Since her age divided by 7 results in a remainder of 0, her age must be a multiple of 7. If her age is $ n $, we notice that $ n-1 $ must be a multiple of 2, 3, 4, and 6. The least common multiple of those numbers is 12, so $ n-1 $ must be a multiple of 12. The multiples of 12 less than 75 are 12, 24, 36, 48, and 60. Adding 1 results in 13, 25, 37, 49, and 61, where 49 is the only multiple of 7. So Rosa is $ \boxed{49} $ years old. OR We look for a multiple of 7 that is not divisible by 2, 3, 4, or 6. First we list all odd multiples of 7 less than 75, which are 7, 21, 35, 49, and 63. Since 21 and 63 are multiples of 3, we're left with 7, 35, and 49 as possibilities. Only $ \boxed{49} $ has a remainder of 1 when divided by 2, 3, 4, or 6.