MathRevolution wrote:
[
Math Revolution GMAT math practice question]
\(|√3-2|+|3-√2|+|5+√3|+|1-√2|=?\)
\(A. 0\)
\(B. 2√2\)
\(C. 2√3\)
\(D. 9\)
\(E. 11\)
|a-b| = the distance between a and b.
|a+b| = |a-(-b)| = the distance between a and -b.
|√3-2| + |3-√2| + |5+√3| + |1-√2|
= |5+√3| + |√3-2| + |1-√2| + |3-√2|
= |√3+5| + |√3-2| + |1-√2| + |3-√2|
=
|√3-(-5)| + |√3-2| +
|1-√2| + |3-√2|The red terms constitute the sum of the following two distances:
-5<----->√3<----->2
The sum of these two distances = the distance between -5 and 2 = 7.
The blue terms constitute the sum of the following two distances:
1<----->√2<----->3
The sum of these two distances = the distance between 1 and 3 = 2.
Thus:
Sum of all 4 terms = 7+2 = 9.
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