Re: HOT Competition 4 Sep/8PM: What is the median of all the values of x
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04 Sep 2020, 19:46
What is the median of all the values of x, which satisfy ||x–3|–5|=3 ?
A. 1
B. 2
C. 3
D. 5
E. 6
Solution:
||x-3|-5| = 3 can be broken down into two cases,
Case 1: |x-3| = 8
Case 2: |x-3| = 2
Case 1 can be expanded further to two more cases,
Case A: x-3 = 8 ---> x = 11
Case B: x-3= -8 ---> x = 5
In the same way, Case 2 can be expanded further to two more cases,
Case C: x-3 = 2 ---> x = -1
Case D: x-3= -2 ---> x = 1
We have to plug the results for Cases A, B, C and D to verify which of those satisfy the original equation. After plugging the values, only Case A (x = 11), Case B (x = 5) and Case D (x = 1) satisfied the original equation. The median of those numbers {1,5,11} is 5.
Hence the answer is D.