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dMAT Mathematical Equations: working backwards

Every item is single-choice, which means the answer is already on the screen. Where the algebra is messy, testing an option is frequently faster than solving — and it cannot go wrong in the way a misremembered method can.

Start in the middle

  1. Order the options by size if they are not already.
  2. Test the middle one.
  3. If it is too large, the answer is below it — three options gone in one test.
  4. If too small, the answer is above it.

Two tests resolve five ordered options. Solving the equation may take longer and carries more risk of an arithmetic slip along the way.

When to solve instead

  • When the options are expressions rather than numbers — substitute a value instead.
  • When substituting is itself laborious.
  • When the algebra is two clean lines, in which case solve it.
  • When the question asks for a relationship rather than a value.

Where options are algebraic, pick a convenient number — avoiding 0 and 1, which make several expressions agree — compute the answer numerically, and see which expression produces it.

Working backwards — FAQs

2 questions

The middle one when they are ordered by size. It eliminates the most.

Not for algebraic options or relationship questions. There, substitute a number instead.

More mathematical equations question types

Sources

Written from the test board's own published material and checked on 1 October 2026.

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