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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