Visual SolutionPYQ 2023 · Apr 15 Shift 1Standard

Question

The total number of three-digit numbers, divisible by 3, which can be formed using the digits 1, 3, 5, 8, if repetition of digits is allowed, is

(A)

21

(B)

20

(C)

22

(D)

18

Solution Path

Classify digits mod 3, enumerate valid residue triples:

1 + 1 + 8 + 12 = 22

01Question Setup

1/4

Three-digit numbers from

\{1, 3, 5, 8\}

with repetition, divisible by 3.

\text{Count} = \;?

02Mod 3 Residues

2/4

Residue 0:

\{3\}

, Residue 1:

\{1\}

, Residue 2:

\{5, 8\}

. Need digit sum

\equiv 0 \pmod{3}

Classify by residue mod 3

03Count CasesKEY INSIGHT

3/4

(0,0,0): 1

(1,1,1): 1

(2,2,2): 8

(0,1,2): 12

. Total

= 22

1 + 1 + 8 + 12 = 22

04Final Answer

4/4

Total

= 22

\boxed{22}

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