Question

Is integer \( x \) a prime number? Statement (I): \( 47 < x < 53 \)
Statement (II): \( x > 1 \)

• A. Statement (I) alone is sufficient.
• B. Statement (II) alone is sufficient.
• C. Both statements (I) and (II) are sufficient.
• D. Neither statement is sufficient.

Hint:

Data sufficiency does not require the answer to be "Yes." If the provided information allows you to conclude "No" definitively, the statement is still considered sufficient.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The task is to find the final direction and minimum distance from the origin after a series of directional movements.


Step 2: Key Formula or Approach:
Map out the trajectory using cardinal directions (North, South, East, West) and compute the net displacement via elementary geometry.


Step 3: Detailed Explanation:
Assume the starting location is \(O\).
1. The individual moves 10 km North from \(O\) to point \(A\).
2. A right turn (facing East) is followed by a 5 km walk to point \(B\).
3. Another right turn (facing South) leads to a 10 km walk to point \(C\).
This trajectory outlines a rectangle \(OABC\), where opposite sides \(OA\) and \(BC\) are parallel and measure 10 km each.
Since the 10 km Northward movement is perfectly canceled by the 10 km Southward movement, the net vertical displacement is zero.
The endpoint \(C\) lies directly to the East of the origin \(O\).
The distance from the start is the length of segment \(OC\), which matches the length of \(AB\), equaling 5 km.
Therefore, the person is located 5 km East of the starting point.


Step 4: Final Answer:
The correct choice is (A).