how many positive integers not exceeding 2001 are multiples of 3 or 4 but not 5
the numbers divisible by 3 = 667
by 4 = 500
by 4 = 500
if you draw your Venn Diagram you will find
the numbers divisible by 3 = 667
by 4 = 500
by 5 = 400
by 12 = 166
by 60 = 33 that means
by 15 = 133
by 20= 100
so the required answer will be 401+133+267=801
To find the number of positive integers not exceeding 2001 that are multiples of 3 or 4 but not 5, we can use the principle of inclusion-exclusion.
Step 1: Count the multiples of 3 not exceeding 2001.
To find the number of multiples of 3, we divide 2001 by 3:
2001 / 3 = 667
There are 667 multiples of 3 not exceeding 2001.
Step 2: Count the multiples of 4 not exceeding 2001.
To find the number of multiples of 4, we divide 2001 by 4:
2001 / 4 = 500.25
Since we are looking for positive integers, we round down to the nearest whole number:
500
There are 500 multiples of 4 not exceeding 2001.
Step 3: Count the multiples of 5 not exceeding 2001.
To find the number of multiples of 5, we divide 2001 by 5:
2001 / 5 = 400.2
Since we are looking for positive integers, we round down to the nearest whole number:
400
There are 400 multiples of 5 not exceeding 2001.
Step 4: Apply the principle of inclusion-exclusion.
To find the number of positive integers that are multiples of 3 or 4 but not 5, we need to subtract the number of multiples of 5 from the sum of the numbers of multiples of 3 and 4. However, we have counted the multiples of 3 and 4 that are also multiples of 5 twice, so we need to add them back once.
Number of multiples of 3 or 4 = Number of multiples of 3 + Number of multiples of 4 - Number of multiples of 5
= 667 + 500 - 400
= 767
Therefore, there are 767 positive integers not exceeding 2001 that are multiples of 3 or 4 but not 5.
I do not know ?
It looks like a pretty hard...... Question