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

 It is currently 23 Sep 2018, 20:54

### 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

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

# If xy < 3, is x < 1?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49323
If xy < 3, is x < 1?  [#permalink]

### Show Tags

26 Jan 2014, 10:37
1
4
00:00

Difficulty:

5% (low)

Question Stats:

85% (00:59) correct 15% (01:12) wrong based on 468 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:
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!

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 49323
Re: If xy < 3, is x < 1?  [#permalink]

### Show Tags

26 Jan 2014, 10:38
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.

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
_________________
Director
Joined: 03 Feb 2013
Posts: 887
Location: India
Concentration: Operations, Strategy
GMAT 1: 760 Q49 V44
GPA: 3.88
WE: Engineering (Computer Software)
Re: If xy < 3, is x < 1?  [#permalink]

### Show Tags

26 Jan 2014, 11:47
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 Application Experience : http://gmatclub.com/forum/hardwork-never-gets-unrewarded-for-ever-189267-40.html#p1516961

Manager
Joined: 20 Dec 2013
Posts: 244
Location: India
Re: If xy < 3, is x < 1?  [#permalink]

### Show Tags

26 Jan 2014, 23:03
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
Joined: 10 Apr 2012
Posts: 42
Concentration: Finance
Schools: Goizueta '19 (I)
WE: Analyst (Commercial Banking)
Re: If xy < 3, is x < 1?  [#permalink]

### Show Tags

28 Jan 2014, 03:07
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.

Math Expert
Joined: 02 Sep 2009
Posts: 49323
Re: If xy < 3, is x < 1?  [#permalink]

### Show Tags

01 Feb 2014, 09:07
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.

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
_________________
Intern
Status: Into the last good fight
Joined: 22 Feb 2012
Posts: 17
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

19 Nov 2014, 16:18
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.

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.

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

SVP
Joined: 26 Mar 2013
Posts: 1808
If xy < 3, is x < 1?  [#permalink]

### Show Tags

08 Jun 2017, 14:47
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

Manager
Joined: 10 Apr 2018
Posts: 105
Re: If xy < 3, is x < 1?  [#permalink]

### Show Tags

14 Sep 2018, 17:37
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)

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
Re: If xy < 3, is x < 1? &nbs [#permalink] 14 Sep 2018, 17:37
Display posts from previous: Sort by

# If xy < 3, is x < 1?

## Events & Promotions

 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®.