Module · Arithmetic & Number Properties
Chapter 10: Averages & Mixtures
Arithmetic
4 topics
What this chapter covers
The 4 topics below make up Averages & Mixtures on the GRE. Click any topic to open its notes, examples and practice test.
Study material & tests
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Formula Reference Sheet
This chapter
Averages
| Arithmetic mean | average = sum ÷ count |
|---|---|
| Sum from average | sum = average × count |
| Weighted average | (n₁a₁ + n₂a₂) / (n₁ + n₂) |
| New average after adding a value | (old sum + new value) / (count + 1) |
Mixtures & alligation
| Alligation ratio | n₁ : n₂ = (a₂ − M) : (M − a₁) (M = mixture mean) |
|---|---|
| Concentration | pure component ÷ total amount |
| Replacement (repeated) | remaining = original × (1 − r/V)ⁿ |
| Mean of two equal groups | (a₁ + a₂) / 2 (weights equal) |
GRE reference
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