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

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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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GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4015
Re: x + y = 8. Does x = 3?  [#permalink]

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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
No information about z.
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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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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Hello from the GMAT Club BumpBot!

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