Solving the Number Analogy Problem: Finding the Pattern

The question asks us to find the number that completes the analogy based on the relationship between the given pairs. The analogy is presented as 19 : 34 :: 5 : 6 :: 27 : ?

This means the relationship between 19 and 34 is the same as the relationship between 5 and 6, and this same relationship should apply between 27 and the missing number.

Analyzing the Given Number Pairs

Let's look closely at the first two pairs provided:

1. Pair 1: 19 : 34
   We need to figure out how 34 is related to 19. Let's try common arithmetic operations.
2. Pair 2: 5 : 6
   Similarly, let's find the relationship between 5 and 6.

Identifying the Numerical Reasoning Pattern

Let's test a few potential patterns for the second pair, as it involves smaller numbers and might be simpler:

• Addition: \(5 + 1 = 6\).
• Multiplication: \(5 \times 1 + 1 = 6\).

Now let's see if either of these simple patterns works for the first pair, 19 : 34.

• If we use simple addition (+1): \(19 + 1 = 20\). This is not 34.
• Let's consider other relationships for 19 and 34. How about multiplying 19 by a small number and adding or subtracting?
• Try multiplying 19 by 2: \(19 \times 2 = 38\). From 38, how do we get 34? \(38 - 4 = 34\).
• So, the potential pattern for the first pair is \(N \times 2 - 4\). Let's test this pattern on the second pair (5 : 6).
• Apply \(N \times 2 - 4\) to 5: \(5 \times 2 - 4 = 10 - 4 = 6\).

This pattern, \(N \times 2 - 4\), works for both the first pair (19 to 34) and the second pair (5 to 6). This confirms that this is likely the underlying numerical reasoning rule for this analogy.

Applying the Pattern to Find the Missing Number

Now we need to apply the same pattern, \(N \times 2 - 4\), to the fifth number, 27, to find the sixth number (the missing number).

Let the missing number be \(X\). According to the pattern:

\(27 \times 2 - 4 = X\)

Step-by-Step Calculation:

1. Multiply 27 by 2: \(27 \times 2 = 54\)

2. Subtract 4 from the result: \(54 - 4 = 50\)

So, the missing number is 50.

Comparing with the Options

Let's check our calculated missing number against the given options:

1. 50
2. 67
3. 52
4. 63

Our calculated number, 50, matches option 1.

Therefore, the complete analogy is 19 : 34 :: 5 : 6 :: 27 : 50.

Revision Table: Number Analogy Pattern

Additional Information: Number Analogy Tips

Number analogy questions test your ability to identify the relationship between pairs of numbers and apply that relationship to a new pair. Here are some common patterns to look for:

• Arithmetic Operations: Addition, subtraction, multiplication, division.
• Squaring/Cubing: The second number might be the square or cube of the first, or related to the square/cube.
• Number Series Logic: Look for patterns involving consecutive numbers, prime numbers, composite numbers, etc.
• Digit Operations: Sometimes the pattern involves the sum, difference, or product of the digits of the number.
• Combinations: The pattern might be a combination of the above, like \(N^2 + C\) or \(N \times A + B\).

Practice analyzing different types of number relationships to improve your pattern identification skills in logical reasoning problems.