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

It is currently 17 Oct 2018, 15:38

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

S99-18

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49968
S99-18  [#permalink]

Show Tags

New post 16 Sep 2014, 01:53
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

41% (02:24) correct 59% (01:41) wrong based on 73 sessions

HideShow timer Statistics

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49968
Re: S99-18  [#permalink]

Show Tags

New post 16 Sep 2014, 01:53
Official Solution:


We can solve this problem either by algebra or by number-plugging. 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?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
Joined: 19 Aug 2014
Posts: 2
Location: United States
Concentration: Entrepreneurship, General Management
Schools: Schulich '15
GMAT 1: 730 Q49 V41
WE: Other (Other)
GMAT ToolKit User
Re: S99-18  [#permalink]

Show Tags

New post 01 Oct 2014, 02:41
We can solve this problem either by algebra or by number-plugging. 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
Intern
avatar
B
Joined: 27 Jan 2016
Posts: 4
Location: India
Schools: Duke '20
GMAT 1: 700 Q50 V38
GPA: 4
Re: S99-18  [#permalink]

Show Tags

New post 17 Oct 2016, 08:13
Shoudn't the question have specified that the integers can't be 0?
Intern
Intern
avatar
Joined: 17 Oct 2014
Posts: 5
Re: S99-18  [#permalink]

Show Tags

New post 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
User avatar
V
Joined: 02 Sep 2009
Posts: 49968
Re: S99-18  [#permalink]

Show Tags

New post 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?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
B
Joined: 11 Aug 2018
Posts: 1
Re: S99-18  [#permalink]

Show Tags

New post 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
GMAT Club Bot
Re: S99-18 &nbs [#permalink] 02 Oct 2018, 12:53
Display posts from previous: Sort by

S99-18

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Moderators: chetan2u, Bunuel



Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.