Question

Select the related numbers from the given alternative
42 : 56 :: 110 : ____ ?

• A. 132
• B. 136
• C. 144
• D. 148

Hint:

Many number analogy questions rely on patterns of squares and products of consecutive integers:
\(42 = 6 \times 7\) and \(56 = 7 \times 8\).
\(110 = 10 \times 11\) and next is \(11 \times 12 = 132\).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Number analogy questions require identifying the mathematical relationship or pattern in the first pair and applying that same pattern to the second pair.

Step 2: Detailed Explanation:
Let us analyze the numbers in the first pair: 42 and 56.
We can express these numbers as products of consecutive integers:
\[ 42 = 6 \times 7 \]
\[ 56 = 7 \times 8 \]
Alternatively, we can express them as:
\[ 42 = 6^2 + 6 \]
\[ 56 = 7^2 + 7 \]
This shows a progression from \(n(n+1)\) to \((n+1)(n+2)\), where \(n = 6\).
Now let us apply this same pattern to the second pair starting with 110:
\[ 110 = 10 \times 11 = 10^2 + 10 \]
Here, the base integer is \(n = 10\).
Following the established pattern, the next number must be:
\[ (10+1) \times (11+1) = 11 \times 12 \]
\[ 11 \times 12 = 132 \]
Alternatively:
\[ 11^2 + 11 = 121 + 11 = 132 \]
This matches Option A.

Step 3: Final Answer:
The missing number is 1