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

 It is currently 17 Jan 2019, 03:14

### 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

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### The winning strategy for a high GRE score

January 17, 2019

January 17, 2019

08:00 AM PST

09:00 AM PST

Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL.
• ### Free GMAT Strategy Webinar

January 19, 2019

January 19, 2019

07:00 AM PST

09:00 AM PST

Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

# If y≠1, is x=1?

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

### Hide Tags

Intern
Status: Impossible is just an opinion
Joined: 31 Oct 2012
Posts: 44
Location: Ukraine
Concentration: Strategy, Marketing
GMAT 1: 590 Q47 V24
GMAT 2: 650 Q47 V34
GMAT 3: 670 Q49 V31
GMAT 4: 690 Q48 V37
GPA: 3.8
WE: Marketing (Consumer Products)
If y≠1, is x=1?  [#permalink]

### Show Tags

11 Oct 2013, 10:50
7
56
00:00

Difficulty:

(N/A)

Question Stats:

59% (01:55) correct 41% (01:55) wrong based on 1119 sessions

### HideShow timer Statistics

If y≠1, is x=1?

(1) x^2 + y^2 = 1
(2) y = 1 - x
##### Most Helpful Expert Reply
Math Expert
Joined: 02 Sep 2009
Posts: 52210
If y≠1, is x=1?  [#permalink]

### Show Tags

11 Oct 2013, 11:44
21
5
lucbesson wrote:
lucbesson wrote:
If y≠1, is x=1?

(1) $$X^2 + Y^2 = 1$$
(2) $$y = 1 - X$$

Hi Guys! I need your help!

My logic is following:
(1) not sufficient equation is virtually a circle around (0,0) point with the radius 1. If y ≠ 1, than x can be almost anything within following limits [-1;0) & (0;1]
(2) not sufficient: consider y = 0 => x=1; y = 3 => x=-2

(1)+(2) Substitute Y from (2) in (1):
$$X^2 + (1-X)^2=1$$
...
$$2X (X-1) = 0$$

Hense X= 0 or X = 1.

Not sufficient?

PLS Help!

The point is that x=0 is not a valid solution. For x = 0, from y = 1 - x it follows that y = 1 but we are told in the stem that y ≠ 1. Thus x can only be 1. Sufficient.

Answer: C.

Does this make sense?
_________________
##### Most Helpful Community Reply
Intern
Joined: 14 Apr 2013
Posts: 9
Location: United States
Concentration: Operations, Technology
WE: Programming (Computer Software)
Re: If y≠1, is x=1?  [#permalink]

### Show Tags

26 May 2014, 01:59
15
8
statement 1
$$x^2 + y^2 = 1$$
Not sufficient here Y can be 0 or here x and y can have the values as \sqrt{1/2}.

statement 2
y = 1 - x.
Not sufficient, again Y can be 0 of Y can be 3 and x can be 2.

combining the 2,
$$x^2 + y^2 = 1$$,
$$x^2 + y^2 + 2xy - 2xy = 1$$,
$$(x + y)^2 -2xy = 1$$,

from second statement x + y = 1,
1 - 2xy = 1,
2xy = 0,
xy=0
either x or y is 0

if x is 0 then y = 1 (from statement 2), but this is not possible as the question stem.

hence y = 0 and x = 1.

Answer option c
_________________

Regards,
Fugitive

##### General Discussion
Intern
Status: Impossible is just an opinion
Joined: 31 Oct 2012
Posts: 44
Location: Ukraine
Concentration: Strategy, Marketing
GMAT 1: 590 Q47 V24
GMAT 2: 650 Q47 V34
GMAT 3: 670 Q49 V31
GMAT 4: 690 Q48 V37
GPA: 3.8
WE: Marketing (Consumer Products)
Re: If y≠1, is x=1?  [#permalink]

### Show Tags

11 Oct 2013, 11:05
lucbesson wrote:
If y≠1, is x=1?

(1) $$X^2 + Y^2 = 1$$
(2) $$y = 1 - X$$

Hi Guys! I need your help!

