Sets Relations And Functions Question 103
Let $ A={x|x\le 9,x\in \mathbb{N}} $ . 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?
Options:
A) 12
B) 21
C) 27
D) 30
Show Answer
Answer:
Correct Answer: D
Solution:
Given $ A={x:x\le 9,x\in N}={1,2,3,4,5,6,7,8,9} $ Total possible multiple of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27 But 3 and 27 are not possible because 3 and 27 cannot be expressed as such that $ a+b+c $ is a multiple of 3
$ 6\to 1+2+3 $
$ 9\to 2+3+4,5+3+1,6+2+1 $
$ 12\to 9+2+1,8+3+1,7+1+4,7+2+3 $
$ 6+4+2,6+5+1,5+4+3 $
$ 15\to 9+4+2,9+5+1,8+6+1,8+5+2, $
$ 8+4+3,7+6+2,7+5+3,6+5+4 $
$ 18\to 9+8+1,9+7+2,9+6+3, $
$ 9+5+4,8+7+3,8+6+4,7+6+5 $
$ 21\to 9+8+4,9+7+5,8+7+6 $
$ 24\to 9+8+7 $
Hence, the total number of largest possible subsets is 30.
BETA
