In a certain code, ‘256’ means ‘you are good’; ‘637’ means ‘we are bad’ and…
2023
In a certain code, ‘256’ means ‘you are good’; ‘637’ means ‘we are bad’ and ‘358’ means ‘good and bad’. Which of the following digits represents ‘and’ in that code?
Answer: C. 8 — Concept: A sentence-substitution code replaces every word of a sentence by a fixed digit, and the digits are not necessarily listed in the order of the words.…
- A.
2
- B.
5
- C.
8
- D.
More than one of the above
- E.
None of the above
Attempted by 6 students.
Show answer & explanation
Correct answer: C
Concept: A sentence-substitution code replaces every word of a sentence by a fixed digit, and the digits are not necessarily listed in the order of the words. Because the pairing is one-to-one and stays the same in every statement, the reliable handle is comparison: a digit that two coded statements have in common must stand for the word that those same two statements have in common.
Application: compare the three coded statements pair by pair.
‘256’ → you are good and ‘637’ → we are bad have the digit 6 in common and the word ‘are’ in common, so 6 = are.
‘256’ → you are good and ‘358’ → good and bad have the digit 5 in common and the word ‘good’ in common, so 5 = good.
‘637’ → we are bad and ‘358’ → good and bad have the digit 3 in common and the word ‘bad’ in common, so 3 = bad.
The statement ‘358’ stands for the words good, and, bad. With 5 = good and 3 = bad already fixed, the digit that remains in that statement, 8, must stand for ‘and’.
Cross-check: the three statements together fix every digit of the code.
Digit | Word |
|---|---|
2 | you |
3 | bad |
5 | good |
6 | are |
7 | we |
8 | and |
Reading the codes back with this table gives ‘256’ = you are good, ‘637’ = we are bad and ‘358’ = good and bad, so all three statements are satisfied at the same time. Because the pairing is one-to-one, no second digit can also stand for ‘and’, and ‘and’ is not left without a digit.
Therefore the digit that represents ‘and’ in this code is 8.