How many 2-digit numbers are multiples of 2 but not 4?
23
pooop
How many two-digit numbers have unit digits 2, but are nor multiples of 4
69
23
To find the number of 2-digit numbers that are multiples of 2 but not 4, we can break it down into steps:
Step 1: Determine the range of 2-digit numbers.
A 2-digit number means any number between 10 and 99 (inclusive). So, the range is from 10 to 99.
Step 2: Identify the multiples of 2 within the range.
To find the multiples of 2, we need to consider the evens numbers within the range. The even numbers are those which are divisible by 2. In this case, it means numbers that end with 0, 2, 4, 6, or 8. Since we are looking for multiples of 2, we can exclude numbers ending with 0 since they are also multiples of 5, and we need numbers not divisible by 4. So, we consider the possibilities of numbers ending with 2, 4, 6, or 8.
The numbers ending with 2 that fall within the range are: 12, 22, 32, ..., 92. (Total: 9 numbers)
The numbers ending with 4 that fall within the range are: 14, 24, 34, ..., 94. (Total: 9 numbers)
The numbers ending with 6 that fall within the range are: 16, 26, 36, ..., 96. (Total: 9 numbers)
The numbers ending with 8 that fall within the range are: 18, 28, 38, ..., 98. (Total: 9 numbers)
Step 3: Count the numbers that are multiples of 2 but not 4.
From the numbers listed above, we need to exclude the numbers that are also multiples of 4 (those divisible by 4). The numbers divisible by 4 in each set are 24, 44, 64, 84 for the numbers ending with 2, 4, 6, and 8 respectively.
So, for each set, we subtract the count of numbers divisible by 4 from the total count:
For the numbers ending with 2: 9 - 1 = 8 numbers
For the numbers ending with 4: 9 - 2 = 7 numbers
For the numbers ending with 6: 9 - 2 = 7 numbers
For the numbers ending with 8: 9 - 2 = 7 numbers
Step 4: Calculate the total count.
To get the total count, we add the counts from each set:
8 + 7 + 7 + 7 = 29
So, there are a total of 29 two-digit numbers that are multiples of 2 but not 4.
there are 90 2-digit numbers, right?
half of them are even (multiples of 2)
1/4 of them are multiples of 4
so, that leaves 1/4 that are even, but not multiples of 4.
almost. why not exactly?