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If y≠0 and x/y=3, then (x-y)/x=?

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If y≠0 and x/y=3, then (x-y)/x=? [#permalink]

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If \(y≠0\) and \(\frac{x}{y}=3\), then \(\frac{(x-y)}{x}\)=?

A. \(-2\)
B. \(-1\)
C. \(\frac{-2}{3}\)
D. \(\frac{2}{3}\)
E. \(1\)
[Reveal] Spoiler: OA

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If y≠0 and x/y=3, then (x-y)/x=? [#permalink]

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New post 15 May 2017, 00:48
MathRevolution wrote:
If \(y≠0\) and \(\frac{x}{y}=3\), then \(\frac{(x-y)}{x}\)=?

A. \(-2\)
B. \(-1\)
C. \(\frac{-2}{3}\)
D. \(\frac{2}{3}\)
E. \(1\)

\(\frac{(x-y)}{x}\)=\(\frac{1-y}{x}\)=\(\frac{1-1}{3}\)=\(\frac{2}{3}\)=
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If y≠0 and x/y=3, then (x-y)/x=? [#permalink]

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New post 16 May 2017, 06:20
MathRevolution wrote:
If \(y≠0\) and \(\frac{x}{y}=3\), then \(\frac{(x-y)}{x}\)=?

A. \(-2\)
B. \(-1\)
C. \(\frac{-2}{3}\)
D. \(\frac{2}{3}\)
E. \(1\)


Method I

\(\frac{x}{y}=3\), multiply both sides by y

x = 3y, substitute this value into \(\frac{(x-y)}{x}\):

\(\frac{(3y-y)}{3y}\)

= \(\frac{2y}{3y}\) = \(\frac{2}{3}\)

Method II

\(\frac{x}{y}=3\) ==>

By cross multiplying or reciprocal, \(\frac{y}{x}\) = \(\frac{1}{3}\)

Then, \(\frac{(x-y)}{x}\) = \(\frac{x}{x}\) - \(\frac{y}{x}\)

Simplify: 1 - \(\frac{1}{3}\) = \(\frac{2}{3}\)

Answer
[Reveal] Spoiler:
D

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Re: If y≠0 and x/y=3, then (x-y)/x=? [#permalink]

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New post 16 May 2017, 06:32
MathRevolution wrote:
If \(y≠0\) and \(\frac{x}{y}=3\), then \(\frac{(x-y)}{x}\)=?

A. \(-2\)
B. \(-1\)
C. \(\frac{-2}{3}\)
D. \(\frac{2}{3}\)
E. \(1\)


Let \(x = 6\) and \(y = 2\)

So, \(\frac{x}{y}=3\)

Now, \(\frac{(x-y)}{x}\)

\(= \frac{6 - 2}{6}\)

\(= \frac{4}{6}\)

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

Thus, answer must be (D) \(\frac{4}{6}\)
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Expert Post
Math Revolution GMAT Instructor
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Re: If y≠0 and x/y=3, then (x-y)/x=? [#permalink]

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New post 17 May 2017, 00:33
==> You get \(\frac{x}{y}=3\), \(x=3y\), then \(\frac{(x-y)}{x}=\frac{(3y-y)}{3y}=\frac{2y}{3y}=\frac{2}{3}\).

The answer is D.
Answer: D
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Re: If y≠0 and x/y=3, then (x-y)/x=? [#permalink]

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New post 17 May 2017, 02:53
If y≠0 and \(\frac{x}{y}\) = 3 , then \(\frac{(x-y)}{x}\)
A. −2
B. −1
C. −\(\frac{2}{3}\)
D. \(\frac{2}{3}\)
E. 1


\(\frac{x}{y}\) = 3 ; x = 3y
\(\frac{(x-y)}{x}\) [Substitute x = 3y]
\(\frac{3y - y}{3y}\) = \(\frac{2y}{3y}\) = \(\frac{2}{3}\)
Answer D...

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Re: If y≠0 and x/y=3, then (x-y)/x=?   [#permalink] 17 May 2017, 02:53
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