How many 3 digit numbers are divisible by 4?a)256b)225c)198d)252e)120C...
B) 225
Explanation: A number is divisible by 4 when its last two digits are divisible by 4 For this the numbers should have their last two digits as 00, 04, 08, 12, 16, … 96 By the formula, a = a + (n-1)d 96 = 0 + (n-1)*4 n = 25 so there are 25 choices for last 2 digits and 9 choices (1-9) for the 1st digit so total 9*25
How many 3 digit numbers are divisible by 4?a)256b)225c)198d)252e)120C...
To find the number of 3-digit numbers divisible by 4, we need to consider the divisibility rule of 4. A number is divisible by 4 if the last two digits of the number are divisible by 4.
Let's analyze the possible values for the last two digits of a 3-digit number.
- The first digit can be any number from 1 to 9 (excluding 0) since a 3-digit number cannot start with 0.
- The second digit can be any number from 0 to 9, as there are no restrictions.
Now, we need to determine the number of possible pairs of two digits that are divisible by 4.
- To have a two-digit number divisible by 4, the last two digits can be the following possibilities: 04, 08, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96.
- There are 24 possible pairs.
Next, we need to consider the first digit. Since it cannot be zero, there are 9 possible values for the first digit.
To find the total number of 3-digit numbers divisible by 4, we multiply the number of possibilities for each digit:
9 (possible values for the first digit) * 10 (possible values for the second digit) * 24 (possible pairs of two digits) = 2160
However, we need to consider that some of these numbers may have repeating digits or zeroes. Therefore, we need to eliminate these cases.
- If the second digit is zero, the first digit can be any number from 1 to 9, giving us 9 possibilities.
- If there is a repeating digit, the second digit can be any number from 0 to 9 (excluding the repeating digit), giving us 9 possibilities.
- If there are two repeating digits, the second digit can be any number from 0 to 9 (excluding the repeating digits), giving us 8 possibilities.
So, the final number of 3-digit numbers divisible by 4 is:
2160 - 9 (numbers with a zero as the second digit) - 9 (numbers with repeating digits) - 8 (numbers with two repeating digits) = 2134
Since none of the given options matches the calculated value, it seems there might be an error in the options provided.