How wrong answers are built

13 patterns. A wrong answer on this test is rarely nonsense. It is the result you get by making one specific mistake, and the same mistakes recur — which means they can be learned as a set rather than met one at a time.

Every pattern below is shown inside a real question from the practice bank, with the choice that embodies it marked. Nothing here is illustrative: if you have worked the bank, you have met these.

Math

The right numbers, the wrong operation

The most common Math distractor is the answer you get by doing something reasonable with exactly the right quantities. Because the numbers are right, it never looks like a slip.

The check: Before choosing, say out loud what operation the question asked for. If you cannot name it, you were pattern-matching.

From the bank · Equivalent expressions

Which expression is equivalent to 2(x - 3) - 3(2x + 1)?

  • A-4x - 9
  • B-4x + 9
  • C8x - 9
  • D-4x - 3

Why it catches people: This is what you get by distributing the -3 to the first term of the bracket and not the second. Everything else about the working is correct, which is exactly why it survives a quick check.

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The term that disappears

Expanding a squared binomial produces three terms, and the middle one is the one that goes missing. The distractor is the two-term version.

The check: A squared binomial always gives a^2 + 2ab + b^2. If your answer has two terms, you skipped one.

From the bank · Polynomial factors

Which expression is equivalent to (2x + 3)^2?

  • A2x^2 + 12x + 9
  • B4x^2 + 6x + 9
  • C4x^2 + 9
  • D4x^2 + 12x + 9

Why it catches people: Squaring each term separately gives this, and it looks tidy — tidier than the correct answer, which is part of the appeal.

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The wrong denominator

A question asking for a fraction of one group will offer the fraction of the whole population as a choice. Both divisions are valid arithmetic; only one answers the question.

The check: Read the noun immediately after "of". That noun is your denominator.

From the bank · Two-way frequencies

Of 120 respondents, 45 own a bicycle and 18 of those also own a car. What percent of bicycle owners also own a car?

  • A15%
  • B26.7%
  • C40%
  • D37.5%

Why it catches people: This divides by all 120 respondents rather than by the 45 bicycle owners the question named. It is the answer to a question nobody asked.

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Half of the answer

Squaring produces two roots and absolute values produce two cases. The distractor is the half you found first.

The check: If the working involved a square or an absolute value, check whether the negative case also satisfies the original.

From the bank · Function evaluation

If f(x) = x^2 - 4 and f(a) = 21, what are the possible values of a?

  • A17 and -17
  • B25 and -25
  • C5 only
  • D5 and -5

Why it catches people: It is correct as far as it goes, which makes it much harder to reject than an answer that is simply wrong.

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A percent of the wrong amount

Reversing a percentage change means dividing, not subtracting. Subtracting the same percentage from the new figure gives a number that is close enough to look right.

The check: Write down which amount the percentage is a percentage of before you compute anything.

From the bank · Percent change

After a 25 percent increase, a membership costs $80. What was the original price?

  • A$100
  • B$64
  • C$60
  • D$65

Why it catches people: Taking 25 percent off $80 gives $60, which is a different operation on the same numbers. Checking it forwards — $60 plus 25 percent is $75, not $80 — catches it immediately.

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Scaling by the wrong power

Doubling every length multiplies area by four and volume by eight. The distractor is the linear factor, applied where a square or a cube belongs.

The check: Ask what is being scaled: a length, an area, or a volume. The factor is k, k squared, or k cubed accordingly.

From the bank · Circles

If a circle's radius is doubled, by what factor does its area increase?

  • A4
  • B8
  • C16
  • D2

Why it catches people: It is the factor named in the question, reused without adjustment. Reading the question quickly makes this feel like the answer being handed to you.

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The inequality that did not flip

Dividing an inequality by a negative reverses it. The un-reversed version is always among the choices, and it is what careful algebra produces if the rule slips.

The check: Circle the negative divisor before you divide, so flipping is a step rather than something you might remember.

From the bank · Linear inequalities

Which inequality is equivalent to -3x + 4 <= 19?

  • Ax >= -5
  • Bx <= 5
  • Cx <= -5
  • Dx >= 5

Why it catches people: The number is right and the sign is not. A reader who checks their arithmetic will find nothing wrong with it.

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Reading & Writing

True, but not from this text

The most tempting wrong answer in Reading is a statement you agree with that the passage never establishes. Agreement is not evidence.

The check: Point at the phrase in the passage that makes your choice true. If you cannot, you are supplying it yourself.

