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Hong KongWorking backwards from the options, and when it fails
Working backwards means testing the options in the stem instead of solving forward. It is fast on Mathematics items with a single unknown and useful on English Language Skills, where you read each version in place. On Reading it fails, because the options are built to look supported.
The options are not just answers. They are four pieces of information you were handed before you started, and on some items using them is faster than ignoring them.
On other items it is how you get caught.
Where it works: Mathematics with one unknown
If a stem asks for a single value and gives you four candidates, you can test them rather than solve for them. Substitute, check the condition, move on. It converts an algebra problem into an arithmetic check, which most people are faster and more reliable at.
Start from the middle. Order the options by size, try the second or third, and the result usually tells you whether you need a bigger or smaller value, which kills two options at once. Two substitutions typically settle it, and Mathematics gives 2.86 minutes an item on our arithmetic - enough room for that and a check.
| Item shape | Work backwards? | Why |
|---|---|---|
| Solve for x, four numeric options | Yes | Substitution is a check rather than a derivation |
| Word problem asking for one quantity | Yes | Testing a value against the story is often clearer than modeling it |
| Which expression represents the situation | No | Nothing to substitute. Build the expression yourself, then match |
| Mean, median or probability of a data set | No | One computation gives the answer directly. Testing four is slower |
| Systems of equations | Sometimes | A candidate pair either satisfies both equations or it does not, and that is quick to check |
The trap inside the technique
Wrong options on Mathematics items are built from real calculations - the value you get by stopping a step short, by inverting a conversion, by dropping a sign. That is the point of a distractor.
So when you substitute an option and it satisfies part of the stem, you have not finished. Check it against the whole condition, including the final clause about what was asked for. An option that solves the equation while answering the wrong question will pass a careless substitution test comfortably.
Where it works differently: English Language Skills
On a sentence-correction item the technique is not substitution, it is reading. Take each option and read the whole sentence with that version in place, silently but completely. Not the option on its own. The sentence.
This catches the family of distractors that fix one problem and create another, because the new error usually appears somewhere other than the portion being changed. Read only the changed words and you will not see it.
The cost is time, and this subtest has the least of it: about eighty seconds an item. Four full readings will not fit. So use it as a tiebreaker between the two options you have left rather than as your first move, and eliminate the obvious two by rule first.
Where it fails: Reading
Here is the strong opinion on this page. Working backwards from the options on a Reading item is not a slower method, it is the wrong method, and it is the specific behavior the distractors are designed to punish.
Reading distractors are true statements. They repeat the passage's own vocabulary. They sit at the wrong scope, or answer a different question, or push an inference one step past what the text supports. Every one of them is built to look supported when you go looking for support, and going looking for support is exactly what working backwards means.
The method that works on Reading runs the other way. Read the stem, decide what the answer should be before you look at the options, then find the option that matches your own formulation. If you cannot form an answer without the options, go back to the passage rather than to the option list.
On Reading, forming your own answer before reading the options is worth more than any elimination rule. It gives you something to compare against, so an option that reuses the passage's wording has to actually match your answer rather than merely feel familiar.
Two things the option list tells you for free
- Units. If three options are in feet and one is in square feet, the odd one is an area and the item probably was not about area. This is the cheapest elimination available on Mathematics and most candidates never look
- Spread. Options clustered tightly around one value usually mean a place-value or sign error is the intended trap. Options spanning orders of magnitude usually mean a conversion is
The rule underneath all of it
Use the options as evidence on items where the answer is a value, and ignore them until you have your own answer on items where it is a judgment. Mathematics is mostly the first kind. Reading is entirely the second. English Language Skills sits in between, which is why it repays a bit of thought about which item you are looking at.
Common questions
Should I plug the answers back in on FTCE Math questions?
On items asking for a single value, yes. Order the options by size and start in the middle, so a result that is too large or too small eliminates two at once. Mathematics allows 2.86 minutes an item on our arithmetic, which leaves room.
Does working backwards help on FTCE Reading questions?
No, and it actively hurts. Reading distractors are true statements that reuse the passage's wording, so hunting for support finds it for several options. Form your own answer from the stem first, then look for the option that matches it.
How do I use elimination on English Language Skills questions?
Eliminate by rule first, then read the whole sentence with each of the two survivors in place. Reading only the changed portion misses the distractor family that fixes one error and introduces another elsewhere in the sentence.
Can the options themselves give away the answer?
Sometimes. Mixed units are a free elimination, since an area answer in square feet cannot answer a perimeter question. Options clustered tightly together suggest the intended trap is a place-value or sign error rather than a method error.
Is it worth checking my answer against the options before finishing?
Check that your value appears, because if it does not you have made an error and you know immediately. Do not treat a match as confirmation, though: every wrong option is somebody's arithmetic, so your answer appearing proves only that the mistake was anticipated.