In a certain code, the phrase "ja ki mo pe" means "at a frog's leap", "mo la ki so" means "take a leap ahead" and "re bo ja na" means "insects are frog's diet". In this language, which code word stands for the English word "at"?

Introduction / Context:
This again is a code language problem where each English word is represented by a distinct code word. We are given three coded sentences and their English meanings. The goal is to determine which code corresponds specifically to the word "at". The approach relies on comparing sentences, finding common words, and mapping them to common codes. Once enough words are mapped, we can assign the code for "at" by elimination.

Given Data / Assumptions:

• "ja ki mo pe" = "at a frog's leap".
• "mo la ki so" = "take a leap ahead".
• "re bo ja na" = "insects are frog's diet".
• Each English word has one unique code, and each code stands for exactly one English word.
• The mapping is consistent across all three sentences.

Concept / Approach:
We compare sentences that share common English words to see which code words they share. First, we identify the code for "frog's" by comparing sentences 1 and 3. Next, we identify the code for "leap" and "a" by comparing sentences 1 and 2. The code for "at" is then deduced as the leftover code in the first sentence which is not shared with any other sentence and which does not match any other word. This is a systematic use of intersection followed by elimination.

Step-by-Step Solution:
Step 1: Compare sentence 1 ("at a frog's leap") with sentence 3 ("insects are frog's diet"). Step 2: Common English word is "frog's". Step 3: Common code between "ja ki mo pe" and "re bo ja na" is "ja". So "frog's" → "ja". Step 4: Now compare sentence 1 ("at a frog's leap") with sentence 2 ("take a leap ahead"). Step 5: Common English words are "a" and "leap". Step 6: Common codes between "ja ki mo pe" and "mo la ki so" are "ki" and "mo". So "a" and "leap" map to "ki" and "mo" in some order. Step 7: In sentence 1, the four code words are "ja, ki, mo, pe" corresponding to "frog's, a, leap, at". We now know that: "frog's" → "ja", "a"/"leap" → "ki"/"mo". Step 8: The only English word left in sentence 1 is "at", and the only unused code word in that sentence is "pe". Step 9: Therefore, "at" must be represented by "pe".

Verification / Alternative check:
With the mapping "frog's" → "ja" and "at" → "pe", you can check that the remaining words in sentence 2 and 3 can be mapped consistently to the remaining codes. "leap" and "a" match "ki" and "mo" between sentences 1 and 2, and "insects", "are", and "diet" can map uniquely to "re", "bo", and "na". No contradiction arises and each code word retains a single meaning, confirming that "pe" is the correct code for "at".

Why Other Options Are Wrong:
Option A ("ja") corresponds to "frog's", as seen from the intersection of sentences 1 and 3. Options C ("bo") and D ("re") only appear in sentence 3 and correspond to other words like "insects" or "diet" or "are". Option E ("la") appears only in sentence 2 and is not present in sentence 1, so it cannot encode any word from sentence 1, including "at". Only "pe" remains as the unique and consistent code for "at".

Common Pitfalls:
Students sometimes try to guess code words based on frequency instead of strict intersections, or they mistakenly assume multiple meanings for the same code word. Another common mistake is to overlook that "frog's" appears in both sentence 1 and 3 and therefore must be mapped first. As always, carefully listing common words and common codes and then proceeding by elimination helps avoid these missteps.

Final Answer:
Thus, the code word for "at" in this language is pe.