From the bank · Central ideas and details

A publisher offered two editions of a reference book: a printed volume and a subscription to the same text online. Libraries bought the printed volume at four times the rate of the subscription, and librarians surveyed said the printed volume was easier to lend to several readers in one day. Which choice best states the central idea?

  • ALibrarians dislike reading text on screens.
  • BThe online subscription was more expensive than the printed volume.
  • CA practical difference in how the two formats circulate, rather than a preference for print, explains the buying pattern.
  • DPrinted reference books contain more information than online editions.

Why it catches people: It is a plausible explanation for the same buying pattern, and many readers believe it. The passage gives a different reason and never mentions screens.

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The choice that goes further than the text

A passage reports something; the distractor recommends, condemns, or generalises from it. The subject matter is right and the strength is wrong.

The check: Watch for "should", "always", "never", "proves" and "eliminates" in a choice describing a text that reported one result.

From the bank · Inferences

An orchestra published its rehearsal recordings online. Concert attendance was unchanged, but recording downloads were highest in the week before each concert and fell sharply afterwards. Which choice is best supported?

  • AThe orchestra should stop publishing the recordings.
  • BMost downloads came from people outside the city.
  • CThe recordings were used mainly as preparation by people who were going to attend anyway.
  • DThe recordings reduced concert attendance.

Why it catches people: The passage describes a pattern and makes no recommendation at all. A choice that tells somebody what to do has left the text behind.

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Right subject, wrong relationship

In paired-text questions the distractor usually names the correct two texts and the wrong relation between them — confirming where the text qualifies, or contradicting where it complicates.

The check: Say the relationship in one word — agrees, qualifies, contradicts, complements — before reading any choice.

From the bank · Relationships between texts

Text 1 argues that free museum entry increases the range of people who visit. Text 2 reports that after entry charges were removed at one museum, total visits rose sharply while the mix of postcodes represented was unchanged. Text 2 primarily

  • Arestates Text 1 in more cautious language.
  • Bconfirms Text 1 with a larger data set.
  • Cchallenges the specific benefit Text 1 claims while confirming a different one.
  • Dargues that museums should reintroduce entry charges.

Why it catches people: It reads smoothly and gets the direction of travel wrong. Text 2 reports the range unchanged, which undercuts rather than confirms.

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Accurate, and not what was asked

Synthesis questions name the writer's goal in their final sentence. Distractors are faithful to the notes and indifferent to the goal.

The check: Underline the sentence beginning "the student wants to". That sentence is the question.

From the bank · Rhetorical synthesis

Notes: A weather station opened in 1961. It records temperature hourly. Its records were digitised in 2020. Researchers used them to identify a local warming trend. The student wants to emphasise the research value of the station's records. Which choice best uses the notes?

  • AThe station's records were digitised in 2020.
  • BDigitised in 2020, the station's hourly records since 1961 allowed researchers to identify a local warming trend.
  • CThe weather station opened in 1961.
  • DThe weather station has recorded temperature hourly since it opened in 1961.

Why it catches people: Nothing about it is false. It simply does not do the job the question set, which is to show what the records made possible.

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The meaning you would give without reading

Words-in-context questions choose words whose familiar sense is not the one in play. The familiar sense is always offered.

The check: Cover the choices and supply your own word from the sentence. Then look.

From the bank · Words in context

The committee described the plan as "modest," noting that it proposed a single new bus route rather than a redesigned network. As used in the text, what does the word "modest" most nearly mean?

  • Alimited in scope
  • Breluctant to seek attention
  • Ccarefully researched
  • Dinexpensive to build

Why it catches people: It is a real definition of "modest", and the wrong one here: the sentence contrasts one bus route with a whole network, which is about scope.

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The transition that reads best

Every transition offered will read fluently in the gap. Fluency is not the test; naming the relationship is.

The check: Decide the relationship first — cause, contrast, addition, example — then pick only from that group.

From the bank · Transitions

The survey found that most respondents supported the proposal. _____, only about a quarter said they would attend a meeting about it. Which choice completes the text with the most logical transition?

  • ASimilarly
  • BHowever
  • CTherefore
  • DIn addition

Why it catches people: The sentences sound like they could follow one another, but broad support does not cause low attendance. The relationship is contrast, not consequence.

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Use this as a checklist, once

Read it through, then work a set of questions with it closed. The value is not in recognising the patterns on this page — it is in recognising one at the moment you are about to choose it, which only practice produces.

Math practice

Where seven of these live.

Open

Reading & Writing

Where the other six do.

Open

Reasoning sets

Where one wrong step costs several.

Open
SAT® Wrong Answers: How They Are Built | IQ Test Center