Solving Number Pattern Reasoning Questions

This question asks us to find the missing number in a given pattern. We are provided with three sets of numbers, and we need to identify the relationship between the numbers within each set to find the missing value in the third set. The note specifies that operations should be performed on the whole numbers as given, without breaking them down into individual digits.

Analyzing the Given Number Sets

The three sets of numbers are:

• (7, 5, 10)
• (2, 1, 5)
• (16, 6, ?)

We need to find a pattern that relates the first two numbers in a set to the third number.

Identifying the Pattern

Let's examine the first set: (7, 5, 10).

We need to perform an operation or a sequence of operations on 7 and 5 to get 10. Let's consider some possibilities:

• Adding the numbers: $7 + 5 = 12$ (Not 10)
• Subtracting the numbers: $7 - 5 = 2$ (Not 10)
• Multiplying the numbers: $7 \times 5 = 35$ (Not 10)
• Trying combinations of operations. What if we find the difference and then multiply?

Let's try subtracting the second number from the first number and then multiplying the result by a constant factor:

$(7 - 5) = 2$

If we multiply this difference by 5, we get:

$2 \times 5 = 10$

This matches the third number in the first set (10).

Testing the Pattern on the Second Set

Let's test this potential pattern on the second set: (2, 1, 5).

According to the pattern, we subtract the second number (1) from the first number (2) and then multiply the result by 5.

$(2 - 1) = 1$

Now, multiply by 5:

$1 \times 5 = 5$

This result (5) matches the third number in the second set. The pattern seems consistent.

Applying the Pattern to Find the Missing Number

Now we apply the established pattern to the third set: (16, 6, ?).

Using the pattern (First Number - Second Number) $\times$ 5 = Third Number:

First Number = 16

Second Number = 6

Difference = $16 - 6 = 10$

Multiply the difference by 5:

$10 \times 5 = 50$

So, the missing number is 50.

Verifying the Answer with Options

The calculated missing number is 50. Let's look at the given options:

1. 32
2. 50
3. 45
4. 24

The number 50 is present as option 2.

Conclusion

The pattern observed is that the third number in each set is obtained by subtracting the second number from the first number and then multiplying the result by 5.

For (7, 5, 10): $(7 - 5) \times 5 = 2 \times 5 = 10$

For (2, 1, 5): $(2 - 1) \times 5 = 1 \times 5 = 5$

For (16, 6, ?): $(16 - 6) \times 5 = 10 \times 5 = 50$

Therefore, the missing number is 50.

Revision Table: Number Pattern Analysis

Additional Information: Solving Pattern Reasoning Problems

Pattern reasoning questions are common in logical and quantitative aptitude tests. They require identifying a mathematical or logical relationship between numbers or elements. Here are some tips for solving such problems:

• Look for simple arithmetic operations: Start by checking for addition, subtraction, multiplication, or division between adjacent numbers or between corresponding numbers in sets.
• Consider combinations: The pattern might involve a combination of operations, like subtraction followed by multiplication, or squaring numbers, etc.
• Look for a constant: Sometimes, a constant number is added, subtracted, multiplied, or divided in each step or set.
• Analyze differences or ratios: Calculate the differences between consecutive numbers or the ratios to see if a pattern emerges.
• Consider positions: For sequences, the position of the number can sometimes be part of the pattern (e.g., $n^2$, $2n+1$).
• Apply consistently: Once you find a potential pattern, test it rigorously on all given examples before applying it to find the missing element.
• Read notes carefully: Pay attention to any specific rules provided, like the one in this question about not breaking down digits.

Practicing various types of pattern problems helps in developing the ability to quickly spot the underlying rule.