Adam's age is a multiple of 10 this year.
His age 7 years ago was a multiple of 7.
Adam's age is between 70 and 80.
- In how many years' time will Adam's age be a multiple of 4?
- How many years ago was Adam's age a multiple of 3?
(a)
Multiple of 10: 10, 20, 30, 40, 50, 60, 70
Multiple of 10 (-7): 3, 13, 23, 33, 43, 53, 63
Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63
Adam's age this year = 70
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72
Number of years' time when Adam will be a multiple of 4
= 72 - 70
= 2
(b)
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69
Least number of years ago when Adam's age was a multiple of 3
= 70 - 69
= 1
Answer(s): (a) 2; (b) 1