Which of the following numbers will replace the question mark (?) in the given series:
\
20, 25, 25, 35, 30, 45, ?, 55, 40?

Question

Which of the following numbers will replace the question mark (?) in the given series:  
\
 20, 25, 25, 35, 30, 45, ?, 55, 40?

Accepted Answer

Let's analyze the series: 20, 25, 25, 35, 30, 45, ?, 55, 40

Step 1: Separate the series into two interleaved sequences:  
- Odd positions: 20 (1st), 25 (3rd), 30 (5th), ? (7th), 40 (9th)   
- Even positions: 25 (2nd), 35 (4th), 45 (6th), 55 (8th)
 
Step 2: Analyze the odd position sequence:
20, 25, 30, ?, 40  
The pattern here is increasing by 5:  
20 + 5 = 25  
25 + 5 = 30  
30 + 5 = 35 (missing number)  
35 + 5 = 40

Step 3: Analyze the even position sequence:
25, 35, 45, 55  
The pattern is increasing by 10:  
25 + 10 = 35  
35 + 10 = 45  
45 + 10 = 55

Step 4: Therefore, the missing number at the 7th position is 35.

However, the options given are 50, 60, 30, 35. The correct missing number is 35.

Rechecking the series with 35 at the 7th position:
20, 25, 25, 35, 30, 45, 35, 55, 40

But the 3rd term is 25, which is the same as the 2nd term, which breaks the pattern.

Alternative approach:  
Look at the differences between consecutive terms:  
25 - 20 = +5    
25 - 25 = 0   
35 - 25 = +10   
30 - 35 = -5   
45 - 30 = +15   
? - 45 = ?  
55 - ? = ?  
40 - 55 = -15

The pattern of differences seems to be alternating positive and negative:    
+5, 0, +10, -5, +15, ?, ?, -15

The positive differences increase by 5: +5, +10, +15    
The negative differences seem to be -5, then missing, then -15

Assuming the missing negative difference is -10:  
? - 45 = -10 => ? = 35  
55 - ? = +20 (which does not fit the pattern)

Alternatively, if the missing number is 50:  
? = 50  
Then 55 - 50 = +5  
Differences: +5, 0, +10, -5, +15, +5, +5, -15 (doesn't fit well)

If the missing number is 60:
? = 60  
55 - 60 = -5   
Differences: +5, 0, +10, -5, +15, +15, -5, -15   (doesn't fit well)

If the missing number is 30:  
? = 30  
55 - 30 = +25  
Doesn't fit the pattern.

Given the best fit is 35, but 35 is option 4, so the correct answer is 35.

Hence, the missing number is 35.

Answer

Answer

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