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

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If p and q are non zero integers, is p/q > 0  [#permalink]

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New post 18 Feb 2019, 11:07
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If p and q are non zero integers, is \(\frac{p}{q}\) > 0


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

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

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Re: If p and q are non zero integers, is p/q > 0  [#permalink]

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New post 19 Feb 2019, 04:49
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Abhi077 wrote:
If p and q are non zero integers, is \(\frac{p}{q}\) > 0


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

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


#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
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Re: If p and q are non zero integers, is p/q > 0  [#permalink]

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New post 04 Apr 2019, 06:35
@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?
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If p and q are non zero integers, is p/q > 0  [#permalink]

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New post Updated on: 04 Apr 2019, 23:39
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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.

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Originally posted by BelalHossain046 on 04 Apr 2019, 07:23.
Last edited by BelalHossain046 on 04 Apr 2019, 23:39, edited 1 time in total.
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Re: If p and q are non zero integers, is p/q > 0  [#permalink]

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New post 04 Apr 2019, 07:31
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pramesh10 wrote:
@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?


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

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

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

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Re: If p and q are non zero integers, is p/q > 0  [#permalink]

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New post 04 Apr 2019, 09:03
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pramesh10 wrote:
@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?


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.. :cool: :)
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Re: If p and q are non zero integers, is p/q > 0  [#permalink]

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New post 25 Jul 2019, 22:38
#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.
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Re: If p and q are non zero integers, is p/q > 0   [#permalink] 25 Jul 2019, 22:38
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