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

It is currently 12 Dec 2018, 11:05

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 December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • The winning strategy for 700+ on the GMAT

     December 13, 2018

     December 13, 2018

     08:00 AM PST

     09:00 AM PST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.
  • GMATbuster's Weekly GMAT Quant Quiz, Tomorrow, Saturday at 9 AM PST

     December 14, 2018

     December 14, 2018

     09:00 AM PST

     10:00 AM PST

    10 Questions will be posted on the forum and we will post a reply in this Topic with a link to each question. There are prizes for the winners.

If xy < 3, is x < 1?

  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: 51121
If xy < 3, is x < 1?  [#permalink]

Show Tags

New post 26 Jan 2014, 09:37
1
6
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

84% (01:16) correct 16% (01:25) wrong based on 494 sessions

HideShow timer Statistics

The Official Guide For GMAT® Quantitative Review, 2ND Edition

If xy < 3, is x < 1?

(1) y > 3
(2) x < 3

Data Sufficiency
Question: 56
Category: Algebra Inequalities
Page: 157
Difficulty: 600


GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
1. Please provide your solutions to the questions;
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

_________________

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 Sep 2009
Posts: 51121
Re: If xy < 3, is x < 1?  [#permalink]

Show Tags

New post 26 Jan 2014, 09:38
SOLUTION

If xy < 3, is x < 1?

(1) y > 3. If x were \(\geq{1}\), then xy would be more than or equal to 3, which would contradcit the condition that xy < 3. Thus x must be less than 1. Sufficient.

(2) x < 3. Not sufficient: consider x=y=0 and x=2 and y=0. Not sufficient.

Answer: A.

Similar questions to practice:
if-xy-4-is-x-2-1-y-1-2-y-x-129251.html
if-ab-7-is-b-166192.html
if-xy-is-less-than-3-is-x-less-than-61629.html
_________________

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

Director
Director
User avatar
B
Joined: 03 Feb 2013
Posts: 851
Location: India
Concentration: Operations, Strategy
GMAT 1: 760 Q49 V44
GPA: 3.88
WE: Engineering (Computer Software)
Reviews Badge
Re: If xy < 3, is x < 1?  [#permalink]

Show Tags

New post 26 Jan 2014, 10:47
1
Bunuel wrote:


Statement 1) y > 3 and if xy < 3, then X has to be < 1 (One of the variable has to compensate for the increase in other variable).
Sufficient.

Statement 2) x < 3
As there is no information of y, we cannot determine if x < 1
So insufficient.

Hence Option A)
_________________

Thanks,
Kinjal
My Debrief : http://gmatclub.com/forum/hardwork-never-gets-unrewarded-for-ever-189267.html#p1449379
My Application Experience : http://gmatclub.com/forum/hardwork-never-gets-unrewarded-for-ever-189267-40.html#p1516961
Linkedin : https://www.linkedin.com/in/kinjal-das/

Please click on Kudos, if you think the post is helpful

Manager
Manager
avatar
Joined: 20 Dec 2013
Posts: 230
Location: India
Re: If xy < 3, is x < 1?  [#permalink]

Show Tags

New post 26 Jan 2014, 22:03
From S1:y>3=>x=fraction/negative integer=>x<1.Sufficient
From S2:x<3=>x=2,1,0...depending on y.It cannot be said whether x<1 or >1.Hence insufficient.
Ans.A
Intern
Intern
avatar
Joined: 10 Apr 2012
Posts: 40
Concentration: Finance
Schools: Goizueta '19 (I)
WE: Analyst (Commercial Banking)
Reviews Badge
Re: If xy < 3, is x < 1?  [#permalink]

Show Tags

New post 28 Jan 2014, 02:07
1
Statement (1). By number picking strategy, if y>3 and xy<3, then X is always less than 1. Sufficient

Statement (2). X can be greater or less than 1 and still xy<3 holds. Insufficient.

Answer A
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51121
Re: If xy < 3, is x < 1?  [#permalink]

Show Tags

New post 01 Feb 2014, 08:07
SOLUTION

If xy < 3, is x < 1?

(1) y > 3. If x were \(\geq{1}\), then xy would be more than or equal to 3, which would contradcit the condition that xy < 3. Thus x must be less than 1. Sufficient.

