How many 7's are there in the following number series which are preceded by an even number but not followed by any odd number ? 437523721367542742712276572

Question

Accepted Answer

To determine how many '7's in the given number series are preceded by an even number but not followed by any odd number, we need to analyze the series step by step according to the given conditions.

The number series is: 437523721367542742712276572

Let's break down the series and identify the '7's that meet the criteria:

1. **437523721367542742712276572**

- **First '7'**: In "437", '7' is preceded by '3' (odd), so it doesn't meet the criteria.
   - **Second '7'**: In "5237", '7' is preceded by '2' (even) and followed by '3' (odd), so it doesn't meet the criteria.
   - **Third '7'**: In "2372", '7' is preceded by '3' (odd), so it doesn't meet the criteria.
   - **Fourth '7'**: In "7213", '7' is preceded by '2' (even) and followed by '1' (odd), so it doesn't meet the criteria.
   - **Fifth '7'**: In "3675", '7' is preceded by '6' (even) and followed by '5' (odd), so it doesn't meet the criteria.
   - **Sixth '7'**: In "5427", '7' is preceded by '2' (even) and followed by '4' (even), so it meets the criteria.
   - **Seventh '7'**: In "4274", '7' is preceded by '4' (even) and followed by '2' (even), so it meets the criteria.
   - **Eighth '7'**: In "7427", '7' is preceded by '4' (even) and followed by '2' (even), so it meets the criteria.
   - **Ninth '7'**: In "2712", '7' is preceded by '2' (even) and followed by '1' (odd), so it doesn't meet the criteria.
   - **Tenth '7'**: In "1227", '7' is preceded by '2' (even) and followed by '6' (even), so it meets the criteria.
   - **Eleventh '7'**: In "2765", '7' is preceded by '6' (even) and followed by '5' (odd), so it doesn't meet the criteria.
   - **Twelfth '7'**: In "6572", '7' is preceded by '5' (odd), so it doesn't meet the criteria.

From the analysis, we find that there are **4** '7's that are preceded by an even number and not followed by an odd number. These are the sixth, seventh, eighth, and tenth '7's in the series.

**Explanation of Options:**

- **Option 1 (3)**: Incorrect because we identified 4 '7's that meet the criteria, not 3.
- **Option 2 (4)**: Correct because there are exactly 4 '7's that meet the criteria.
- **Option 3 (1)**: Incorrect because there are more than 1 '7' that meet the criteria.
- **Option 4 (2)**: Incorrect because there are more than 2 '7's that meet the criteria.

Thus, the correct answer is Option 4, which states that there are 4 '7's that meet the specified conditions.