In the following number sequence, how many times an odd number is immediately followed by an even number? 5 3 8 4 7 9 6 5 3 9 2 7 8 2 1 4 5 6 3 8 2 6 5 8 6 7
8
Counting Odd Followed by Even Numbers in a Sequence
The question asks us to find the number of times an odd number is immediately followed by an even number in the given number sequence. To solve this, we need to examine each pair of adjacent numbers in the sequence.
The given number sequence is: 5 3 8 4 7 9 6 5 3 9 2 7 8 2 1 4 5 6 3 8 2 6 5 8 6 7
We will go through the sequence from left to right and check each pair of consecutive numbers. A pair satisfies the condition if the first number is odd and the second number is even.
Let's analyze the sequence pair by pair:
- (5, 3): 5 is odd, 3 is odd. Does not meet the condition.
- (3, 8): 3 is odd, 8 is even. Meets the condition. Count = 1.
- (8, 4): 8 is even, 4 is even. Does not meet the condition.
- (4, 7): 4 is even, 7 is odd. Does not meet the condition.
- (7, 9): 7 is odd, 9 is odd. Does not meet the condition.
- (9, 6): 9 is odd, 6 is even. Meets the condition. Count = 2.
- (6, 5): 6 is even, 5 is odd. Does not meet the condition.
- (5, 3): 5 is odd, 3 is odd. Does not meet the condition.
- (3, 9): 3 is odd, 9 is odd. Does not meet the condition.
- (9, 2): 9 is odd, 2 is even. Meets the condition. Count = 3.
- (2, 7): 2 is even, 7 is odd. Does not meet the condition.
- (7, 8): 7 is odd, 8 is even. Meets the condition. Count = 4.
- (8, 2): 8 is even, 2 is even. Does not meet the condition.
- (2, 1): 2 is even, 1 is odd. Does not meet the condition.
- (1, 4): 1 is odd, 4 is even. Meets the condition. Count = 5.
- (4, 5): 4 is even, 5 is odd. Does not meet the condition.
- (5, 6): 5 is odd, 6 is even. Meets the condition. Count = 6.
- (6, 3): 6 is even, 3 is odd. Does not meet the condition.
- (3, 8): 3 is odd, 8 is even. Meets the condition. Count = 7.
- (8, 2): 8 is even, 2 is even. Does not meet the condition.
- (2, 6): 2 is even, 6 is even. Does not meet the condition.
- (6, 5): 6 is even, 5 is odd. Does not meet the condition.
- (5, 8): 5 is odd, 8 is even. Meets the condition. Count = 8.
- (8, 6): 8 is even, 6 is even. Does not meet the condition.
- (6, 7): 6 is even, 7 is odd. Does not meet the condition.
After checking all adjacent pairs in the number sequence, we found that the condition (odd number immediately followed by an even number) is met 8 times.
The pairs that satisfy the condition are (3, 8), (9, 6), (9, 2), (7, 8), (1, 4), (5, 6), (3, 8), and (5, 8).
Therefore, an odd number is immediately followed by an even number 8 times in the given sequence.
Revision Table: Key Points for Sequence Analysis
When analyzing number sequences for specific patterns like odd followed by even, keep these points in mind:
| Step | Description | Importance |
|---|---|---|
| Understand the Condition | Clearly identify what pattern you are looking for (e.g., odd followed by even). | Ensures you are checking for the correct pattern. |
| Check Adjacent Pairs | Analyze numbers two at a time, looking at a number and the one immediately after it. | The condition specifies "immediately followed by". |
| Systematic Scan | Go through the sequence from start to finish without skipping any pairs. | Avoids missing any occurrences of the pattern. |
| Careful Counting | Keep a clear count as you find each instance of the pattern. | Ensures accuracy in the final answer. |
Additional Information on Number Patterns
Number sequence questions often test your ability to identify patterns. The odd/even pattern is one type, but others include:
- Arithmetic Progression: Where the difference between consecutive terms is constant (e.g., 2, 4, 6, 8...).
- Geometric Progression: Where the ratio between consecutive terms is constant (e.g., 3, 9, 27, 81...).
- Fibonacci Sequence: Where each number is the sum of the two preceding ones (starting typically with 0 and 1 or 1 and 1) (e.g., 0, 1, 1, 2, 3, 5, 8...).
- Simple Arithmetic: Adding, subtracting, multiplying, or dividing a fixed number or a sequence of numbers.
- Alternating Patterns: Different rules applying to alternate numbers or alternate pairs.
Understanding the properties of numbers, like being odd or even, is fundamental to solving many types of number sequence and logical reasoning problems.
Important Questions from Number Arrangement
Select the set in which the numbers are related in the same way as are the numbers of the given sets.
( 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.)
(5, 60, 70)
(9, 108, 126)
How many 5s are there in the following number sequence which are immediately preceded by 7 and immediately followed by 6?
5 6 4 6 4 5 6 4 6 7 7 5 6 4 5 7 5 4 4 5 7 4 6 5 4
Select the option in which the numbers are related in the same way as are the numbers in the given set.
(131, 142, 153)
How many 5's are there in the given sequence which are neither immediately preceded by 1 nor immediately followed by 3?
1 3 5 5 3 1 4 8 3 6 7 7 1 5 3 1 5 3 8
Look at this series: G2, J8 _______ P32, S50 So what would be appropriate to fill in the blanks?
A. M12
B. H12
C. N10
D. Q10
