Decoding the Code Language Pattern

This problem involves a code language where words are transformed based on a specific pattern. We are given two examples of words and their coded forms: 'FRISK' coded as 'THLIQ' and 'MOADS' coded as 'QODQB'. We need to find the code for 'WAGER'.

Let's analyze the patterns by looking at the alphabetical position of each letter (A=1, B=2, ..., Z=26).

Analyzing the First Example: FRISK to THLIQ

The shifts applied to the letters in 'FRISK' to get 'THLIQ' are: +14, +16, +3, +16, +6.

Analyzing the Second Example: MOADS to QODQB

The shifts applied to the letters in 'MOADS' to get 'QODQB' are: +4, +0, +3, +13, +9.

Identifying the Pattern of Shifts

Let's list the shifts for each position across the two examples:

• Position 1: +14 (for F), +4 (for M)
• Position 2: +16 (for R), +0 (for O)
• Position 3: +3 (for I), +3 (for A)
• Position 4: +16 (for S), +13 (for D)
• Position 5: +6 (for K), +9 (for S)

We can observe a consistent pattern for Position 3: the shift is always +3.

Let's look closer at Positions 4 and 5:

• Position 4 shifts: +16, +13. The difference is $13 - 16 = -3$.
• Position 5 shifts: +6, +9. The difference is $9 - 6 = +3$.

It appears there might be a sequence of shifts applied based on the position in the word, possibly evolving across the examples provided. Assuming the third word 'WAGER' is the next in this implicit sequence, let's see if we can deduce its shifts.

• Position 3 shift is consistently +3. So, for G in WAGER, the shift will be +3.
• Position 4 shifts decrease by 3 (-3). If this pattern continues, the next difference might decrease by 1, i.e., -2. So, the shift for Position 4 in WAGER could be $13 + (-2) = +11$. (Sequence: +16, +13, +11)
• Position 5 shifts increase by 3 (+3). If this pattern continues, the next difference might decrease by 1, i.e., +2. So, the shift for Position 5 in WAGER could be $9 + (+2) = +11$. (Sequence: +6, +9, +11)

Now let's consider the options for WAGER. The third letter of WAGER is G(7). Applying a +3 shift: G(7) + 3 = 10, which corresponds to the letter J. All options have J as the third letter, supporting this finding.

Let's calculate the letters for Positions 4 and 5 using the derived shifts (+11 and +11):

• Position 4: E(5) + 11 = 16, which corresponds to the letter P.
• Position 5: R(18) + 11 = 29. Since there are 26 letters, we calculate $29 \pmod{26} = 3$, which corresponds to the letter C.

So, the last three letters of the coded word for WAGER should be JPC. Looking at the options, only option 3 ends with JPC.

Let's assume the shifts for Positions 1 and 2 in WAGER result in the first two letters of option 3 (C and Y), and attempt to find the full pattern.

• Position 1: W(23) coded as C(3). Shift = $3 - 23 = -20 \equiv +6 \pmod{26}$.
• Position 2: A(1) coded as Y(25). Shift = $25 - 1 = +24$.

The full sequence of shifts for WAGER, based on the correct option, is +6, +24, +3, +11, +11.

Let's look at the sequence of shifts for each position again:

• Position 1: +14, +4, +6 (Differences: -10, +2)
• Position 2: +16, +0, +24 (Differences: -16, +24)
• Position 3: +3, +3, +3 (Differences: +0, +0) - Consistent!
• Position 4: +16, +13, +11 (Differences: -3, -2) - Pattern: subtract 3, then subtract 2.
• Position 5: +6, +9, +11 (Differences: +3, +2) - Pattern: add 3, then add 2.

While the patterns for Positions 1 and 2 are not as simple as for Positions 3, 4, and 5, the shifts +6 and +24 for WAGER's first two letters seem to fit with the specific coded word CYJPC.

Based on the consistent pattern for Position 3 and the observed sequence of shifts for Positions 4 and 5 matching the end of option 3, and assuming the shifts for Positions 1 and 2 are +6 and +24 respectively for WAGER, we can code WAGER.

Coding WAGER

Apply the shifts +6, +24, +3, +11, +11 to the letters of WAGER (W, A, G, E, R):

• W (Position 23) + 6 = 29 $\equiv$ 3 (Position of C)
• A (Position 1) + 24 = 25 (Position of Y)
• G (Position 7) + 3 = 10 (Position of J)
• E (Position 5) + 11 = 16 (Position of P)
• R (Position 18) + 11 = 29 $\equiv$ 3 (Position of C)

Combining the resulting letters, we get CYJPC.

Conclusion

The coded word for 'WAGER' is 'CYJPC' based on the positional shift pattern observed across the given examples.

Coding Decoding Problem Revision Table

Additional Information on Letter Coding

Letter coding is a common type of question in logical reasoning and verbal ability tests. These codes replace letters in a word with other letters based on a specific rule or pattern. Identifying this underlying pattern is key to solving the problem.

Common types of letter coding patterns include:

• Shifting: Each letter is shifted forward or backward by a fixed number of positions in the alphabet (e.g., +2 for every letter).
• Different Shifts: Each letter is shifted by a different number, often following a sequence (+1, +2, +3, ... or +2, -1, +2, -1, ...). The shift might depend on the position of the letter in the word or whether it's a vowel or a consonant.
• Reversal: The order of letters is reversed, and sometimes shifts are applied after reversal.
• Substitution: Each letter is directly substituted with another specific letter (e.g., A always becomes Z, B always becomes Y).
• Positional Value: The code might be based on the alphabetical position of the letters, sometimes involving sums, differences, or simple arithmetic operations on these values.

Solving letter coding problems requires careful observation, comparing the input word and its code, and testing different potential rules or combinations of rules. Sometimes, as in this problem, the pattern for different positions might follow different sub-patterns or sequences.