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

 It is currently 20 Jun 2019, 13:09 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  If x^2+y^2=1, is x+y=1 ? (1) xy=0 (2) y=0

Author Message
TAGS:

Hide Tags

Intern  Joined: 30 Aug 2010
Posts: 13
If x^2+y^2=1, is x+y=1 ? (1) xy=0 (2) y=0  [#permalink]

Show Tags

11 00:00

Difficulty:   55% (hard)

Question Stats: 59% (01:27) correct 41% (01:15) wrong based on 649 sessions

HideShow timer Statistics

If x^2+y^2=1, is x+y=1 ?

(1) xy=0
(2) y=0

Originally posted by rraggio on 15 Sep 2010, 07:37.
Last edited by Bunuel on 17 May 2012, 01:19, edited 1 time in total.
Edited the OA
Math Expert V
Joined: 02 Sep 2009
Posts: 55732
Re: If x^2+y^2=1, is x+y=1 ?  [#permalink]

Show Tags

3
2
rraggio wrote:
If x^2+y^2=1, is x+y=1 ?

(1) xy=0
(2) y=0

Thanks!

I think answer B is not correct.

(1) $$xy=0$$ --> either $$x=0$$ or $$y=0$$:
if $$x=0$$, then $$x^2+y^2=y^2=1$$ and $$y=1$$ or $$y=-1$$, so $$x+y=0+1=1$$ (answer YES) or $$x+y=0-1=-1$$ (answer NO);
if $$y=0$$, then $$x^2+y^2=x^2=1$$ and $$x=1$$ or $$x=-1$$, so $$x+y=1+0=1$$ (answer YES) or $$x+y=-1+0=-1$$ (answer NO);

(2) $$y=0$$ --> $$x^2+y^2=x^2=1$$ and $$x=1$$ or $$x=-1$$, so $$x+y=1+0=1$$ (answer YES) or $$x+y=-1+0=-1$$ (answer NO). Two different answers. No sufficient.

(1)+(2) $$xy=0$$ and $$y=0$$ --> $$y=0$$ and $$x=1$$ or $$x=-1$$, so $$x+y=1+0=1$$ (answer YES) or $$x+y=-1+0=-1$$ (answer NO). Two different answers. No sufficient.

_________________
General Discussion
Manager  Joined: 20 Jul 2010
Posts: 206
Re: If x^2+y^2=1, is x+y=1 ?  [#permalink]

Show Tags

D can be true only when problem says x and y are positive.
_________________
If you like my post, consider giving me some KUDOS !!!!! Like you I need them
Math Expert V
Joined: 02 Sep 2009
Posts: 55732
If x^2+y^2=1, is x+y=1 ? (1) xy=0 (2) y=0  [#permalink]

Show Tags

1
saxenashobhit wrote:
D can be true only when problem says x and y are positive.

Both $$x$$ and $$y$$ cannot be positive as it would contradict the statements.

For D to be the answer the question should ask "is $$x+y>1$$?" instead of "is $$x+y=1$$?".
_________________
Manager  Joined: 30 Aug 2010
Posts: 85
Location: Bangalore, India
Re: If x^2+y^2=1, is x+y=1 ?  [#permalink]

Show Tags

For the given Question, The answer shud be "E".

(x+y)^2=X^2+y^2+2xy=1+2xy ==> x+y = sqrt(1+2xy)

1) xy=0 ==> x+y = sqrt(1+0) = +1 (or) -1 ===> Not Suff.
2) y=0 ==> clearly Not suff.

1&2 No new info.

Had the qtn been "IS |X+Y| = 1", then the answer whould have been "A" as shown above.

Hope it is clear.
Senior Manager  Joined: 31 Mar 2010
Posts: 394
Location: Europe
Re: If x^2+y^2=1, is x+y=1 ?  [#permalink]

Show Tags

If I may,

x^2+y^2=1 is the formula of a circle centered on (0,0) with radius 1.

