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 the last numbers is 4. What is the average of the three numbers?
Option 1: 2
Option 2: 3.5
Option 3: 3
Option 4: 2.5
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Correct Answer: 3
Solution : Let the numbers in order be a, b, and c. According to the question, a + b = 2 × 2 = 4-----------(i) b + c = 2 × 3 = 6-----------(ii) c + a = 2 × 4 = 8-----------(iii) On adding (i), (ii), and (iii), we get, 2 (a + b + c) = 4 + 6 + 8 = 18 $\therefore$ a + b + c = $\frac{18}{2}$ = 9 So, the required average = $\frac{9}{3}$ = 3 Hence, the correct answer is 3.
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