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27 Apr 2023, 08:30
Kudos
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
47% (01:56) correct
53%
(02:13)
wrong
based on 55
sessions
History
Date
Time
Result
Not Attempted Yet
If |x + 5| = |y + 5|, what is the value of x + y ?
(1) xy < 0
(2) x > 3 and y < 3
(1) xy < 0
(2) x > 3 and y < 3
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
27 Apr 2023, 13:27
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Bunuel
|x + 5| = |y+5|
When (x + 5) and (y+5) share the same positive-negative sign ⇒
x + 5 = y + 5
x = y
When (x + 5) and (y+5) share opposite positive-negative sign ⇒
x + 5 = -(y + 5)
x + 5 = - y - 5
x + y = -10
Statement 1
(1) xy < 0
x and y share opposite positive-negative signs. This we can conclude that \(x \ne y\).
Hence, for the premise to hold true, x + y =-10
The statement alone is sufficient to find the sum of x and y. We can eliminate B, C, and E.
Statement 2
(2) x > 3 and y < 3
As x and y have no overlap in their range, we can conclude that \(x \ne y\).
Hence, for the premise to hold true, x + y =-10
The statement alone is sufficient to find the sum of x and y.
Option D
27 Apr 2023, 22:36
Kudos
Bookmarks
Bunuel
Solution:
Pre Analysis:
- We are given \(|x + 5| = |y + 5|\)
- We can square both the sides and get \((x+5)^2=(y+5)^2\)
\(⇒x^2+25+10x=y^2+25+10y\)
\(⇒x^2-y^2+10x-10y=0\)
\(⇒(x+y)(x-y)+10(x-y)=0\)
\(⇒(x-y)(x+y+10)=0\) - So, either \(x=y\) or \(x+y=-10\) or BOTH
Statement 1: \(xy < 0\)
- From this we can be sure that \(x≠y\)
- Therefore, \(x+y=-10\)
- Thus, statement 1 alone is sufficient and we can eliminate options B, C and E
Statement 2: \(x > 3\) and \(y < 3\)
- From this we can be sure that \(x≠y\)
- Therefore, \(x+y=-10\)
- Thus, statement 2 alone is also sufficient
Hence the right answer is Option D
