{ 30,31,32,....,100 }
How many numbers in the above set are divisible by 8 ?
a. 9
b. 10
c. 11
d. 12
e. 13
please answer and explain
Multiples of 8:
32, 40, 48, 56, 64, 72, 80, 88, 96
only 1 in 8 will be divisible, so divide by 8.
(100-30+1)/8 = 8.8
so, there appear to be only 8 multiples of 8 in that set.
But, the non-multiples on either end take up some of the candidate spots. So, start just after the smallest multiple of 8:
(100-31)/8 = 8.6
So, there are 8 multiples of 8 between 33 and 100, as well. Add in 32, and we have 9 altogether:
32 40 48 56 64 72 80 88 96
To determine how many numbers in the set {30, 31, 32, ..., 100} are divisible by 8, we need to find the count of numbers that satisfy the given condition.
To find numbers that are divisible by 8, we look for numbers that have a remainder of 0 when divided by 8.
We can start by finding the smallest number in the set that is divisible by 8. In this case, it is 32. Then, we find the largest number in the set that is divisible by 8. In this case, it is 96.
To find the count of numbers between 32 and 96 inclusive that are divisible by 8, we can subtract 31 (the number before 32) from 96, divide the result by 8, and add 1 to include the starting number 32.
(96 - 31) ÷ 8 + 1 = 13
So, there are 13 numbers in the set {30, 31, 32, ..., 100} that are divisible by 8.
Therefore, the answer is e. 13.