KA-0045Back-solve from the answer choices
5 points, difficulty 3 of 3Level 5–6about 90sA number is 4 more than a third of itself. Which of the choices is that number?
Hints
Take them one at a time. The first gives nothing away.
1A nudge
Test a choice instead of solving.
2The strategy
The answer is one of the five. Take a middle choice, find a third of it, add 4, and see whether you land back on the number you started with.
3The full solution
Test 12: a third is 4, and 4 + 4 = 8, not 12, so 12 is too big. Test 6: a third is 2, and 2 + 4 = 6. That works.
Solution
The reliable way
Back-solve. Take a choice, find a third of it, add 4, and check whether you land back on the same number. For 12: a third is 4, and 4 + 4 = 8, which is not 12, so 12 is too big. For 6: a third is 2, and 2 + 4 = 6 - it works. Starting from a middle choice tells you which direction to move next. The transferable idea: on a multiple-choice paper, checking an answer is often far cheaper than deriving it.
The elegant way
Writing n = n/3 + 4 gives 2n/3 = 4, so n = 6 - worth doing as a check even when you back-solved.
Why this is on the test: Back-solving is a contest skill in its own right, and knowing when checking beats deriving is worth several marks across a paper.