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Question

Select the option that is related to the third term in the same way as the second term is related to the first term.

SMART : QOYTR : : LOGIC : ?

This question was previously asked in
SSC Selection Post 2021 Question Paper (09-Feb-2022) (Shift-1)
The correct answer is

JQEKA

Analogy Question Solution: Decoding Letter Patterns

This question asks us to find the word that relates to LOGIC in the same way that QOYTR relates to SMART. This is a type of analogy question often found in logical reasoning sections of exams. To solve it, we need to identify the pattern or rule applied to transform SMART into QOYTR and then apply the same rule to LOGIC.

Analyzing the Relationship: SMART to QOYTR

Let's look at how each letter in SMART changes to the corresponding letter in QOYTR. We can consider the position of each letter in the English alphabet (A=1, B=2, ..., Z=26).

Letter from SMART Position Letter in QOYTR Position Change
S 19 Q 17 \(17 - 19 = -2\)
M 13 O 15 \(15 - 13 = +2\)
A 1 Y 25 \(25 - 1 = 24\). However, \(1 - 2 = -1\). In alphabetical order, moving 2 steps back from A gives Z (1 step) and then Y (2 steps). So, the shift is -2. \(1 - 2 \equiv -1 \equiv 25 \pmod{26}\)
R 18 T 20 \(20 - 18 = +2\)
T 20 R 18 \(18 - 20 = -2\)

The pattern of changes between corresponding letters is consistently -2, +2, -2, +2, -2.

Applying the Pattern to LOGIC

Now we apply the identified pattern (-2, +2, -2, +2, -2) to each letter of LOGIC.

Letter from LOGIC Position Pattern Shift New Position Calculation New Letter
L 12 -2 \(12 - 2 = 10\) J (10th letter)
O 15 +2 \(15 + 2 = 17\) Q (17th letter)
G 7 -2 \(7 - 2 = 5\) E (5th letter)
I 9 +2 \(9 + 2 = 11\) K (11th letter)
C 3 -2 \(3 - 2 = 1\) A (1st letter)

Following the pattern, the word LOGIC transforms into JQEKA.

Comparing with Options

Let's check if JQEKA matches any of the given options:

  1. JPEKA
  2. JPEJA
  3. JQEKA
  4. JQFKA

The calculated word JQEKA matches option 3.

Conclusion

The pattern connecting SMART to QOYTR is a sequential letter shift of -2, +2, -2, +2, -2 for each letter. Applying this exact pattern to LOGIC results in the word JQEKA. Therefore, JQEKA is related to LOGIC in the same way QOYTR is related to SMART.


Revision Table: Analogy Patterns

Concept Description Example (SMART:QOYTR)
Letter Analogy Relating words based on patterns in their letters or positions. Identifying the shift pattern (-2, +2, -2, +2, -2).
Position-based Pattern The rule depends on the alphabetical position of letters. S (19) → Q (17) shows a shift of -2 based on position.
Cyclic Shift When shifting letters backwards from A or forwards from Z, the alphabet wraps around. A (1) shifted by -2 results in Y (25).

Additional Information: Solving Letter Series and Analogies

Letter series and analogy questions test your logical reasoning and pattern recognition skills. Here are some common types of patterns you might encounter:

  • Positional Shifts: Adding or subtracting a fixed number or a varying sequence of numbers to the letter positions (like in this problem).
  • Reverse Order: The letters are simply reversed.
  • Alphabetical Grouping: Letters are grouped, and operations are applied within groups (e.g., shifting all vowels by +1, all consonants by -1).
  • Skipping Letters: A fixed number of letters are skipped between consecutive letters in the series or analogy.
  • Vowel/Consonant Patterns: Rules might apply differently to vowels and consonants.
  • Mirror Image: The second term might be a form of mirror image or reversal of the first.

To effectively solve these problems, it's helpful to:

  • Know the alphabetical order and position of each letter quickly.
  • Look for consistent changes between corresponding letters.
  • Consider different types of patterns (addition, subtraction, multiplication, division, squaring positions, or combining rules).
  • Check if the pattern is uniform across all letters or varies based on position (like 1st letter, 2nd letter, etc.).
  • Practice with various examples to recognise common patterns faster.
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