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

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

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

(1) q^2 > p
(2) q - p < 0
Spoiler: OA
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Re: If p is a positive integer, is p + 2 > q? [#permalink]

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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.

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

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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.

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

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

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New post 29 Sep 2013, 16:08
Expert's post
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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Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

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New post 08 Feb 2018, 15:46
The options are not listed.
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Re: If p is a positive integer, is p + 2 > q? [#permalink]

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New post 08 Feb 2018, 20:59
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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.
D. EACH 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.
Ultimate GMAT Quantitative Megathread

Hope this helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Re: If p is a positive integer, is p + 2 > q?   [#permalink] 08 Feb 2018, 20:59
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