KA-0063Divisibility rules: 2, 3, 4, 5, 9, 10
4 points, difficulty 2 of 3Level 3–4about 75sWhich of these numbers can be divided exactly by both 4 and 9?
Hints
Take them one at a time. The first gives nothing away.
1A nudge
Test both rules on each number.
2The strategy
For 4, look at the last two digits. For 9, add the digits and see whether the total is a multiple of 9. A number has to pass both tests, not just one.
3The full solution
144: the last two digits are 44, which is a multiple of 4, and 1 + 4 + 4 = 9. So 144 passes both.
Solution
The reliable way
Apply both tests to each choice. Divisible by 4 means the last two digits form a multiple of 4; divisible by 9 means the digits add to a multiple of 9. 96 passes the 4 test only. 117 and 153 pass the 9 test only. 132 passes the 4 test but its digits add to 6. 144 has last two digits 44, a multiple of 4, and digits adding to 9. The transferable idea: an and question needs both tests run, and the first pass is not the answer.
The elegant way
A number divisible by both 4 and 9 is divisible by 36, and 144 is 4 times 36.
Why this is on the test: Students routinely stop at the first rule that passes; making both rules necessary is what turns a recall question into a checking one.