How many numbers between 101 and 1001 is divisible by 6 but not by 15?
Answers
Numbers between 101 and 1001 which are divisible by 6,
The first number is 102 while the last number is 996
This can be written in the form of an A.P.
102,108,114,.......................,996
Here, first term(a)=102
Last term (l)=996
Common difference(d)=6
We know that
an=a+(n-1)d
996=102+(n-1)6
=>894=6n-6
=>n=150 ....................Eq.(1)
Now the numbers which are divisible by 6 and 15 will be their LCM which is equal to 30
So, the first and last number divisible by 30 will be 120 and 990 respectively ,
This can be written in the form of an A.P.
120,150,....................,990.
Here,first term(a)=120
last term(l)=990
common difference(d)=30
We know that
an=a+(n-1)d
=>990=120+(n-1)30
=>870=30n-30
=>n=30 .................Eq.(2)
Subtracting Eq.(2) from Eq.(1)
We get 120 which the number of numbers which are divisible by 6 and not by 15 between 101 and 1001.
Answer: The number of numbers between 101 and 1001 that are divisible by 6 but not by 15 is 90.
Step-by-step explanation:
To find the number of numbers between 101 and 1001 that are divisible by 6 but not by 15, we need to follow a few steps.
Step 1: Find the first number that is divisible by 6 in the given range.
The first number that is divisible by 6 in the given range is 102.
Step 2: Find the last number that is divisible by 6 in the given range.
The last number that is divisible by 6 in the given range is 996.
Step 3: Find the number of numbers that are divisible by 6 in the given range.
To find the number of numbers that are divisible by 6 in the given range, we need to divide the last number that is divisible by 6 (996) by 6 and subtract it from the first number that is divisible by 6 (102) divided by 6 and add 1 to it.
So, the number of numbers that are divisible by 6 in the given range = [(996/6) - (102/6) + 1] = 149.
Step 4: Find the number of numbers that are divisible by 15 in the given range.
To find the number of numbers that are divisible by 15 in the given range, we need to divide the last number that is divisible by 15 (990) by 15 and subtract it from the first number that is divisible by 15 (105) divided by 15 and add 1 to it.
So, the number of numbers that are divisible by 15 in the given range = [(990/15) - (105/15) + 1] = 59.
Step 5: Find the number of numbers that are divisible by 6 and not by 15 in the given range.
The number of numbers that are divisible by 6 and not by 15 in the given range = the number of numbers that are divisible by 6 in the given range - the number of numbers that are divisible by 15 in the given range.
So, the number of numbers that are divisible by 6 and not by 15 in the given range = 149 - 59 = 90.
Therefore, the number of numbers between 101 and 1001 that are divisible by 6 but not by 15 is 90.
View more such questions :
https://brainly.in/question/35595436
#SPJ2