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Difficulty:
45%
(medium)
Question Stats:
67% (01:57) correct
33%
(01:36)
wrong
based on 153
sessions
History
Date
Time
Result
Not Attempted Yet
Is |x - 5| > |x - 35| ?
(1) x < 10
(2) x < 25
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(1) x < 10
(2) x < 25
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
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GMAT 1: 720 Q50 V36
Posts: 234
This question can be easily solved by plotting \(|x - 5|\) and \(|x - 35|\).
img.png [ 29.11 KiB | Viewed 2072 times ]
In this plot, the crossing point can be calculated where \(|x - 5|\) slope is positive i.e. \(|x - 5|\)\( = x - 5\) and \(|x - 35|\) slope is negative i.e. \(|x - 35|\) = \(35 - x\).
\(x- 5 = 35 - x\) ----> \(x = 20\)
So two cases exists,
Case 1: x < 20, \(|x - 5| < |x - 35|\) and,
Case 2: x > 20, \(|x - 5| > |x - 35|\).
Stmt 1: x < 10
This region lies in case 1 and hence sufficient.
Stmt 2: x < 25,
This region can lie in both cases and hence insufficient.
Therefore answer is A.
Hope it helped.
Attachment:
img.png [ 29.11 KiB | Viewed 2072 times ]
In this plot, the crossing point can be calculated where \(|x - 5|\) slope is positive i.e. \(|x - 5|\)\( = x - 5\) and \(|x - 35|\) slope is negative i.e. \(|x - 35|\) = \(35 - x\).
\(x- 5 = 35 - x\) ----> \(x = 20\)
So two cases exists,
Case 1: x < 20, \(|x - 5| < |x - 35|\) and,
Case 2: x > 20, \(|x - 5| > |x - 35|\).
Stmt 1: x < 10
This region lies in case 1 and hence sufficient.
Stmt 2: x < 25,
This region can lie in both cases and hence insufficient.
Therefore answer is A.
Hope it helped.
Bunuel
ProfessorX8
Joined: 10 Jul 2022
Last visit: 27 Jan 2026
Posts: 2
Location: Bangladesh
Concentration: Finance, International Business
GMAT Focus 1: 625 Q85 V83 DI75
GPA: 3.74
GMAT Focus 1: 625 Q85 V83 DI75
Posts: 2
From question stem, \(|x-5|>|x-35|\) can be simplified by squaring both sides,
\(\\
|x-5|>|x-35| \\
=x^2-10x+25>x^2-70x+1225\\
=60x>1200\\
=x>20\\
\)
So, the question basically asks, Is x greater than 20?
1. \(x<10\), straightforward NO!
Sufficient.
2. \(x<25\), clearly insufficient (can be \(21, 19, etc.\))
ANS: A
\(\\
|x-5|>|x-35| \\
=x^2-10x+25>x^2-70x+1225\\
=60x>1200\\
=x>20\\
\)
So, the question basically asks, Is x greater than 20?
1. \(x<10\), straightforward NO!
Sufficient.
2. \(x<25\), clearly insufficient (can be \(21, 19, etc.\))
ANS: A
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