Number Analogy: Understanding the Problem

The question asks us to identify the relationship between the numbers in the given sets: (6, 22, 14) and (8, 30, 19). We need to find a set from the options where the numbers share the exact same relationship. A key rule is that operations must be performed on the whole numbers themselves, not by breaking them down into individual digits.

Pattern Identification: Analyzing the Given Sets

Let's examine the relationship in the first set (6, 22, 14). Let the three numbers be A, B, and C, where A=6, B=22, and C=14. We need to find a rule that connects these three numbers.

• Consider sums, differences, or products of the numbers.
• $A + C = 6 + 14 = 20$. The middle number is 22. $20 + 2 = 22$. This suggests a possible rule: $A + C + 2 = B$. Let's check the second set.

Now, let's check this possible rule $A + C + 2 = B$ with the second set (8, 30, 19). Here, A=8, B=30, and C=19.

• $A + C + 2 = 8 + 19 + 2 = 27 + 2 = 29$. The middle number is 30. Since $29 \neq 30$, this rule is incorrect.

Let's look for another pattern. Let's try combinations of multiplication and addition/subtraction.

• Maybe the middle number (B) is related to A and C by multiplication and then addition/subtraction.
• Consider the form $xA + yC = B$. Let's use the two given sets to form equations:
• Set 1: (6, 22, 14) → $6x + 14y = 22$
• Set 2: (8, 30, 19) → $8x + 19y = 30$

We now have a system of two linear equations with two variables, $x$ and $y$:

$6x + 14y = 22$ (Equation 1)

$8x + 19y = 30$ (Equation 2)

Let's simplify Equation 1 by dividing by 2:

$3x + 7y = 11$ (Equation 3)

Now, we can solve for $x$ and $y$ using substitution or elimination. Let's use elimination. Multiply Equation 3 by 8 and Equation 2 by 3:

$(3x + 7y = 11) \times 8 \implies 24x + 56y = 88$

$(8x + 19y = 30) \times 3 \implies 24x + 57y = 90$

Subtract the first new equation from the second new equation:

$(24x + 57y) - (24x + 56y) = 90 - 88$

$y = 2$

Now substitute $y=2$ back into Equation 3 ($3x + 7y = 11$):

$3x + 7(2) = 11$

$3x + 14 = 11$

$3x = 11 - 14$

$3x = -3$

$x = -1$

So the relationship appears to be $A \times (-1) + C \times 2 = B$, which can be written as $2C - A = B$. Let's verify this rule with the original sets.

• For (6, 22, 14): $2 \times 14 - 6 = 28 - 6 = 22$. This matches the middle number.
• For (8, 30, 19): $2 \times 19 - 8 = 38 - 8 = 30$. This also matches the middle number.

The rule is consistently $B = 2C - A$.

Testing Options: Applying the Number Set Rule

Now we apply the rule $B = 2C - A$ to each of the given options to find the set that follows the same pattern.

• Option 1: (12, 46, 27)
  • A=12, B=46, C=27
  • Calculate $2C - A = 2 \times 27 - 12 = 54 - 12 = 42$
  • The calculated value (42) is not equal to B (46). This option does not follow the rule.
• Option 2: (4, 18, 11)
  • A=4, B=18, C=11
  • Calculate $2C - A = 2 \times 11 - 4 = 22 - 4 = 18$
  • The calculated value (18) is equal to B (18). This option follows the rule.
• Option 3: (7, 26, 17)
  • A=7, B=26, C=17
  • Calculate $2C - A = 2 \times 17 - 7 = 34 - 7 = 27$
  • The calculated value (27) is not equal to B (26). This option does not follow the rule.
• Option 4: (9, 34, 22)
  • A=9, B=34, C=22
  • Calculate $2C - A = 2 \times 22 - 9 = 44 - 9 = 35$
  • The calculated value (35) is not equal to B (34). This option does not follow the rule.

Based on the analysis, only Option 2 follows the identified rule $B = 2C - A$.

Conclusion: Identifying the Correct Set

The set (4, 18, 11) is related in the same way as the sets (6, 22, 14) and (8, 30, 19), following the rule $B = 2C - A$.

Number Analogy Revision Table

Additional Information on Number Analogy

Number analogy questions are common in logical reasoning and quantitative aptitude sections of competitive exams. They test your ability to observe numbers and identify the underlying pattern or relationship. Common patterns include:

• Basic arithmetic operations (addition, subtraction, multiplication, division).
• Operations involving squares or cubes of numbers.
• Combinations of different operations.
• Relationships between the first and second number, first and third, or all three.
• Rules applied sequentially or simultaneously.

The key to solving these problems is a systematic approach:

• Analyze the given examples carefully.
• Try simple relationships first (sums, differences, basic multiples).
• If simple methods don't work, look for more complex combinations (like $xA + yC = B$).
• Once a potential rule is found, test it against ALL given examples to ensure it holds consistently.
• Apply the validated rule to each option to find the matching set.

Practicing different types of number analogy problems helps in recognizing patterns more quickly.