Four of the following five are alike in a certain way and thus form a group. Find the one which doesn’t belong to the group?

Study the following information carefully and answer the questions given below:

Riya starts walking from point Z towards west for 11m to reach point Y. Then, she turns right and walks for 4m to reach point X. Then she again turns right and walks for 14m to reach point W and then finally she turns towards south and walks for 6m to reach point V.

Karan starts walking towards north for 2m from point Z to reach at point U. Then, he takes right and left turn and walks for 6m and 9m to reach point T and S respectively. Then, he takes left turn and walks for 5m to reach point R. -

The correct answer option is XV.

To determine which pair does not belong to the group, let us plot the positions of all points on a 2D Cartesian plane taking point Z as the origin (0, 0).

Step 1: Determine the coordinates of Riya's path

1. Point Z: (0, 0)
2. Riya walks West for 11 m to reach Point Y: (-11, 0)
3. She turns Right (North) and walks for 4 m to reach Point X: (-11, 4)
4. She turns Right (East) and walks for 14 m to reach Point W: (-11 + 14, 4) = (3, 4)
5. Finally, she turns South and walks for 6 m to reach Point V: (3, 4 - 6) = (3, -2)

Step 2: Determine the coordinates of Karan's path

1. From Point Z (0, 0), Karan walks North for 2 m to reach Point U: (0, 2)
2. He turns Right (East) and walks 6 m to reach Point T: (0 + 6, 2) = (6, 2)
3. He turns Left (North) and walks 9 m to reach Point S: (6, 2 + 9) = (6, 11)
4. He turns Left (West) and walks 5 m to reach Point R: (6 - 5, 11) = (1, 11)

Step 3: Analyze the relative directions for each pair

• YU: U (0, 2) lies to the North-East of Y (-11, 0).
• ZW: W (3, 4) lies to the North-East of Z (0, 0).
• US: S (6, 11) lies to the North-East of U (0, 2).
• XV: V (3, -2) lies to the South-East of X (-11, 4).

In all options except XV, the second point is located in the North-East direction relative to the first point. In XV, the second point is located in the South-East direction.

Therefore, XV is the one that does not belong to the group.