Question : Three numbers are such that the average of the first two numbers is 2, the average of the last two numbers is 3 and the average of the first and last number is 4, then the average of the three numbers is equal to:
Option 1: 2
Option 2: 3.5
Option 3: 3
Option 4: 2.5
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Correct Answer: 3
Solution :
Let the three numbers be $x,y,$ and $z$.
The average of the first two numbers is 2.
$⇒x+y=2×2=4$
The average of the last two numbers is 3 and the average of the first and last numbers is 4.
$⇒y+z=2×3=6$
$⇒x+z=2×4=8$
Adding the above equations, we get,
$2(x+y+z)=18$
$\therefore (x+y+z)=9$
So, the average of three numbers $=\frac{(x+y+z)}{3}=\frac{9}{3}=3$
Hence, the correct answer is 3.
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