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# If x/y = 2/3, then (x - y)/x?

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Intern
Joined: 18 Feb 2005
Posts: 40
If x/y = 2/3, then (x - y)/x?  [#permalink]

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21 Oct 2005, 00:42
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87% (00:46) correct 13% (01:19) wrong based on 386 sessions

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If $$\frac{x}{y} = \frac{2}{3}$$, then $$\frac{x - y}{x}$$?

A. -1/2
B. -1/3
C. 1/3
D. 1/2
E. 5/2
##### Most Helpful Expert Reply
Math Expert
Joined: 02 Sep 2009
Posts: 61189
Re: If x/y = 2/3, then (x - y)/x?  [#permalink]

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17 Sep 2013, 18:17
5
1
njss750 wrote:
If x/y =2/3, then (x-y)/x?

A. -1/2
B. -1/3
C. 1/3
D. 1/2
E. 5/2

x/y=2/3 --> y/x=3/2.

$$\frac{x-y}{x}=1-\frac{y}{x}=1-\frac{3}{2}=-\frac{1}{2}$$.

Answer: A.
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##### General Discussion
VP
Joined: 24 Sep 2005
Posts: 1274
Re: If x/y = 2/3, then (x - y)/x?  [#permalink]

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21 Oct 2005, 00:54
njss750 wrote:
x/y =2/3, then (x-y)/x?
-1/2, -1/3, 1/3, 1/2, 5/2

Since this was in the last few probs of OG, thot that x/y could also be interpreted as x=-2 and y=-3 and therefore x/y can be equal to 2/3. OG proved me wrong, but is this a theoretical possibility?

we have this law of fraction:
a/b=c/d= (a-c)/(b-d)

x/y=2/3 ---> x/2=y/3= (x-y)/(2-3)=(x-y)/(-1) ---> (x-y)/x= -1/2
VP
Joined: 24 Sep 2005
Posts: 1274
Re: If x/y = 2/3, then (x - y)/x?  [#permalink]

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21 Oct 2005, 00:55
hik, i thought too complicatedly ....you're right, ywilfred!
Intern
Joined: 04 Sep 2013
Posts: 10
Re: If x/y = 2/3, then (x - y)/x?  [#permalink]

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17 Sep 2013, 18:02
laxieqv wrote:
njss750 wrote:
x/y =2/3, then (x-y)/x?
-1/2, -1/3, 1/3, 1/2, 5/2

Since this was in the last few probs of OG, thot that x/y could also be interpreted as x=-2 and y=-3 and therefore x/y can be equal to 2/3. OG proved me wrong, but is this a theoretical possibility?

we have this law of fraction:
a/b=c/d= (a-c)/(b-d)

x/y=2/3 ---> x/2=y/3= (x-y)/(2-3)=(x-y)/(-1) ---> (x-y)/x= -1/2

will you please explain this rule i couldn't find it anywhere on the internet? also i am not familiar with it either

i have solved it like this:x/y=2/3
x-y/x=x/x-y/x
1-2/3=3-2/3
so the answer is 1/3............. am i right?? :s
Intern
Joined: 29 May 2013
Posts: 5
Re: If x/y = 2/3, then (x - y)/x?  [#permalink]

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17 Sep 2013, 18:24
x/y=2/3, then y/x=3/2.
(x-y)/x = x/x-y/x = 1-3/2 = -1/2
Intern
Joined: 04 Sep 2013
Posts: 10
Re: If x/y = 2/3, then (x - y)/x?  [#permalink]

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18 Sep 2013, 09:52
i got it!!! thanks guys!!!!
Manager
Joined: 25 Sep 2012
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Re: If x/y = 2/3, then (x - y)/x?  [#permalink]

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19 Sep 2013, 02:49
1
I solved it like this...

x/y = 2/3
so x = 2 and y = 3
substitute and get the answer -1/2
Intern
Joined: 21 Nov 2013
Posts: 1
Re: If x/y = 2/3, then (x - y)/x?  [#permalink]

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21 Nov 2013, 18:59
I'm still confused. Where does the 1 come from?
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Re: If x/y = 2/3, then (x - y)/x?  [#permalink]

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21 Nov 2013, 20:32
2
2
sdlucas wrote:
I'm still confused. Where does the 1 come from?

You separate out the numerator.

$$\frac{(x-y)}{x} = \frac{x}{x} - \frac{y}{x} = 1 - \frac{y}{x} = 1 - \frac{3}{2} = -\frac{1}{2}$$
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Joined: 25 Jan 2016
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Location: United States (OH)
GPA: 3.7
Re: If x/y = 2/3, then (x - y)/x?  [#permalink]

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19 Apr 2016, 15:12
did i get lucky? or can this be a correct approach.

I cross multiplied to get 3x=2y. I then divided by 3 to get 2/3y and just plugged that into where ever x was
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Re: If x/y = 2/3, then (x - y)/x?  [#permalink]

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19 Apr 2016, 21:12
1
ross14 wrote:
did i get lucky? or can this be a correct approach.

I cross multiplied to get 3x=2y. I then divided by 3 to get 2/3y and just plugged that into where ever x was

Yes, the approach is fine. You are eliminating one variable, bringing it all in terms of a single variable and then cancelling it off to get a value.
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Re: If x/y = 2/3, then (x - y)/x?  [#permalink]

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29 Oct 2017, 10:15
1
njss750 wrote:
If x/y =2/3, then (x-y)/x?

A. -1/2
B. -1/3
C. 1/3
D. 1/2
E. 5/2

Replace x = 2 & y = 3

So, $$\frac{(x-y)}{x} = \frac{2 - 3}{2} = -\frac{1}{2}$$

Hence, answer will be (A) $$-\frac{1}{2}$$
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Re: If x/y = 2/3, then (x - y)/x?  [#permalink]

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15 Sep 2019, 02:11
njss750 wrote:
If x/y =2/3, then (x-y)/x?

A. -1/2
B. -1/3
C. 1/3
D. 1/2
E. 5/2

Given: x/y =2/3

Asked: (x-y)/x=?

$$\frac{x}{y} =\frac{2}{3}$$
$$\frac{x-y}{x} = \frac{-1}{2}$$

IMO A
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Joined: 12 Dec 2019
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Re: If x/y = 2/3, then (x - y)/x?  [#permalink]

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12 Dec 2019, 17:11
(x/y) - (y/y)
----------------- =
(x/y)

2/3 - 1
----------------- =
2/3

-1/2

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Re: If x/y = 2/3, then (x - y)/x?  [#permalink]

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01 Jan 2020, 18:43
njss750 wrote:
If $$\frac{x}{y} = \frac{2}{3}$$, then $$\frac{x - y}{x}$$?

A. -1/2
B. -1/3
C. 1/3
D. 1/2
E. 5/2

Cross-multiplying, we have:

3X = 2Y

Thus, we can let X = 2 and Y = 3, so we have:

(2 - 3)/2 = -1/2

Alternate Solution:

(X-Y)/X = X/X - Y/X = 1 - Y/X

Since X/Y = 2/3, Y/X = 3/2, so 1 - Y/X = 1 - 3/2 = -1/2.

Answer: A
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Re: If x/y = 2/3, then (x - y)/x?   [#permalink] 01 Jan 2020, 18:43
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