XAT 2014 — QA & DI Question 6

|X + 7| + |X – 8| = 16
For X ≥ 8, |X + 7| = X + 7 and |X – 8| = X – 8
∴ |X – 7| + |X – 8| = X + 7 + X – 8 = 2X – 1
2X – 1 = 16

$\therefore X=\frac{17}{2}$

For -7 ≤ x < 8,
∴ |X + 7| = X + 7 & |X – 8| = 8 – X
∴ |X + 7| = |X – 8| = X + 7 + 8 – X = 15 ≠ RHS
0 ≤ x < 8 is not possible.
-7 ≤ x < 0
∴ |X + 7| = 7 + X & |X – 8| = -X + 8
16 = |X + 7| + |X – 8| = 7 + X – X +  8 = 15
∴ -7 ≤ x < 0 is not possible.
Now, x < -8 |X + 7| = - 7 – x |X – 8| = -X + 8
∴ |X + 7| + |X – 8| = - 7 – X – X + 8 = 1 – 2X = 16
⇒ 2X = -15 ⇒ X = -7.5
Hence, option (b).