Mar 20 07:00 AM PDT  09:00 AM PDT Join a FREE 1day workshop and learn how to ace the GMAT while keeping your fulltime job. Limited for the first 99 registrants. Mar 20 09:00 PM EDT  10:00 PM EDT Strategies and techniques for approaching featured GMAT topics. Wednesday, March 20th at 9 PM EDT Mar 23 07:00 AM PDT  09:00 AM PDT Christina scored 760 by having clear (ability) milestones and a trackable plan to achieve the same. Attend this webinar to learn how to build trackable milestones that leverage your strengths to help you get to your target GMAT score.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 53721

Question Stats:
42% (02:23) correct 58% (01:39) wrong based on 78 sessions
HideShow timer Statistics



Math Expert
Joined: 02 Sep 2009
Posts: 53721

Re: S9918
[#permalink]
Show Tags
16 Sep 2014, 01:53
Official Solution: We can solve this problem either by algebra or by numberplugging. Let's use algebra. All four variables can be expressed in terms of just one variable, since they are consecutive integers and we know their order. If we keep \(p\) as the basic variable, then \(q = p + 1\), \(r = p + 2\), and \(s = p + 3\). Now we can rephrase the question: Is \(pr \lt qs\)? Is \(p(p + 2) \lt (p + 1)(p + 3)\)? Is \(p^2 + 2p \lt p^2 + 4p + 3\)? Is \(2p \lt 4p + 3\)? Is \(0 \lt 2p + 3\)? Is \(3 \lt 2p\)? Is \(\frac{3}{2} \lt p\)? Since \(p\) is an integer, the question is answered "yes" if \(p = 1\) or greater, and "no" if \(p = 2\) or less. Statement (1): SUFFICIENT. We rephrase the statement similarly. \(pq \lt rs\) \(p(p + 1) \lt (p + 2)(p + 3)\) \(p^2 + p \lt p^2 + 5p + 6\) \(0 \lt 4p + 6\) \(0 \lt 2p + 3\) \(\frac{3}{2} \lt p\) This is precisely the same condition as asked in the question. Thus, we can answer the question definitively. Statement (2): INSUFFICIENT. Again, we rephrase the statement similarly. \(ps \lt qr\) \(p(p + 3) \lt (p + 1)(p + 2)\) \(p^2 + 3p \lt p^2 + 3p + 2\) \(0 \lt 2\) Since 0 is always less than 2, no matter the value of \(p\), the statement is always true. Thus, we do not gain any information that would help us answer the question. Answer: A
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 19 Aug 2014
Posts: 2
Location: United States
Concentration: Entrepreneurship, General Management
WE: Other (Other)

Re: S9918
[#permalink]
Show Tags
01 Oct 2014, 02:41
We can solve this problem either by algebra or by numberplugging. Let's use algebra. All four variables can be expressed in terms of just one variable, since they are consecutive integers and we know their order. If we keep p as the basic variable,
Bunuel  how do you suggest to solve this by number plugging.
Also im not great at using number plugging to solve questions and generally take the algaebric ways which costs me more time and is very unfeasibe in some questions.
Are you aware of a bank of questions for me to practice number plugging and also some tips and tricks about the same. Thanks in advance . You are a saviour.



Intern
Joined: 27 Jan 2016
Posts: 4
Location: India
GPA: 4

Re: S9918
[#permalink]
Show Tags
17 Oct 2016, 08:13
Shoudn't the question have specified that the integers can't be 0?



Intern
Joined: 17 Oct 2014
Posts: 5

Re: S9918
[#permalink]
Show Tags
25 Nov 2016, 02:53
if we use number plugging method the ans will be B 1st statement: pq<rs let the values be 1,2,3,4 then 2<12 its true. assumen values be 2,1,0,1 then 2>0 the statement is not sufficient.
2nd statement: ps<qr values be 1,2,3,4 then 4<6 true. values be 2,1,0,1 then 2<0 hence statement is sufficient. please help me where i am wrong



Math Expert
Joined: 02 Sep 2009
Posts: 53721

Re: S9918
[#permalink]
Show Tags
25 Nov 2016, 06:17
pratistha29 wrote: if we use number plugging method the ans will be B 1st statement: pq<rs let the values be 1,2,3,4 then 2<12 its true. assumen values be 2,1,0,1 then 2>0 the statement is not sufficient.
2nd statement: ps<qr values be 1,2,3,4 then 4<6 true. values be 2,1,0,1 then 2<0 hence statement is sufficient. please help me where i am wrong With 1,2,3,4 you have and YES answer to the question (\(pr \lt qs\)) while with 2,1,0,1 you get a NO answer to the question (\(pr \gt qs\)). This means that the second statement is not sufficient.
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 11 Aug 2018
Posts: 6

Re: S9918
[#permalink]
Show Tags
02 Oct 2018, 12:53
If we wish to use number plugging, then we have to consider 4 different cases for values for p q r s.
Case 1 : 1, 2, 3, 4
Case 2 : 4, 3, 2, 1
Case 3 : 2, 1, 0, 1
Case 4 : 1, 0, 1, 2
[NOTICE the difference between case 3 and 4 carefully]
Now, check for statement 1 : pq<rs
For all the cases for which pq<rs holds true, pr<qs should give the same answer [either YES or NO]. Here, it does. Hence, SUFFICIENT.
Now, check for statement 2 : ps<qr
Here, all the cases for which ps<qr holds true donot give the same answer to 'Is pr<qs ?'. Hence, INSUFFICIENT.
Therefore, the answer ====> A