This should help you answer the problem more easily PS: the answer is definitely E. Typos happen.
Manager  Joined: 29 Oct 2010
Posts: 67
Re: If x^2+y^2=1, is x+y=1 ?  [#permalink]

Show Tags

Intern  Joined: 14 Nov 2011
Posts: 10
Re: If x^2+y^2=1, is x+y=1 ? (1) xy=0 (2) y=0 Thanks  [#permalink]

Show Tags

IMO Answer is D.. Here's why:

x^2+y^2= 1

X^2+y^2 can be written as (x+y)^2-2xy

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

From statement 1, xy=0 we get (x+y)^2 = 1
From statement 2, y=0 we get (x+y)^2 = 1

Thus (x+y)=1-----> Square root of both sides

Both statements are sufficient.
Math Expert V
Joined: 02 Sep 2009
Posts: 55732
Re: If x^2+y^2=1, is x+y=1 ? (1) xy=0 (2) y=0 Thanks  [#permalink]

Show Tags

pratk wrote:
IMO Answer is D.. Here's why:

x^2+y^2= 1

X^2+y^2 can be written as (x+y)^2-2xy

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

From statement 1, xy=0 we get (x+y)^2 = 1
From statement 2, y=0 we get (x+y)^2 = 1

Thus (x+y)=1 -----> Square root of both sides

Both statements are sufficient.

The answer to this question is E, not D.

Consider two sets of numbers, which satisfy stem, as well as both statements and give different values of x+y:
If $$y=0$$ and $$x=1$$ then $$x+y=1+0=1$$;
If $$y=0$$ and $$x=-1$$ then $$x+y=-1+0=-1$$.

Now, the problem in your solution (the red part) is that (x+y)^2=1 means that x+y=1 OR x+y=-1 (you forgot to consider negative root). Basically the same way as x^2=4 means that x=2 or x=-2.

Hope it's clear.
_________________
Intern  Joined: 14 Nov 2011
Posts: 10
Re: If x^2+y^2=1, is x+y=1 ? (1) xy=0 (2) y=0 Thanks  [#permalink]

Show Tags

Yes Bunuel, what you mention is correct and I also thought about it that way and this would hold true if ther question would have been phrased differently- perhaps something like : "What is the value of x?" However the question simply asks: is x+y=1? And based on my post above, the answer to that question is Yes using both statements independently.

Not sure if my thinking is correct, guess I have been doing alot of critical reasoning questions so my mind is working in a different way.

Any thoughts?
Math Expert V
Joined: 02 Sep 2009
Posts: 55732
Re: If x^2+y^2=1, is x+y=1 ? (1) xy=0 (2) y=0 Thanks  [#permalink]

Show Tags

pratk wrote:
Yes Bunuel, what you mention is correct and I also thought about it that way and this would hold true if ther question would have been phrased differently- perhaps something like : "What is the value of x?" However the question simply asks: is x+y=1? And based on my post above, the answer to that question is Yes using both statements independently.

Not sure if my thinking is correct, guess I have been doing alot of critical reasoning questions so my mind is working in a different way.

Any thoughts?

No, your thinking is not correct. It's seems that you have some problem with this type of DS question. It's a YES/NO DS question. In a Yes/No Data Sufficiency question, statement(s) is sufficient if the answer is “always yes” or “always no” while a statement(s) is insufficient if the answer is "sometimes yes" and "sometimes no".

Now, we have that even when statements are taken together x+y can equal to 1 as well as -1. So, both statements are not sufficient to give definite YES or definite NO answer to the question whether x+y=1.

Hope it's clear.
_________________
Intern  Joined: 14 Nov 2011
Posts: 10
Re: If x^2+y^2=1, is x+y=1 ? (1) xy=0 (2) y=0  [#permalink]

Show Tags

Thanks for the explanation. I get it now.
Guess I need to practice more of these Always Yes/No type.
Manager  Affiliations: Project Management Professional (PMP)
Joined: 30 Jun 2011
Posts: 135
Location: New Delhi, India

Show Tags

eybrj2 wrote:
If x^2+y^2=1, is x+y=1 ?

