Is y = 7?

[Gmat_mission]

Is y = 7?

(1) x - 4 = 0
(2) (x - 3)(y - 7) = 0

[spoiler]OA=C[/spoiler].

Why is not sufficient the second statement? May someone helps me? Thanks.

[Vincen]

Hello Gmat_mission.

Here, we have to say if y is equal to 7 or not.

(1) x - 4 = 0

This statement implies that x=4. This doesn't give us information about y. Then it is NOT SUFFICIENT.

(2) (x - 3)(y - 7) = 0

Here we have two options: x=3 or y=7. Since y can be 7 or not, this statement is NOT SUFFICIENT.

Now, if we use both statements together we will get that necessary y=7. Therefore, here we get a unique answer. SUFFICIENT.

Hence, we have that the correct answer is the option C.

I hope it helps.

[Brent@GMATPrepNow]

Is y = 7?

(1) x - 4 = 0
(2) (x - 3)(y - 7) = 0

Target question: Is y = 7?

Statement 1: x - 4 = 0
In other words, x = 4
Since we have no information about y, statement 1 is NOT SUFFICIENT

Statement 2: (x - 3)(y - 7) = 0
This tells us that EITHER x = 3 OR y = 7
So, y COULD equal 7, or y might not equal 7

For example, consider these two possible cases:
Case a: x = 2 and y = 7. Notice that these values satisfy the equation (x - 3)(y - 7) = 0. In this case, the answer to the target question is YES. y DOES equal 7
Case b: x = 3 and y = 2. Notice that these values satisfy the equation (x - 3)(y - 7) = 0. In this case, the answer to the target question is NO. y does NOT equal 7
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 2 tells us that EITHER x = 3 OR y = 7
Statement 1 tells us that x = 4
Since statement 1 eliminates the possibility that x = 3, it MUST be the case that y = 7
In other words, the answer to the target question is YES. y DOES equal 7
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent