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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, 21:59
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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 15 Mar 2018, 22:00
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. \(\frac{1}{x} - 1\)


7. Algebra



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New to the Math Forum?
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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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, 23:42
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, 05:18
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, 03:38
\(\frac{a}{b}\)= 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 = &nbs [#permalink] 18 Mar 2018, 03:38
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