Algebra guide: Question 5 Page 89: Two values of X

[SherryK835]

Hello,
The data sufficiency question asks:

What is x?
1. x=4y-4
2. xy=8

Putting together the two statements, we get a quadratic equation, that tells us that x=8 or x=-4

The answer in the book is E. Is this because there are two values for x?
Does that mean until and unless we can get only one value of x, the statements are insufficient?

What if the question is in a word problem, and x represents the number of oranges. Then in that case it can only be a positive number, so we can disregard x=-4. In this scenario, do we then have sufficient information to determine what x is?

Thanks for all your help.

[SherryK835]

Hi,
Just wanted to check if someone had time to take a look at this. Hoping it didnt get lost in the queue

[RonPurewal]

Does that mean until and unless we can get only one value of x, the statements are insufficient?

correct.

What if the question is in a word problem, and x represents the number of oranges. Then in that case it can only be a positive number, so we can disregard x=-4. In this scenario, do we then have sufficient information to determine what x is?

also correct; if common sense implies restrictions, then those restrictions apply.