GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Oct 2019, 23:29

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 25 Sep 2018
Posts: 428
Location: United States (CA)
Concentration: Finance, Strategy
GMAT 1: 640 Q47 V30
GPA: 3.97
WE: Investment Banking (Investment Banking)
If p and q are non zero integers, is p/q > 0  [#permalink]

### Show Tags

18 Feb 2019, 11:07
9
00:00

Difficulty:

35% (medium)

Question Stats:

67% (01:28) correct 33% (01:35) wrong based on 165 sessions

### HideShow timer Statistics

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

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

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

_________________
Why do we fall?...So we can learn to pick ourselves up again
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5021
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If p and q are non zero integers, is p/q > 0  [#permalink]

### Show Tags

19 Feb 2019, 04:49
1
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
Intern
Joined: 10 Jan 2019
Posts: 2
Re: If p and q are non zero integers, is p/q > 0  [#permalink]

### Show Tags

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?
Manager
Joined: 11 Feb 2013
Posts: 149
GMAT 1: 490 Q44 V15
GMAT 2: 690 Q47 V38
GPA: 3.05
WE: Analyst (Commercial Banking)
If p and q are non zero integers, is p/q > 0  [#permalink]

### Show Tags

Updated on: 04 Apr 2019, 23:39
1
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

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.
Manager
Joined: 11 Feb 2013
Posts: 149
GMAT 1: 490 Q44 V15
GMAT 2: 690 Q47 V38
GPA: 3.05
WE: Analyst (Commercial Banking)
Re: If p and q are non zero integers, is p/q > 0  [#permalink]

### Show Tags

04 Apr 2019, 07:31
1
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

Posted from my mobile device
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5021
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If p and q are non zero integers, is p/q > 0  [#permalink]

### Show Tags

04 Apr 2019, 09:03
2
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..
Intern
Joined: 29 Oct 2018
Posts: 1
Re: If p and q are non zero integers, is p/q > 0  [#permalink]

### Show Tags

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
Re: If p and q are non zero integers, is p/q > 0   [#permalink] 25 Jul 2019, 22:38
Display posts from previous: Sort by