Question

Consider the following statements :

1. The sum of 5 consecutive integers can be 100.

2 The product of three consecutive natural numbers can be equal to their sum.

Which of the above statements is/are correct ? 

1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2

Answer 1

Correct Answer - Option 3 : Both 1 and 2

 

Let us assume 5 consecutive numbers as n - 2, n - 1, n, n + 1, n + 2

⇒ (n - 2) + (n - 1) + n + (n + 1) + (n + 2) = 100

⇒ 5n = 100 

⇒ n = 20

So the numbers are 18, 19, 20, 21, 22 and statement 1 is correct.

Let us assume 3 consecutive numbers as n - 1, n, n + 1

⇒ (n - 1) + n + (n +1) = (n - 1)× n× (n + 1)

⇒ 3n = n³ - n

⇒ n(n² - 4) = 0 ⇒ n = 0 or n = -2 or n =2

Since number are natural so n = 0 and n = -2 is not possible,

So, the numbers are 1, 2 and 3 and statement 2 is correct.

Hence, option 3 is correct.