Question

In a code language, \(m^{\text{th}}\) letter is coded as \((m-1)^{\text{th}}\) letter if \(m\) is odd and \((m+1)^{\text{th}}\) letter if \(m\) is even. Then which word is coded as ‘LDZMR’? 

• A. MEALS
• B. TRIMS
• C. MEATS
• D. TRAIN

Hint:

When decoding is confusing, test the given options by applying the coding rule directly.

Answer 1

The Correct Option is A

Concept:
We need to find the original word whose code is \[ \text{LDZMR} \] The easiest method is to test the options using the given rule.

Step 1: Test MEALS. Letters of MEALS are: \[ M,\ E,\ A,\ L,\ S \] Their positions are: \[ M=13,\quad E=5,\quad A=1,\quad L=12,\quad S=19 \]

Step 2: Apply the coding rule. Since \(M=13\) is odd: \[ M\rightarrow L \] Since \(E=5\) is odd: \[ E\rightarrow D \] Since \(A=1\) is odd: \[ A\rightarrow Z \] Since \(L=12\) is even: \[ L\rightarrow M \] Since \(S=19\) is odd: \[ S\rightarrow R \]

Step 3: Form the code. \[ \text{MEALS}\rightarrow \text{LDZMR} \] This matches the given code.

Step 4: Final answer. \[ \boxed{\text{MEALS}} \]