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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If y = (x^(-1) – 1)/(x^(-1) + 1), what is x in terms of y?

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Manager  P
Joined: 29 Oct 2019
Posts: 212
If y = (x^(-1) – 1)/(x^(-1) + 1), what is x in terms of y?  [#permalink]

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Difficulty:   15% (low)

Question Stats: 90% (01:52) correct 10% (02:53) wrong based on 20 sessions

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If $$y = \frac{x^{-1} – 1}{ x^{-1} + 1}$$, what is x in terms of y?

(A) $$\frac{y – 1}{y + 1}$$

(B) $$\frac{y + 1}{y – 1}$$

(C) $$\frac{1- y}{1 + y}$$

(D) $$\frac{1+ y}{1 - y}$$

(E) $$\frac{y}{y + 1}$$

Source: GMAT Quantum

Originally posted by sjuniv32 on 13 Feb 2020, 18:28.
Last edited by Bunuel on 13 Feb 2020, 23:08, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert V
Joined: 02 Aug 2009
Posts: 8295
Re: If y = (x^(-1) – 1)/(x^(-1) + 1), what is x in terms of y?  [#permalink]

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sjuniv32 wrote:
If y = $$\frac{x^{-1} – 1}{ x^{-1} + 1}$$, what is x in terms of y?

(A) $$\frac{y – 1}{y + 1}$$

(B) $$\frac{y + 1}{y – 1}$$

(C) $$\frac{1- y}{1 + y}$$

(D) $$\frac{1+ y}{1 - y}$$

(E) $$\frac{y}{y + 1}$$

Source: GMAT Quantum

Two ways..

1) simplify..
y = $$\frac{x^{-1} – 1}{ x^{-1} + 1}=\frac{\frac{1}{x}-1}{\frac{1}{x}+1}=\frac{\frac{1-x}{x}}{\frac{x+1}{x}}=\frac{1-x}{x+1}$$...
So $$y(x+1)=1-x.....yx+y=1-x....yx+x=1-y....x=\frac{1-y}{1+y}$$

2) Take a value for x...
Let x=1/2
y = $$\frac{x^{-1} – 1}{ x^{-1} + 1}=\frac{\frac{1}{2}^{-1}-1}{\frac{1}{2}^{-1}+1}=\frac{2-1}{2+1}=\frac{1}{3}$$

A will give -1/3
C. $$\frac{1- y}{1 + y}=\frac{1-\frac{1}{2}}{1+\frac{1}{2}}=\frac{\frac{1}{2}}{\frac{3}{2}}=\frac{1}{3}$$

C
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GMATWhiz Representative G
Joined: 07 May 2019
Posts: 387
Location: India
Re: If y = (x^(-1) – 1)/(x^(-1) + 1), what is x in terms of y?  [#permalink]

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sjuniv32 wrote:
If y = $$\frac{x^{-1} – 1}{ x^{-1} + 1}$$, what is x in terms of y?

(A) $$\frac{y – 1}{y + 1}$$

(B) $$\frac{y + 1}{y – 1}$$

(C) $$\frac{1- y}{1 + y}$$

(D) $$\frac{1+ y}{1 - y}$$

(E) $$\frac{y}{y + 1}$$

Source: GMAT Quantum

Solution

• $$y = \frac{(x^{-1} – 1)}{ (x^{-1} +1)}$$
$$⟹ y = ({\frac{1}{x} - 1})/({\frac{1}{x}+1})$$
$$⟹ y = \frac{(1 – x)}{(1+x)}$$
$$⟹ y(1+x) = (1 – x)$$
$$⟹ y+ yx= 1 – x$$
$$⟹ x(1 +y) = (1-y)$$
$$⟹ x= \frac{(1-y)}{ (1+y)}$$
Thus, the correct answer is Option C
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