Study the given pattern carefully and select the number that can replace the question mark> in it. 11 13 17 33 35 39 189 191 ?
195
This solution explains how to find the missing number in the given numerical pattern by analyzing the relationship between numbers in each row.
Understanding the Number Pattern Puzzle
The task is to identify the missing number represented by the question mark (?) in the provided sequence. The numbers are arranged in rows, and we need to discover the pattern governing this arrangement.
The given pattern is:
- 11 13 17
- 33 35 39
- 189 191 ?
Analyzing the Pattern Within Each Row
Let's examine the relationship between the numbers listed horizontally in each row.
- Row 1: 11, 13, 17
- To get from the first number (11) to the second number (13), we add 2: $11 + 2 = 13$.
- To get from the second number (13) to the third number (17), we add 4: $13 + 4 = 17$.
- The pattern for Row 1 is: Add 2, then add 4.
- Row 2: 33, 35, 39
- To get from the first number (33) to the second number (35), we add 2: $33 + 2 = 35$.
- To get from the second number (35) to the third number (39), we add 4: $35 + 4 = 39$.
- The pattern for Row 2 is the same as Row 1: Add 2, then add 4.
We have identified a consistent pattern across the first two rows: each row starts with a number, the next number is obtained by adding 2, and the number after that is obtained by adding 4 to the second number.
Applying the Pattern to Find the Missing Number
We can now apply this identified pattern (add 2, then add 4) to the third row to find the missing number.
- The third row starts with the number 189.
- First, we add 2 to the starting number: $189 + 2 = 191$. This matches the second number given in the third row.
- Next, we add 4 to this second number (191) to find the missing number: $191 + 4 = 195$.
So, the missing number in the pattern is 195.
Matching the Result with the Options
The calculated missing number is 195. Let's compare this with the given options:
- Option 1: 203
- Option 2: 199
- Option 3: 217
- Option 4: 195
The calculated number, 195, corresponds to Option 4.
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