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SSC CGL 2024 PYQ — Question 66

SSC CGL - 09 Sep 2024 - Shift 3 • Quantitative Aptitude • Q66

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If x, y and z are positive numbers and x + y + z = 1, then the least value of 1x+1y+1z{1\over x} + {1\over y} + {1\over z} is:

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Correct answer: C

Explanation

The correct answer is Option 3 i.e. 9.

We know that,

Arithmetic mean ≥ Harmonic mean

⇒ (x+y+z)3(x + y + z)\over3 ≥ 31x+1y+1z3\over{{1\over x} + {1\over y} + {1\over z}}

⇒ 131\over3 ≥ 31x+1y+1z3\over{{1\over x} + {1\over y} + {1\over z}}

⇒ 1x+1y+1z{1\over x} + {1\over y} + {1\over z} ≥ 9

So, 

The least value of 1x+1y+1z{1\over x} + {1\over y} + {1\over z} is 9