Another inequality based question

[xerocoool]

1) In the following problem

If | x^2 * y | = | (-w) * z |, then which of the following could be true ?

Indicate all possible values

A) x^2 = wz
B) | x^2 * y| = | (-w) * z |
C) - (wz) = wz
D) | - x^2 | = | (-w) * z |
E) - w = z
F) x^2 = - | y |

Ans) A,C,D,E
My doubt is,
Answer choice "B" is an valid answer right ? (The book says A,C,D,E)
Suppose I consider X=1, Y=1, Z=1, W=1
which satisfies the main condition | x^2 * y | = | (-w) * z | => 1
Plugging those values into answer choice "B" we get,
| 1 * 1 | = | (-1) * 1 |
1 =1

Thanks

[tommywallach]

Hey Xero,

As written, (B) is the same as the inequality given in the original question...

Where is this from? Or did you copy it down wrong?

-t

[xerocoool]

Hi Tommy,

It's from Princeton 1014 - Integer Properties.

Just cross checked, option (B) is the same as the original equation. Could be an error ?

Thanks
Xero

[tommywallach]

Looks like it! Silly Princeton...

-t

[xerocoool]

Hi Tommy,

What is the right method of handling such absolute value questions (mostly with 3 or more variables).

I believe, we cannot solve for such equations and have to plug in values to prove "D"

For ex.
For the equation | x^2 * y | = | (-w) * z |
we need to test x^2 = wz

Do we need to just pick values for ex. x= 1, y=1, z=1, w=1 : plug back into both equations and check whether it holds true (depending on the question "must be" or "could be")

Or should we actually try solving the main equation ? try to simplify it or something (quite confusing)


Thanks

[tommywallach]

Hey Xero,

You wouldn't do a question like this without considering the answer choices. The work involved with "solving" something like that is pretty intense. Instead, I would work backwards from the answer choices, applying logic and only occasionally checking values.

For example:

If | x^2 * y | = | (-w) * z |, then which of the following could be true ?

A) x^2 = wz

If w = 1, z = 1, x = 1, y = 1, then A is true. Done.

C) - (wz) = wz

If everything is 0, this is fine.

Et cetera. Your original impulse to just go through answers considering values is the most logical to me.

-t

[xerocoool]

Thanks for the review.