Question

Sean

a

,

b

,

c

,

d

números reales con

|a - b| = 2

,

|b - c| = 3

,

|c - d| = 4

. ¿Cuál es la suma de todos los valores posibles de

|a - d|

?

Let

a,

b,

c,

and

d

be real numbers with

|a - b| = 2,

|b - c| = 3,

and

|c - d| = 4.

What is the sum of all possible values of

|a - d|?

9

12

15

18

24

Escribe

a - d

= (a - b) + (b - c) + (c - d)

= \pm 2 \pm 3 \pm 4

.

Write

a - d

= (a - b) + (b - c) + (c - d)

= \pm 2 \pm 3 \pm 4

Enumera los distintos valores de

|\pm 2 \pm 3 \pm 4|

.

List the distinct values of

|\pm 2 \pm 3 \pm 4|

Como

a - d

= (a-b) + (b-c) + (c-d)

= \pm 2 \pm 3 \pm 4,

los valores absolutos posibles son

\begin{aligned} 2+3+4 &= 9, \\ 2+3-4 &= 1, \\ 2-3+4 &= 3, \\ -2+3+4 &= 5. \end{aligned}

Su suma es

9 + 1 + 3 + 5 = 18

.

Así, la respuesta correcta es D.

Since

a - d

= (a-b) + (b-c) + (c-d)

= \pm 2 \pm 3 \pm 4,

the possible absolute values are

\begin{aligned} 2+3+4 &= 9, \\ 2+3-4 &= 1, \\ 2-3+4 &= 3, \\ -2+3+4 &= 5. \end{aligned}

Their sum is

9 + 1 + 3 + 5 = 18.

Thus, the correct answer is D.