How is the word **‘dwarf’** definitely coded in the given code language?

I. In a certain code language, **‘the dwarf planet’** is coded as **‘cq sd ap’** and **‘the solar energy’** is coded as **‘kb og sd’**.

II. In a certain code language, **‘only dwarf planet’** is coded as **‘cq ap st’**, and **‘the coldest planet’** is coded as **‘sd cq yt’**.

Question

How is the word **‘dwarf’** definitely coded in the given code language?

I. In a certain code language, **‘the dwarf planet’** is coded as **‘cq sd ap’** and **‘the solar energy’** is coded as **‘kb og sd’**.

II. In a certain code language, **‘only dwarf planet’** is coded as **‘cq ap st’**, and **‘the coldest planet’** is coded as **‘sd cq yt’**.

Accepted Answer

**Solution:**

1. From statement I:
   - ‘the dwarf planet’ is coded as ‘cq sd ap’
   - ‘the solar energy’ is coded as ‘kb og sd’

Common word: ‘the’ appears in both phrases.
   Common code: ‘sd’ appears in both codes.
   Therefore, ‘the’ = ‘sd’.

2. From statement II:
   - ‘only dwarf planet’ is coded as ‘cq ap st’
   - ‘the coldest planet’ is coded as ‘sd cq yt’

Common word: ‘planet’ appears in both phrases.
   Common code: ‘cq’ appears in both codes.
   Therefore, ‘planet’ = ‘cq’.

3. Using statement I:
   - ‘the dwarf planet’ = ‘cq sd ap’
   - We know ‘the’ = ‘sd’ and ‘planet’ = ‘cq’ (from statement II), so ‘dwarf’ must be ‘ap’.

4. Using statement II:
   - ‘only dwarf planet’ = ‘cq ap st’
   - ‘planet’ = ‘cq’, so ‘dwarf’ = ‘ap’ again.

Hence, both statements together are required to conclusively determine that **‘dwarf’ is coded as ‘ap’**.

**Answer:** D. The data in both statement I and II together are necessary to answer the question.

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