A number, x, equals 80% of the average of 5, 7, 14 and a number y. If

Question

A number, x, equals 80% of the average of 5, 7, 14 and a number y. If the average of x and y is 26, then what is the value of y ?

(A) 13 
(B) 26
(C) 39
(D) 40
(E) 41

ash124 · Answer

Understand the Question: 
  x = .8(5+7+14+y)/4. --(1)
 (x +y)/2 = 26--(2) 
 The value of y ?

Solve eqn. (1) & (2)
x-.2y =5.2
x + y = 52
Sub. (1) - (2)
1.2y = 46.8 
  y = 39

Answer: C

chiefab · Answer

---> x=0.8*(26+y)/4
 5x-y=26...i
----> (x+y)/2=26
 x+y=52
 x=52-y...ii

Solve for y; y=39

IMO answer is (c)39

BrushMyQuant · Answer

Theory

➡ Average or Arithmetic Mean = Sum of all the Values / Total Number of Values 
 ➡ Sum of All the values = Average * Total Number of Values

A number, x, equals 80% of the average of 5, 7, 14 and a number y

Average of 5, 7, 14 and y =  \frac{Sum}{4} 
=> Average of 5, 7, 14 and y =  \frac{5 + 7 + 14 + y}{4}  =  \frac{26 + y}{4}

x = 80% of the Average of 5, 7, 14 and y = 80% * Average of 5, 7, 14 and y =  \frac{80}{100}  *  \frac{26 + y}{4} 
=  \frac{4}{5}  *  \frac{26 + y}{4}  =  \frac{26 + y}{5}

=> x =  \frac{26 + y}{5}  ...(1)

The average of x and y is 26

Average =  \frac{Sum}{2}  =  \frac{x + y}{2}  = 26
=> x + y = 26*2 = 52

Substituting value of x from (1) we get

\frac{26 + y}{5}  + y = 52
=>  \frac{26 + y + 5y}{5}  = 52
=> 26 + 6y = 5*52 = 260
=> 6y = 260 - 26 = 234
=> y =  \frac{234}{6}  = 39

So,  Answer will be C .
Hope it helps!

Watch the following video to Learn the Basics of Statistics

https://www.youtube.com/watch?v=Cvy_HHw4KIs

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