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

It is currently 17 Feb 2019, 10:05

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
Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
  • Free GMAT Algebra Webinar

     February 17, 2019

     February 17, 2019

     07:00 AM PST

     09:00 AM PST

    Attend this Free Algebra Webinar and learn how to master Inequalities and Absolute Value problems on GMAT.
  • Valentine's day SALE is on! 25% off.

     February 18, 2019

     February 18, 2019

     10:00 PM PST

     11:00 PM PST

    We don’t care what your relationship status this year - we love you just the way you are. AND we want you to crush the GMAT!

If a and b are positive numbers, is a < b?

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

Hide Tags

 
Manager
Manager
User avatar
G
Joined: 01 Sep 2016
Posts: 193
GMAT 1: 690 Q49 V35
GMAT ToolKit User Reviews Badge
If a and b are positive numbers, is a < b?  [#permalink]

Show Tags

New post Updated on: 17 Jun 2017, 02:10
3
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

67% (02:00) correct 33% (01:58) wrong based on 109 sessions

HideShow timer Statistics

If a and b are positive numbers, is a < b?

(1) a < b/2 + 2
(2) a < b/2 -2

_________________

we shall fight on the beaches,
we shall fight on the landing grounds,
we shall fight in the fields and in the streets,
we shall fight in the hills;
we shall never surrender!


Originally posted by bkpolymers1617 on 17 Jun 2017, 01:45.
Last edited by Bunuel on 17 Jun 2017, 02:10, edited 1 time in total.
Renamed the topic and edited the question.
Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3341
Location: India
GPA: 3.12
Premium Member
Re: If a and b are positive numbers, is a < b?  [#permalink]

Show Tags

New post 17 Jun 2017, 02:45
Given a and b are positive numbers, we need to find out if a < b?

(1) a < b/2 + 2
Equation can be re-written as a-2 < b/2
For values a = b = 10 statement a<b is false as a=b
Similarly, for values a = 3,b=3.2 statement a<b is true
Hence, not sufficient.

(2) a < b/2 - 2
Equations can be rewritten as a+2 < b/2
If a=b=any value, the equation a+2 < b/2 will not stand.
If a>b for any positive number, the equation a+2 < b/2 will not stand.
Only when a<b, this statement stands.

Hence this statement alone is sufficient.(Option B)
_________________

You've got what it takes, but it will take everything you've got

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 52906
Re: If a and b are positive numbers, is a < b?  [#permalink]

Show Tags

New post 17 Jun 2017, 03:09
If a and b are positive numbers, is a < b?

(1) a < b/2 + 2. If b = 2 and a = 2, then answer is NO but if b = 4 and a = 1, then the answer is YES. Not sufficient.

(2) a < b/2 - 2. Notice that b/2 is less than b, so b/2 - 2 is even less. So, even if b/2 - 2 is greater than a, then so must be b alone. Sufficient.

Answer: B.
_________________

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

Senior Manager
Senior Manager
User avatar
G
Joined: 06 Jul 2016
Posts: 366
Location: Singapore
Concentration: Strategy, Finance
GMAT ToolKit User Premium Member
Re: If a and b are positive numbers, is a < b?  [#permalink]

Show Tags

New post 17 Jun 2017, 03:18
S1 -> if b = 2 then a < 3 so it can be 2 but if b = 4, a < 6 so it can be 5 and can be 1. Insufficient

S2 -> b = 2 then a < -1, if b = 4 a < 0. Sufficient.

Answer is B.


Sent from my iPhone using GMAT Club Forum
_________________

Put in the work, and that dream score is yours!

CEO
CEO
User avatar
D
Joined: 11 Sep 2015
Posts: 3431
Location: Canada
Re: If a and b are positive numbers, is a < b?  [#permalink]

Show Tags

New post 17 Jun 2017, 07:38
Top Contributor
bkpolymers1617 wrote:
If a and b are positive numbers, is a < b?

(1) a < b/2 + 2
(2) a < b/2 - 2


Target question: Is a < b?

Given: a and b are positive numbers

Statement 1: a < b/2 + 2
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of a and b that satisfy statement 1. Here are two:
Case a: a = 0 and b = 2, in which case a < b
Case b: a = 2.5 and b = 2, in which case a > b
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, read my article: http://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: a < b/2 - 2
Since b is POSITIVE, we know that b/2 < b
We can also say that b/2 - 2 < b/2
We can COMBINE these inequalities to get: a < b/2 - 2 < b/2 < b
If we ignore the middle parts, we see that a < b
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer:

RELATED VIDEO

_________________

Test confidently with gmatprepnow.com
Image

Intern
Intern
avatar
B
Joined: 08 Aug 2018
Posts: 41
Location: India
GMAT 1: 720 Q49 V40
GPA: 4
WE: Engineering (Energy and Utilities)
CAT Tests
Re: If a and b are positive numbers, is a < b?  [#permalink]

Show Tags

New post 15 Oct 2018, 06:17
Bunuel wrote:
If a and b are positive numbers, is a < b?

(1) a < b/2 + 2. If b = 2 and a = 2, then answer is NO but if b = 4 and a = 1, then the answer is YES. Not sufficient.

(2) a < b/2 - 2. Notice that b/2 is less than b, so b/2 - 2 is even less. So, even if b/2 - 2 is greater than a, then so must be b alone. Sufficient.

Answer: B.


Dear brunel
Any tips in deciding the numbers to test the inequalities? i am taking too much in agreeing on the numbers to test the DS questions. thanks in advance
GMAT Club Bot
Re: If a and b are positive numbers, is a < b?   [#permalink] 15 Oct 2018, 06:17
Display posts from previous: Sort by

If a and b are positive numbers, is a < b?

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


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®.