Let $a, b, c, d$ are real numbers such that $| a - b | = 2, | b - c | = 3, | c - a | = 4$ . Then the sum of all possible values of $| a - d |$ is

9

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18

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24

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30

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Solution

The correct option is C $18$
$| a - b | = 2, | b - c | = 3, | c - d | = 4$
$a - b = \pm 2$
$b - c = \pm 3$
$c - d = \pm 4$
possible values of $(a - d)$ are $\pm 9, \pm 5, \pm 3$
$| a - d | = 9, 5, 3, 1$
Sum of all possible values are $18$

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