Quantity Comparison (Q1 vs Q2)
Master Quantity Comparison (Q1 vs Q2). Solve two independent quantities and compare them ($>, <, =, \ge, \le$). Covers Quadratic, Arithmetic, and Geometry.
Model 1: The Comparison Framework
- The Core: You are given two quantities, Quantity I and Quantity II. You must find their values and compare them.
- Options Standard:
A) Quantity I > Quantity II
B) Quantity I < Quantity II
C) Quantity I тЙе Quantity II
D) Quantity I тЙд Quantity II
E) Quantity I = Quantity II or No Relation - Strategy: Do NOT estimate unless gap is huge. Calculate exact values. If Q1 depends on a variable range (e.g., ), test ALL cases against Q2.
Example:
Q: Q1: Value of x if . Q2: Value of y if .
Solution: Q1: . Q2: . Compare: +5=5, -5<5. So .
Model 2: Quadratic Inequalities
- Sign Method: Use sign of constants to predict root signs. (+,+) roots < (-,+) roots? No, verify values.
- Range Comparison: If Q1 is an interval [a, b] and Q2 is [c, d], compare endpoints. Overlap usually means 'No Relation'.
- Common Trap: (always +ve), but if , . Watch out for these definitions.
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