# Need some help with some math problems

## Main Question or Discussion Point

Hello,

I was hoping I could get some help with some questions that I am struggling with for a test...

1. If a number is expressed in binary, which of the following is a necessary and sufficient condition to test whether it is divisible by 2?

a. If the number does not end in 0
b. If the alternating sum of the digits is 0 or divisible by 3
c. If the number includes an even number of 1's and an even number of 0's
d. If the number, when converted to decimal form, has the sum of its digits divisible by 3

2. If A=(1, 2, 3) and B=(3, 4, 5) how many elements are in the intersection of A and B?

a. 0
b. 1
c. 3
d. 5

3. What is the sum of the 10 binomial coefficients of the form C(9, k)?

a. 45
b. 362,880
c. 512
d. 1,729

4. There are 93 students in a class; 42 like Math, while 41 like English. If 30 students don't like either subject, how many students like both?

a. 10
b. 20
c. 41
d. The answer cannot be determined from the data given

Thank you very much,
Elisabeth