If p and q are non zero integers, is p/q > 0

GIVEN Neither P nor q is ZERO.
When p/q >0: if (1) p and q are both positive or (2) p and q are both negative.
In short, if both p and q are of SAME SIGN, p/q is positive.

Statement 1:|p^3|=|q^3|
Learning point : In case of determining positive or negative sign, ODD POWER IS USELESS (if the base is NON ZERO).

Because, in case of odd power, if the base is negative, resulting output will definitely be negative, and if the base is positive , resulting output will definitely be positive.
For example,
(a). (-2)^3=-8 [here base is negative (-2) & resulting output is also negative (-8)]

(b). (2)^3=8 [here base is positive (2) & resulting output is also positive (8)]

Back the statement 1, now it becomes |p|=|q|. That means following two distances are equal
(I) the distance between 0 and p,
(II) the distance between 0 and q,
That means, both p and q are the same point (for example 2&2 or -2 &-2) or opposite direction values (for example 2 and -2).
So p and q can be same direction or opposite direction. So statement 1 is insufficient.

Posted from my mobile device

Even if p=1and q=(-1), |p^3|=|q^3|

|(1)^3|=|1|=1

And |(-1)^3|=|(-1)|=1

Posted from my mobile device

pramesh10

If p and q are non zero integers, is p/q > 0


(1) |p^3| = |q^3|

(2) |p + q| = |p| + |q|

#1
|p^3| = |q^3|
the above relation can be considered valid when both p & q are either +ve /-ve or opposite sign integers , in that case p/q >0 wont stand always true as there is a possiblity of having either of p or q as -ve integer . you can test with p=2 , q=2 , p=-2, q=2 , p = 2, q=-2 or p=q=-2 ..

#2
|p + q| = |p| + |q|
this relation would stand true and valid only when both p & q are +ve integers , p=2,q=2
so our question of whether p/q>0 will be yes
so this statement is sufficient

hope this helps..

#2
|p + q| = |p| + |q|
this relation would stand true when both p & q have the same sign.
For eg: p= -5, q= -3
|p+q|=8
|p|=5
|q|=3
|p|+ |q| = 8
Thus, p/q will always be positive. p/q>0
Hence the answer is B.