Select the number from among the given options that can replace the question mark (?) in the following series. 264, 288, 312, ?, 360, 384
336
Finding the Missing Number in the Series
The question asks us to identify the number that should replace the question mark (?) in the given series: 264, 288, 312, ?, 360, 384.
To solve a number series problem, we need to find the underlying pattern that relates the numbers in the sequence.
Analyzing the Number Series Pattern
Let's look at the differences between consecutive terms in the series where the numbers are known.
- Difference between the second and first term: \(288 - 264\)
- Difference between the third and second term: \(312 - 288\)
- Difference between the sixth and fifth term: \(384 - 360\)
| Terms | Difference |
|---|---|
| 288 and 264 | \(288 - 264 = 24\) |
| 312 and 288 | \(312 - 288 = 24\) |
| 384 and 360 | \(384 - 360 = 24\) |
From the calculations above, we observe a consistent difference of 24 between consecutive terms. This suggests that the series is an arithmetic progression where each term is obtained by adding 24 to the previous term.
Calculating the Missing Term
Following this pattern, the missing term (?) should be obtained by adding 24 to the term before it, which is 312.
Missing Term = Term before ? + 24
Missing Term = \(312 + 24\)
Missing Term = \(336\)
Verifying the Pattern
Let's verify if adding 24 to the calculated missing term (336) gives the next term in the series, which is 360.
\(336 + 24 = 360\)
Yes, it matches the given series. The pattern holds true.
Thus, the missing number in the series is 336.
Conclusion
The series is 264, 288, 312, 336, 360, 384, with a common difference of 24.
Looking at the given options, the number 336 is one of the choices.
The final answer is 336.
| Option | Value | Matches Missing Term? |
|---|---|---|
| 1 | 324 | No |
| 2 | 348 | No |
| 3 | 342 | No |
| 4 | 336 | Yes |
Revision Table: Number Series Concepts
| Concept | Description | Example Pattern |
|---|---|---|
| Arithmetic Series | Each term is obtained by adding a fixed number (common difference) to the previous term. | Adding a constant value (e.g., +5, -10) |
| Geometric Series | Each term is obtained by multiplying the previous term by a fixed number (common ratio). | Multiplying by a constant value (e.g., ×2, ×0.5) |
| Difference Series | The differences between consecutive terms follow a pattern (e.g., arithmetic, geometric). | Differences are +2, +4, +6, ... |
| Mixed Series | Combinations of different patterns (e.g., alternating operations, multiple series). | Alternating + / × operations |
Additional Information: Solving Number Series
Solving number series problems often involves identifying the rule that generates the sequence. Here are some common strategies:
- Calculate the differences between consecutive terms. If the differences are constant, it's an arithmetic series. If the differences themselves form a pattern, analyze that pattern.
- Calculate the ratios between consecutive terms. If the ratios are constant, it's a geometric series.
- Look for patterns involving squares, cubes, prime numbers, or Fibonacci numbers.
- Consider alternating patterns or combined operations (e.g., add then subtract, multiply then add).
- Break down complex series into simpler sub-series if possible.
Practice with different types of series helps in quickly recognizing patterns.
Important Questions from Number Series
- In the following number-pairs, the second number is obtained by applying certain mathematical operations to the first number. Which numbers should replace X and Y so that the pattern followed by the two numbers on the left side of :: is the same as that on the right side of :: ?
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 - Operations on 13 such as adding /subtracting /multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
X : 676 :: 17 : Y - Which of the following options should come in place of the question mark (?) in the given series to make it logically complete?
125, 128, 133, 140, 149,? - What should come in place of the question mark (?) in the given series?
801 800 792 765 701 ? - What should come in place of the question mark (?) in the given series?
101 110 121 134 149 ? - What should come in place of the question mark (?) in the given series?
40, 48, 58, 66, 76, ?
