Question

Four positive integers are given. Select any three of these integers, find their arithmetic average, and add this result to the fourth integer. Thus the numbers $29,23,21and17$ are obtained. One of the original integers is:

• A. $19$
• B. $21$
• C. $23$
• D. $29$
• E. $17$

Answer 1

Answer: (B)

$21$

Solving the system
$\frac{1}{3}(a+b+c)+d=29;\frac{1}{3}(b+c+d)+a=23$
$\frac{1}{3}(c+d+a)+b=21;\frac{1}{3}(d+a+b)+c=17,$
we obtain $a=12,b=9,c=3,d=21$. Thus (b) is the correct choice.