#Numbers-13

If eggs are removed from a basket two, three, four, five, six at a time, there remain respectively one, two, three, four and five eggs respectively. But if eggs are removed seven at a time, no eggs remain. What is the least number of eggs that could have been in the basket?

Solution-

Number of eggs in the basket = 2a+1 = 3b+2 =4c+3 = 5d+4 = 6e+5=7k
Now,common difference among the remainders is 1,
So, number will be of the form = LCM(2,3,4,5,6) - Common Difference
                                                     = 60p - 1
Now, we have to find the least number, (60p -1) must be divisible by 7
for p = 2
60p-1 = 119 is divisible by 7
Hence,119 is the least number of eggs that could have been in the basket.

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