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

It is currently 22 Sep 2018, 14:00

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 y≠1, is x=1?

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

Hide Tags

Senior Manager
Senior Manager
User avatar
P
Joined: 24 Aug 2016
Posts: 319
Location: India
Concentration: Entrepreneurship, Operations
GMAT 1: 540 Q49 V16
GMAT 2: 640 Q47 V31
GMAT 3: 630 Q48 V28
GPA: 3.4
GMAT ToolKit User Reviews Badge CAT Tests
Re: If y ≠ 1, is x = 1 ?  [#permalink]

Show Tags

New post 09 May 2018, 15:39
1
FillFM wrote:
If y ≠ 1, is x = 1 ?


(1) \(x^2\) + \(y^2\) = 1
(2) y = 1 – x



(1) \(x^2\) + \(y^2\) = 1

Case 01 , y=2, x= \(\sqrt{(1- 2^2)}\) = \(\sqrt{(-3)}\)
Case 02 , y=0, x= \(\sqrt{(1- 0^2)}\) = \(\sqrt{(1)}\) = \(+1\) or \(-1\).... Thus (NS)

(2) y = 1 – x[/m]
Case 01 , y=2, \(x= 1-2 = -1\)
Case 02 , y=0, \(x= 1-0 = 1\).... Thus (NS)

(1) +(2) = =>

from (2) \(x+y=1\)
or \((x+y)^2= 1\)
or \(x^2+y^2+2*x*y =1\)
or \(1+2*x*y =1\) ( substituting \(x^2\) + \(y^2\) = \(1\) from (1))
or \(2*x*y =0\)

Now as y ≠ 1..... x has to be 0. Thus x is not 1. ......................Thus sufficient...... Hence I would go for option C.
_________________

Please let me know if I am going in wrong direction.
Thanks in appreciation.

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49303
Re: If y≠1, is x=1?  [#permalink]

Show Tags

New post 09 May 2018, 21:33
Manager
Manager
avatar
S
Joined: 10 Jan 2013
Posts: 87
Location: India
Concentration: General Management, Strategy
GMAT 1: 600 Q43 V30
GPA: 3.95
GMAT ToolKit User Reviews Badge
Re: If y≠1, is x=1?  [#permalink]

Show Tags

New post 15 Jul 2018, 02:53
MDK wrote:
If y≠1, is x=1?

(1) x^2 + y^2 = 1
(2) y = 1 - x


My take-

stmt 1.

given y is not equal to 1, for stmt 1 to be true, y can be zero but x can be +1 or -1.

Not sufficient

stmt 2.

y= 1-x is also not sufficient. could be any value

combining

convert 2. x= 1-y

(1-y)^2 + y^2 = 1

1 + y^2 -2y + y^2 = 1

2y(y-1)=0
y=1 (not possible)

therefore 2y=0 or y=0

therefore x=1 ( as per question stem)

C
Senior Manager
Senior Manager
avatar
S
Joined: 04 Aug 2010
Posts: 277
Schools: Dartmouth College
Re: If y≠1, is x=1?  [#permalink]

Show Tags

New post 15 Jul 2018, 03:37
2
A very fast approach is to GRAPH the two statements.
x² + y² = r² is the equation for a circle that is centered at the origin and has a radius of r.
y = mx + b is the equation of a line with a slope of m and a y-intercept of b.

Statement 1: x² + y² = 1
This is the equation for a circle that is centered at the origin and has a radius of 1:
Image
The question prompt indicates that y≠1.
Thus, (x,y) can be any point on the circle other than (0,1).
Since it's possible that (x,y) = (1,0) or that (x.y) = any other point on the circle other than (0,1), INSUFFICIENT.

Statement 2: y = 1-x
Rephrased in the form of y = mx + b:
y = -x + 1.
This is the equation of a line with a slope of -1 and a y-intercept of 1:
Image
The question prompt indicates that y≠1.
Thus, (x,y) can be any point on the line other than (0,1).
Since it's possible that (x,y) = (1,0) or that (x.y) = any other point on the line other than (0,1), INSUFFICIENT.

Statements combined:
Overlaying the graphs, we get;
Image
Of the 2 points of intersection, only (1,0) is viable.
Thus, x=1.
SUFFICIENT.


_________________

GMAT and GRE Tutor
Over 1800 followers
Click here to learn more
GMATGuruNY@gmail.com
New York, NY
If you find one of my posts helpful, please take a moment to click on the "Kudos" icon.
Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.

GMAT Club Bot
Re: If y≠1, is x=1? &nbs [#permalink] 15 Jul 2018, 03:37

Go to page   Previous    1   2   [ 24 posts ] 

Display posts from previous: Sort by

If y≠1, is x=1?

  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®.