Anatomy of a wrong answer
Reviewing a missed question by reading the right answer teaches you that question. Reading why each wrong option exists teaches you the twelve questions that will catch you the same way. Here are three, taken apart.
01Why the wrong options are there at all
A test writer starts from the correct answer and then works backwards into the most likely errors. That is why the options often differ by a single sign, a single power, or a single denominator. The options are not a set of four possibilities; they are a set of four stories about how the question can go wrong, and only one of them ends well.
02Example one: the probability with a hidden group
A survey of 200 residents finds 120 own a dog, 70 own a cat, and 40 own both. One resident is chosen at random. What is the probability they own neither? The correct answer is one quarter: at least one pet accounts for 120 + 70 - 40, which is 150 people, leaving 50 of the 200, and 50/200 simplifies to 1/4. Now read the options as mistakes. Three quarters is 150/200, which is the probability of owning at least one pet, the exact complement of the question. One fifth is 40/200, which uses only the people who own both, treating the overlap as if it were the whole group. Eleven twentieths is 110/200, which counts the people who own exactly one pet and quietly discards the overlap entirely. Each wrong option is a real, complete, wrong line of reasoning. The question is testing whether you can find the group that is left over after the union, not whether you can add two numbers.
03Example two: the absolute value that had a condition
Which value of x satisfies both the absolute value of x equals 4 and x is less than zero? The correct answer is -4. The other three options are: 2, which comes from halving 4 instead of solving the equation at all; 4, which is a genuine solution of the absolute value but ignores the condition; and -2, which looks like the negative answer and is the trap for anyone who solved nothing and merely copied the negative sign. Notice that both real solutions appear among the options. That is deliberate, and it is the signature of a question with a condition attached: the test wants to see whether you applied the second sentence, not whether you can solve the first.
04Example three: the radius that was left squared
The endpoints of a diameter of a circle are (-2, 1) and (4, 9). What is the radius? The distance between the endpoints is 10, so the radius is 5, and 5 is the correct answer. The distractors map the whole journey: 10 is the diameter, which is the distance without the halving step; 25 is the squared radius, which is the value that appears in the circle equation; and 50 is the squared diameter, which is the number you get from the distance formula before taking the root. None of these is arbitrary. Each is a place where a student stops one step early, and all three are useful answers in some other question. This is why checking the units and the question wording matters more here than redoing the arithmetic.
05Reading your own mistakes this way
When you miss a question, do not just read the solution. Cover it, decide which option you would have picked, and name the story that produced it. Was it a step you stopped early, a condition you ignored, or a quantity you answered instead of the one asked? That name is the thing to practise, and it is more valuable than the question itself, because the same story will appear again with numbers you have never seen.
06What this changes in practice
It changes what you do after checking an answer. Instead of asking whether you were right, ask what the other three options were for. When you can explain why each wrong option is attractive, you have understood the question at the level the test is measuring, which is judgement rather than procedure.
07Questions
Why are wrong answers often close to the right one?
Because they are generated from the errors the question is designed to catch. A distractor that is far from correct would not tempt anyone, so the wrong options are the results of stopping one step early or applying the wrong rule.
Should I review the questions I got right?
Yes, quickly. If you cannot say why the other options are wrong, you got it right by recognition rather than by method, and the same question with different numbers may go the other way.
How do I use this while practising?
After each miss, name the mistake in one of three words: unknown, slipped, or misread. Then review the wrong options and match each one to a story. That habit converts a miss into a rule.
Does this help on the harder second module?
Most of all there. The hard module rarely asks for more arithmetic; it puts the deciding information in the wording, which is exactly what distractor analysis trains.
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