There are 6 such numbers.

Quick check using digit sums

A number is:

  • divisible by 3 if the sum of its digits is divisible by 3
  • divisible by 9 if the sum of its digits is divisible by 9

We want: “divisible by 3 but not by 9” → digit sum divisible by 3 but not by 9. Let’s test each:

  1. 2133 → 2+1+3+3=92+1+3+3=92+1+3+3=9 → divisible by 9 ❌
  2. 2343 → 2+3+4+3=122+3+4+3=122+3+4+3=12 → divisible by 3, not by 9 ✅
  3. 3474 → 3+4+7+4=183+4+7+4=183+4+7+4=18 → divisible by 9 ❌
  4. 4131 → 4+1+3+1=94+1+3+1=94+1+3+1=9 → divisible by 9 ❌
  5. 5286 → 5+2+8+6=215+2+8+6=215+2+8+6=21 → divisible by 3, not by 9 ✅
  6. 5340 → 5+3+4+0=125+3+4+0=125+3+4+0=12 → divisible by 3, not by 9 ✅
  7. 6336 → 6+3+3+6=186+3+3+6=186+3+3+6=18 → divisible by 9 ❌
  8. 7347 → 7+3+4+7=217+3+4+7=217+3+4+7=21 → divisible by 3, not by 9 ✅
  9. 8115 → 8+1+1+5=158+1+1+5=158+1+1+5=15 → divisible by 3, not by 9 ✅
  10. 9276 → 9+2+7+6=249+2+7+6=249+2+7+6=24 → divisible by 3, not by 9 ✅

Final count

Numbers divisible by 3 but not by 9 are:

  • 2343, 5286, 5340, 7347, 8115, 9276

So, the answer is: 6.