What number will come in place of question mark in this series? 100, 115, ?, 150, 170, 185 A. 135 B. 130 C. 140 D. 145
A
Solving the Number Series Question
The question asks us to find the missing number in the given series:
100, 115, ?, 150, 170, 185
To solve this type of number series problem, we need to identify the pattern or rule that governs the sequence of numbers. Often, this pattern is found by looking at the difference between consecutive terms.
Finding the Pattern in the Number Series
Let's calculate the differences between the given consecutive terms:
- Difference between the second and first term: \(115 - 100 = 15\)
- Difference between the sixth and fifth term: \(185 - 170 = 15\)
- Difference between the fifth and fourth term: \(170 - 150 = 20\)
We have the differences for the first step (+15), the last step (+15), and the second to last step (+20). Let the missing number be \(x\). The series is 100, 115, \(x\), 150, 170, 185.
The differences look like this:
100 \(\xrightarrow{+15}\) 115 \(\xrightarrow{?}\) \(x\) \(\xrightarrow{?}\) 150 \(\xrightarrow{+20}\) 170 \(\xrightarrow{+15}\) 185
Notice that the differences are 15 and 20, and they seem to appear in some order. Let's consider a pattern where the differences alternate between 15 and 20.
- Starting with 100, add 15: \(100 + 15 = 115\). This matches the second term.
- Next, following the alternating pattern, add 20 to the second term: \(115 + 20 = 135\). This could be the missing number.
- Now, add 15 to this result: \(135 + 15 = 150\). This matches the fourth term.
- Next, add 20 to the fourth term: \(150 + 20 = 170\). This matches the fifth term.
- Finally, add 15 to the fifth term: \(170 + 15 = 185\). This matches the sixth term.
The pattern of adding 15 and then 20 alternately perfectly fits the given series:
\(100 \xrightarrow{+15} 115 \xrightarrow{+20} 135 \xrightarrow{+15} 150 \xrightarrow{+20} 170 \xrightarrow{+15} 185\)
Therefore, the missing number in the series is 135.
Checking the Options
The options provided are:
- A. 135
- B. 130
- C. 140
- D. 145
Our calculated missing number, 135, matches Option A.
Conclusion
The number that comes in place of the question mark in the series 100, 115, ?, 150, 170, 185 is 135.
Revision Table: Number Series Analysis
| Term Number | Term Value | Difference from Previous Term |
|---|---|---|
| 1 | 100 | - |
| 2 | 115 | \(115 - 100 = 15\) |
| 3 | 135 (Calculated) | \(135 - 115 = 20\) |
| 4 | 150 | \(150 - 135 = 15\) |
| 5 | 170 | \(170 - 150 = 20\) |
| 6 | 185 | \(185 - 170 = 15\) |
Additional Information: Types of Number Series Patterns
Number series questions are common in aptitude tests and logical reasoning sections. Understanding different types of patterns can help solve them quickly. Some common types include:
- Arithmetic Series: A constant difference between consecutive terms (e.g., 2, 4, 6, 8...).
- Geometric Series: A constant ratio between consecutive terms (e.g., 2, 4, 8, 16...).
- Difference Series: The differences between consecutive terms form their own pattern, which might be an arithmetic series, geometric series, or another type (like the alternating difference pattern seen in this question).
- Square/Cube Series: The terms are squares or cubes of natural numbers, or related to them (e.g., 1, 4, 9, 16... or 1, 8, 27, 64...).
- Fibonacci Series: Each term is the sum of the two preceding terms (e.g., 0, 1, 1, 2, 3, 5, 8...).
- Mixed Series: A combination of two or more patterns, sometimes applied alternately to terms.
Practice is key to recognizing these various number series patterns.
Important Questions from Missing Number
Select the number that can replace the question mark (?) in the following pattern.
5
6
7
8
9
115
206
?
502
719
What function does the public key serve in digital signature verification?
Which of the following is an example of multi-factor authentication for PC security?
Find the missing term in the following question:
Which of the following numbers will replace the question mark (?) in the given series?
43, 45, 48, 53, 60, 71, ?