(1) xy=0
(2) y=0

Hi eybrj

(X+Y)^2= X^2+Y^2+2*X*Y

1) Since XY=0
(X+Y)^2= X^2+Y^2+0=1
=> (X+Y)= +1 or -1
So no unique Solution

2) Since y=0
(X+Y)^2= X^2+0+0=X^2

X^2=1
=> X= +1 or -1
=> X+Y= +1 or -1

So no unique solution

Combining 1) & 2) only gives XY term to be zero hence the solution can't
be determined so E is the answer

Best
Vaibhav
_________________
Best
Vaibhav

If you found my contribution helpful, please click the +1 Kudos button on the left, Thanks
Intern  Joined: 18 May 2013
Posts: 12
WE: Consulting (Consulting)
Re: If x^2+y^2=1, is x+y=1 ?  [#permalink]

Show Tags

Bunuel wrote:
rraggio wrote:
If x^2+y^2=1, is x+y=1 ?

(1) xy=0
(2) y=0

Thanks!

I think answer B is not correct.

(1) $$xy=0$$ --> either $$x=0$$ or $$y=0$$:
if $$x=0$$, then $$x^2+y^2=y^2=1$$ and $$y=1$$ or $$y=-1$$, so $$x+y=0+1=1$$ (answer YES) or $$x+y=0-1=-1$$ (answer NO);
if $$y=0$$, then $$x^2+y^2=x^2=1$$ and $$x=1$$ or $$x=-1$$, so $$x+y=1+0=1$$ (answer YES) or $$x+y=-1+0=-1$$ (answer NO);

(2) $$y=0$$ --> $$x^2+y^2=x^2=1$$ and $$x=1$$ or $$x=-1$$, so $$x+y=1+0=1$$ (answer YES) or $$x+y=-1+0=-1$$ (answer NO). Two different answers. No sufficient.

(1)+(2) $$xy=0$$ and $$y=0$$ --> $$y=0$$ and $$x=1$$ or $$x=-1$$, so $$x+y=1+0=1$$ (answer YES) or $$x+y=-1+0=-1$$ (answer NO). Two different answers. No sufficient.

Hi Bunuel,

In one of posts, I read that "square root function can not give negative result"

So in the solution above, is it ok to assume that Under root Y Square (or X Square) will have 2 values: one positive and one negative.

Regards

Rohan
Math Expert V
Joined: 02 Sep 2009
Posts: 55732
Re: If x^2+y^2=1, is x+y=1 ?  [#permalink]

Show Tags

RohanKhera wrote:
Bunuel wrote:
rraggio wrote:
If x^2+y^2=1, is x+y=1 ?

(1) xy=0
(2) y=0

Thanks!

I think answer B is not correct.

(1) $$xy=0$$ --> either $$x=0$$ or $$y=0$$:
if $$x=0$$, then $$x^2+y^2=y^2=1$$ and $$y=1$$ or $$y=-1$$, so $$x+y=0+1=1$$ (answer YES) or $$x+y=0-1=-1$$ (answer NO);
if $$y=0$$, then $$x^2+y^2=x^2=1$$ and $$x=1$$ or $$x=-1$$, so $$x+y=1+0=1$$ (answer YES) or $$x+y=-1+0=-1$$ (answer NO);

(2) $$y=0$$ --> $$x^2+y^2=x^2=1$$ and $$x=1$$ or $$x=-1$$, so $$x+y=1+0=1$$ (answer YES) or $$x+y=-1+0=-1$$ (answer NO). Two different answers. No sufficient.

(1)+(2) $$xy=0$$ and $$y=0$$ --> $$y=0$$ and $$x=1$$ or $$x=-1$$, so $$x+y=1+0=1$$ (answer YES) or $$x+y=-1+0=-1$$ (answer NO). Two different answers. No sufficient.

Hi Bunuel,

In one of posts, I read that "square root function can not give negative result"

So in the solution above, is it ok to assume that Under root Y Square (or X Square) will have 2 values: one positive and one negative.

Regards

Rohan

I guess you are confused by the part where we have $$x=1$$ or $$x=-1$$ from $$x^2=1$$.

