Many questions.

[Celsion]

1) How to solve problems similar to this: What is the remainder of [unparseable or potentially dangerous latex formula]? or the remainder of [unparseable or potentially dangerous latex formula]?
2) 12% of 466[unparseable or potentially dangerous latex formula]?
3) Number of proper subsets of the set {M,A,T,H} or any set for the matter? I though it was [unparseable or potentially dangerous latex formula].
4) A problem type similar to 3), "Set A has 15 proper subsets. How many elements are in Set A?"
5) "Set A has 8 distinctive elements. How many proper subsets with at least one element does set A have?"

Number 3-5 are all similar. Sorry for all the questions, I just really want to improve at number sense. Thanks if you can answer them all.

[bradp]

1) do each term remainder 4 separately

9^2 mod 4 = 1 mod 4
7 mod 4 = 3 mod 4
5 mod 4 = 1 mod 4
1 - 3 * 1 = -2 mod 4 = remainder 2

6 is divisible by 3 so all of 6^4 * 5^3 is 0 mod 3. -16 is -1 mod 3 --> remainder 2

2) 1% of 466 2/3 is 4 2/3, multiply that by 12

3) proper subsets is 2^n - 1. One of the subsets is a set identical to set A, so it isn't proper (definition of proper subset)


4) 15 = 2^n - 1, n = 4

5) set A has 256 total subsets. One of those subsets is the empty set {} (does not have at least one element). Then there's the improper one (see above)

2^8 = 256, subtract 2 = 254