My logic is following:
(1) not sufficient equation is virtually a circle around (0,0) point with the radius 1. If y ≠ 1, than x can be almost anything within following limits [-1;0) & (0;1]
(2) not sufficient: consider y = 0 => x=1; y = 3 => x=-2

(1)+(2) Substitute Y from (2) in (1):
$$X^2 + (1-X)^2=1$$
...
$$2X (X-1) = 0$$

Hense X= 0 or X = 1.

Not sufficient?

PLS Help!
Senior Manager
Joined: 13 Jun 2013
Posts: 275
Re: If y is not equal to 1, is x = 1?  [#permalink]

### Show Tags

26 Nov 2014, 01:37
4
3
vasili wrote:
If y is not equal to 1, is x = 1?

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

Quote:
Please help.

st.1 here different values of x and y can satisfy the equation $$x^2 + y^2 =1$$. for example

x=$$\frac{1}{\sqrt{2}}$$
y=$$\frac{1}{\sqrt{2}}$$

as x is not equal to 1. hence answer to the original question is no.

also, x=1 and y=0 will satisfy this equation. as x=1, thus answer to the original question is yes.

x=-1 and y=0 will satisfy this equation. as x is not equal to 1, thus answer to the original question is no.

st. 2
y= 1-x again different values are possible. hence not sufficient

combining st.1 and st.2

put y=1-x in $$x^2+y^2=1$$

$$x^2 +1+x^2-2x=1$$
$$2(x^2-2x)=0$$
$$x(x-1)=0$$

x=0 or x=1

but x=0 is not possible, as y is not equal to 1. hence x=1. thus answer should be C
Manager
Joined: 06 Aug 2013
Posts: 73
Re: If y≠1, is x=1?  [#permalink]

### Show Tags

26 Nov 2014, 01:46
Bunuel wrote:
lucbesson wrote:
lucbesson wrote:
If y≠1, is x=1?

(1) $$X^2 + Y^2 = 1$$
(2) $$y = 1 - X$$

Hi Guys! I need your help!

My logic is following:
(1) not sufficient equation is virtually a circle around (0,0) point with the radius 1. If y ≠ 1, than x can be almost anything within following limits [-1;0) & (0;1]
(2) not sufficient: consider y = 0 => x=1; y = 3 => x=-2

(1)+(2) Substitute Y from (2) in (1):
$$X^2 + (1-X)^2=1$$
...
$$2X (X-1) = 0$$

Hense X= 0 or X = 1.

Not sufficient?

PLS Help!

The point is that x=0 is not a valid solution. For x=1, from y=1-x it follows that y=1 but we are told in the stem that y≠1. Thus x can only be 1. Sufficient.

Answer: C.

Does this make sense?

bunuel,
i have a doubt here...
x^2 + y^2 = 1
and
y = 1-x
=> x+y = 1 squaring both sides
=> x^2 + y^2 + 2xy = 1 substituting x^2 + y^2 = 1
=> 1 + 2xy = 1
=> 2xy = 0
=> xy = 0
now x can be anything on the basis of the above equatn
hence getting E. what am i missing

secondly, what might be the level of this question??

would really appreciate your help.
thanks.
Intern
Joined: 21 Nov 2014
Posts: 31
Location: Viet Nam
GMAT 1: 760 Q50 V44
Re: If y is not equal to 1, is x = 1?  [#permalink]

### Show Tags

26 Nov 2014, 02:16
11
2
My quick thought. Look at the picture, there are only two points satisfy the condition (1,0) and (0,1) but y is not equal 1 then only x = 1, y = 0 satisfy the conditions.
The answer is C, and you can come up with the answer in 30 seconds.
Attachments

is x=1.png [ 4.56 KiB | Viewed 37059 times ]

_________________

GMAT Group for Vietnamese:

https://www.facebook.com/groups/644070009087525/

Intern
Joined: 30 Oct 2014
Posts: 2
Location: India
GMAT 1: 670 Q48 V34
WE: Analyst (Computer Software)
Re: If y is not equal to 1, is x = 1?  [#permalink]

### Show Tags

26 Nov 2014, 03:17
4
vasili wrote:
If y is not equal to 1, is x = 1?

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

Quote:
Please help.

In the question it is given that y can take ANY VALUE except 1.

