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30 May 2019, 12:53
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Difficulty:
75%
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Question Stats:
59% (03:02) correct
41%
(03:06)
wrong
based on 64
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In an apartment complex, the number of people aged 51 years and above is 30 and there are at most 39 people whose ages are below 51 years. The average age of all the people in the apartment complex is 38 years. What is the largest possible average age, in years, of the people whose ages are below 51 years?
A. 25
B. 26
C. 27
D. 28
E. 29
A. 25
B. 26
C. 27
D. 28
E. 29
30 May 2019, 13:37
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nick1816
In an apartment complex, the number of people aged 51 years and above is 30 and there are at most 39 people whose ages are below 51 years. The average age of all the people in the apartment complex is 38 years. What is the largest possible average age, in years, of the people whose ages are below 51 years?
A. 25
B. 26
C. 27
D. 28
E. 29
A. 25
B. 26
C. 27
D. 28
E. 29
Let the avg age for people <51 yrs of age = x
We know, Sum of all ages = Avg age of total group * total members = 38n (where, n = total members)
Since, sum will remain the same for 'total group' and for 'group<51' + 'group >=51'
We get,
39x + 30* 51 = 38n
(we assume 51 to be average age for group>=51 since it is the smallest value for this group and thus will enable us to get the largest value for the other group)
x= [(38*69) - (30*51)] / 39
x= 28
Option D.
General Discussion
07 Jun 2019, 01:17
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In the following solution, the two groups of occupants are referred to as Groups A (those whose ages are 51 or more years) and B(those whose ages are below 51 years). It is assumed that the average age and the number of occupants in B are 'x' years and 'y' respectively.
SOLUTION
01. Since the average age of all occupants is fixed it stands to reason that the lowest average age be assumed for the occupants of A in order to maximize the average age of the occupants of B. Thus the total age of all occupants in A is 51*30=1530. Total age of occupants in B is, of course, x*y.
02. (Total age of all occupants in the apartment complex)/(Total number of occupants in the complex)=Average age of all occupants
(1530+xy)/(30+y)=38---> xy=38y-390---> x=(38y-390)/y---> x=38-(390/y). In order to maximize the value of 'x' we have to minimize the value of 390/y which means that we have to maximize the value of 'y'. But the maximum value of 'y' is limited to 39. Therefore:
x=38-(390/39)=38-10=28.
Ans: D
SOLUTION
01. Since the average age of all occupants is fixed it stands to reason that the lowest average age be assumed for the occupants of A in order to maximize the average age of the occupants of B. Thus the total age of all occupants in A is 51*30=1530. Total age of occupants in B is, of course, x*y.
02. (Total age of all occupants in the apartment complex)/(Total number of occupants in the complex)=Average age of all occupants
(1530+xy)/(30+y)=38---> xy=38y-390---> x=(38y-390)/y---> x=38-(390/y). In order to maximize the value of 'x' we have to minimize the value of 390/y which means that we have to maximize the value of 'y'. But the maximum value of 'y' is limited to 39. Therefore:
x=38-(390/39)=38-10=28.
Ans: D
