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03 Feb 2020, 05:01
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E
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Difficulty:
35%
(medium)
Question Stats:
70% (01:44) correct
30%
(01:39)
wrong
based on 155
sessions
History
Date
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Not Attempted Yet
If \(a ≠ 0\), is \(b < a < c\) ?
(1) \(b < |a| < c\)
(2) \(|b| < |a| < |c|\)
(1) \(b < |a| < c\)
(2) \(|b| < |a| < |c|\)
03 Feb 2020, 05:22
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Both Statements will be true if b=1, a=2 and c=3, and in that case b < a < c. But both Statements will also be true if b = 1, a = -2 and c = 3, and in that case a is smaller than b and c. So the answer is E.
03 Feb 2020, 06:40
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Bunuel
We need to check if: \(b < a < c\)
Statement 1: \(b < |a| < c\)
Since \(|a|\) is less than \(c\), it must be true that \(c > 0\)
However, \(b\) may be positive or negative
Say: \(b = -2, a = -4, c = 8\) --- choose values so that \(|a| > |b|\) but \(a < b < 0\)
These values satisfy \(b < |a| < c\) but the required question: If \(b < a < c\) is NOT true
Say: \(b = -6, a = -4, c = 8\) --- choose values so that \(|a| < |b|\) but \(b < a < 0\)
These values satisfy \(b < |a| < c\) and the required question: If \(b < a < c\) is also true
Thus, statement 1 is Insufficient
Statement 2: \(|b| < |a| < |c|\)
Say: \(b = 1, a = 2, c = 3\) --- choose all positive values
These values satisfy \(|b| < |a| < |c|\) and the required question: If \(b < a < c\) is true
Say: \(b = -1, a = -2, c = -3\) --- choose all negative values
These values satisfy \(|b| < |a| < |c|\) but the required question: If \(b < a < c\) is NOT true
Thus, statement 2 is Insufficient
Combining the statements: We have:
\(b < |a| < c\) ... (Statement 1)
\(|b| < |a| < |c|\) ... (Statement 2)
Say: \(b = 1, a = 2, c = 3\) --- choose all positive values
These values satisfy \(b < |a| < c\) and \(|b| < |a| < |c|\) and the required question: If \(b < a < c\) is true
Say: \(b = -1, a = -2, c = 3\) --- choose values so that \(|a| > |b|\) but \(a < b < 0 and c > |a| > 0\)
These values satisfy \(b < |a| < c\) and \(|b| < |a| < |c|\) but the required question: If \(b < a < c\) is NOT true
Thus, combining statements is also Insufficient
Answer E
