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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

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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