Maths Class!!

Number Theory Level 2

One day, in my maths class, my teacher wrote six variables a,b,c,d, e and f on the blackboard. She said " Let a, b, c, d, e and f be six consecutive integers. When one of them is erased, the sum of the remaining five integers is 2014. You have to find the sum of the digits of the integer that was erased".

She gave the class 10 minutes to the class to figure out the question. Then she asked me to give the answer.

But I was clueless! Can you help me find the answer?


The answer is 5.

Krishna Ramesh by Krishna Ramesh , 22, India

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2 solutions

Ramiel To-ong
Sep 29, 2015

nice approach

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Krishna Ramesh
May 4, 2014

Let the numbers be x, x+1, x+2, x+3, x+4 and x+5.

So, now we have to remove one of these integers such that the sum of the remaining integers is equal to 2014 and x comes as a whole number

By, trial and error, on removing x+1, we get 5x+14=2014 which gives us x=400

so, the removed integer is 401, having sum of digits=5.

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