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# (x−y)(y−x+1) = ?

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Intern
Joined: 22 Mar 2017
Posts: 15
(x−y)(y−x+1) = ?  [#permalink]

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Updated on: 07 Jun 2017, 19:58
2
00:00

Difficulty:

35% (medium)

Question Stats:

68% (01:16) correct 32% (01:32) wrong based on 152 sessions

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(x−y)(y−x+1) = ?

(1) x−y=2

(2) y−x+1=−1

Originally posted by Nathanlambson on 07 Jun 2017, 14:21.
Last edited by Bunuel on 07 Jun 2017, 19:58, edited 1 time in total.
Renamed the topic.
CEO
Joined: 11 Sep 2015
Posts: 3431
Re: (x−y)(y−x+1) = ?  [#permalink]

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07 Jun 2017, 14:35
2
Top Contributor
Nathanlambson wrote:
(x − y)(y − x + 1) = ?

(1) x−y=2

(2) y−x+1=−1

Target question: What is the value of (x − y)(y − x + 1)?

Statement 1: x−y = 2
Great. We already have half of the expression of (x − y)(y − x + 1)
Take x−y = 2 and multiply both sides by -1 to get: -x+y = -2
Rewrite as: y - x = -2
Add 1 to both sides: y - x + 1 = -1
So, (x − y)(y − x + 1) = (2)(-1) = -2
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: y−x+1=−1
Once again, we're given half of the expression of (x − y)(y − x + 1)
Take y−x+1=−1 subtract 1 from both sides to get: y−x=−2
Multiply both sides by -1 to get: -y+x = 2
Rewrite as: x - y = 2
So, (x − y)(y − x + 1) = (2)(-1) = -2
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent
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Re: (x−y)(y−x+1) = ?  [#permalink]

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04 Sep 2018, 18:29
Nathanlambson wrote:
(x−y)(y−x+1) = ?

(1) x−y=2

(2) y−x+1=−1

$$? = \left( {x - y} \right)\left( {y - x + 1} \right)$$

$$\left( 1 \right)\,\,\,\boxed{x - y = 2}\,\,\,\, \Rightarrow \,\,\,y - x = - 2\,\,\,\, \Rightarrow \,\,\,\boxed{y - x + 1 = - 2 + 1}$$

$$? = 2 \cdot \left( { - 2 + 1} \right)\,\,\,\,\,{\text{SUF}}.$$

$$\left( 2 \right)\,\,\boxed{y - x + 1 = - 1}\,\,\, \Rightarrow \,\,\,y - x = - 2\,\,\,\, \Rightarrow \boxed{x - y = 2}\,\,$$

$$? = 2 \cdot \left( { - 1} \right)\,\,\,\,{\text{SUF}}.$$

The above follows the notations and rationale taught in the GMATH method.

Regards,
fskilnik.
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Re: (x−y)(y−x+1) = ?   [#permalink] 04 Sep 2018, 18:29
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# (x−y)(y−x+1) = ?

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