Consider the given question and decide which of the following statements is sufficient to answer the question. What is the code for PQR? Statements: I. ABC represents BCD; DEF represents EFG. II. LMN represents MNO; OPQ represents PQR.
Either I or II is sufficient to answer the question.
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
| Concept | Explanation | Application Here |
|---|---|---|
| Data Sufficiency | Evaluating if given data (statements) is sufficient to answer a question. | Checking if Statement I, Statement II, or both can determine the code for PQR. |
| Coding-Decoding | Problems finding rules or patterns that transform words/numbers into codes. | Identifying the letter shift pattern in the given examples. |
| Sufficiency | A statement is sufficient if it provides a unique, definite answer to the question. | Both statements independently provided a unique code (QRS) for PQR. |
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.
Important Questions from Data Sufficiency
Which of the following statement is correct?
I. The value of 1002 - 992 + 982 - 972 + 962 - 952 + 942 - 932 + ...... + 222 - 212 is 4840.
II. The value of
\(\left(k^2+ \frac{1}{k^2} \right) \left(k- \frac{1}{k} \right) \left(k^4+ \frac{1}{k^4} \right) \) \(\left(k+ \frac{1}{k} \right)\left(k^4- \frac{1}{k^4} \right)\) is \(k^{16}- \frac{1}{k^{16}}\).
Given below is a question followed by two statements I and II. Read both statements carefully to decide which one of them is sufficient to answer the question.
Six people - A, B, C, D, E and F are sitting in a straight line facing north. Who sits to the immediate left of D?
(I) A sits second from one of the extreme ends of the line. Only two people sit between A and B. E sits to the immediate right of C.
(II) C sits third from the left end of the line. Only one person sits between C and F. E sits third to the right of F.
Please read the below equation and select an appropriate option from the following.
x + y = 10 ; y = x - 2
Quantity A is x.
Quantity B is y.
A lady wants to buy the following items in the given price range-
1. Tomato between Rs. 40 and Rs. 45 per kg.
2. Grapes in the price range of Rs. 80 and Rs. 90 per kg.
3. Milk packets at Rs. 23 per liter.
In which shop from the following will she definitely get all her items/
A. Shop S sells tomato at Rs. 22.5 per half kg, Grapes at Rs. 82 per kg and milk at Rs. 24 per liter.
B. Shop H sells grapes at Rs. 21 per quarter kg, milk at 12.5 per half litre and tomato at Rs. 22 per half kg.
C. Shop O sells milk at Rs. 11.5 per half litre, tomato at 21 per half kg and grapes at Rs. 43 per half kg.
D. Shop P sells tomato at Rs. 23.5 per half kg, grapes at Rs. 85 per kg and milk at Rs. 23 per litre.You are given a question and two statements. Identify which of the statements is/are sufficient to answer the question.
Question:
When is Yuvi's wedding anniversary?
Statements:
1: On the 7 th day of a month.
2. The month has 29 days only in a leap year.
