Question

In a certain code language, 'EGKMZBLNDF' is coded as 'FLAME38' and 'QSHJFHGISU' is coded as 'RIGHT124'. How will 'DFEGFHGIHJ' be coded in that language?

• A. EFGHI35
• B. EFIGH36
• C. EIHFG24
• D. EGHIF70

Hint:

In complex coding-decoding questions, break the problem into parts (e.g., letters and numbers). If the logic derived from examples is inconsistent, try applying the simplest and most direct logic to the question at hand, as the examples might be flawed.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
We need to decipher the rules of a code language from two given examples and apply those rules to a new input string to find its corresponding code. The code consists of a word part and a number part.
Step 2: Key Formula or Approach:
We will analyze the transformation from the source string to the coded word and number separately. We'll use the positional values of letters in the alphabet (A=1, B=2, C=3, ...).
Step 3: Detailed Explanation:
Part 1: Decoding the Word
Let's analyze the first example: 'EGKMZBLNDF' \(\rightarrow\) 'FLAME'. The source has 10 letters, the code has 5. This suggests pairs of letters are being combined. Let's look at the positional values:

Pair 1: E(5), G(7) \(\rightarrow\) Average is \((5+7)/2 = 6\), which is F.
Pair 2: K(11), M(13) \(\rightarrow\) Average is \((11+13)/2 = 12\), which is L.
Pair 3: Z(26), B(2) \(\rightarrow\) Average is \((26+2)/2 = 14\), which is N. This doesn't match 'A'. Let's try treating the alphabet as circular, so after Z comes A. If B is treated as 28 (26+2), the average is \((26+28)/2=27\), which corresponds to A. This is a possible interpretation.
Pair 4: L(12), N(14) \(\rightarrow\) Average is \((12+14)/2 = 13\), which is M.
Pair 5: D(4), F(6) \(\rightarrow\) Average is \((4+6)/2 = 5\), which is E.
The logic seems to be taking the average of the positions of consecutive pairs of letters. Let's verify with the second example: 'QSHJFHGISU' \(\rightarrow\) 'RIGHT'.

Pair 1: Q(17), S(19) \(\rightarrow\) Average is \((17+19)/2 = 18\), which is R.
Pair 2: H(8), J(10) \(\rightarrow\) Average is \((8+10)/2 = 9\), which is I.
Pair 3: F(6), H(8) \(\rightarrow\) Average is \((6+8)/2 = 7\), which is G.
Pair 4: G(7), I(9) \(\rightarrow\) Average is \((7+9)/2 = 8\), which is H.
Pair 5: S(19), U(21) \(\rightarrow\) Average is \((19+21)/2 = 20\), which is T.
The logic for the word part is confirmed. Part 2: Decoding the Number
Let's analyze the number part.

Example 1: 'FLAME' \(\rightarrow\) 38. Let's sum the positional values of 'FLAME': F(6)+L(12)+A(1)+M(13)+E(5) = 37. The code is 38. This is (Sum + 1).
Example 2: 'RIGHT' \(\rightarrow\) 124. Let's sum the positional values of 'RIGHT': R(18)+I(9)+G(7)+H(8)+T(20) = 62. The code is 124. This is (Sum \(\times\) 2).
The rule for the number is not consistent across the examples, which suggests a flawed question. However, in such cases, often a simpler logic is intended for the question being asked. Let's try one more logic: the number is simply the sum of the positional values of the final coded word's letters. This would mean the numbers in the examples are slightly off. Let's apply this simple logic to our target word. Part 3: Applying the Rules to 'DFEGFHGIHJ'
Word Part:

DF: \((4+6)/2 = 5\) \(\rightarrow\) E
EG: \((5+7)/2 = 6\) \(\rightarrow\) F
FH: \((6+8)/2 = 7\) \(\rightarrow\) G
GI: \((7+9)/2 = 8\) \(\rightarrow\) H
HJ: \((8+10)/2 = 9\) \(\rightarrow\) I
The coded word is 'EFGHI'. Number Part: Assuming the simplest intended logic is to sum the positions of the letters in the final coded word: Sum = E(5) + F(6) + G(7) + H(8) + I(9) = 35. Step 4: Final Answer:
Combining the word and the number, we get 'EFGHI35'. This matches option (A).