If p and r are integers, p does not equal 0, and p = -r, which of the following must be true?

Question

p p>r
p+r<0
p-r<0
pr<0

Answer 1

OK
Of you think of it as as p = (-1)r, you can see that p and r will be the same with one difference - their sign.

Since p cannot be 0, you can't have p*r =0.

Now, p+r = 0 since, if you added r to both sides you get this formula. So the first two answers cannot be true, since, p or r could be negative and make the statements false.

Conversely, since we already know that p+r =0, anwers three and four also are false.

So that leaves the last answer and it is true:
p*r will always be <0.

Hope that helps.

Answer 2

pr < 0

Answer 3

only pr < 0

Answer 4

p = -r just means they are opposites (like 5 and -5) thus adding them will equal 0.

only one that must hold true is pr < 0 since a neg*pos = neg

Answer 5

I would say pr<0
if p = -1 then r = 1 (-1 = -(1))
and if p = 1 then r = -1 (1=-(-1))

so if p is positive then r must be negative and vice versa,
if you multiply a positive and a negative integer the answer will always be negative.

Answer 6

pr < 0, since p = -r, then pr = -p², which is always negative

The first two and the fourth can be false since we don't know which, p or r, is positive.

The third is false. p + r = 0

Answer 7

p -r < r True

p>r => -r > r False

p+r -r + r < 0 False

p - r <0 => -r - r <0 True

pr<0 => -r x r <0 => -r^2 <0 True

Answer 8

pr<0.

Consider p = 2 and r = -2.

Also, consider p = -2 and r = 2.
Given the statement above, we don't know whether pr.
p-r = 2p
p + r = 0.