If x and y are non-zero integers

[hima.batavia]

If x and y are non-zero integers and |x| + |y| = 32, what is xy?

(1) -4x - 12y = 0

(2) |x| - |y| = 16


I don't understand why you assume that x and y are opposite signs based on simplifying the first expression.

Thanks!
Hima

[jnelson0612]

Hi Hima,
Take a look at the first expression, statement 1. You have
-4x - 12y = 0.

If I add 12y to both sides, I get -4x = 12y. If I divide both sides by -4, I get x=-3y.

If x = -3y, then we have the following two scenarios. Either:
a) x is positive and y is negative
OR
b) x is negative and y is positive

Notice how it is impossible for both to be negative or positive.

I hope this helps!

[hima.batavia]

Thanks Jamie!

I have a follow-up question. Why do you convert them back to absolute values? When do you use that technique as a general rule?

Cheers,
Hima

[jnelson0612]

Thanks Jamie!

I have a follow-up question. Why do you convert them back to absolute values? When do you use that technique as a general rule?

Cheers,
Hima

Hi Hima,
Sorry, I'm not understanding your question "why do you convert them back to absolute values?" Can you elaborate?

Thank you!

[rite2deepti]

Thanks Jamie!

I have a follow-up question. Why do you convert them back to absolute values? When do you use that technique as a general rule?

Cheers,
Hima

Hi Hima,
Sorry, I'm not understanding your question "why do you convert them back to absolute values?" Can you elaborate?

Thank you!

What is the OA I am getting B as my answer

[jnelson0612]

rite2deepti, the correct answer is A.

See this link to read the full explanation: cat-question-opposite-signs-t1514.html

Thank you,

[PoonamS895]

I'm not sure why statement 2 is not sufficient.

[RonPurewal]

I'm not sure why statement 2 is not sufficient.

all you can figure out from statement 2 (plus the prompt) is that |x| = 24 and |y| = 8.
this means that x could be either 24 or –24, and y could be either 8 or –8.
thus there are two different possible values of xy (with opposite signs).