The sum of thirty-two consecutive natural numbers is a perfect square. What is the least possible sum of the smallest and the largest of the thirty-two numbers?

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Solution

The correct option is C 49
Let the numbers be $a, a + 1, a + 2, . . . . . ., a + 31.$
Sum of these numbers $32 a + \frac{31 \times 32}{2} = 16 (2 a + 31)$
As 16 is a perfect square, the least possible value of 2a + 31 = 49.
Therefore, a = 9 and a + 31 = 40.
The least possible sum = 49.

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The sum of thirty-two consecutive natural numbers is a perfect square. What is the least possible sum of the smallest and the largest of the thirty-two numbers?

The correct option is C 49Let the numbers be a,a+1,a+2,......,a+31. Sum of these numbers 32a+31×322=16(2a+31) As 16 is a perfect square, the least possible value of 2a + 31 = 49. Therefore, a = 9 and a + 31 = 40. The least possible sum = 49.

The correct option is C 49
Let the numbers be $a, a + 1, a + 2, . . . . . ., a + 31.$
Sum of these numbers $32 a + \frac{31 \times 32}{2} = 16 (2 a + 31)$
As 16 is a perfect square, the least possible value of 2a + 31 = 49.
Therefore, a = 9 and a + 31 = 40.
The least possible sum = 49.