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

It is currently 23 Sep 2018, 17:10

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

If negative integer a is multiplied by b and the result is greater tha

  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: 49320
If negative integer a is multiplied by b and the result is greater tha  [#permalink]

Show Tags

New post 29 Jun 2018, 02:12
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

70% (01:21) correct 30% (01:29) wrong based on 182 sessions

HideShow timer Statistics

If negative integer a is multiplied by b and the result is greater than 0 but less than |a|, then which of the following must be true of b?


A. \(b > 1\)

B. \(0 < b < 1\)

C. \(-1 < b < 0\)

D. \(b < a\)

E. \(|b| < a\)

_________________

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

Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6802
If negative integer a is multiplied by b and the result is greater tha  [#permalink]

Show Tags

New post 29 Jun 2018, 03:14
1
3
Bunuel wrote:
If negative integer a is multiplied by b and the result is greater than 0 but less than |a|, then which of the following must be true of b?


A. \(b > 1\)

B. \(0 < b < 1\)

C. \(-1 < b < 0\)

D. \(b < a\)

E. \(|b| < a\)


If a*b>0, where a<0, so b is also <0

If ab<|a|, square both sides
\(a^2b^2<a^2.......a^2b^2-a^2<0....a^2(b^2-1)<0\)
Since a^2>0, so \(b^2-1<0........b^2<1\)
Range of b is -1<b<1....
But b is negative, so -1<b<0


Other way
Substitute a as -2
So -2b<|-2|.............-2b<2..........divide both sides by -2...
\(\frac{-2b}{-2}>\frac{2}{-2}...............b>-1\)
Since b<0....-1<b<0

C
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Director
Director
User avatar
G
Joined: 31 Oct 2013
Posts: 578
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: If negative integer a is multiplied by b and the result is greater tha  [#permalink]

Show Tags

New post 29 Jun 2018, 08:05
1
Bunuel wrote:
If negative integer a is multiplied by b and the result is greater than 0 but less than |a|, then which of the following must be true of b?


A. \(b > 1\)

B. \(0 < b < 1\)

C. \(-1 < b < 0\)

D. \(b < a\)

E. \(|b| < a\)



I think conceptual understanding is a must to work out this question. Few points can be made based on the information given:

1. a is negative . b must also be negative.
2. Absolute value of a is greater than the product of a and b.
3. we know that negative times negative yields positive result.

Let assume the value of a and b.

a = -4 and b = -2

so, ab = 8 but it is stated in the question that |a| > ab . So, b can't be a integer rather it's a fraction.

a = -4
b = -\(\frac{1}{2}\)

a*b = (-4)*(-1/2)
= 2
and |a| > 2.

Thus , b is a negative fraction.

Option C is the best answer.
Intern
Intern
avatar
B
Joined: 08 Oct 2017
Posts: 24
GMAT ToolKit User CAT Tests
Re: If negative integer a is multiplied by b and the result is greater tha  [#permalink]

Show Tags

New post 29 Jun 2018, 09:05
Keep in mind - a -ve and |a|>ab>0
implies -- b has to be -ve
For a*b to be less than |a| - b has to be -ve fraction < 1
Senior SC Moderator
avatar
V
Joined: 22 May 2016
Posts: 1979
Premium Member CAT Tests
If negative integer a is multiplied by b and the result is greater tha  [#permalink]

Show Tags

New post 29 Jun 2018, 10:04
1
Bunuel wrote:
If negative integer a is multiplied by b and the result is greater than 0 but less than |a|, then which of the following must be true of b?


A. \(b > 1\)

B. \(0 < b < 1\)

C. \(-1 < b < 0\)

D. \(b < a\)

E. \(|b| < a\)

Use a negative integer for \(a\)
in order to simplify the arithmetic

Let \(a=-3\)
\(|-3|= 3\)

(1) the result of \(a*b\) is greater than 0
\(a*b>0\)
\((-3*b)>0\)
= \(0<(-3*b)\)

(2) the result of \(a*b\) is less than \(|a|\)
\(a*b<|a|\)
\((-3*b)<3\)

(3) Combine:
\(0<(-3*b)<3\)
Divide all terms by -3, flip the signs
\(0>b>-1\)
= \(-1<b<0\)

Answer C
_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"

GMAT Club Bot
If negative integer a is multiplied by b and the result is greater tha &nbs [#permalink] 29 Jun 2018, 10:04
Display posts from previous: Sort by

If negative integer a is multiplied by b and the result is greater tha

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

Events & Promotions

PREV
NEXT


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®.