AndreG wrote:
If |a - b| = |b - c| = 2 , what is |a - c| ?
(1) \(a \lt b \lt c\)
(2) \(c - a \gt c - b\)
(C) 2008 GMAT Club - m16#37
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
Question
In the original question, there are 3 variables and 2 equations. Thus D is most likely.
For the condition 1), \(| a - b | = b - a = 2\) and \(| b - c | = c - b = 2\).
When we add two equations \(c - a = ( b - a ) + ( c - b ) = c - a = 4\).
Thus \(| a - c | = 4\).
The condition 1) is sufficient.
For the condition 2) \(c - a > c - b\) is equivalent to \(-a > -b\) or \(a < b\).
However, we don't know anything about c from the condition 2).
There two cases that satisfy \(| a - b | = | b - c | = 2\).
----a----b----c---->
---a,c----b--------->
Thus \(|a-c| = c - a = ( c - b ) + ( b - a ) = 2 + 2 = 4\) or \(| a - c | = 0\).
The condition 2) is sufficient.
Therefore the answer is A.
For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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