Why is an applied glossary more useful than a simple list?
The GMAT and GRE both include quantitative reasoning in English, but have different scopes and formats. This glossary covers basic relationships useful for reading both tests. It does not make their content or calculator rules interchangeable; see the test-specific guides.
When a word trips you up, connect it to a relationship and a counterexample. “At least five” includes five, unlike “more than five.” If you cannot distinguish these sets, knowing the French translation is not enough.
The following examples apply these relationships. Also pay attention to number punctuation in English prompts: a period can be a decimal separator. Rewrite units and numbers clearly in your scratch work without changing their value.
Which words should you be able to translate into math immediately?
Learn each row with its example, then make up an example of your own. The last column highlights a distinction that can change the answer.
| English term | Meaning and notation | What to check |
|---|---|---|
| Integer | Integer: …, −2, −1, 0, 1, 2, … | Does not mean positive |
| Even / odd | Even / odd | Zero is even |
| Factor / multiple | Factor / multiple | 3 is a factor of 12; 12 is a multiple of 3 |
| Remainder | Remainder: 17 = 5 × 3 + 2 | For a positive divisor d: 0 ≤ remainder < d |
| At least / no less than | At least: x ≥ a | Equality included |
| At most / no more than | At most: x ≤ a | Equality included |
| Fewer than / less than | Strictly less than: x < a | Equality excluded |
| Ratio of A to B | Ratio A:B, or A/B for B ≠ 0 | Order matters: A then B |
| Increased by | Increased by | Distinguish from “increased to,” which gives the final value |
| Average (arithmetic mean) | Arithmetic mean | Total divided by count |
| Consecutive integers | Consecutive integers: n, n + 1, n + 2 | Consecutive even integers increase by 2 |
| Twice / half | Twice / half | Identify the quantity being compared |
How can you turn a sentence into a condition?
Do not immediately write down an arbitrary operation. First name the unknown, then translate the relationship in the correct direction.
A workshop needs at least 47 labels. Labels are sold in packs of 8. What is the least number of packs the workshop must buy?
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The solution, step by step
6 packs.
The method in action
- We need 8p ≥ 47, where p is an integer. Five packs give 40 labels, which is not enough; six give 48, which is enough.
- The quotient 47/8 is not a whole number of packs to buy. “At least” sets a minimum to reach; it is not a rounding-to-nearest instruction.
Lea has 7 fewer cards than twice the number of cards Omar has. Omar has 15 cards. How many cards does Lea have?
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The solution, step by step
23 cards.
The method in action
- Twice the number Omar has is 2 × 15 = 30. Seven fewer than that is 30 − 7 = 23.
- 7 − 30 reverses the comparison. 2 × (15 − 7) subtracts before doubling, which the sentence does not say.
The pitfall
A familiar word can hide a precise constraint
“Positive integer” adds two conditions: integer and strictly positive. A value such as 0.5 is positive but not an integer; zero is an integer but is not strictly positive. If a sufficiency question allows real numbers, you cannot test only integers.
Also pay attention to “percent of” versus “percent greater than.” The first gives a portion; the second keeps the base and adds a portion. The wording differs only slightly, but the equations differ substantially.
Which quantity is the reference?
The next mini-problem practices a comparison, not a change over time. Both quantities exist simultaneously.
Quantity A is 25 percent greater than quantity B. If B is 64, what is A?
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The solution, step by step
80.
The method in action
- A equals B plus 25% of B: A = 1.25 × 64 = 80.
- 16 is only 25% of B. 48 would be 25% less. “Greater” means adding to the base.
- Check: A − B = 16 and 16/64 = 25%. The denominator is correctly the reference quantity B.
Key takeaways
- Connect each term to a relationship and its limits.
- Reread thresholds and the order of comparisons.
- Keep GMAT and GRE rules distinct.