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If (3/a)/(1/(b/5) + (6/b)) = 9/22

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Bunuel
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If (3/a)/(1/(b/5) + (6/b)) = 9/22 [#permalink] New post  28 Sep 2021, 02:30
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If \(\frac{\frac{3}{a}}{\frac{1}{\frac{b}{5}} + \frac{6}{b}} = \frac{9}{22}\), what is the value of \(\frac{b}{a}\) ?

(A) \(\frac{11}{3}\)

(B) \(\frac{3}{11}\)

(C) \(\frac{2}{3}\)

(D) \(\frac{3}{2}\)

(E) \(\frac{9}{11}\)
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BrentGMATPrepNow
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Re: If (3/a)/(1/(b/5) + (6/b)) = 9/22 [#permalink] New post  28 Sep 2021, 06:59
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Bunuel wrote:
If \(\frac{\frac{3}{a}}{\frac{1}{\frac{b}{5}} + \frac{6}{b}} = \frac{9}{22}\), what is the value of \(\frac{b}{a}\) ?

(A) \(\frac{11}{3}\)

(B) \(\frac{3}{11}\)

(C) \(\frac{2}{3}\)

(D) \(\frac{3}{2}\)

(E) \(\frac{9}{11}\)


Important property: : \(\frac{1}{(\frac{a}{b})}=\frac{b}{a}\)

When we apply the property we get: \(\frac{\frac{3}{a}}{\frac{5}{b}+\frac{6}{b}} = \frac{9}{22}\)

Now simplify the denominator on the left side: \(\frac{\frac{3}{a}}{\frac{11}{b}} = \frac{9}{22}\)

Rewrite the left side as follows: \((\frac{3}{a})(\frac{b}{11}) = \frac{9}{22}\)

Simplify the left side: \(\frac{3b}{11a} = \frac{9}{22}\)

Multiply both sides of the equation by \(\frac{11}{3}\) to get: \(\frac{b}{a} = \frac{3}{2}\)

Answer: D
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Re: If (3/a)/(1/(b/5) + (6/b)) = 9/22 [#permalink]
28 Sep 2021, 06:59
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