Square root function can not give negative result --> $$\sqrt{some \ expression}\geq{0}$$, for example $$\sqrt{x^2}\geq{0}$$ --> $$\sqrt{4}=2$$ (not +2 and -2).

In contrast, the equation $$x^2=25$$ has TWO solutions, +5 and -5, because both 5^2 and (-5)^2 equal to 25.

Hope it's clear.
_________________
Intern  Joined: 18 May 2013
Posts: 12
WE: Consulting (Consulting)
Re: If x^2+y^2=1, is x+y=1 ?  [#permalink]

Show Tags

So you mean that a square root operation results in 2 solution (positive and negative) only in case of an equation ? And otherwise (in case of non equation) there is only one solution i.e. positive ?

Regards,

Rohan
Math Expert V
Joined: 02 Sep 2009
Posts: 55732
Re: If x^2+y^2=1, is x+y=1 ?  [#permalink]

Show Tags

RohanKhera wrote:
So you mean that a square root operation results in 2 solution (positive and negative) only in case of an equation ? And otherwise (in case of non equation) there is only one solution i.e. positive ?

Regards,

Rohan

Not sure I understand what you mean. Anyway:

$$x^2=4$$ --> $$x=2$$ or $$x=-2$$.

$$\sqrt{x}=4$$ --> $$x=16$$. Or $$x=\sqrt{4}$$ --> $$x=2$$.
_________________
Intern  Joined: 25 Jan 2014
Posts: 44
GMAT 1: 600 Q44 V29 GMAT 2: 710 Q48 V38 GPA: 3.35
WE: Analyst (Computer Software)
Re: If x^2+y^2=1, is x+y=1 ? (1) xy=0 (2) y=0  [#permalink]

Show Tags

1
Bunuel

Similar question but couldnt find any thread

If y is not equal to 1, is x=1?

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

Statement 1 is clearly not sufficient, as y can be 1/2 or 0, so x can be +3/4 , -3/4 or +1/-1
Similar statement 2 alone is not sufficient

Even when you combine both

y = 1-x
x+y =1
squaring both sides
(x+y)^2 = 1
x^2 +y^2 + 2xy = 1

from (1),
1 + 2xy = 1, hence xy =0
so x could be 1, 2, 3... and y could be 0, not sufficient.

But is OA is C. I am not sure how
Math Expert V
Joined: 02 Sep 2009
Posts: 55732
Re: If x^2+y^2=1, is x+y=1 ? (1) xy=0 (2) y=0  [#permalink]

Show Tags

gaurav1418z wrote:
Bunuel

Similar question but couldnt find any thread

If y is not equal to 1, is x=1?

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

Statement 1 is clearly not sufficient, as y can be 1/2 or 0, so x can be +3/4 , -3/4 or +1/-1
Similar statement 2 alone is not sufficient

Even when you combine both

y = 1-x
x+y =1
squaring both sides
(x+y)^2 = 1
x^2 +y^2 + 2xy = 1

from (1),
1 + 2xy = 1, hence xy =0
so x could be 1, 2, 3... and y could be 0, not sufficient.

But is OA is C. I am not sure how

From xy=0, x=0, y=0 or both. But if x=0, then from y=1-x, we get that y=1 but we are told that y≠1, thus x≠0. Hence y=0 and from y=1-x, we get that x=1.

This question is discussed here: if-y-1-is-x-161421.html

Hope it helps.
_________________
Intern  Joined: 25 Jan 2014
Posts: 44
GMAT 1: 600 Q44 V29 GMAT 2: 710 Q48 V38 GPA: 3.35
WE: Analyst (Computer Software)
Re: If x^2+y^2=1, is x+y=1 ? (1) xy=0 (2) y=0  [#permalink]

Show Tags

Thanks as always Bunuel, yes it helps. Cheers and have a good day Re: If x^2+y^2=1, is x+y=1 ? (1) xy=0 (2) y=0   [#permalink] 22 May 2014, 03:12

Go to page    1   2    Next  [ 24 posts ]

Display posts from previous: Sort by

If x^2+y^2=1, is x+y=1 ? (1) xy=0 (2) y=0  