Question Details

Directions: Read the following information carefully and answer the questions given below:

Anita starts cycling from point A in the west direction. After travelling 4m, she reaches point B. From point B, she takes a left turn and rides 3m to reach point C. From point C, she turns right and travels 6m to reach point D. From point D, she takes a right turn and travels 9m to reach point E.

Benny starts cycling from point P in the north direction. After travelling 6m, he reaches point Q. From point Q, he takes a left turn and rides 5m to reach point R. From point R, he takes a left turn and rides 10m to reach point S. Now, from point S, he takes a right turn and travels 3m to reach point E.

Four of the following five pairs of points are alike in a certain way based on the given information and thus form a group. Which one does not belong to that group?

Options

A

A, E

B

D, S

C

C, P

D

S, Q

E

E, R

Show Answer

Correct Answer :

Option A

A, E

Solution :

The correct answer is A, E.

Step 1: Determine the position coordinates for Anita's path.
Let point A be at origin (0, 0), taking East as +x, West as -x, North as +y, and South as -y.
- Anita starts at point A(0, 0) and travels 4m West to reach point B(-4, 0).
- From B, she turns left (South) and travels 3m to reach point C(-4, -3).
- From C, she turns right (West) and travels 6m to reach point D(-10, -3).
- From D, she turns right (North) and travels 9m to reach point E(-10, 6).

Step 2: Determine the position coordinates for Benny's path.
Since Benny ends his journey at point E(-10, 6), we can work backward from E:
- Benny travels from point S right (West) 3m to reach E. Tracing backward (East 3m) gives point S(-7, 6).
- Benny travels from point R left (South) 10m to reach S. Tracing backward (North 10m) gives point R(-7, 16).
- Benny travels from point Q left (West) 5m to reach R. Tracing backward (East 5m) gives point Q(-2, 16).
- Benny travels from point P North 6m to reach Q. Tracing backward (South 6m) gives point P(-2, 10).

Step 3: Analyze the relative direction of the second point with respect to the first point for each given pair.
1. D, S: S(-7, 6) is located +3m East and +9m North of D(-10, -3). Thus, S is in the North-East direction of D.
2. C, P: P(-2, 10) is located +2m East and +13m North of C(-4, -3). Thus, P is in the North-East direction of C.
3. S, Q: Q(-2, 16) is located +5m East and +10m North of S(-7, 6). Thus, Q is in the North-East direction of S.
4. E, R: R(-7, 16) is located +3m East and +10m North of E(-10, 6). Thus, R is in the North-East direction of E.
5. A, E: E(-10, 6) is located -10m West and +6m North of A(0, 0). Thus, E is in the North-West direction of A.

Conclusion:
In all pairs except A, E, the second point is situated in the North-East direction relative to the first point. In the pair A, E, point E is in the North-West direction relative to point A. Therefore, A, E does not belong to the group.

Unlock Our Free Library

Access expert-curated educational resources and study materials—completely free.

Ask AI Tutor
5 left
Q1 View Question & Options
AI Tutor is solving this question...
Reading question context & options...