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 : ?
JQEKA
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.
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.
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.
Let's check if JQEKA matches any of the given options:
The calculated word JQEKA matches option 3.
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.
| 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). |
Letter series and analogy questions test your logical reasoning and pattern recognition skills. Here are some common types of patterns you might encounter:
To effectively solve these problems, it's helpful to:
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