Use every condition and test the answer
Handle strict inequalities, integer restrictions, signs, counting and algebraic identities without losing a condition.
The idea
An equation describes a relationship; the conditions decide which solutions are allowed. A nonzero denominator, a positive-integer requirement or the word strictly can change the answer. When counting, decide what distinguishes two outcomes before applying a formula. After solving, substitute into the original statement, not just into an intermediate equation. A boundary check often catches a one-unit error that correct arithmetic alone cannot.
A method to try
- List the domain before manipulating an expression: integer or real, positive or unrestricted, zero allowed or forbidden.
- Use equality to locate a boundary, then restore the actual inequality. Positive profit means more than break-even, not equal to it.
- When dividing an inequality by a negative number, reverse the inequality sign. Retain whether each endpoint is included.
- For a must-be-true claim, try small values with different magnitudes while preserving the stated signs. A single counterexample rejects a universal claim.
- For counting and probability, specify ordered or unordered outcomes and whether selection replaces an item. Count each valid outcome exactly once.
- Use prime factors for integer conditions. A perfect square has even exponents for every prime. For two positive integers, their product equals their greatest common divisor multiplied by their least common multiple; check that a candidate satisfies both given values.
- Check all candidates in the original problem and retain units. A symbolic expression can be evaluated without finding every unknown separately.
- Use the optional 45-minute section as fixed practice. In the official exam, review becomes available after answering all questions in a section if time remains, and up to three answers can be edited. This practice tool allows freer movement.
Follow the reasoning.
A workshop has fixed costs of 840 currency units. Each item sold costs a further 9 currency units and produces revenue of 24 currency units. What is the fewest whole number of items it must sell to earn more than 300 currency units in profit?
- Define n as a whole-number count of items. Profit is 24n − (840 + 9n) = 15n − 840.
- The phrase more than 300 creates a strict inequality: 15n − 840 > 300, or 15n > 1,140.
- Dividing by positive 15 gives n > 76. The smallest whole number allowed is therefore 77.
- Check the boundary: n = 76 gives exactly 300 profit, so it fails. For n = 77, profit is 1,155 − 840 = 315, which meets the target.
Think it through first.
How many integers n satisfy −2 < n/3 ≤ 2?
Show the explanation
12 integers.
Multiply by positive 3 to obtain −6 < n ≤ 6. The integers run from −5 through 6 inclusive; their count is 6 − (−5) + 1 = 12.
Make it your own
After section B, identify one answer that failed because of a condition rather than arithmetic. Write the missing condition and show why the tempting alternative fails. Correct-answer totals are feedback for these fixed items; they do not convert to official GMAT scores or percentiles.
This lesson is one part of a short starter pathway. It does not cover the full exam syllabus or establish a predicted score.
Official references
These provider and publisher links explain the exam or underlying concepts. Our lessons and questions are original, independent practice.
View 4 references and checked dates
- GMAC: exam structure (opens in a new tab)Checked 2026-10-06
- GMAC: exam content (opens in a new tab)Checked 2026-10-06
- GMAC: official preparation (opens in a new tab)Checked 2026-09-20
- GMAC: calculator and note-taking policies (opens in a new tab)Checked 2026-10-06