If we look at the first statement $$x^2 + y^2 = 1$$, we are provided with a equation of a circle with center at (0,0) and radius 1. This circle will intersect x axis at points (1,0) and (-1,0) and y axis at (0,1) and (0,-1). Over the entire circumference of the circle there are infinite number of points that will satisfy statement 1 even if we exclude one specific point where value of y is 1. Therefore statement ONE alone is not sufficient.

Moving on to second statement $$y = 1 - x$$, we are provided with a equation of a line passing through points (0,1) and (1,0). Yet again there are infinite number of points that will satisfy statement 2 even if we exclude one specific point where value of y is 1. Therefore statement TWO alone is not sufficient.

Now when we combine both first and second statement we get two specific points [i.e. (0,1) and (1,0)] where these curves meet. We are given that y is not equal to 1. Hence we are left with one unique value (1,0). Therefore answer option (c) is correct.

I have also uploaded the image of containing both the figures.

-----------------------------------------------------------
+1 Kudos if you find the reply useful.
Attachments

File comment: Figure of circle and line

Figure circle and line.JPG [ 10.85 KiB | Viewed 37043 times ]

Math Expert
Joined: 02 Sep 2009
Posts: 52210
If y≠1, is x=1?  [#permalink]

### Show Tags

26 Nov 2014, 04:41
arnabs wrote:
Bunuel wrote:
lucbesson wrote:

Hi Guys! I need your help!

My logic is following:
(1) not sufficient equation is virtually a circle around (0,0) point with the radius 1. If y ≠ 1, than x can be almost anything within following limits [-1;0) & (0;1]
(2) not sufficient: consider y = 0 => x=1; y = 3 => x=-2

(1)+(2) Substitute Y from (2) in (1):
$$X^2 + (1-X)^2=1$$
...
$$2X (X-1) = 0$$

Hense X= 0 or X = 1.

Not sufficient?

PLS Help!

The point is that x=0 is not a valid solution. For x=1, from y=1-x it follows that y=1 but we are told in the stem that y≠1. Thus x can only be 1. Sufficient.

Answer: C.

Does this make sense?

bunuel,
i have a doubt here...
x^2 + y^2 = 1
and
y = 1-x
=> x+y = 1 squaring both sides
=> x^2 + y^2 + 2xy = 1 substituting x^2 + y^2 = 1
=> 1 + 2xy = 1
=> 2xy = 0
=> xy = 0
now x can be anything on the basis of the above equatn
hence getting E. what am i missing

secondly, what might be the level of this question??

would really appreciate your help.
thanks.

The very post you are quoting answers the question.

xy = 0 means that x = 0 or y = 0. But x = 0 is not a valid solution. If x = 0, from y = 1 - x it follows that y=1 but we are told in the stem that y≠1. Thus y = 0 and from y = 1 - x it follows that x = 1.

As for the difficulty level of the question: stats in the original post say that it's a 700 level question.
_________________
Manager
Joined: 31 Jul 2014
Posts: 128
GMAT 1: 630 Q48 V29
Re: If y≠1, is x=1?  [#permalink]

### Show Tags

28 Nov 2014, 23:45
vasili wrote:
If y is not equal to 1, is x = 1?

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

Hi
I am not sure if this is correct solution, someone kindly help

If y is not equal to 1, is x = 1?
1) x^2 + y^2 = 1
2) y = 1 - x

------------------------------------------------
Statement1
x^2 + y^2 = 1
y=0 , x=1 --> x=1 Yes
but y and x need not be integers so y = x = sqrt(0.5) --> x=1 No
------------------------------------------------
Statement2
y = 1 - x
x=1, Y=0 --> x=1 Yes
x=0.5 , Y = 0.5 --> x=1 No
--------------------------------------------------
1+2
Here I checked all ranges

Case1
If x=0 then Y=1 which can not be true
So x=1 and Y=0
x=1 Yes

Case2
x between 0 and 1
x=0.1 y=0.9
x=0.5 y=0.5
x=0.9 y=0.1
As we know number between 0 and 1 , then x2<x so in this case x^2 + y^2 <> 1
so we cant consider this range

Case3
x between 0 and -1
this will be same as case2 , because square will be same for + and -ve