(2) x < 3. Not sufficient: consider x=y=0 and x=2 and y=0. Not sufficient.

Answer: A.

Similar questions to practice:
if-xy-4-is-x-2-1-y-1-2-y-x-129251.html
if-ab-7-is-b-166192.html
if-xy-is-less-than-3-is-x-less-than-61629.html
_________________

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
Status: Into the last good fight
Joined: 22 Feb 2012
Posts: 17
Location: Bangladesh
GMAT 1: 550 Q42 V24
GMAT 2: 550 Q44 V23
GMAT 3: 540 Q41 V24
Re: If xy < 3, is x < 1?  [#permalink]

Show Tags

New post 19 Nov 2014, 15:18
If xy < 3, is x < 1?

(1) y > 3. If x were \(\geq{1}\), then xy would be more than or equal to 3, which would contradict the condition that xy < 3. Thus x must be less than 1. Sufficient.

(2) x < 3. Not sufficient: consider x=y=0 and x=2 and y=0. Not sufficient.

Answer: A.


I'm a bit confused after analyzing another similar question with different solution

In st1, why negative values of x are not being considered ? I came up with answer "E", considering negative values of x

However, just when I was convinced that, values of x and y need to be assumed positive in this type of prompt, I met the following question

Is xy < 6?

(1) x < 3 and y < 2.
(2) 1/2 < x < 2/3 and y^2 < 64.

Data Sufficiency, Question: 68, Page: 157, OG quant review 2nd edition

SOLUTION

Is xy < 6?

(1) x < 3 and y < 2 --> now, if both x and y are equal to zero then xy=0<6 and the answer will be YES but if both x and y are small enough negative numbers, for example -10 and -10 then xy=100>6 and the answer will be NO. Not sufficient.

(2) \frac{1}{2}<x<\frac{2}{3} and y^2<64, which is equivalent to -8<y<8 --> even if we take the boundary values of x and y to maximize their product we'll get: xy=\frac{2}{3}*8\approx{5.3}<6, so the answer to the question "is xy<6?" will always be YES. Sufficient.

Answer: B.


Here, both the positive and negative values of x and y have been considered.

Bunuel can you please explain the contradiction ?
SVP
SVP
User avatar
D
Joined: 26 Mar 2013
Posts: 1910
Reviews Badge CAT Tests
If xy < 3, is x < 1?  [#permalink]

Show Tags

New post 08 Jun 2017, 13:47
If xy < 3, is x < 1?

(1) y > 3

Let y = 4.......4x <3.......x <3/4< 1....Yes

Let y = 100...100x <3....x <0.03 <1...Yes

Always Yes

Sufficient

(2) x < 3

Let x =1/3........1/3 y < 3 ......y < 8/3.......Answer is yes

Let x = 2...........2 y < 3........y < 2/3........Answer is NO

Insufficient

Answer: A
Manager
Manager
User avatar
G
Joined: 10 Apr 2018
Posts: 180
Re: If xy < 3, is x < 1?  [#permalink]

Show Tags

New post 14 Sep 2018, 16:37
Hi,

here are my two cents for this questions

We should know two rules for this for one of the method to solve algebrically

1. if a>b & c<d then From one inequality it is possible to subtract term wise another inequality of the opposite sense retaining the sense of inequality from which the other was subtracted ..

Here is what i mean Say a>b & c<d then a-c > b-d.

2. 1. if a>b & c>d then Two inequality having same sense may be added term wise Here is what it will be a+c>b+d

So
From Stamt 1:
xy < 3 ---- (i)
and
y >3 -----(ii)

(i)- (ii)
Using rule 1 we have
xy-y<0
y(x-1)<0
so wither y<0 and or x-1<0
since y>3 it must be that x-1<0 or x<1
So sufficient.

From Stmt 2:
X<3-------(iii)

adding (i) and (iii)
xy+x<6
x(y+1)<6
so we have
x<6 and or y+1<6
or x<6 and or y<5
or we have
x<3 and or y<5
we can't say if x<1
Hence insufficient.

Probus
GMAT Club Bot
Re: If xy < 3, is x < 1? &nbs [#permalink] 14 Sep 2018, 16:37
Display posts from previous: Sort by

If xy < 3, is x < 1?

  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®.