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If x > 1 and a/b = 1 - 1/x, then b/a =

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If x > 1 and a/b = 1 - 1/x, then b/a =  [#permalink]

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New post 15 Mar 2018, 22:59
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A
B
C
D
E

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  15% (low)

Question Stats:

91% (00:45) correct 9% (01:44) wrong based on 47 sessions

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Re: If x > 1 and a/b = 1 - 1/x, then b/a =  [#permalink]

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New post 15 Mar 2018, 23:00
Bunuel wrote:
If \(x > 1\) and \(\frac{a}{b} = 1 - \frac{1}{x}\), then \(\frac{b}{a} =\)

A. x

B. x - 1

C. \(\frac{x - 1}{x}\)

D. \(\frac{x}{x - 1}\)

E. \(\frac{1}{x} - 1\)


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Re: If x > 1 and a/b = 1 - 1/x, then b/a =  [#permalink]

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New post 16 Mar 2018, 00:42
Bunuel wrote:
If \(x > 1\) and \(\frac{a}{b} = 1 - \frac{1}{x}\), then \(\frac{b}{a} =\)

A. x

B. x - 1

C. \(\frac{x - 1}{x}\)

D. \(\frac{x}{x - 1}\)

E. \(\frac{1}{x} - 1\)


a/b = (x-1)/x

i.e. b/a = x/(x-1)

Answer: option D
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If x > 1 and a/b = 1 - 1/x, then b/a =  [#permalink]

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New post 16 Mar 2018, 06:18
Bunuel wrote:
If \(x > 1\) and \(\frac{a}{b} = 1 - \frac{1}{x}\), then \(\frac{b}{a} =\)

A. x

B. x - 1

C. \(\frac{x - 1}{x}\)

D. \(\frac{x}{x - 1}\)

E. \(\frac{1}{x} - 1\)

We are asked for the reciprocal of \(\frac{a}{b}\).

We can take the reciprocal of RHS only if RHS expression is a single number or a single fraction.

(If fractions are added or subtracted on RHS, find the sum or difference. Then flip the resultant fraction.)
\(\frac{a}{b} = 1 - \frac{1}{x}\)

\(\frac{a}{b} = (\frac{1}{1}*\frac{x}{x}) - (\frac{1}{x}*\frac{x}{x})\)

\(\frac{a}{b} = \frac{x}{x}-\frac{1}{x}\)

\(\frac{a}{b} = \frac{(x-1)}{x}\)

\(\frac{b}{a} = \frac{x}{(x-1)}\)


Answer D

Or use \(\frac{1}{a}-\frac{1}{b}=\frac{b-a}{ab}\). From original fractions, use numbers in the denominator. Subtract first number from second number (b-a) for the new numerator. Multiply the numbers (ab) for the new denominator.
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Re: If x > 1 and a/b = 1 - 1/x, then b/a =  [#permalink]

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New post 18 Mar 2018, 04:38
\(\frac{a}{b}\)= 1-\(\frac{1}{x}\)

\(\frac{a}{b}\)= \(\frac{x-1}{x}\)

Inverse the above equation

\(\frac{b}{a}\)=\(\frac{x}{x-1}\)

Answer: D.
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Re: If x > 1 and a/b = 1 - 1/x, then b/a =   [#permalink] 18 Mar 2018, 04:38
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