Question

There are between 50 and 60 eggs in a basket. When Mohammed counts by 3's, there are 2 eggs left over. When he counts by 5's there are 4 left over. How many eggs are there in the basket?

Answer 1

Hello There!

3 : 48, 51, 54, 57, 60
5: 50, 55, 60

Choose a number that satisfies both:

59

When divided by 3 it has a remainder of 2
When divided by 5 it has a remainder of 4.

There are 59 eggs in the basket.

Hope This Helps You!
Good Luck :)

Answer 2

The correct answer is:

59

Step-by-step explanation:

The numbers between 50 and 60 that are divisible by 3 are

51, 54, 57, 60

The numbers between 50 and 60 that are divisible by 5 are

50, 55, 60

We know that when he counts by 3s, he has 2 left over; this means the number he counts to is 2 fewer than the number of eggs. This means, counting by 3s, we could have

51+2, 54+2, 57+2, or 60+2 = 53, 56, 59, 62

62 is not an option, since we know we have between 50 and 60 eggs; this gives us 53, 56 or 59.

We also know that when he counts by 5s, he has 4 left over; this means the number he counts to is 4 fewer than the number of eggs. This means, counting by 5s, we could have

50+4, 55+4, 60+4, or 54, 59, 64

64 is not an option, since we know we have between 50 and 60 eggs; this gives us 54 or 59.

The only number in both lists is 59, so this must be the answer.