Finding the Code for PQR: A Data Sufficiency Problem

This question asks us to determine which of the given statements, or both, are sufficient to find the code for the letters PQR. We are presented with two statements, each providing examples of words and their corresponding codes. We need to analyze the information in each statement to identify a coding pattern and see if that pattern allows us to deduce the code for PQR.

Analysis of Statement I for PQR Code

Statement I gives us the following information:

• ABC represents BCD
• DEF represents EFG

Let's look at the relationship between the original words and their codes in these examples. Observing the letters, we can see a consistent transformation:

• A in ABC corresponds to B in BCD (A shifts to the next letter, B)
• B in ABC corresponds to C in BCD (B shifts to the next letter, C)
• C in ABC corresponds to D in BCD (C shifts to the next letter, D)

The same pattern appears in the second example:

• D in DEF corresponds to E in EFG (D shifts to E)
• E in DEF corresponds to F in EFG (E shifts to F)
• F in DEF corresponds to G in EFG (F shifts to G)

This pattern is a simple letter shift where each letter in the original word is replaced by the next letter in the English alphabet (a shift of +1 position).

Applying this identified pattern from Statement I to find the code for PQR:

• P shifts to Q
• Q shifts to R
• R shifts to S

Thus, according to the pattern derived from Statement I, the code for PQR is QRS.

Since Statement I provides enough information to identify a clear pattern and determine the code for PQR, Statement I alone is sufficient to answer the question.

Analysis of Statement II for PQR Code

Statement II gives us these examples:

• LMN represents MNO
• OPQ represents PQR

Let's analyze the relationship between the original words and their codes in these examples as well:

• L in LMN corresponds to M in MNO (L shifts to M)
• M in LMN corresponds to N in MNO (M shifts to N)
• N in LMN corresponds to O in MNO (N shifts to O)

The second example confirms the pattern:

• O in OPQ corresponds to P in PQR (O shifts to P)
• P in OPQ corresponds to Q in PQR (P shifts to Q)
• Q in OPQ corresponds to R in PQR (Q shifts to R)

Statement II also establishes the same coding pattern: each letter in the original word is shifted one position forward in the alphabet to get the code.

Applying this pattern from Statement II to find the code for PQR:

• P shifts to Q
• Q shifts to R
• R shifts to S

Thus, according to the pattern derived from Statement II, the code for PQR is QRS.

Since Statement II provides enough information to identify a clear pattern and determine the code for PQR, Statement II alone is sufficient to answer the question.

Determining Overall Sufficiency for PQR Code

Based on our analysis:

• Statement I alone provides a consistent pattern (letter shift +1) that determines the code for PQR to be QRS. Therefore, Statement I is sufficient.
• Statement II alone also provides a consistent pattern (letter shift +1) that determines the code for PQR to be QRS. Therefore, Statement II is sufficient.

Since the question can be answered using the information in Statement I alone OR the information in Statement II alone, either statement is sufficient.

Therefore, either Statement I or Statement II is sufficient to answer the question.

Revision Table: Key Concepts in Data Sufficiency and Coding

Additional Information: Understanding Letter Shift Codes

Letter shift is a fundamental concept in coding and cryptography. The simplest type, as seen in this problem, is a Caesar cipher with a shift of +1. More complex variations exist:

• Shift Amount: The shift can be any number (e.g., +3, -2, +10). The alphabet wraps around (e.g., a shift of +1 for Z would be A).
• Direction of Shift: Shifts can be forward (+ N) or backward (- N).
• Key Word: The shift amount might be determined by a keyword or phrase.
• Position-Based Shift: The shift might vary depending on the position of the letter in the word (e.g., the first letter shifts by +1, the second by +2, etc.).

Solving coding-decoding problems like this relies heavily on pattern recognition. Carefully comparing the original words and their codes, letter by letter and position by position, is key to unlocking the coding rule.