Case4
x >=1 here again x^2 + y^2 <> 1
so we cant consider this range

x<=-1 here again x^2 + y^2 <> 1
so we cant consider this range

Hence only x=1 and Y=0 works
IMO C

Someone please confirm if it is correct.
Manager
Status: Kitchener
Joined: 03 Oct 2013
Posts: 89
Location: Canada
Concentration: Finance, Finance
GPA: 2.9
WE: Education (Education)
Re: If y≠1, is x=1?  [#permalink]

### Show Tags

09 Apr 2015, 05:41
MDK wrote:
If y≠1, is x=1?

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

But if we take the sqroot of both side in statment 1 we will get x+y=1

so, x=1,y=0 or x=4,y=-3 so statment 1 insuff

statment 2 also y could be equal to -3 when x=4

and y=0 when x=1 so statment 2 insuff

both statment 1and 2 insuff where x could be equal to 1 or 4 so the answer is E
_________________

Click +1 Kudos if my post helped

Math Expert
Joined: 02 Sep 2009
Posts: 52210
Re: If y≠1, is x=1?  [#permalink]

### Show Tags

09 Apr 2015, 05:52
23a2012 wrote:
MDK wrote:
If y≠1, is x=1?

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

But if we take the sqroot of both side in statment 1 we will get x+y=1

so, x=1,y=0 or x=4,y=-3 so statment 1 insuff

statment 2 also y could be equal to -3 when x=4

and y=0 when x=1 so statment 2 insuff

both statment 1and 2 insuff where x could be equal to 1 or 4 so the answer is E

Did you test whether x=4 and y=-3 satisfy x^2 + y^2 = 1?

If you take the square root from x^2 + y^2 = 1, you'd get $$\sqrt{x^2 + y^2}= 1$$, not x + y = 1.
_________________
Director
Joined: 07 Aug 2011
Posts: 535
Concentration: International Business, Technology
GMAT 1: 630 Q49 V27
Re: If y≠1, is x=1?  [#permalink]

### Show Tags

09 Apr 2015, 07:08
MDK wrote:
If y≠1, is x=1?

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

(1) x^2 + y^2 = 1
y^2= 1-x^2
X will be 0 when Y=-1 (cannot be 1)
X can be +/- 1 when Y=0.
insufficient.

(2) y = 1 - x
Y can be 0 in which case X=1 , Y can be 2 in which case X=-1 .
not sufficient.

x^2 + (1-x)^2 = 1
2x(x-1)=0
X = 0 or 1

Since Y cannot be 1 so X cannot be 0 .
hence X=1

Ans: C
_________________

Thanks,
Lucky

_______________________________________________________
Kindly press the to appreciate my post !!

Senior Manager
Joined: 02 Dec 2014
Posts: 371
Location: Russian Federation
Concentration: General Management, Economics
GMAT 1: 640 Q44 V33
WE: Sales (Telecommunications)
Re: If y≠1, is x=1?  [#permalink]

### Show Tags

19 May 2015, 14:21
manpreetsingh86 wrote:
vasili wrote:
If y is not equal to 1, is x = 1?

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

Quote:
Please help.

st.1 here different values of x and y can satisfy the equation $$x^2 + y^2 =1$$. for example

x=$$\frac{1}{\sqrt{2}}$$
y=$$\frac{1}{\sqrt{2}}$$

as x is not equal to 1. hence answer to the original question is no.

also, x=1 and y=0 will satisfy this equation. as x=1, thus answer to the original question is yes.

x=-1 and y=0 will satisfy this equation. as x is not equal to 1, thus answer to the original question is no.

st. 2
y= 1-x again different values are possible. hence not sufficient

combining st.1 and st.2

put y=1-x in $$x^2+y^2=1$$

$$x^2 +1+x^2-2x=1$$
$$2(x^2-2x)=0$$
$$x(x-1)=0$$

x=0 or x=1

but x=0 is not possible, as y is not equal to 1. hence x=1. thus answer should be C

Hi manpreetsingh86! The correct version of the bold part is 2(x^2-x)=0. In your solution 2 in the brackets is wrong since you factor out 2 already. Please correct
_________________

"Are you gangsters?" - "No we are Russians!"

Manager
Joined: 21 Feb 2012
Posts: 57
Re: If y≠1, is x=1?  [#permalink]

### Show Tags

20 May 2015, 04:43
Quick soln

Statement 1: Circle with infinite values for x when y is not 1. reject.

