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In the following number sequence, how ma...

In the following number sequence, how many such even numbers are there which are exactly divisible by its immediate preceding number but not exactly divisible by its immediate following number?
3 8 4 1 5 7 2 8 3 4 8 9 3 9 4 21 5 8 2

A

one

B

Two

C

Three

D

Four

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to analyze the given sequence of numbers and identify the even numbers that meet the specified conditions. The conditions are: 1. The even number must be exactly divisible by its immediate preceding number. 2. The even number must not be exactly divisible by its immediate following number. Let's break down the solution step by step: ### Step 1: Identify the even numbers in the sequence The given sequence is: 3, 8, 4, 1, 5, 7, 2, 8, 3, 4, 8, 9, 3, 9, 4, 21, 5, 8, 2 The even numbers in this sequence are: - 8 - 4 - 2 - 8 - 4 - 8 - 2 ### Step 2: Check each even number against the conditions 1. **For the first even number (8)**: - Preceding number: 3 (3 does not divide 8) - Following number: 4 (8 is divisible by 4) - **Does not meet conditions.** 2. **For the second even number (4)**: - Preceding number: 8 (8 is divisible by 4) - Following number: 1 (4 is divisible by 1) - **Does not meet conditions.** 3. **For the third even number (2)**: - Preceding number: 7 (7 does not divide 2) - Following number: 8 (2 is not divisible by 8) - **Does not meet conditions.** 4. **For the fourth even number (8)**: - Preceding number: 2 (2 divides 8) - Following number: 3 (8 is not divisible by 3) - **Meets conditions.** 5. **For the fifth even number (4)**: - Preceding number: 8 (8 is divisible by 4) - Following number: 8 (4 is divisible by 8) - **Does not meet conditions.** 6. **For the sixth even number (8)**: - Preceding number: 4 (4 divides 8) - Following number: 9 (8 is not divisible by 9) - **Meets conditions.** 7. **For the seventh even number (2)**: - Preceding number: 21 (21 does not divide 2) - Following number: None (there is no number after 2) - **Does not meet conditions.** ### Step 3: Count the even numbers that meet the conditions From our checks, we found that the even numbers that meet the conditions are: - The first 8 (preceded by 2 and followed by 3) - The second 8 (preceded by 4 and followed by 9) Thus, there are **2 even numbers** that satisfy the conditions. ### Final Answer The total number of even numbers that are exactly divisible by their immediate preceding number but not by their immediate following number is **2**. ---
To solve the problem, we need to analyze the given sequence of numbers and identify the even numbers that meet the specified conditions. The conditions are: 1. The even number must be exactly divisible by its immediate preceding number. 2. The even number must not be exactly divisible by its immediate following number. Let's break down the solution step by step: ### Step 1: Identify the even numbers in the sequence ...
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