

(E) At least one dietician earned more than the highest-paid Happywell physical therapist last year. - Incorrect - We cannot infer this.

Answer: C

daboo343 · Answer

Simple Mathematics
and only answer choice C confirms that

CJWORK · Answer

C is clear to be the answer.

A- we could have agreed, if the passage had said that there are only 2 departments
B - We got too little information
C - Yes! 
D - Could be but cannot say
E - Could be but cannot say

DharLog · Answer

At Happywell, Inc., last year the average annual salary for dieticians was $50,000, while the average annual salary for physical therapists was $42,000. The average annual salary for all Happywell employees last year was $40,000.

If the information above is correct, which one of the following conclusions can properly be drawn on the basis of it?

(A) There were more physical therapists than dieticians at Happywell last year.

(B) There was no dietician at Happy well last year who earned less than the average for a physical therapist.

(C) At least one Happywell employee earned less than the average for a physical therapist last year.

(D) At least one physical therapist earned less than the lowest-paid Happywell dietician last year.

(E) At least one dietician earned more than the highest-paid Happywell physical therapist last year.

All options ecxept C are too extreme. To each one of them we can find counterargument

Source: LSAT
------------

SonalSinha803 · Answer

(A) There were more physical therapists than dieticians at Happywell last year. - clearly uncertain. We don't know about other professionals at Happwell. So, there is a possibility that other professionals are also there or only two of them are there. Eliminate.

(B) There was no dietician at Happy well last year who earned less than the average for a physical therapist. - Really cannot say this. Eliminate.

(C) At least one Happywell employee earned less than the average for a physical therapist last year. - definitely. Only then the overall average is 40000 that is less than 42000 and 50000. Correct.

(D) At least one physical therapist earned less than the lowest-paid Happywell dietician last year. - may be or may be not.

(E) At least one dietician earned more than the highest-paid Happywell physical therapist last year. - may be or may be not.

Thus, C is the best option.

Sent from my Lenovo K53a48 using  GMAT Club Forum mobile app

goaltop30mba · Answer

GMATNinjaTwo   GMATNinja   AjiteshArun

Hey guys

hope you all are doing well.

I have been practising gmat CR for quite sometime and have noticed that i am not too comfortable with quantitative based questions. Hence i decided to practice just these type of questions so as to achieve max possible clarity. Though this isn't an official question, I would still like to understand a certain thing or two about this specific question. First of all, I am aware of the concept of weighted average since it is tested in quant pretty often. I thought i was okay with the concept of weighted averages until this question.

From what i know about the weighted average, it must be close the average of a group with more weight. It is given to us that the overall average is $40000. This overall average salary of both the therapists and the physicians is closer to the average salary of the therapists than to the average of salary of the dieticians. This means that the number the number of therapists must be greater than the number of dieticians.

Is there something more to this concept because i do notice that the weighted average ideally should be between $42000 and $46000, but in this case it is even lower than lowest of the given two averages ie lower than $42000 ?

This also makes me think that is this really a weighted average question?

PS: I know that this isn't an official question, but it will be great if you guys help me with this

looking forward to hearing from you all.

best regards,

Thelionking1234 · Answer

This is basically a weighted average verbal question.

If all employees have the exact average amount as a salary (42000 or 50000) then the overall average would lie in between 42000 and 50000, and not less than 42000. So there must be at least one employee who got the salary less than the average amount.

You can do the same by calculating, assuming a few examples.

hence C is the correct answer.

Trishal · Answer

in this question i also think that option a is correct. if there are 5 therapists and 1 dietician then the average salary will be 40000. will there be any case when a option is negated?

Tifosi · Answer

Answer analysis
A. We cannot infer the number when averages are given. Hence  incorrect 
B. There is the possibility of a dietician to earn less than average of a physical therapist, and then a dietician has a high salary to counter this low salary and still maintain the average. Hence  incorrect 
 C . yes, that is why the average of all employees is lower than any average
D. Consider this case... Two dieticians, one earns 90,000 and the other earns 10,000. Still the average is 50000. Now the other physical therapists all earn 42000 and the average remains 42000. So, this option fails and hence  incorrect 
E. Consider this case... Two physical therapists, one earns 83000 and the other earns 1000. Still the average is 42000. Now the other dieticians all earn 50000and the average remains 50000. So, this option fails and hence  incorrect

CrackverbalGMAT · Answer

Hi Trishal

As per the question stem:

Average salary of dieticians = $ 50,000
Average salary of physical therapists = $ 42,000
Average salary of all employees = $ 40,000

If there were only dieticians and physical therapists (no matter in what number, including the case you have stated), the average salary of all employees cannot be $40,000 - it has to be between $50,000 and $42,000. For the case you have stated, the average salary would be $43,333.

Therefore, for average salary of all employees to be $40,000, there must be other employees whose average salary is <$40,000.

Option (A) states that there were more physical therapists than dieticians. We cannot be sure of this as this. For example, consider the following case:

Number of dieticians = 1
Number of physical therapists = 1
Number of other employees = 3
Average salary of other employees = $36,000

This would satisfy the conditions given in the stimulus, and there aren't more physical therapists than dieticians. Hope this clarifies.

hientranzx · Answer

At Happywell, Inc., last year the average annual salary for dieticians was $50,000, while the average annual salary for physical therapists was $42,000. The average annual salary for all Happywell employees last year was $40,000.

dieticians: $50,000
therapists: $42,000
all employees: $40,000 
--> There are someone who salary is lower than S40,000 --> C is the correcct one

If the information above is correct, which one of the following conclusions can properly be drawn on the basis of it?

(A) There were more physical therapists than dieticians at Happywell last year.

(B) There was no dietician at Happy well last year who earned less than the average for a physical therapist.

(C) At least one Happywell employee earned less than the average for a physical therapist last year.

(D) At least one physical therapist earned less than the lowest-paid Happywell dietician last year.

(E) At least one dietician earned more than the highest-paid Happywell physical therapist last year.

BLTN · Answer

Just a small adjustment to the nice explanation given by Lucky2783.
Why A cannot be inference?

From the stimulus we can infer that if the average of dieticians 50k and av of physical therapistsis 42k then the total averave will be between 50k....... 42k

Concerning the answer A
 
How it can be the case that the total average something between 50k....... 42k but the actual is 40?
So, there is another group of workers whose salary below the 42k.
In this case, we cannnot deduce # of "physical therapists"> that of "dieticians" or not. 
Because we need 3d group with average below 42k to match the argument.

Hence, the equation will be following,

(50000*N + 42000*K + "<42k"*NG ) /(N+K+NG) = 40000
Where NG is a NewGroup

At Happywell, Inc., last year the average annual salary for dieticians

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At Happywell, Inc., last year the average annual salary for dieticians

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