Step 1: Understand the mathematical relationship
Let the sum of first N natural numbers be S. The formula is:
The student added one number (let's call it x) twice. Therefore, the reported sum is:
Since x is one of the numbers from the set {1,2,3,…,N}, we know that 1≤x≤N.
Step 2: Find the approximate value of N
Since x is positive, the actual sum S must be less than 700.
\frac{N(N + 1)}{2} < 700
We look for a number N such that N2≈1400. Since 372=1369 and 382=1444, let's test N=37:
This is already greater than 700, so N must be smaller. Let's test N=36:
Step 3: Calculate the repeated number x
Using N=36 and S=666:
Since x=34 is less than or equal to N=36, this is a valid solution.
Step 4: Find the sum of the digits of x
The number added twice is 34.
Final Answer:
The sum of the digits of the repeated number is 7.
Correct Option: (c)
