In a plane, line X is perpendicular to line Y and parallel to line Z; line U is perpendicular to both lines V and W; line X is perpendicular to line V. Which one of the following statements is correct ?

(a) Z, U and W are parallel.
(b) X, V and Y are parallel.
(c) Z, V and U are all perpendicular to W.
(d) Y, V and W are parallel. ✓ UPSC's answer

Why the answer is (d)

• Since X is perpendicular to Y and parallel to Z, Z is also perpendicular to Y.

• Since U is perpendicular to both V and W, V and W are parallel to each other.

• Since X is perpendicular to V and V is parallel to W, X is perpendicular to W; since X is parallel to Z, Z is perpendicular to W.

• Since Y and V are both perpendicular to X, Y and V are parallel; with V parallel to W, Y, V and W are all parallel.

• Therefore option (d) is correct.

Why the other options are wrong

(a) Z, U and W are parallel.: Z and U are both perpendicular to W, so they cannot be parallel to W.
(b) X, V and Y are parallel.: X is perpendicular to both V and Y, so X cannot be parallel to either of them.
(c) Z, V and U are all perpendicular to W.: V is parallel to W, not perpendicular to W, so Z, V and U are not all perpendicular to W.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2015, held on 23 August 2015. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.