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 :
Sum & Product of Consecutive Integers
Problem Part 1 – Five Consecutive Integers
Let’s say the first integer is x.
The next four numbers are: x+1, x+2, x+3, and x+4
The sum of these five numbers is 5x + 10
If this sum equals 100, then:
5x + 10 = 100
Solving for x: x = 18
Therefore, the five consecutive integers are: 18, 19, 20, 21, 22
Problem Part 2 – Numbers 1, 2, and 3
Sum: 1 + 2 + 3 = 6
Product: 1 × 2 × 3 = 6
Conclusion:
Both statements are correct since:
1. We found five consecutive integers that sum to 100
2. For numbers 1, 2, and 3, their sum equals their product
