Project ForgeGeneral Aptitude
Quantitative Aptitude
GATE 2024
Medium
For positive non-zero real variables x and y, if ln((x+y)/2) = (1/2)[ln(x) + ln(y)], then the value of x/y + y/x is
- A1
- B1/2
- 2
- D4
Explanation
The RHS equals ln(√(xy)), so the equation says (x+y)/2 = √(xy) — the arithmetic mean equals the geometric mean, which for positive reals happens if and only if x = y (equality case of AM-GM). Substituting x = y: x/y + y/x = 1 + 1 = 2.
Source: GATE CS 2024 Session 2 (CS2) (2024)
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