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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Question : If the square of the sum of three positive consecutive natural numbers exceeds the sum of their squares by 292, what is the largest of the three numbers?
Option 1: 5
Option 2: 6
Option 3: 3
Option 4: 8
Question : The sum of three consecutive integers is 51. The middle one is:
Option 1: 14
Option 2: 15
Option 3: 16
Option 4: 17
Question : The sum of three consecutive even numbers is 28 more than the average of these three numbers. Then the smallest of these three numbers is:
Option 1: 6
Option 2: 12
Option 3: 14
Option 4: 16
Question : If the three numbers in the ratio 3 : 2 : 5 such that the sum of the squares is equal to 1862, then which number is the middle one?
Option 2: 14
Option 3: 13
Option 4: 15
Question : The sum of two numbers is equal to 25 and their difference is 20. The ratio of the two numbers is:
Option 1: 9 : 1
Option 2: 7 : 9
Option 3: 3 : 5
Option 4: 2 : 7
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