In each of the following question a number series is a given. After the series, a number is given followed by (a),(b),(c),(d) and (e). You have to complete the series starting with the number given following the sequence of the given series. Then answer the given questions.
200 184 193 157 182 118 167
150 (a) (b) (c) (d) (e)
. Which of the following numbers will cone in place of (e) ?

Options

A. 132
B. 115
C. 68
D. 117

Answer

To solve the given number series problem, we will analyze the provided series and find the pattern to determine the missing values, specifically the value that will replace (e).

### Given Series:
200, 184, 193, 157, 182, 118, 167

### Steps to Solve:

1. **Identify the Pattern:**
- Let's look at the differences between consecutive numbers:
- 200 to 184: 200 - 184 = 16 (decrease)
- 184 to 193: 193 - 184 = 9 (increase)
- 193 to 157: 193 - 157 = 36 (decrease)
- 157 to 182: 182 - 157 = 25 (increase)
- 182 to 118: 182 - 118 = 64 (decrease)
- 118 to 167: 167 - 118 = 49 (increase)

- The differences are:
- Decrease: 16, 36, 64
- Increase: 9, 25, 49

2. **Recognize the Pattern in Differences:**
- The decrease values (16, 36, 64) are squares of 4, 6, and 8 respectively (4^2, 6^2, 8^2).
- The increase values (9, 25, 49) are squares of 3, 5, and 7 respectively (3^2, 5^2, 7^2).

3. **Continuing the Pattern:**
- The next decrease should be the square of 10 (10^2 = 100).
- The next increase should be the square of 9 (9^2 = 81).

4. **Starting with 150:**
- Now we will start with the number 150 and apply the identified pattern.
- First, we decrease by 16 (the first decrease):
- 150 - 16 = 134 (this will be (a))
- Next, we increase by 9 (the first increase):
- 134 + 9 = 143 (this will be (b))
- Next, we decrease by 36 (the second decrease):
- 143 - 36 = 107 (this will be (c))
- Next, we increase by 25 (the second increase):
- 107 + 25 = 132 (this will be (d))
- Finally, we decrease by 64 (the third decrease):
- 132 - 64 = 68 (this will be (e))

### Conclusion:
The value that will replace (e) is **68**.