NEW HERE? LEARN MORE
closeclose
Last visit was: 28 Apr 2024, 03:44 It is currently 28 Apr 2024, 03:44
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

If xy ≠ 0. Is x + y = 0 ? (1) x is reciprocal of y. (2) x ≠ 1.

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92964
Own Kudos [?]: 619590 [1]
Given Kudos: 81613
Send PM
CAT Tests Forum Quiz Mode
If xy ≠ 0. Is x + y = 0 ? (1) x is reciprocal of y. (2) x ≠ 1. [#permalink] New post   10 Dec 2018, 02:21
Expert Reply
00:00
A
B
C
D
E

Difficulty:

35% (medium)

Question Stats:

62% (01:16) correct 38% (01:25) wrong based on 106 sessions
Hide Show timer Statistics
If xy ≠ 0. Is x + y = 0 ?

(1) x is reciprocal of y.
(2) x ≠ 1.
ShowHide Answer
Official Answer
A
User avatar
P
eswarchethu135
Senior Manager
Senior Manager
Joined: 13 Jan 2018
Posts: 279
Own Kudos [?]: 403 [1]
Given Kudos: 20
Location: India
Concentration: Operations, General Management
Schools: EDHEC Sept 2019 Intake (A) Erasmus '20 IE Jan20 Intake (A)
GMAT 1: 580 Q47 V23
GMAT 2: 640 Q49 V27
GPA: 4
WE:Consulting (Consulting)
Send PM
Reviews Badge
Re: If xy ≠ 0. Is x + y = 0 ? (1) x is reciprocal of y. (2) x ≠ 1. [#permalink] New post   10 Dec 2018, 02:53
1
Bookmarks
Statement 1) x = \(\frac{1}{y}\)

is x+y = 0?

\(\frac{1}{y}\) + y = 0

\(\frac{1+y^2}{y}\) = 0

Now \(xy \neq{0}\)

i.e, either of x or y cannot be 0.

So in \(\frac{1+y^2}{y}\) , \(y^2\) will be positive and 1+positive value is some other positive value. Now this entire value is divided by y (which is not 0). This fraction can never be equal to 0.

\(\frac{1+y^2}{y} \neq{0}\)

So SUFFICIENT.

Statement 2) \(x \neq{1}\)

Clearly INSUFFICIENT.

OPTION: A
User avatar
L
Archit3110
GMAT Club Legend
GMAT Club Legend
Joined: 18 Aug 2017
Status:You learn more from failure than from success.
Posts: 8022
Own Kudos [?]: 4100 [0]
Given Kudos: 242
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
Send PM
GMAT ToolKit User CAT Tests
Re: If xy ≠ 0. Is x + y = 0 ? (1) x is reciprocal of y. (2) x ≠ 1. [#permalink] New post   10 Dec 2018, 05:06
Bunuel wrote:
If xy ≠ 0. Is x + y = 0 ?

(1) x is reciprocal of y.
(2) x ≠ 1.


from 1 :

x=1/y
or xy=1

and given x+y=0
we can say
1/y+y=0
1+y^2=0
y=+/-1

so for any value of y we would get reciprocal value of x hence sufficient..

from 2:
x ≠ 1
no info of y so in sufficient..

IMO A
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6818
Own Kudos [?]: 29968 [2]
Given Kudos: 799
Location: Canada
Send PM
Re: If xy ≠ 0. Is x + y = 0 ? (1) x is reciprocal of y. (2) x ≠ 1. [#permalink] New post   10 Dec 2018, 07:58
2
Kudos
Expert Reply
Top Contributor
Bunuel wrote:
If xy ≠ 0. Is x + y = 0 ?

(1) x is reciprocal of y.
(2) x ≠ 1.


Target question: Is x + y = 0 ?

Given: xy ≠ 0
IMPORTANT: xy ≠ 0 tells us that neither x nor y equals zero.
So, in order for x+y to equal zero, we need one value (x or y) to be POSITIVE, and the other value to be NEGATIVE.

Statement 1: x is reciprocal of y.
Let's focus on the sign (negative or positive) of each value.
There are two possible cases:
Case a: y is NEGATIVE. Since x = 1/y, we can see that x must be NEGATIVE too. So, x + y = NEGATIVE + NEGATIVE = some negative number. In this case, the answer to the target question is NO, it is NOT the case that x+y = 0
Case b: y is POSITIVE. Since x = 1/y, we can see that x must be POSITIVE too. So, x + y = POSITIVE + POSITIVE = some positive number. In this case, the answer to the target question is NO, it is NOT the case that x+y = 0
Since both possible cases yield THE SAME answer to the target question, statement 1 is SUFFICIENT

Statement 2: x ≠ 1
There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = 2 and y = -2. In this case, the answer to the target question is YES, it IS the case that x+y = 0
Case b: x = 2 and y = -1. In this case, the answer to the target question is NO, it is NOT the case that x+y = 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32715
Own Kudos [?]: 822 [0]
Given Kudos: 0
Send PM
Re: x is not equal to 0. Is x+y=0? 1. x is reciprocal of y. 2. x [#permalink] New post   18 Nov 2020, 07:08
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: x is not equal to 0. Is x+y=0? 1. x is reciprocal of y. 2. x [#permalink]
18 Nov 2020, 07:08
Moderator:
Bunuel
Math Expert
92964 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions