KA-0131Back-solve from the answer choices
4 points, difficulty 2 of 3Level 3–4about 60sTwice a number, with 3 added, gives 17. Which of the choices is the number?
Hints
Take them one at a time. The first gives nothing away.
1A nudge
Test a choice rather than solving.
2The strategy
The answer is one of the five, so pick a middle one, double it, add 3, and see whether you land on 17. The result tells you which way to move next.
3The full solution
Test 10: double is 20, plus 3 is 23 - too big. Test 7: double is 14, plus 3 is 17. That works.
Solution
The reliable way
Back-solve. Take the middle choice, 10: doubling gives 20, plus 3 is 23, which overshoots 17 - so the number is smaller. Try 7: doubling gives 14, plus 3 is 17. That is it. Starting in the middle means one test tells you which direction to go. The transferable idea: on a multiple-choice paper, checking a candidate is often cheaper than deriving the answer, and starting in the middle halves the work.
The elegant way
Undoing gives (17 - 3) divided by 2 = 7, which is worth doing as a check even after back-solving.
Why this is on the test: Deciding whether to test or to derive is a real exam skill, and starting from choice A rather than the middle wastes the information each test gives.