Statement 2: Line with infinite values for x when y is not 1. reject

Combines statement: Only two point of intersection (0,1) and (1,0). Thus solvable.

As pointed in the above posts the easiest way is the graphical way in most of these type of questions. I think we should not even think on the track of solving equations.
_________________

Regards
J

Do consider a Kudos if you find the post useful

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8787
Location: Pune, India
Re: If y≠1, is x=1?  [#permalink]

### Show Tags

20 May 2015, 22:17
1
1
MDK wrote:
If y≠1, is x=1?

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

Something to think about here:

y is "not 1" is an unusual information. There is no reason for which it needs to be "not 1" such as (y - 1) in denominator.

(1) x^2 + y^2 = 1
x can take many values since this is an equation in two variables. y will take corresponding value(s). What we need to check is whether x can be 1. The only time the statement may be sufficient is if x is 1 only when y = 1.
Put x = 1, you get y = 0.
So x may or may not be 1. Insufficient

(2) y = 1 - x
Similarly, x and y may take infinite different value. When x = 1, y = 0 here. So again, x may or may not be 1. Not sufficient.

Using both, x^2 + (1-x)^2 = 1
x(x - 1) = 0
Either x is 0 or 1. But if x is 0, y is 1 which is not allowed. So x must be 1.

Answer (C)
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

Manager
Joined: 13 Dec 2013
Posts: 154
Location: United States (NY)
Concentration: General Management, International Business
GMAT 1: 710 Q46 V41
GMAT 2: 720 Q48 V40
GPA: 4
WE: Consulting (Consulting)
Re: If y≠1, is x=1?  [#permalink]

### Show Tags

22 Mar 2017, 20:03
MDK wrote:
If y≠1, is x=1?

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

1) y=0, x=1 then yes
y=(sqroot0.5)^2, x=y=(sqroot0.5)^2, then no

2) Clearly insuff. 4=1-(-3) then no, 0=1-1, then yes

1)&2) (1-x)^2 + x^2 = 1
x^2-x=0
x=1 or x=0 but y cannot be 1 so from y=1-x, x must be 1.
Intern
Joined: 05 Mar 2015
Posts: 49
Location: Azerbaijan
GMAT 1: 530 Q42 V21
GMAT 2: 600 Q42 V31
GMAT 3: 700 Q47 V38
Re: If y≠1, is x=1?  [#permalink]

### Show Tags

26 Aug 2017, 03:53
If y ≠ 1, is x = 1?

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

(2) y=1-x

It is obvious that neither statement alone is sufficient. Now, let's look two statements together.

Think about it x+y = 1 but x^2 + y^2 = 1. Can you think of a pair of two numbers whose sum is 1. But when you square those numbers and add together the results, you again get 1? The only pair 1 and 0

Since y can't be 1, x must be 1
Intern
Joined: 24 Jul 2017
Posts: 47
Location: India
WE: Information Technology (Computer Software)
Re: If y≠1, is x=1?  [#permalink]

### Show Tags

02 Oct 2017, 02:40
Got this question in GMATPrep EP1 and below is the approach I followed:
1. x^2 + y^2 = 1
Not given that x and y are integers. Hence, two cases possible:
a. If y = 0, x = 1 or x = -1
b. If y =1/sqrt2 , x = 1/sqrt2. Not sufficient

2. y = 1-x
x can take any value except for zero. Hence not sufficient.

(1) + (2),
x^2 + y^2 = 1 and y = 1-x
We know that (x+y)^2 = x^2 + y^2 + 2xy
1^2 = 1 + 2xy
2xy = 0
Given that y ≠ 1, for xy to be zero x has to be 1. Sufficient

Hence option C.

Kudos if it helps
Manager
Joined: 22 Jun 2017
Posts: 71
Location: Brazil
GMAT 1: 600 Q48 V25
GPA: 3.5
WE: Engineering (Energy and Utilities)
If y ≠ 1, is x = 1 ?  [#permalink]

### Show Tags

09 May 2018, 14:00
If y ≠ 1, is x = 1 ?

(1) $$x^2$$ + $$y^2$$ = 1
(2) y = 1 – x
If y ≠ 1, is x = 1 ? &nbs [#permalink] 09 May 2018, 14:00

Go to page    1   2    Next  [ 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

 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®.