While adding the first few continuous natural numbers, a candidate missed one of the numbers and wrote the answer as 177. What was the number missed ?

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Submitted by examrobotsa on

Q: 70 (IAS/2009)
While adding the first few continuous natural numbers, a candidate missed one of the numbers and wrote the answer as 177. What was the number missed ?

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,8,18,7,6,8,5

keywords: 

{'first few continuous natural numbers': [0, 0, 1, 0], 'numbers': [0, 1, 0, 0], 'number': [0, 0, 0, 2]}

The problem is essentially asking for a number that must have been skipped when summing the first few natural numbers resulting in a total of 177. The formula for the sum of the first `n` natural numbers is n*(n+1)/2. The value closest to 177 using this formula comes at n=19, yielding 190. Hence, we subtract 177 from 190, which equals to 13. So, the candidate must have missed the number 13 when adding them up. Looking at the options:

Option 1: 11 - If the missed number was 11, the sum would have been 179, which is not the case.

Option 2: 12 - If the missed number was 12, the sum would have been 178, which isn`t our target number.

Option 3: 13 - As explained above, if the missed number was 13, the sum would be 177 which is our target number.

Option 4: 14 - If the missed number was 14, the sum would have been 176, which isn`t the required total.

Hence, The correct answer is option 3.