Four girls P, Q, R and S are studying languages in a University. P is learning French and Dutch. Q is learning Chinese and Japanese. R is learning Spanish and French. S is learning Dutch and Japanese. Given that: French is easier than Dutch; Chinese is harder than Japanese; Dutch is easier than Japanese, and Spanish is easier than French. Based on the above information, which girl is learning the most difficult pair of languages?
Q
This problem requires us to determine which of the four girls is studying the most difficult pair of languages. To find the answer, we first need to establish a clear order of difficulty for all the languages mentioned based on the given clues.
Language Difficulty Relationships
We are given the following relationships about the difficulty of the languages:
- French is easier than Dutch. This can be represented as: $\text{French} < \text{Dutch}$.
- Chinese is harder than Japanese. This means: $\text{Chinese} > \text{Japanese}$.
- Dutch is easier than Japanese. This implies: $\text{Dutch} < \text{Japanese}$.
- Spanish is easier than French. So: $\text{Spanish} < \text{French}$.
Establishing Overall Language Order
Let's combine these individual relationships to form a comprehensive order of language difficulty from the easiest to the hardest:
- Starting with "Spanish is easier than French", we have: $\text{Spanish} < \text{French}$.
- Next, "French is easier than Dutch" extends our sequence: $\text{Spanish} < \text{French} < \text{Dutch}$.
- Following that, "Dutch is easier than Japanese" further extends the order: $\text{Spanish} < \text{French} < \text{Dutch} < \text{Japanese}$.
- Finally, "Chinese is harder than Japanese" tells us that Chinese is the most difficult language among all, surpassing Japanese in difficulty.
Therefore, the complete order of language difficulty from easiest to hardest is:
$\text{Spanish} < \text{French} < \text{Dutch} < \text{Japanese} < \text{Chinese}$
Girls and Their Language Pairs
Let's list the languages that each girl is learning:
| Girl | Languages Learning |
|---|---|
| P | French and Dutch |
| Q | Chinese and Japanese |
| R | Spanish and French |
| S | Dutch and Japanese |
Evaluating Language Pair Difficulty
Now, using our established overall difficulty order ($\text{Spanish} < \text{French} < \text{Dutch} < \text{Japanese} < \text{Chinese}$), we will evaluate the difficulty of each girl's language pair:
- P's languages: French and Dutch. Based on our order, Dutch ($\text{Dutch}$) is harder than French ($\text{French}$).
- Q's languages: Chinese and Japanese. According to our order, Chinese ($\text{Chinese}$) is harder than Japanese ($\text{Japanese}$). Notably, Chinese is also the most difficult language in the entire set.
- R's languages: Spanish and French. In this pair, French ($\text{French}$) is harder than Spanish ($\text{Spanish}$).
- S's languages: Dutch and Japanese. From our ranking, Japanese ($\text{Japanese}$) is harder than Dutch ($\text{Dutch}$).
Identifying Most Difficult Pair
To determine which girl is learning the most difficult pair of languages, we need to identify the pair that contains the language (or languages) highest on our difficulty scale.
- For P, the more difficult language is Dutch.
- For Q, the more difficult language is Chinese.
- For R, the more difficult language is French.
- For S, the more difficult language is Japanese.
Comparing the "harder" language from each girl's pair against our overall difficulty order ($\text{Spanish} < \text{French} < \text{Dutch} < \text{Japanese} < \text{Chinese}$), it is clear that Chinese is the most difficult language overall. Girl Q is the only one studying Chinese (along with Japanese).
Therefore, Q is learning the most difficult pair of languages (Chinese and Japanese).
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