What is the value of w? 1) w<0 2) w^2=100

[AsadA969]

What is the value of w?
1) w<0
2) w^2=100

Correct Answer C.

Source: TargetTestPrep

[AsadA969]

What is the value of w?
1) w<0
2) w^2=100

Correct Answer C.

Source: TargetTestPrep

Can you explain the statement 2, please? My explanation says that w= ±10. If I consider the value of w= +10 too, will the statement 2 contradict statement 1 where the value of w is only negative value?

[StaceyKoprince]

Good question—this is an important point to understand.

Statement 1 says that w is negative.
Statement 2 days that w is either +10 or –10.

Those two statements don't contradict—rather, they partially overlap. They contain some information that is in common. And then, when you put them together, you're able to narrow down to just one value. That's why the correct answer is (C).

This would be the equivalent in the real world of saying something like:
Her age is odd.
She is either 25 or 26 years old.

Using just the first fact, you don't know how old she is. Using just the second fact, you don't know how old she is. But if you combine the two facts, now you know how old she is.

A contradiction would be something like this:
(1) w is negative
(2) w is positive

There is no way for any single value to work with these two facts—there is no value that is both negative and positive. So these are contradictory facts.

Likewise, this is a contradiction:
Her age is odd.
She is 26 or 28 years old.

There's no way to reconcile those two sets of facts.