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# If p is a positive integer, is p + 2 > q?

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Intern
Joined: 14 Mar 2013
Posts: 46
Location: United States
GMAT Date: 12-03-2013
WE: General Management (Retail)
If p is a positive integer, is p + 2 > q?  [#permalink]

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28 Sep 2013, 09:31
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Difficulty:

35% (medium)

Question Stats:

71% (01:50) correct 29% (02:03) wrong based on 192 sessions

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If p is a positive integer, is p + 2 > q?

(1) q^2 > p
(2) q - p < 0
Manager
Joined: 29 Apr 2013
Posts: 94
Location: India
Concentration: General Management, Strategy
GMAT Date: 11-06-2013
WE: Programming (Telecommunications)
Re: If p is a positive integer, is p + 2 > q?  [#permalink]

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28 Sep 2013, 09:59
2
If p is a positive integer, is p + 2 > q?

(1) $$q^2$$ > p
(2) q - p < 0

Statement 1: $$q^2$$ is always positive irrespective of whether q is positive or negative. So let's plugin values:
q=-2 and p=1
$$q^2$$ = 4 --> 4 > 1
p+2 = 1 + 2 = 3 ---> 3 > -2 --> p+2 > q

Again, q = 4, p = 1
$$q^2$$ = 16 --> 16 > 1
p+2 = 1 + 2 = 3 ---> 3 is not greater than 4 --> (p+2) not greater than q. So statement 1 alone is insufficient.

Statement 2:
q - p < 0
q < p or p > q
As p is a positive integer, so if p > q then p+2 is definitely greater than q. So statement 2 alone is sufficient.

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Collection of some good questions on Number System

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Joined: 02 Sep 2009
Posts: 50007
Re: If p is a positive integer, is p + 2 > q?  [#permalink]

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29 Sep 2013, 12:09
If p is a positive integer, is p + 2 > q?

(1) q^2 > p. If p=1 and q=100, then p+2<q but if p=1 and q=-100, then p+2>q. Not sufficient.

(2) q - p < 0 --> p>q. Since p is greater than q, then p+2 (greater number than p) is also greater than q. Sufficient.

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Re: If p is a positive integer, is p + 2 > q?  [#permalink]

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29 Sep 2013, 15:55
Could someone please let me know why we can't subtract statement 1 from the question, or what I am doing incorrectly?

For some reason, this isn't getting to the correct solution.

P + 2>q
- (P< q^2)
_________

2 > q - q^2

2 > q(1 - q)

Which always seems to hold true. If q > 1, then 2 > (some negative); If 0<q<1, then 2 > (some number between 0 and 1); and if q < 0, then 2 > (some negative). For q = 0 or q = 1, 2 > 0.

Where's the flaw in my logic? Help would be greatly appreciated. Thanks
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Joined: 02 Sep 2009
Posts: 50007
Re: If p is a positive integer, is p + 2 > q?  [#permalink]

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29 Sep 2013, 16:08
grant1377 wrote:
Could someone please let me know why we can't subtract statement 1 from the question, or what I am doing incorrectly?

For some reason, this isn't getting to the correct solution.

P + 2>q
- (P< q^2)
_________

2 > q - q^2

2 > q(1 - q)

Which always seems to hold true. If q > 1, then 2 > (some negative); If 0<q<1, then 2 > (some number between 0 and 1); and if q < 0, then 2 > (some negative). For q = 0 or q = 1, 2 > 0.

Where's the flaw in my logic? Help would be greatly appreciated. Thanks

p + 2 > q is NOT given. That is what we need to establish.
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Posts: 13
Re: If p is a positive integer, is p + 2 > q?  [#permalink]

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08 Feb 2018, 15:46
The options are not listed.
Math Expert
Joined: 02 Sep 2009
Posts: 50007
Re: If p is a positive integer, is p + 2 > q?  [#permalink]

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08 Feb 2018, 20:59
1
Missyy wrote:
The options are not listed.

This is a data sufficiency question. Options for DS questions are always the same.

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

I suggest you to go through the following posts:
ALL YOU NEED FOR QUANT.

Hope this helps.
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Re: If p is a positive integer, is p + 2 > q? &nbs [#permalink] 08 Feb 2018, 20:59
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