\(19384: 31506 :: 28493:?\)
40615
Number Analogy Explained
This question is a type of number analogy problem. In such problems, we are given a pair of numbers that share a specific mathematical or logical relationship. We need to identify this relationship and then apply the same logic to another number to find the missing number in the second pair.
The given analogy is:
\(19384 : 31506 :: 28493 : ?\)
Finding the Logical Pattern
Let's examine the relationship between the first pair of numbers, \(19384\) and \(31506\). We will look at the digits of the first number and see how they transform into the digits of the second number.
Consider the digits of \(19384\) one by one and compare them with the digits of \(31506\) at the corresponding positions:
- First digit: The digit \(1\) in \(19384\) corresponds to the digit \(3\) in \(31506\). The operation is \(1 + 2 = 3\).
- Second digit: The digit \(9\) in \(19384\) corresponds to the digit \(1\) in \(31506\). The operation is \(9 + 2 = 11\). When results exceed \(9\), we use the unit digit, which is equivalent to applying modulo \(10\) arithmetic: \(11 \pmod{10} = 1\).
- Third digit: The digit \(3\) in \(19384\) corresponds to the digit \(5\) in \(31506\). The operation is \(3 + 2 = 5\).
- Fourth digit: The digit \(8\) in \(19384\) corresponds to the digit \(0\) in \(31506\). The operation is \(8 + 2 = 10\). Using modulo \(10\) arithmetic, \(10 \pmod{10} = 0\).
- Fifth digit: The digit \(4\) in \(19384\) corresponds to the digit \(6\) in \(31506\). The operation is \(4 + 2 = 6\).
The identified pattern is that each digit of the first number is increased by \(2\). If the sum of a digit and \(2\) is greater than \(9\), the unit digit of the sum is taken (i.e., modulo \(10\) operation is applied).
Applying the Pattern to \(28493\)
Now, we apply the same rule (add \(2\) to each digit, using modulo \(10\) for results greater than \(9\)) to the second number, \(28493\), to find the missing number.
Let's process each digit of \(28493\):
- First digit: \(2 + 2 = 4\).
- Second digit: \(8 + 2 = 10\). Applying modulo \(10\), the result is \(0\).
- Third digit: \(4 + 2 = 6\).
- Fourth digit: \(9 + 2 = 11\). Applying modulo \(10\), the result is \(1\).
- Fifth digit: \(3 + 2 = 5\).
Combining these resulting digits in order, we obtain the number \(40615\).
Missing Number Identification
We compare our calculated result, \(40615\), with the given options:
- Option 1: \(39615\)
- Option 2: \(41706\)
- Option 3: \(40617\)
- Option 4: \(40615\)
Our calculated result matches Option 4.
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Important Questions from Reasoning Analogy
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Withdraw : ExtractSelect the word-pair that best represents a similar relationship to the one expressed in the pair of words given below.
Duleep Trophy : Cricket
Select the set in which the numbers are related in the same way as are the numbers of the following sets.
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