If a 0, b 0, and 2c = (a/b)^(1/2), what is the value of b?

Question

If a > 0, b > 0, and  2c = \sqrt{\frac{a}{b}} , what is the value of b?

(1) a = 8 and c = 2 
(2) c^2/a = 1/2

HardWorkBeatsAll · Answer

Squaring the given equation,

4*c^2 = a/b

So,

b = a/4c^2

In order to find b, we need a/c^2.

Either of (1) and (2) can be used to get this ratio. So,  (D) - EACH ALONE IS SUFFICIENT

Anonamy · Answer

How is stmt 2 sufficient, would someone kindly explain? Thx

Bunuel · Answer

From the stem:  2c = \sqrt{\frac{a}{b}} ;

Square:  4c^2=\frac{a}{b} ;

From (2): c^2/a = 1/2;

c^2 = a/2.

Substitute:  4*\frac{a}{2}=\frac{a}{b} ;

2=\frac{1}{b} ;

b = 1/2.

ganand · Answer

Hi  vikasp99 ,

Thank you for posting the question. 
Please use math mode for writing formulas. Read the following post:

Writing Mathematical Formulas in the GMAT Club Forums

If a>0, b>0, and  2c = \sqrt{\frac{a}{b}} , what is the value of b?

(1) a = 8 and c = 2

2c = \sqrt{\frac{a}{b}} \Rightarrow 4 = \sqrt{\frac{8}{b}} \Rightarrow b = \frac{1}{2} . Sufficient.

(2)  \frac{c^{2}}{a} = \frac{1}{2} 
 
 \Rightarrow a = 2 c^{2}

we know  2c = \sqrt{\frac{a}{b}} . Square both sides :  4c^{2} = \frac{a}{b} \Rightarrow 4c^{2} = \frac{2c^{2}}{b} \Rightarrow b = \frac{1}{2}

Sufficient.

Answer: D

Thanks.

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If a > 0, b > 0, and 2c = (a/b)^(1/2), what is the value of b?

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