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

It is currently 21 Feb 2019, 16:34

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
  • Online GMAT boot camp for FREE

     February 21, 2019

     February 21, 2019

     10:00 PM PST

     11:00 PM PST

    Kick off your 2019 GMAT prep with a free 7-day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th.
  • Free GMAT RC Webinar

     February 23, 2019

     February 23, 2019

     07:00 AM PST

     09:00 AM PST

    Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT

If a < b < 0, which of the following must be true?

  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: 53063
If a < b < 0, which of the following must be true?  [#permalink]

Show Tags

New post 21 Apr 2015, 05:01
2
7
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

65% (01:49) correct 35% (01:54) wrong based on 287 sessions

HideShow timer Statistics

Retired Moderator
User avatar
Joined: 06 Jul 2014
Posts: 1229
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33
GMAT 2: 740 Q50 V40
GMAT ToolKit User Premium Member
Re: If a < b < 0, which of the following must be true?  [#permalink]

Show Tags

New post 21 Apr 2015, 07:21
1
2
Bunuel wrote:
If a < b < 0, which of the following must be true?

A. a^2 < b^2
B. b − 10 < a
C. b + a > a
D. ab < b^2
E. ab < a^2

Kudos for a correct solution.


a) \(a^2<b^2\); \(a^2-b^2<0\) false because \(|a|>|b|\)
b) \(b − 10 < a\); \(b<a+10\) false if \(|a|-|b| > 10\)
c) \(b + a > a\); \(b > 0\) false
d) \(ab < b^2\) false because \(|b| < |a|\)
e) \(ab < a^2\) true because \(|a|>|b|\)

And answer is E
_________________

Simple way to always control time during the quant part.
How to solve main idea questions without full understanding of RC.
660 (Q48, V33) - unpleasant surprise
740 (Q50, V40, IR3) - anti-debrief ;)

Director
Director
User avatar
Joined: 07 Aug 2011
Posts: 529
Concentration: International Business, Technology
GMAT 1: 630 Q49 V27
GMAT ToolKit User
Re: If a < b < 0, which of the following must be true?  [#permalink]

Show Tags

New post 21 Apr 2015, 08:18
1
Bunuel wrote:
If a < b < 0, which of the following must be true?

A. a^2 < b^2
B. b − 10 < a
C. b + a > a
D. ab < b^2
E. ab < a^2

Kudos for a correct solution.


A. a^2 < b^2 --> (a+b)(a-b) < 0 --> (-ive)*(-ive)<0 ; NO
B. b − 10 < a --> b-a<10,let a=-1000 and b=-1; then b-a=999 . NO
C. b + a > a --> b>0 ; NO
D. ab < b^2 --> b*(a-b) <0; (-ive)*(-ive)<0 ; NO
E. ab < a^2 --> a*(b-a)<0; (-ive)*(+ive) <0 YESSSSSSSS!!. this is our answer.
Director
Director
avatar
P
Joined: 21 May 2013
Posts: 661
Re: If a < b < 0, which of the following must be true?  [#permalink]

Show Tags

New post 21 Apr 2015, 23:04
1
Bunuel wrote:
If a < b < 0, which of the following must be true?

A. a^2 < b^2
B. b − 10 < a
C. b + a > a
D. ab < b^2
E. ab < a^2

Kudos for a correct solution.


A. a^2<b^2. Put a=-2,b=-1, 4>1.Not true
B. b-10<a. Put a=-25,b=-3. -13>-25.Not true
C.b+a>a. Put b=-1,a=-2, -3<-2. Not true
D. ab<b^2. Put b=-1,a=-2, ab=2 and b^2=1. Not true
E.ab<a^2. Always true. Put b=-2,a=-5. ab=10, a^2=25. True
Answer E
Current Student
User avatar
B
Joined: 25 Nov 2014
Posts: 98
Concentration: Entrepreneurship, Technology
GMAT 1: 680 Q47 V38
GPA: 4
Re: If a < b < 0, which of the following must be true?  [#permalink]

Show Tags

New post 22 Apr 2015, 00:16
1
picking no for a and b :
a b OpA
-2 -1 4<1 NT
-1.5 -.5 2.25<.25 NT
-20 -1 400<1 NT

similarly work out the table for other options.. Thus we see that putting these nos of a and b in A, B, C, D give Not True(NT) or maybe true ans. E gives true always. Thus E.
_________________

Kudos!!

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 53063
Re: If a < b < 0, which of the following must be true?  [#permalink]

Show Tags

New post 27 Apr 2015, 02:13
Bunuel wrote:
If a < b < 0, which of the following must be true?

A. a^2 < b^2
B. b − 10 < a
C. b + a > a
D. ab < b^2
E. ab < a^2

Kudos for a correct solution.


VERITAS PREP OFFICIAL SOLUTION:

E. In this problem you should see that a and b are both negative numbers, and that a has a greater absolute value (it's further from zero) than b does. So when you square a, you'll end up with a larger positive number than when you multiply a by a lesser-absolute-value b. So choice E must be true. Choosing numbers can help exemplify:

a = -10, b = -5

Would mean that a^2 = 100 and ab = 50, so a^2 is bigger.

Even if you try with fractions (always a good idea to consider), a = -3/4 and b = -1/2 yields:

a^2 = 9/16 (greater than 1/2)

ab = 3/8 (less than 1/2)

Proving E to be true. For the incorrect answers:

A) Since a has a larger absolute value, when it's squared it will be larger than b-squared.

B) Because you don't know the relative values of a and b, you can't determine that moving b 10 places to the left will reduce it past a.

C) Adding a negative number (b) to a will make it smaller, not larger, than the original a.

D) See demonstration above.
_________________

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

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 9879
Premium Member
Re: If a < b < 0, which of the following must be true?  [#permalink]

Show Tags

New post 21 Dec 2017, 19:17
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: If a < b < 0, which of the following must be true?   [#permalink] 21 Dec 2017, 19:17
Display posts from previous: Sort by

If a < b < 0, which of the following must be true?

  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®.