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# x + y = 8. Does x = 3?

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Math Expert
Joined: 02 Sep 2009
Posts: 58434
x + y = 8. Does x = 3?  [#permalink]

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11 Aug 2016, 06:48
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Difficulty:

15% (low)

Question Stats:

82% (01:37) correct 18% (01:53) wrong based on 167 sessions

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x + y = 8. Does x = 3?

(1) 2x + z = 8
(2) 3y − 4z = 7

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Posts: 4015
Re: x + y = 8. Does x = 3?  [#permalink]

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11 Aug 2016, 07:32
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Bunuel wrote:
x + y = 8. Does x = 3?

(1) 2x + z = 8
(2) 3y − 4z = 7

Target question: Does x = 3

Given: x + y = 8

Statement 1: 2x + z = 8
So, statement 1 is NOT SUFFICIENT

NOTE: If we're not quite convinced that statement 1 is not sufficient, we might TEST some values.
Case a: x = 1, y = 7, and z = 6 (satisfies the given info AND statement 1). In this case x = 1
Case b: x = 0, y = 8, and z = 8 (satisfies the given info AND statement 1). In this case x = 2
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 3y − 4z = 7
Once again, we have no information about z.
So, statement 2 is NOT SUFFICIENT

ONCE AGAIN, if we're not quite convinced that statement 1 is not sufficient, we might TEST some values.
Case a: x = 7, y = 1, and z = 1 (satisfies the given info AND statement 2). In this case x = 7
Case b: x = 3, y = 5, and z = 2 (satisfies the given info AND statement 2). In this case x = 3
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Given: x + y = 8, which means y = 8 - x
Statement 2: 3y − 4z = 7. Replace y with 8 - x to get: 3(8 - x ) - 4z = 7
Simplify to get: -3x - 4z = -17
Statement 1: 2x + z = 8

Since we now have two equations with 2 variables (-3x - 4z = -17 and 2x + z = 8), AND those 2 equations are not equivalents, we COULD solve this system for x, which means we COULD answer the target question.
Since we COULD answer the target question with certainty, the combined statements are SUFFICIENT

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Re: x + y = 8. Does x = 3?  [#permalink]

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11 Aug 2016, 07:52
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Bunuel wrote:
x + y = 8. Does x = 3?

(1) 2x + z = 8
(2) 3y − 4z = 7

(1) 2x + z = 8; here three equation required to solve the equation,but we have two only(along with x+y=8) ,Not Sufficient

(2) 3y − 4z = 7 ; here three equation required to solve the equation,but we have two only(along with x+y=8) ,Not Sufficient

(1) + (2) Now we have total three equation ,So we can easily get three individual value(x,y and z).Sufficient

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Re: x + y = 8. Does x = 3?  [#permalink]

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08 Aug 2018, 12:11
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Re: x + y = 8. Does x = 3?   [#permalink] 08 Aug 2018, 12:11
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