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09 Nov 2022, 02:30
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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:
35%
(medium)
Question Stats:
57% (01:34) correct
43%
(01:35)
wrong
based on 61
sessions
History
Date
Time
Result
Not Attempted Yet
Is x < 0 ?
(1) |x - 21| < 5
(2) |x - 20| > 3
(1) |x - 21| < 5
(2) |x - 20| > 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
09 Nov 2022, 03:00
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Is x < 0 ?
(1) |x - 21| < 5
Two cases:
\(x-21<5……..x<26\)
\(21-x<5………x>16\)
Combined cases => \(16<x<26\)
x>0 in entire range.
Sufficient
(2) |x - 20| > 3
Two cases:
\(x-20>3……..x>23\)
\(20-x>3………x<17\)
Combined cases => x<17 and x>23
So, x can be less than 0 and greater than 0 too.
Insufficient
A
(1) |x - 21| < 5
Two cases:
\(x-21<5……..x<26\)
\(21-x<5………x>16\)
Combined cases => \(16<x<26\)
x>0 in entire range.
Sufficient
(2) |x - 20| > 3
Two cases:
\(x-20>3……..x>23\)
\(20-x>3………x<17\)
Combined cases => x<17 and x>23
So, x can be less than 0 and greater than 0 too.
Insufficient
A
09 Nov 2022, 03:10
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Statement 1
(1) |x - 21| < 5
If the inequality is of the form |x-a| < b
The value of x will lie between a-b and a+b.
Range of x is between (21-5) and (21+5)
So x lies between 16 and 26. Is x < 0, the answer is a definite no.
Hence statement 1 is sufficient and we can eliminate B, C and E.
(2) |x - 20| > 3
If the inequality is of the form |x-a| > b
The values of x will be
In this case, x > 23 or x < 17
Hence x can take positive as well as negative values.
The statement is not sufficient and we can eliminate D.
Option A
(1) |x - 21| < 5
If the inequality is of the form |x-a| < b
The value of x will lie between a-b and a+b.
Range of x is between (21-5) and (21+5)
So x lies between 16 and 26. Is x < 0, the answer is a definite no.
Hence statement 1 is sufficient and we can eliminate B, C and E.
(2) |x - 20| > 3
If the inequality is of the form |x-a| > b
The values of x will be
- x > a + b
- x < a - b
In this case, x > 23 or x < 17
Hence x can take positive as well as negative values.
The statement is not sufficient and we can eliminate D.
Option A
