Question

Once upon a time and old lady went to sell her eggs at the local market. When asked how many, she had she replied I can't count past 100 but I know that: If you divide the number of eggs by 2 there will be one egg left. If you divide the number of eggs by 3 there will be one egg left If you divide the number of eggs by 4 there will be one egg left. If you divide the number of eggs by 5 there will be one egg left. If you divide the number of eggs by 6 there will be one egg left. If you divide the number of eggs by 7 there will be one egg left. If you divide the number of eggs by 8 there will be one egg left. If you divide the number of eggs by 9 there will be one egg left. If you divide the number of eggs by 10 there will be one egg left. Finally if you divide the number of eggs by 11 there will be no eggs left. How many eggs did the old lady have?

Answer 1

25201 eggs

Explanation:

We are told that when the number is divided by 2, 3, 4, 5, 6, 7, 8, 9, 10 there is 1 egg left.

Thus means we have to find the Least common multiple(L.C.M)

L.C.M of 2, 3, 4, 5, 6, 7, 8, 9, 10 is 2520

Since when divided by the numbers above, we have 1 egg remaining, it means the formula to get the total number of eggs will be;

2520x + 1

Where x is any positive integer.

Now, we are told that when you divide the number of eggs by 11 there will be no eggs left.

This is modulo 11.

It means we have to find the smallest number of X for which 2520x + 1 modulo 11 is 0.

The smallest number will be at x = 10

Thus:

Number of eggs = 2520(10) + 1 = 25201

To confirm this; 25201/11 = 2291

No remainder, so it shows that that is truly the number of eggs