Question : If the mean of two numbers is 12, and the difference between the two numbers is 6, find the two numbers.
Option 1: 2 and 22
Option 2: 14 and 10
Option 3: 15 and 9
Option 4: 3 and 24
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Correct Answer: 15 and 9
Solution : Let the two numbers be a and b. Given that the mean of the two numbers is 12, ⇒ $\frac{a + b}{2}$ = 12 ⇒ a + b = 24 ___(1) Given that the difference between the two numbers is 6, ⇒ a – b = 6 ___(2) Adding the above equations, ⇒ 2a = 30 ⇒ a = 15 From equation 2, ⇒ b = a – 6 = 15 – 6 = 9 Hence, the correct answer is 15 and 9.
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Question : What will be the average of all the prime numbers between 9 and 22?
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