How Do You Solve These Common Math Test Questions?

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The discussion centers on solving common math test questions, including divisibility rules for binary numbers, set intersections, binomial coefficients, and basic set theory involving students' subject preferences. Key points include identifying that a binary number is divisible by 2 if it ends in 0, determining the intersection of sets A and B, calculating the sum of binomial coefficients for C(9, k), and applying the principle of inclusion-exclusion to find how many students like both Math and English. Participants emphasize the importance of attempting to solve problems independently before seeking assistance. The thread highlights the need for clear reasoning and understanding of mathematical principles to tackle these questions effectively.
eqlisa
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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
 
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