SATHEE: Quantitative Aptitude Ques 232

Quantitative Aptitude Ques 232

Question: BE, CF are the two medians of $ \Delta ABC $ and G is their point of intersection. EF cuts AG at O. The ratio of AO and OG is equal to

Options:

A) 1 : 3

B) 2 : 3

C) 3 : 1

D) 1 : 2

Show Answer

Answer:

Correct Answer: C

Solution:

F and E are mid-points of AB and AC, respectively So, $ EF\parallel BC $ Also in $ \Delta ADB, $ $ FO\parallel BD $

$ \Rightarrow $ $ \frac{AF}{FB}=\frac{AO}{OD} $

$ \Rightarrow $ $ \frac{AF}{FB}+1=\frac{AO}{OD}+1 $

$ \Rightarrow $ $ \frac{AF+FB}{FB}=\frac{OA+OD}{OD} $

$ \Rightarrow $ $ \frac{AB}{FB}=\frac{AD}{OD} $
$ \Rightarrow $ $ \frac{2FB}{FB}=\frac{AD}{OD} $ So, O is mid-point of AD.

$ \therefore $ $ OA=OD $

$ \Rightarrow $ $ OA=OG+DG $

$ \Rightarrow $ $ OA=OG+\frac{AG}{2} $ $ ( \because \frac{AG}{GD}=\frac{2}{1} ) $

$ \Rightarrow $ $ OA=OG+\frac{AO+OG}{2} $

$ \Rightarrow $ $ 2OA=3OG+AO $
$ \Rightarrow $ $ \frac{AO}{AG}=\frac{3}{1}=3:1 $

Quantitative Aptitude Ques 231

Quantitative Aptitude Ques 233

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