Difficulty: Easy
Correct Answer: 8
Explanation:
Introduction / Context:
This coding and decoding question uses three short code statements where each number sequence corresponds to a phrase. Your task is to determine which digit represents a particular word by comparing these codes. This type of question tests your ability to use set intersections and logical deduction to match words with symbols or digits.
Given Data / Assumptions:
Code 134 means “good and tasty”.
Code 478 means “see good pictures”.
Code 729 means “pictures are faint”.
Each three digit code corresponds to three separate words in the associated phrase.
The same word is always represented by the same digit in all codes in which it appears.
Different words use different digits.
You are asked to find which digit represents the word “see”.
Concept / Approach:
The key idea is that common words across two phrases must correspond to common digits in their codes. By comparing which words and digits are shared between statements, you can map specific digits to words. Once a few mappings are known, the remaining words and digits can be identified by elimination. This question is a direct application of set intersection logic.
Step-by-Step Solution:
Step 1: Write the codes and their meanings clearly.
Step 2: Compare the first two statements: “134” means “good and tasty”, and “478” means “see good pictures”.
Step 3: The common word between these two phrases is “good”. The common digit between 134 and 478 must therefore represent “good”.
Step 4: The digits in 134 are {1, 3, 4} and the digits in 478 are {4, 7, 8}. The only digit common to both codes is 4.
Step 5: Therefore, digit 4 represents the word “good”.
Step 6: Next, compare “478” meaning “see good pictures” with “729” meaning “pictures are faint”. The common word is “pictures”.
Step 7: The digits in 478 are {4, 7, 8}, and the digits in 729 are {7, 2, 9}. The only common digit is 7.
Step 8: Therefore, digit 7 stands for “pictures”.
Step 9: In the code 478, we now know that 4 is “good” and 7 is “pictures”. The remaining digit 8 must stand for the remaining word “see”.
Verification / Alternative check:
You can verify by checking that all mappings are consistent. In code 134, the words are “good and tasty”. We have already assigned 4 to “good”. That means 1 and 3 must stand for “and” and “tasty” in some order. In code 729, the words are “pictures are faint”. We assigned 7 to “pictures”, so 2 and 9 must be “are” and “faint” respectively. No contradiction arises, which confirms our deductions. Therefore, it is consistent that 8 represents “see”.
Why Other Options Are Wrong:
9: This digit appears only in 729, which stands for “pictures are faint”, so it cannot represent “see”.
2: This digit also appears only in 729, so it must represent either “are” or “faint”, not “see”.
1: This digit appears only in 134, which stands for “good and tasty”, again not matching “see”.
Common Pitfalls:
A typical mistake is to try to guess without systematically comparing common words and digits. Some candidates also forget that each word must have a unique digit, so a digit already assigned to one word cannot represent another. Always perform the intersection step carefully, and then use elimination for the remaining words and digits.
Final Answer:
The digit that stands for the word “see” in the given code language is 8.
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