Last visit was: 13 Dec 2024, 10:43 It is currently 13 Dec 2024, 10:43
Home
GMAT
Messages
Tests
Schools
Reviews
Social
Chat
My Profile
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
Back to Forum
Create Topic
605-655 Level|   Absolute Values|         
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 13 Dec 2024
Posts: 97,873
Own Kudos:
685,588
 []
Given Kudos: 88,268
Products:
GMAT Club Tests Forum Quiz
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 97,873
Kudos: 685,588
 []
If |x| = |y|, x + y = ? (1) x - y = 4 (2) x/y = -1 12 Jul 2019, 08:00
Kudos
Add Kudos
4
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

45% (medium)

Question Stats:

61% (01:28) correct 39% (01:28) wrong based on 389 sessions

History

Date
Time
Result
Not Attempted Yet
If \(|x| = |y|\), \(x + y = ?\)


(1) \(x - y = 4\)

(2) \(\frac{x}{y} = -1\)


 

This question was provided by Math Revolution
for the Heroes of Timers Competition

 

ShowHide Answer
Official Answer
D
Most Helpful Reply
User avatar
Kinshook
User avatar
GMAT Club Legend
Joined: 03 Jun 2019
Last visit: 13 Dec 2024
Posts: 5,423
Own Kudos:
4,599
 []
Given Kudos: 161
Location: India
Schools: HBS '22 CBS '22 Wharton '22
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Products:
My Reviews
Schools: HBS '22 CBS '22 Wharton '22
GMAT 1: 690 Q50 V34
Posts: 5,423
Kudos: 4,599
 []
If |x| = |y|, x + y = ? (1) x - y = 4 (2) x/y = -1 Updated on: 13 Jul 2019, 09:30
Originally posted by Kinshook on 12 Jul 2019, 08:16.
Last edited by Kinshook on 13 Jul 2019, 09:30, edited 1 time in total.
4
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Given: |x|=|y|
Question: x+y=?

Statement 1:
x−y=4
Since |x|=|y|
=> x = y or x=-y
x-y=4
x<>y => x=-y
x=2 & y=-2
x+y=0
SUFFICIENT

Statement 2:
x/y=−1
x=-y
x+y=0
SUFFICIENT

IMO D
General Discussion
User avatar
JonShukhrat
User avatar
Joined: 06 Jun 2019
Last visit: 01 Jul 2024
Posts: 313
Own Kudos:
983
 []
Given Kudos: 655
Location: Uzbekistan
Posts: 313
Kudos: 983
 []
If |x| = |y|, x + y = ? (1) x - y = 4 (2) x/y = -1 Updated on: 13 Jul 2019, 05:33
Originally posted by JonShukhrat on 12 Jul 2019, 09:00.
Last edited by JonShukhrat on 13 Jul 2019, 05:33, edited 2 times in total.
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
If |x|=|y|, x+y=?

Since x and y are equal (note: their absolute values are so), let's pick some easy numbers to work with.

ST1 x−y=4
Say x and y are 2 each. 2-2=0 (NO, must be 4). Does not work
Say x and y are (-2) each. (-2)-(-2)=0 (NO, must be 4). Does not work
Say x is (-2) and y is (2). (-2)-2=-4 (NO, must be 4). Does not work
Say x is 2 and y is (-2). 2-(-2)=4, yes it works. So 2+(-2)=0. We have an answer. Sufficient.

ST2 xy=−1
Let's do similar testing.
Say x and y are 2 each. 2/2=1(NO, must be (-1)). Does not work
Say x and y are (-2) each. (-2)/(-2)=1 (NO, must be (-1)). Does not work
Say x is (-2) and y is (2). (-2)/2=-1, yes it works. So, we have -2+2=0. We have an answer.
Say x is 2 and y is (-2). 2/(-2)=-1, yes it works. So 2+(-2)=0. Again, we have an answer. (Although two different sets of value works, both yield the same answer) Sufficient

Hence D
avatar
Ilishar
avatar
Joined: 12 Aug 2017
Last visit: 30 Mar 2020
Posts: 44
Own Kudos:
56
 []
Given Kudos: 75
Concentration: General Management, Marketing
Posts: 44
Kudos: 56
 []
If |x| = |y|, x + y = ? (1) x - y = 4 (2) x/y = -1 12 Jul 2019, 09:19
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Given : |x|=|y|
Find: x+y? (single value should be available)
Analysis:
if x=y then, values are required
if x= -y then, x+y = 0
if -x = y then, x+y =0
(1)Statement 1:
x-y=4
x=y+4 => x not equal to y
we know |x|=|y| thus, we can have values like x(2), y(-2), implying that x+y = 0
Hence, sufficient

(ii) Statement 2:
x/y = -1
x=-y thus, x+y =0
Hence, Sufficient

Final Answer D
User avatar
RusskiyLev
User avatar
Joined: 26 Mar 2019
Last visit: 26 Mar 2022
Posts: 63
Own Kudos:
104
 []
Given Kudos: 142
Location: Azerbaijan
Concentration: Finance, Strategy
Schools: Booth '23 (II)
GMAT 1: 730 Q50 V38
Products:
My Reviews
Schools: Booth '23 (II)
GMAT 1: 730 Q50 V38
Posts: 63
Kudos: 104
 []
If |x| = |y|, x + y = ? (1) x - y = 4 (2) x/y = -1 12 Jul 2019, 09:22
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Quote:
If |x|=|y|, x+y=?


