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GRE Math Challenge #142-(1-x)/(x-1)= 1/x

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sandy
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GRE Math Challenge #142-(1-x)/(x-1)= 1/x [#permalink] New post   Updated on: 20 Feb 2020, 16:34
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\(\frac{(1-x)}{(x-1)}= \frac{1}{x}\)

x is not equal to 1

Quantity A
Quantity B
X
\(-\frac{1}{2}\)




A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

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B

Originally posted by sandy on 15 May 2015, 11:44.
Last edited by Carcass on 20 Feb 2020, 16:34, edited 4 times in total.
Edited by Carcass
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Re: GRE Math Challenge #142 [#permalink] New post   15 May 2015, 13:34
1
sandy wrote:
\((1-x)/(x-1)= 1/x\)

x is not equal to 1

Quantity A: x
Quantity B: -1/2


SOLVE FOR x

Notice that we can take (1-x)/(x-1) and rewrite it as follows:
(1-x)/(x-1) = (-1)(-1 + x)/(x - 1)
= (-1)(x - 1)/(x - 1)
= -1

So, our original equation becomes -1 = 1/x, which means x = -1

So, we get:
Quantity A: -1
Quantity B: -1/2

-1/2 is greater than -1, so the correct answer is
Show: ::
B


Cheers,
Brent
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Re: GRE Math Challenge #142-(1-x)/(x-1)= 1/x [#permalink] New post   09 Aug 2016, 17:33
1
Why did you multiply by (-1) here? to eliminate the fraction?

(-1)(-1 + x)/(x - 1)
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Re: GRE Math Challenge #142-(1-x)/(x-1)= 1/x [#permalink] New post   10 Aug 2016, 04:48
1
Faye214 wrote:
Why did you multiply by (-1) here? to eliminate the fraction?

(-1)(-1 + x)/(x - 1)


To be clear, I'm not multiplying by -1. I'm factoring out -1 from (1 - x)
In other words, I'm REWRITING (1 - x) as (-1)(-1 + x) so that I can eliminate the fraction.

Cheers,
Brent
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GRE Math Challenge #142-(1-x)/(x-1)= 1/x [#permalink] New post   17 Jun 2021, 01:51
GreenlightTestPrep wrote:
sandy wrote:
\((1-x)/(x-1)= 1/x\)

x is not equal to 1

Quantity A: x
Quantity B: -1/2


SOLVE FOR x

Notice that we can take (1-x)/(x-1) and rewrite it as follows:
(1-x)/(x-1) = (-1)(-1 + x)/(x - 1)
= (-1)(x - 1)/(x - 1)
= -1





So, our original equation becomes -1 = 1/x, which means x = -1

So, we get:
Quantity A: -1
Quantity B: -1/2

-1/2 is greater than -1, so the correct answer is
Show: ::
B


Cheers,
Brent



But sir, if question is not mentioned "x is not equal to 1
", then what would be your solution?
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Re: GRE Math Challenge #142-(1-x)/(x-1)= 1/x [#permalink] New post   17 Jun 2021, 07:53
It has to be mentioned. The denominator can't be zero.

kumarneupane4344 wrote:
GreenlightTestPrep wrote:
sandy wrote:
\((1-x)/(x-1)= 1/x\)

x is not equal to 1

Quantity A: x
Quantity B: -1/2


SOLVE FOR x

Notice that we can take (1-x)/(x-1) and rewrite it as follows:
(1-x)/(x-1) = (-1)(-1 + x)/(x - 1)
= (-1)(x - 1)/(x - 1)
= -1





So, our original equation becomes -1 = 1/x, which means x = -1

So, we get:
Quantity A: -1
Quantity B: -1/2

-1/2 is greater than -1, so the correct answer is
Show: ::
B


Cheers,
Brent



But sir, if question is not mentioned "x is not equal to 1
", then what would be your solution?
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Re: GRE Math Challenge #142-(1-x)/(x-1)= 1/x [#permalink] New post   05 May 2023, 10:21
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