A number theory problem by Jai Gupta

Number Theory Level 3

A pack contains N card numbered from1 to N. Two consecutive numbered card are removed from the pack and the sum of the numbers on the remaning cards is 1224.if the smaller of the numbers on the removed cards is K then K-20 is??

Note :an IIT JEE problem 2013


The answer is 5.

Jai Gupta by Jai Gupta , 22, India

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2 solutions 

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for N in range(1,101):
    for K in range(1,101):
        num = N*(N+1)/2 - 2*K - 1
        if num == 1224:
            print K
            print N

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Ansh Bhatt
Nov 2, 2014

N(N+1)/2 - 2K - 1 = 1224........ N(N+1)/2 = 1225 + 2K....... 50 is the smallest value of N which satisfies this equation......... thus we get, 4K = 100.........
thus K - 20 = 5

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