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21 Apr 2024, 10:54
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E
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Difficulty:
25%
(medium)
Question Stats:
77% (01:30) correct
23%
(01:45)
wrong
based on 288
sessions
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Date
Time
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Not Attempted Yet
If \(|a - b| = |b - c| = 2\) and \(a < b < c\), what is the value of \(|a - c|\)?
A. 0
B. 1
C. 2
D. 3
E. 4
A. 0
B. 1
C. 2
D. 3
E. 4
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04 May 2024, 04:00
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Official Solution:
If \(|a - b| = |b - c| = 2\) and \(a < b < c\), what is the value of \(|a - c|\)?
A. 0
B. 1
C. 2
D. 3
E. 4
Given that \(a < b\), we can deduce that \(|a-b| = -(a-b) = 2\), which simplifies to \(b-a = 2\). Similarly, since \(b < c\) is given, we can deduce that \(|b-c| = -(b-c) = 2\), which simplifies to \(c-b = 2\). By adding these two equations: \((b-a) + (c-b) = 2 + 2\), we get \(c-a = 4\). Therefore, \(|a-c| = 4\).
Answer: E
If \(|a - b| = |b - c| = 2\) and \(a < b < c\), what is the value of \(|a - c|\)?
A. 0
B. 1
C. 2
D. 3
E. 4
Given that \(a < b\), we can deduce that \(|a-b| = -(a-b) = 2\), which simplifies to \(b-a = 2\). Similarly, since \(b < c\) is given, we can deduce that \(|b-c| = -(b-c) = 2\), which simplifies to \(c-b = 2\). By adding these two equations: \((b-a) + (c-b) = 2 + 2\), we get \(c-a = 4\). Therefore, \(|a-c| = 4\).
Answer: E
General Discussion
21 Apr 2024, 10:58
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We can draw a line with a, b, c
Distance between a and b b and c each 2
So 4
Posted from my mobile device
Distance between a and b b and c each 2
So 4
Posted from my mobile device