(1) x−y=4

(2) x/y=−1

It is given that |x|=|y|. Hence, either x = y or x = - y.
We need to find out what is x + y?
If x = y, then x + y is 2x or 2y.
If x = -y, then x + y = 0.

Let us analyze the statements separately first and see if it is required to analyze them together.

Statement 1:
x - y = 4.
From this statement we can conclude that x = y + 4, and x is not equal to y. From what we found in the beginning, it means that x = -y. In this case, we can substitute y by -x and write an equation as x + y = x - x = 0.
Statement is sufficient.

Statement 2:
x/y = -1.
From this stament, it can be calculated that x = -1 * y = -y. Here, we can solve it in the same way as we did above in analysis of the first statement.
Statement 2 is sufficient.

As we have both statements sufficient to solve the question, the Answer is D.
User avatar
freedom128
User avatar
Joined: 30 Sep 2017
Last visit: 01 Oct 2020
Posts: 943
Own Kudos:
1,302
 []
Given Kudos: 402
GMAT 1: 720 Q49 V40
GPA: 3.8
Products:
My Reviews
GMAT 1: 720 Q49 V40
Posts: 943
Kudos: 1,302
 []
If |x| = |y|, x + y = ? (1) x - y = 4 (2) x/y = -1 12 Jul 2019, 10:11
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
|x|=|y| --> x^2 = y^2 --> x^2 - y^2 = 0 --> (x-y)(x+y)=0

QUESTION: x+y=?

(1) x−y=4
If (x−y)(x+y)=0 and (x−y)=4, then (x+y) must be 0
(1) is SUFFICIENT

(2) x/y=−1
x/y=−1 --> x = −y --> x+y = 0
(2) is SUFFICIENT


Correct answer is (D)
User avatar
bebs
User avatar
Joined: 18 Jun 2018
Last visit: 03 Dec 2021
Posts: 333
Own Kudos:
201
 []
Given Kudos: 1,283
Concentration: Finance, Healthcare
Schools: Jones '22 (M$) McCombs '22 (WL) Kelley '22 (A$)
Schools: Jones '22 (M$) McCombs '22 (WL) Kelley '22 (A$)
Posts: 333
Kudos: 201
 []
If |x| = |y|, x + y = ? (1) x - y = 4 (2) x/y = -1 12 Jul 2019, 13:24
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Given: |x|=|y|

Question : x+y=0

St 1: x-y = 4 ==> x = 2, y = -2 ==> 2+(-2)=0 ===> sufficient since we can't find any other set of numbers that satisfies St 1 and |x|=|y|.
St 2: \(\frac{x}{y}\)=-1 ==> x=-y ==> x+y=0 ==> sufficient

Therefore, the answer is D.
User avatar
nick1816
User avatar
Retired Moderator
Joined: 19 Oct 2018
Last visit: 12 Dec 2024
Posts: 1,859
Own Kudos:
7,094
 []
Given Kudos: 707
Location: India
Posts: 1,859
Kudos: 7,094
 []
If |x| = |y|, x + y = ? (1) x - y = 4 (2) x/y = -1 12 Jul 2019, 18:26
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Statement 1
|x|=|y| and x-y=4
It implies that x and y gas opposite signs
Hence x+y=0
Sufficient

Statement 2
|x|=|y| and xy=-1
Again we get that x and y are equal in magnitude, but have opposite signs
x+y=0
sufficient

IMO D
User avatar
CareerGeek
User avatar
Joined: 20 Jul 2017
Last visit: 12 Dec 2024
Posts: 1,297
Own Kudos:
3,784
 []
Given Kudos: 162
Location: India
Concentration: Entrepreneurship, Marketing
GMAT 1: 690 Q51 V30
WE:Education (Education)
GMAT 1: 690 Q51 V30
Posts: 1,297
Kudos: 3,784
 []
If |x| = |y|, x + y = ? (1) x - y = 4 (2) x/y = -1 12 Jul 2019, 20:22
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
|x|=|y|
--> x = ± y
--> x = y (or) x = -y

