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10 Jul 2023, 01:30
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A
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:
68% (01:57) correct
32%
(01:31)
wrong
based on 151
sessions
History
Date
Time
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Not Attempted Yet
Is |x - 5| > |x - 35| ?
(1) x < 10
(2) x < 25
(1) x < 10
(2) x < 25
10 Jul 2023, 02:17
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This question can be easily solved by plotting \(|x - 5|\) and \(|x - 35|\).
img.png [ 29.11 KiB | Viewed 1984 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 1984 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
General Discussion
23 Jun 2025, 08:41
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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
