In a certain code language, some statements are coded as given. 1. "Economy growth level down" is coded as "77 42 11 36". 2. "Slow percentage rate range" is coded as "55 91 23 82". 3. "Economy growth rate index range" is coded as "77 64 91 11 82". 4. "Economy range level down" is coded as "36 11 42 82". What is the code for "55 11 77 23 91"?
The correct answer is Option 2: Slow economy growth percentage rate.
We can find the code for each word by comparing the statements where they repeat:
Find "Economy":
"Economy" is common to statements 1, 3, and 4.
The common code among these three statements is 11.
Therefore: Economy = 11
Find "Growth":
Looking at statement 1 ("Economy growth level down" $\to$ 77 42 11 36) and statement 3 ("Economy growth rate index range" $\to$ 77 64 91 11 82), the common words are "Economy" and "growth".
The common codes are 11 and 77. Since Economy = 11, growth = 77.
Find "Range":
"Range" is common to statements 2, 3, and 4.
The common code among these three statements is 82.
Therefore: range = 82
Find "Rate" and "Percentage":
Looking at statement 2 ("Slow percentage rate range" $\to$ 55 91 23 82), since range = 82, the remaining words {"Slow", "percentage", "rate"} correspond to {55, 91, 23}.
Looking at statement 3 ("Economy growth rate index range" $\to$ 77 64 91 11 82), since Economy = 11, growth = 77, and range = 82, the remaining words {"rate", "index"} correspond to {91, 64}.
Comparing these two, the common word is "rate" and the common code is 91.
Therefore: rate = 91
Since rate = 91 and range = 82 from statement 2, the remaining words {"Slow", "percentage"} in statement 2 correspond to {55, 23}.
Now, let's look at our options to match these words:
55: Slow / Percentage
11: Economy
77: Growth
23: Percentage / Slow
91: Rate
Checking Option 2: "Slow economy growth percentage rate"
Slow = 55 (or 23)
economy = 11
growth = 77
percentage = 23 (or 55)
rate = 91
This matches the set of codes 55 11 77 23 91 perfectly.
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