D is the set of all the multiples of 3 between 20 and 100...

[msliwiak]

Word translations problem:
D is the set of all the multiples of 3 between 20 and 100. E is the set of all the factors of 400. Set D and Set E have how many numbers in common?

Could you please explain your answer choice "0" as the correct answer for this problem?

Set D {21,24,27,30....99} - multiples of 3 between 20 and 100
Set E {2,2,2,2,5,5} - all of the factors of 400

So, in search for common numbers of D and E, I factor out members of D, i.e.
21: {7,3} - no common number with E
24: {2,2,2,3} - one common number "2" with E
27: {3,3,3} - no common number with E
30: {2,3,5} - one common number with "2" with E

Therefore, I selected answer: "1" common number.

In your explanation you state: "...that the prime factorization of any member of set E will NOT include the prime number 3." However, "2" is a factor of 400 (set E) and a common number with members of set D, at least 24 and 30. Shouldn't the correct answer be "1" number in common instead of "0"? Please clarify.
Thanks.
Marek Sliwiak

[JonathanSchneider]

Hi Marek. You're doing a good job with the math, but you seem to be having a harder time making sense of the meaning of the words in the problem.

Set A is just multiples of 3, NOT factors of those multiples. As a result, 2 cannot be part of Set A (2 is not a multiple of 3). Moreover, notice that Set B is not simply the prime factors of 400, but ALL factors of 400. Note that there are 15 total factors for the number 400. However, NONE of those 15 numbers is divisible by 3 (because 400 does not have a factor of 3).

Hope that helps.