{ 1,2.3,..........,210 }
How many numbers in the above set are multiples of 3 but not 9 ?
a. 46
b. 47
c. 48
d. 69
e. 70
please answer and explain
There are obviously 70 multiples of 3 (210/3 = 70)
So, how many multiples of 9 are there?
Figure the difference.
210/9=23.333
so 70-23 =47
answer b ?
Looks good to me.
To determine how many numbers in the set {1, 2, 3, ..., 210} are multiples of 3 but not 9, we can follow these steps:
1. Identify the first and last multiples of 3 within the given set.
- The first multiple of 3 in the set is 3.
- The last multiple of 3 in the set is 210.
2. Find the number of multiples of 3 within the set.
- Divide 210 by 3: 210 ÷ 3 = 70
- There are 70 multiples of 3 within the set.
3. Subtract the number of multiples of 3 that are also multiples of 9.
- Divide 210 by 9: 210 ÷ 9 = 23 remainder 3
- There are 23 multiples of 9 within the set.
- To find the number of multiples of 3 and 9, we divide 23 (the number of multiples of 9) by 3 since every third multiple of 9 is also a multiple of 3: 23 ÷ 3 = 7
4. Subtract the number of multiples of 3 and 9 from the total number of multiples of 3.
- 70 (total multiples of 3) - 7 (multiples of both 3 and 9) = 63
Therefore, there are 63 numbers in the set {1, 2, 3, ..., 210} that are multiples of 3 but not 9.
The correct answer is not listed among the options, so there may be a mistake in the provided answer choices.