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

Question

If p and q are non zero integers, is  \frac{p}{q}  > 0

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

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

Archit3110 · Answer

#1
p * q can be both or either be +/- ve integers so value of p/q>0 or <0 possible
insufficient
#2
both p & q have to be +ve integers to be valid
so 
p/q >0 always
sufficient
IMO b

pramesh10 · Answer

@Archit3110- Can you please explain how p and q be both or either be +/- ve integers so value? Based on statement 1, p and q are either both positive or negative. Hence p/q in either cases will be > 0. What am I missing here?

BelalHossain046 · Answer

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

(b). (2)^3=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

BelalHossain046 · Answer

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

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

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

Posted from my mobile device

Archit3110 · Answer

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..

singhpriyasha14 · Answer

#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.

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

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