Question : Directions: If the sum of three consecutive numbers is 15, what is the square of the middle number?
Option 1: 16
Option 2: 25
Option 3: 36
Option 4: 9
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Correct Answer: 25
Solution : Let the three consecutive numbers be a, (a + 1), and (a + 2).
As per the question, the sum of the three consecutive numbers is 15, then –
⇒ a + a + 1 + a + 2 = 15
⇒ 3a + 3 = 15
⇒ 3a = 15 – 3
⇒ 3a = 12
⇒ a = 12 ÷ 3 = 4
Thus, the value of the middle number = (a + 1) = 4 + 1 = 5, and (5)
2
= 25
So, 25 is the required answer. Hence, the second option is correct.
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