What is the direction of D with respect to F?

Statement I: A is in West of B. C is in North-east of D. C is in South of B. F is in West of C.

Statement II: A is in North of E. F is in West of E. E is in North of B. D is in West of E.

Question

What is the direction of D with respect to F?

Statement I: A is in West of B. C is in North-east of D. C is in South of B. F is in West of C.

Statement II: A is in North of E. F is in West of E. E is in North of B. D is in West of E.

Accepted Answer

**Solution:**

We need to find the direction of D with respect to F.

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**Analyze Statement I:**
- A is West of B.
- C is North-east of D.
- C is South of B.
- F is West of C.

From this, we can try to position points:
- Since C is South of B, B is North of C.
- A is West of B.
- C is North-east of D means D is South-west of C.
- F is West of C.

However, the exact relative position of D with respect to F cannot be determined because we do not know the relative positions of F and D directly. We only know F is West of C and D is South-west of C, but the exact direction of D from F is ambiguous.

So, Statement I alone is **not sufficient**.

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**Analyze Statement II:**
- A is North of E.
- F is West of E.
- E is North of B.
- D is West of E.

From this:
- E is North of B.
- A is North of E.
- F is West of E.
- D is West of E.

Since both D and F are West of E, but no information about their relative positions to each other is given, we cannot determine the direction of D with respect to F.

So, Statement II alone is **not sufficient**.

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**Combine Statements I and II:**

From Statement II, we know E is North of B, and both D and F are West of E.

From Statement I, C is South of B, and F is West of C.

Since E is North of B and C is South of B, E is North of C.

F is West of C (Statement I) and West of E (Statement II), so F lies somewhere west between E and C.

D is West of E (Statement II) and South-west of C (Statement I).

Putting all together:
- E is North of B
- C is South of B
- F is West of C and West of E
- D is West of E and South-west of C

Thus, D is South-west of C and West of E, while F is West of C and E.

Since D is South-west of C and F is West of C, D lies to the South of F (because D is South-west of C, F is directly West of C).

Hence, the direction of D with respect to F is **South**.

Therefore, both statements together are **necessary** to answer the question.

**Answer:** Both statements together are necessary to answer the question.

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