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Question

Let A=x|x9,xN. Let B=a,b,c be the subset of A where a+b+c is a multiple of 3. What is the largest possible number of subsets like B?


A

12

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B

21

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C

27

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D

30

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Solution

The correct option is D

30


Explanation for the correct Option(s)

Find the largest possible number of subsets like B

Given,

A=x|x9,xN=1,2,3,4,5,6,7,8,9

B=a,b,c

The total possible multiple of 3 can be expressed as

{3,6,9,12,15,18,21,24,27}

Since 3 and 27 cannot be expressed as such that a+b+c is a multiple of 3 , 3 and 27are not possible.

Remaining possible multiple of 3 are 6,9,12,15,18,21,24, this can be expressed as such that a+b+c as shown below:

61+2+392+3+4,5+3+1,6+2+1129+2+1,8+3+1,7+1+4,7+2+3,6+4+2,6+5+1,5+4+3159+4+2,9+5+1,8+6+1,8+5+2,8+4+3,7+6+2,7+5+3,6+5+4189+8+1,9+7+2,9+6+3,9+5+4,8+7+3,8+6+4,7+6+5.219+8+4,9+7+5,8+7+6249+8+7

From the above subsets, the total largest possible number of subsets are 30.

Hence, the correct answer is option D.


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