Each question is followed by two statements, I and II. Answer each que...
Using statement I alone:
We cannot conclude anything about Qarim as we do not know the direction he is facing.
Thus, statement I alone is not sufficient to answer the question.
Using statement II alone:
We know the number of times Qarim turned and his present direction.
But we don't know the angle at which he is turning.
Thus, statement II alone is not sufficient to answer the question.
Using statement I and II both:
We get the angle at which he is turning also the direction in which he is turning from statement I and his direction at 127839th turn.
As he is facing north after 127839.
After 4 turns in any direction, we will face the same direction as that of the initial.
So, 127839/4 , we get remainder as 3.
He is facing north after 3 anticlockwise turns.
∴ He is facing east initially.
Hence, both statements I and II are necessary to answer.
Hence, option 4.
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Each question is followed by two statements, I and II. Answer each que...
Understanding the Problem
To determine the initial direction Qarim was facing, we need to analyze both statements separately and then together.
Statement I Analysis
- Qarim turned 90 degrees anticlockwise 1,983,862,989 times.
- Each turn of 90 degrees changes the direction:
- 0 turns: North
- 1 turn: West
- 2 turns: South
- 3 turns: East
- 4 turns: North (and so on, repeating every 4 turns).
- To determine the final direction after all turns, we can find the remainder of 1,983,862,989 divided by 4.
- Since this calculation gives a specific remainder, we can determine the final direction but not the initial direction.
Statement II Analysis
- After 127,839 turns, Qarim was facing North.
- Similar to statement I, we can calculate the impact of these turns on his direction.
- Again, we can find the remainder of 127,839 divided by 4 to determine his final direction after these specific turns.
- However, without knowing his initial direction, we cannot conclude definitively about his starting point.
Combining Statements I and II
- By using both statements together, we can establish the sequence of turns and their effects on Qarim's final direction.
- Since both statements provide critical information regarding turns and final direction, we can deduce the initial direction based on the changes.
Conclusion
The correct answer is (4) because both statements combined give enough information to determine the initial direction, while neither statement alone is sufficient.
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