Difficulty: Medium
Correct Answer: 98214
Explanation:
Introduction / Context:
This verbal reasoning problem uses a letter–digit substitution code. Each letter is consistently replaced by a particular digit. By observing two coded words, MASTER and STAMP, we can deduce the mapping for each letter and then use it to encode PASTE.
Given Data / Assumptions:
Concept / Approach:
The key is to align letters of the original words with their corresponding digits in the codes and deduce a one-to-one mapping from each letter to a digit. Once all letters in PASTE are known, we write their digits in that order to get the final code.
Step-by-Step Solution:
Step 1: Map letters from MASTER → 682145.
M → 6, A → 8, S → 2, T → 1, E → 4, R → 5.
Step 2: Confirm this mapping with STAMP → 21869.
STAMP letters: S, T, A, M, P.
Code digits: 2, 1, 8, 6, 9.
We already know S → 2, T → 1, A → 8, M → 6, so P must map to 9.
Step 3: Now encode PASTE using these mappings.
P → 9, A → 8, S → 2, T → 1, E → 4.
Step 4: Write the digits together: 9 8 2 1 4 → 98214.
Verification / Alternative check:
All letters in MASTER and STAMP are accounted for, and there are no conflicts in the mapping. Re-substituting back from digits to letters reconstructs the original words, confirming consistency.
Why Other Options Are Wrong:
Other options alter at least one letter–digit mapping. For example, options that do not start with 9 are immediately wrong because P must map to 9. Any code that changes the internal sequence 8 for A, 2 for S, 1 for T, or 4 for E contradicts the original data.
Common Pitfalls:
Sometimes learners try to treat the numbers as operations (addition or multiplication) rather than as simple substitutions. Another mistake is assuming different codes for the same letter when it appears in multiple words. In this type of problem, the mapping is always consistent.
Final Answer:
Using the same letter–digit coding scheme, PASTE is written as 98214 in that code language.
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