Difficulty: Medium
Correct Answer: HJLN
Explanation:
Introduction / Context:
This question is a letter analogy based on positions in the English alphabet. The group EFGH is related to LNPR in a specific way, and you must find the group of letters that will have the same relationship with ABCD. Such problems test your understanding of alphabet positions and pattern recognition across several letters at once.
Given Data / Assumptions:
Concept / Approach:
We convert each letter to its alphabet position: A as 1, B as 2, and so on up to Z as 26. Then we compare the positions of EFGH with LNPR. If there is a clear incremental pattern, such as adding a certain number to each letter, we can apply that same numerical transformation to ABCD. The aim is to see not only one shift, but the whole sequence of shifts from the first set to the second set of letters.
Step-by-Step Solution:
Step 1: Write the positions for EFGH. E is 5, F is 6, G is 7, and H is 8.
Step 2: Write the positions for LNPR. L is 12, N is 14, P is 16, and R is 18.
Step 3: Find the difference for each corresponding letter. From E(5) to L(12) is +7, from F(6) to N(14) is +8, from G(7) to P(16) is +9, and from H(8) to R(18) is +10.
Step 4: Observe that the increments are increasing by one each time: +7, +8, +9, +10.
Step 5: Now write the positions for ABCD. A is 1, B is 2, C is 3, and D is 4.
Step 6: Apply the same increments. Add 7 to A: 1 + 7 = 8 (H). Add 8 to B: 2 + 8 = 10 (J). Add 9 to C: 3 + 9 = 12 (L). Add 10 to D: 4 + 10 = 14 (N).
Step 7: Combine these letters to get HJLN and compare with the options. This matches option b exactly.
Verification / Alternative check:
Check that no other option can be obtained by applying the same set of increments. If we tried PQRS, HIJK, or EFGH, we would need different, inconsistent shifts from ABCD, which would no longer match the pattern taken from EFGH to LNPR. Also, if we reverse the process from HJLN by subtracting 7, 8, 9, and 10, we get back A, B, C, and D respectively. This two way check confirms that HJLN is the only group that satisfies the defined rule.
Why Other Options Are Wrong:
PQRS would require a constant shift that does not fit the varying increments seen in the original pair. HIJK is simply four consecutive letters and does not reflect the pattern of increasing shifts. EFGH repeats the original group and shows no transformation at all. None of these alternative options replicate the exact +7, +8, +9, +10 shift sequence discovered from the example pair.
Common Pitfalls:
A frequent error is to assume a constant shift for all letters, such as adding the same number to each position, because that pattern is common in simpler problems. Here, the shifts increase by one each time, which is slightly more complex. Carefully computing differences for each corresponding letter, rather than guessing, prevents such mistakes and quickly reveals the intended pattern.
Final Answer:
By applying the same pattern of increments used from EFGH to LNPR, the group ABCD corresponds to HJLN.
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