KA-0011Divisibility rules: 2, 3, 4, 5, 9, 10
4 points, difficulty 2 of 3Level 3–4about 60sThe four-digit number 27_4 is divisible by 3. Which digit could go in the gap?
Hints
Take them one at a time. The first gives nothing away.
1A nudge
Add the digits you already know.
2The strategy
A number is divisible by 3 exactly when its digits add to a multiple of 3. Add the three known digits, then ask what the missing digit must be to push the total onto a multiple of 3.
3The full solution
2 + 7 + 4 = 13. The next multiple of 3 above 13 is 15, so the missing digit is 2. (8 would also work, but it is not offered.)
Solution— no shortcut on this one
The test for 3 is the digit sum. The known digits give 2 + 7 + 4 = 13, so the full digit sum is 13 plus the missing digit. For that to be a multiple of 3 the missing digit must be 2, giving 15, or 5, giving 18, or 8, giving 21. Only 2 is among the choices. The transferable idea: convert a divisibility question into a question about the digit sum.
Why this is on the test: Divisibility rules are pure speed on a timed paper, and the common failure is testing the missing digit instead of the whole digit sum.