Question

A woman was carrying a basket of eggs to the market whena passerby bumped her. She dropped tha basket and all the eggs broke. The passerby, wishing to pay for her lose, asked, '' How many eggs were in your basket?'' " I don't remember exactly'', the woman replied, '' but i do recall that when the i divided number of eggs by 2,3,4,6, there was an egg left over. When i divided the number of eggs by 5 one is more. And also when i took the out in groups of seven, it emptied the basket''. How many eggs are there in the basket? Happy Independance Day

Answer 1

the no. is 49 because when2,3,4,6 is divided by 49 one is left. When 5 is divided with 49 it is one more. that means 50.When 7 is divided it is emptied. Same to you Happy Independance day!!

Answer 2

Let us derive this result  using Algebra.

Number is N.     LCM of 2,3,4,6 =  12.

N = 12 k + 1       for some  k.       --- (1)
N =  5 m - 1     for some  m.         --- (2)

1)  12 k +2  = 5m        =>    5 (m - 2k) = 2 (k+1)
      so   m - 2k  is a multiple of 2    and    k+1  is a multiple of 5.
      So   k = 4, 9, 14, 19 ....
      So   m = 8, 10, 12, 14, 16,...

Then  possible values for N are:  
    49,109,169,229,289,349,409,469... 39,49,59,69,79,89,99,109,119 ...

2)  Check which of these are divisible by 7 and satisfies the conditions.

The number of  eggs:   49  or  469  or  889   ...