Five employees have different salaries. From least to greatest they ar

Question

Five employees have different salaries. From least to greatest they are a, b, c, d, and e. The average (arithmetic mean) of the five salaries is equal to the median. If each person’s salary is increased by as much as the median salary, the new average is equal to the previous high salary. If the average of a, b, and d is $40,000, what is the sum of c and e?

A. $60,000
B. $80,000
C. $90,000
D. $120,000
E. $180,000

A. $60,000
B. $80,000
C. $90,000
D. $120,000
E. $180,000

chetan2u · Answer

Sum = 5c because AVG is equal to median.

c is the median and e is the highest..
When you add median to each number median becomes the largest number, so c+c=e

a+b+c+d+e=5c..........but a+b+d=3*40000 and e=2c
Thus 3*40000+c+2c=5c..........2c=120000......c=60000
c+e=3c=3*60000=180000

E

EgmatQuantExpert · Answer

Solution 
  Given:  
 • Five employees have different salaries. From least to greatest they are a, b, c, d, and e.
• a < b < c < d < e
• (a + b + c + d + e)/5 = median, which is c ……………….. (1)
•  /5 = e …………………. (2)
• (a + b + d)/3 = $40,000 …………………… (3)

To find:  
 • The value of c + e

Approach and Working:   
 • From (1), we get,
 o a + b + c + d + e = 5c ……………. (4)
 
• From (2), we get,
 o a + b + c + d + e + 5c = 5e
o Substituting (4) in the above equation gives, 
  10c = 5e, that is 
 e = 2c …………………. (5)
  
• From (3), we get,
 o a + b + d = $1,20,000 ………………. (6)
 
• Substituting (5) and (6) in (4), we get,
 o $1,20,000 + c + 2c = 5c
o Implies, c = $60,000
o Thus, e = 2 * $60,000 = $1,20,000

Therefore, the value of c + e = $1,80,000

Hence, the correct answer is option E

Answer: E

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Bismarck · Answer

OA:E

\frac{a+b+c+d+e}{5}=c 
 a+b+c+d+e = 5c  ....(1)
 
 \frac{(a+c)+(b+c)+(c+c)+(d+c)+(e+c)}{5}=e  
 a+b+c+d+e+5c=5e  ....(2)

Substituting  (1)  into  (2) , we get

5c+5c=5e 
 10c=5e; 2c=e .....(3)

\frac{a+b+d}{3}= $ 40,000

a+b+d = 3 * $ 40,000 = $ 120,000 ......(4)

Putting (3) and (4) in (1), we get

(a+b+d)+(c)+e = 5c 
 ($ 120,000)+c+2c = 5c 
 ($ 120,000)= 2c 
 e =2c = $ 120,000

c= \frac{$ 120,000}{2} =$ 60,000

c+e = $ 60,000 + $ 120,000 =$ 180,000

wunstepcloser · Answer

Here was my  plug-in approach  which took 2 minutes and 15 seconds:

I noticed that median = average which only happens when numbers are listed in a consecutive pattern.

I plugged in 10, 20, 30,40, 50 for the salaries but then realized that when I doubled the median (30), I could not get to the highest number (50). I then tried 20, 40 ,60, 80 , 100 and it still did not work when I doubled the median as 120 does not equal 100.

So I re-adjusted my numbers once again so that the last number is twice the median and the numbers still have a pattern: 0, 30 , 60 , 90 ,120. When I doubled 60 I could get 120 and my median and average were the same (60). Therefore I added 60 + 120 (c + e) and got 180. Which in this case is $180,000.

A_Nishith · Answer

Let 5 numbers be : a,b,c,d,e.
Given, (a+b+c+d+e)/5 = Avg. = Median 
Now, Because AVG is equal to median(=c).
=> a+b+c+d+e=5c

c is the median and e is the highest..
When you add median to each number median becomes the largest number, 
=> (a+c),(b+c),(c+c),(d+c),(e+c) 
=> c+c=e

a+b+c+d+e=5c..........but a+b+d=3*40000 and e=2c
=> 3*40000+c+2c=5c..........2c=120000...... c=60000
 
 c+e  =3c=3*60000= 180000

Answer: E

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Five employees have different salaries. From least to greatest they ar

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