Which number will replace the question mark (?) in the given series? 55, 68, 81, 94, ?, 120
107
Solving Number Series Questions
Number series questions are common in reasoning sections of competitive exams. To solve them, you need to identify the pattern or rule that connects the numbers in the sequence. Common patterns include addition, subtraction, multiplication, division, squares, cubes, or a combination of these operations, often involving a constant value or a sequence of values.
Analyzing the Given Number Series
The given series is:
55, 68, 81, 94, ?, 120
We need to find the number that replaces the question mark (?). Let's examine the differences between consecutive terms to find the pattern in this number series.
| Term 1 | Term 2 | Difference | Calculation |
|---|---|---|---|
| 55 | 68 | 13 | \(68 - 55 = 13\) |
| 68 | 81 | 13 | \(81 - 68 = 13\) |
| 81 | 94 | 13 | \(94 - 81 = 13\) |
From the calculations above, we can see a consistent difference of 13 between consecutive numbers. This indicates that the series is an arithmetic progression where each term is obtained by adding 13 to the previous term. The common difference is 13.
Finding the Missing Number
To find the missing number, we apply the identified pattern to the last known number before the question mark, which is 94. We add the common difference, 13, to 94:
\(\text{Missing Number} = 94 + 13\)
\(\text{Missing Number} = 107\)
Verifying the Pattern
Let's check if adding 13 to the calculated missing number gives the next number in the series (120):
\(107 + 13 = 120\)
This matches the last number in the given series, confirming that our pattern and the calculated missing number are correct.
Conclusion
The number that replaces the question mark (?) in the series 55, 68, 81, 94, ?, 120 is 107. This is because the series follows a pattern of adding 13 to the previous term.
Revision Table: Key Steps for Number Series
| Step | Action | Purpose |
|---|---|---|
| 1 | Examine the series | Understand the sequence of numbers. |
| 2 | Calculate differences/ratios | Identify potential patterns (arithmetic, geometric, etc.). |
| 3 | Formulate a rule | Define the mathematical relationship between terms. |
| 4 | Apply the rule | Find the missing or next term. |
| 5 | Verify the result | Check if the pattern holds for subsequent terms (if available). |
Additional Information: Types of Number Series
Understanding different types of number series patterns can help solve problems quickly:
- Arithmetic Series: Each term is found by adding a constant value (the common difference) to the previous term. The given series is an example of an arithmetic series.
- Geometric Series: Each term is found by multiplying the previous term by a constant value (the common ratio).
- Fibonacci Series: Each term (after the first two) is the sum of the two preceding terms (e.g., 0, 1, 1, 2, 3, 5, 8...).
- Square/Cube Series: Terms are squares or cubes of consecutive numbers (e.g., 1, 4, 9, 16... or 1, 8, 27, 64...).
- Mixed Series: A combination of two or more patterns, or an alternating pattern.
By practicing with various types of series, you can improve your ability to spot patterns quickly during exams.
Similar Questions
- Choose the missing number in the below series.
100, 95, 90, 85, ?, 75 Which of the following numbers will replace the question mark (?) in the given series?
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Which of the following numbers will replace the question mark (?) in the given series?
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Select the number from among the given options that can replace the question mark (?) in the following series.
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Which number will replace the question mark (?) in the following series?
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From the given options, choose the correct one that will replace the question mark (?) in the following series.
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Select the number from among the given options that can replace the question mark (?) in the following series.
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Important Questions from Number Series
Select the number from among the given options that can replace the question mark (?) in the following series.
15, 45, 75, 105, ?
Identify the number that does NOT belong to the following series.
18, 27, 35, 45, 54
Select the number from among the given options that can replace the question mark (?) in the following series.
37, 41, 50, 66, ?
दिए गए विकल्पों में से वह संख्या चुनिए जो निम्नलिखित श्रृंखला में प्रश्नवाचक चिन्ह (?) को प्रतिस्थापित कर सके।
20, 21, 25, 34,?, 75
Select the correct option that will fill in the blank and complete the series.
45, 49, 58, 74, .........