(1) x − y = 4
--> x & y can have ONLY opposite sign; x is positive & y is negative
--> x = -y
-y - y = 4
--> -2y = 4
--> y = -2
--> x = -(-2) = 2

x + y = 2 - 2 = 0

Sufficient

(2) x/y=−1
--> x & y are of same value, BUT opposite sign
--> x = -y

x + y = -y + y = 0

Sufficient

IMO Option D

Pls Hit Kudos if you like the solution
User avatar
GKomoku
User avatar
Joined: 06 Mar 2018
Last visit: 23 Mar 2022
Posts: 301
Own Kudos:
941
 []
Given Kudos: 3,682
Status:To infinity and beyond
Location: Kazakhstan
Concentration: Technology, Finance
Schools: Stanford '23 Sloan '23
GPA: 3.87
Schools: Stanford '23 Sloan '23
Posts: 301
Kudos: 941
 []
If |x| = |y|, x + y = ? (1) x - y = 4 (2) x/y = -1 12 Jul 2019, 23:22
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post

If |x|=|y|, x+y=?




(1) x−y=4, from this we can get that x and y are opposite signs.
If they both were negative, zero: -2--2=-2+2=0.
If they both were positive aslo x-y=0.
So we infer that both of them need to be opposite signs and x need to be positive. eg: 2--2=2+2=4
We have definite answer, sufficient.

(2) x/y=−1 from this we get x and y different signs, hence x+y=0, sufficient.

D is the answer.

User avatar
shridhar786
User avatar
Joined: 31 May 2018
Last visit: 08 Feb 2022
Posts: 325
Own Kudos:
1,638
 []
Given Kudos: 132
Location: United States
Concentration: Finance, Marketing
Posts: 325
Kudos: 1,638
 []
If |x| = |y|, x + y = ? (1) x - y = 4 (2) x/y = -1 12 Jul 2019, 23:42
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
If |x|=|y| , x+y=?

\(|x|^2\) = \(|y|^2\) (squaring both sides)
\(x^2\) = \(y^2\)
(\(x^2\)-\(y^2\)) = 0
(x-y)(x+y) = 0
(x-y)=0 or (x+y) = 0

STATEMENT (1) x−y=4
this statement tells us that (x-y) ≠ 0
then definitely (x+y) = 0 SUFFICIENT

STATEMENT (2) \(\frac{x}{y}\)=−1
\(\frac{x}{y}\)+1 = 0
\(\frac{(x+y)}{y}\)=0
(x+y)=0 (since y cant be equal to zero)
SUFFICIENT

D is the answer
User avatar
eakabuah
User avatar
Retired Moderator
Joined: 18 May 2019
Last visit: 15 Jun 2022
Posts: 782
Own Kudos:
1,078
 []
Given Kudos: 101
Posts: 782
Kudos: 1,078
 []
If |x| = |y|, x + y = ? (1) x - y = 4 (2) x/y = -1 13 Jul 2019, 01:12
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
If |x|=|y|, then x=y or x=-y
What is x+y?

1. x-y=6
The condition is that x=y or x=-y.
So x-y=6
The values of x and y that satisfy this condition are x=3 and y=-3 and this satisfies the condition x=-y
3-(-3)=6. Hence we can say that x+y=0
Statement 1 alone is sufficient.

Statement 2: x/y=-1
We know that both x and y can be both positive or they both negative or one can be positive while the other is negative.
So we mutiply both sides by y^2 to ensure the signs don’t change.
y^2+xy=0
y(y+x)=0
either y=0, which makes x=0, or y+x=0 which means that x=-y
And this is true for any pairs of x=-y, such as {1,-1; 2,-2; 3,-3; -4,4}
Hence we can say that x+y=0
Statement 2 is therefore sufficient.
Answer imo is D

Posted from my mobile device
User avatar
ArtyomYom
User avatar
Joined: 01 Oct 2018
Last visit: 23 Feb 2021
Posts: 26
Own Kudos:
73
 []
Given Kudos: 104
Posts: 26
Kudos: 73
 []
If |x| = |y|, x + y = ? (1) x - y = 4 (2) x/y = -1 13 Jul 2019, 04:22
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
If |x|=|y|, x+y=?
Possibilities:
x and y can be pos and neg:
'+' + '+' = 2x or 2y
'-' + '-' = 2x or 2y
'+' + '-' = 0
'-' + '+' = 0

(1) x−y=4
if x and y:
'+' '+' = no sence, coz |x|=|y|
'-' '-' = no sence, coz |x|=|y|
'+' '-' = can be x = 2 y = -2
'-' '+' = no sense, coz result need to be negative
SUFFICIENT: '+' + '-' = 0

(2) xy=−1
if x and y:
'+' '+' = no sence, multiple must be positive
'-' '-' = no sence, multiple must be positive
'+' '-' = can be
'-' '+' = can be
SUFFICIENT:
'+' + '-' = 0
'-' + '+' = 0

Answ D
Moderator:
Bunuel
Math Expert
97873 posts