anothor brain teaser better than the last?

Question

there are fewer than 6 DOZEN blow popos in my bag if i count by 2's there is 1 left over if i count by 3's there are 2 left over there is 3 left over if i count by 4's four are left over if i cont by 5's how many blow pops are in my bag

Answer 1

Since 4 is a multiple of 2, (that is, any number, into which four will go evenly, so too with 2) we will disregard 2.

If we then find the common multiple of 3, 4, and 5: 3x4x5=60. If we have one less than any multiple of a number, then that number will divide into the "one less than multiple" number, leaving a remainder one less than the divisor (number).

Thus, of 59:
59 / 5 = 11 and 4/5
59 / 4 = 14 and 3/4
59 / 3 = 19 and 2/3
59 / 2 = 29 and 1/2

Answer 2

59

Answer 3

49

Answer 4

61