Q. 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?
(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2
Correct Answer: (c) Both 1 and 2
Question from UPSC Prelims 2021 CSAT Paper
Explanation :
5 Consecutive Integers Sum
Let’s say the first of these consecutive integers is x. Then the next four are x+1, x+2, x+3, and x+4. The sum of these five numbers is 5x + 10.
If this sum is equal to 100, then we have the equation 5x + 10 = 100. Solving for x gives us x = 18.
So one possible set of five consecutive integers that add up to 100 is {18, 19, 20, 21, 22}. Therefore statement 1 is correct.
Considering statement 2:
We know that, 1 + 2 + 3 = 6 And 1 × 2 × 3 = 6
So, Statement 2 is correct too.
