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

 It is currently 18 Nov 2019, 12:07

### 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

# Are positive integers p and q both greater than n ?

Author Message
TAGS:

### Hide Tags

Manager
Joined: 16 Feb 2010
Posts: 160
Are positive integers p and q both greater than n ?  [#permalink]

### Show Tags

Updated on: 16 Oct 2019, 05:56
3
9
00:00

Difficulty:

45% (medium)

Question Stats:

65% (01:42) correct 35% (01:43) wrong based on 251 sessions

### HideShow timer Statistics

Are positive integers p and q both greater than n ?

(1) p - q is greater than n
(2) q > p

Originally posted by zisis on 14 Jul 2010, 13:40.
Last edited by Bunuel on 16 Oct 2019, 05:56, edited 3 times in total.
Edited the question and added the OA
Math Expert
Joined: 02 Sep 2009
Posts: 59125
Re: Are positive integers p and q both greater than n ?  [#permalink]

### Show Tags

14 Jul 2010, 15:06
6
3
zisis wrote:
are positive integers p and q both greater than n

(1) p-q is greater than n
(2) q>p

Given: $$p=integer>0$$ and $$q=integer>0$$. Question: is $$p>n$$ and $$q>n$$?

(1) $$p-q>n$$. Clearly insufficient.

(2) $$q>p$$, no info about $$n$$. Not sufficient.

(1)+(2) Sum (1) and (2) (we can safely do this as their signs are in the same direction): $$p-q+q>n+p$$ --> $$n<0$$. As given that both $$p$$ and $$q$$ are positive then they are greater than negative $$n$$. Sufficient.

_________________
##### General Discussion
Manager
Joined: 15 Aug 2010
Posts: 70
Location: Moscow, Russia
Schools: top schools
WE 1: Foreign Ministry - 6 years
WE 2: Law Firm - 3 years
Re: Are positive integers p and q both greater than n ?  [#permalink]

### Show Tags

17 Feb 2011, 06:59
(i) Clearly, not sufficient;
(ii) Clearly, not sufficient.

Taken together:
We can subtract two inequalities with different signs:
p-q > n -----p > n+q
q > p -------p < q
Subtract and get 0 > n

Since n is less than zero and p and q are positive integers, then obviously n < p or q
Director
Status: -=Given to Fly=-
Joined: 04 Jan 2011
Posts: 787
Location: India
Schools: Haas '18, Kelley '18
GMAT 1: 650 Q44 V37
GMAT 2: 710 Q48 V40
GMAT 3: 750 Q51 V40
GPA: 3.5
WE: Education (Education)
Re: Are positive integers p and q both greater than n ?  [#permalink]

### Show Tags

Updated on: 22 Feb 2011, 01:00
1
Are p and q both greater than n?

(1) p - q is greater than n
(2) q>p

EDIT:

p and q are positive integers.... I missed that part

Sorry!
_________________

Originally posted by AmrithS on 21 Feb 2011, 23:13.
Last edited by AmrithS on 22 Feb 2011, 01:00, edited 1 time in total.
Manager
Joined: 02 Apr 2010
Posts: 92
Re: Are positive integers p and q both greater than n ?  [#permalink]

### Show Tags

22 Feb 2011, 00:46
1
Are you sure the correct answer is C?

Let's do two cases for which the stated conditions hold.

Case 1: p= 2, q=3
From condition 1 it follows that n < -1, i.e. n is smaller than both p and q.

Case 2: p=-3, q=-2

From condition 1 it follows that n <-1, i.e. it is unclear whether n is smaller or larger than p and q.

Unless the question states that p and q are positive (integers) I think the correct solution is E (not C).
Senior Manager
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 416
Re: Are positive integers p and q both greater than n ?  [#permalink]

### Show Tags

22 Feb 2011, 08:25
Bunuel wrote:
zisis wrote:
are positive integers p and q both greater than n

(1) p-q is greater than n
(2) q>p

Given: $$p=integer>0$$ and $$q=integer>0$$. Question: is $$p>n$$ and $$q>n$$?

(1) $$p-q>n$$. Clearly insufficient.

(2) $$q>p$$, no info about $$n$$. Not sufficient.

(1)+(2) Sum (1) and (2) (we can safely do this as their signs are in the same direction): $$p-q+q>n+p$$ --> $$n<0$$. As given that both $$p$$ and $$q$$ are positive then they are greater than negative $$n$$. Sufficient.

_________________
Senior Manager
Joined: 21 Mar 2010
Posts: 257
Re: Are positive integers p and q both greater than n ?  [#permalink]

### Show Tags

23 Feb 2011, 13:11
Baten80 wrote:
Bunuel wrote:
zisis wrote:
are positive integers p and q both greater than n

(1) p-q is greater than n
(2) q>p

Given: $$p=integer>0$$ and $$q=integer>0$$. Question: is $$p>n$$ and $$q>n$$?

(1) $$p-q>n$$. Clearly insufficient.

(2) $$q>p$$, no info about $$n$$. Not sufficient.

(1)+(2) Sum (1) and (2) (we can safely do this as their signs are in the same direction): $$p-q+q>n+p$$ --> $$n<0$$. As given that both $$p$$ and $$q$$ are positive then they are greater than negative $$n$$. Sufficient.

I second that! In my attempt to solve it i did a whole bunch of things but this was the easiest!
Retired Moderator
Joined: 16 Nov 2010
Posts: 1237
Location: United States (IN)
Concentration: Strategy, Technology
Re: Are positive integers p and q both greater than n ?  [#permalink]

### Show Tags

23 Feb 2011, 18:42
From 1) p-q is greater than n

=> p-n > q (a +ve value) so p > n, but nothing can be inferred about q, so (1) is not sufficient.

From (2) q > p but nothing is given about n, so (2) is not sufficient.

So combining (1) and (2) we can see that q > p > n.

_________________
Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings
Senior Manager
Joined: 08 Jun 2010
Posts: 266
Location: United States
Concentration: General Management, Finance
GMAT 1: 680 Q50 V32
Re: Are positive integers p and q both greater than n ?  [#permalink]

### Show Tags

20 Mar 2012, 18:35
1. A is insufficient because we know p-q>n. This means p>n but q need not be greater than n. We have no further information on q. e.g. 5-2 > 2 but here q = n. So, rule out A.

2. B is insufficient as no information is given on n. So, we can't compare n to p and q.

Together C: we know that q-p MUST be negative and that makes n negative. Since p and q are positive integers its sufficient to answer the question that BOTH p and Q are greater than n.

I suppose the mistake you made is that you didn't read the key word POSITIVE INTEGERS.
Non-Human User
Joined: 09 Sep 2013
Posts: 13602
Re: Are positive integers p and q both greater than n? 1) p-q is  [#permalink]

### Show Tags

16 Oct 2019, 05:56
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: Are positive integers p and q both greater than n? 1) p-q is   [#permalink] 16 Oct 2019, 05:56
Display posts from previous: Sort by