ssarkar wrote:
What is the total number of integers between 100 and 200 that are divisible by 3?
(A) 33
(B) 32
(C) 31
(D) 30
(E) 29
In a set of consecutive integers, you'd expect about 1/3 of the numbers to be divisible by 3, since multiples of 3 are 3 apart, so A is the only reasonable answer here. There are many ways to do this rigorously. We can list all of the multiples of 3 in the given range - here it is useful to know that a number is divisible by 3 if the sum of its digits is divisible by 3. So 102 is the smallest multiple of 3 in the range, and 198 is the largest. We thus need to count how many numbers are in this list:
102, 105, 108, ..., 192, 195, 198
This is an equally spaced list; you can use the formula:
n = (largest - smallest) / ('space') + 1 = (198 - 102) / (3) + 1 = 96/3 + 1 = 32 + 1 = 33
Or if you don't want to use a formula, you could just divide everything in the list by 3:
34, 35, 36, ...., 64, 65, 66
then subtract 33 from each of these numbers:
1, 2, 3, ..., 31, 32, 33
to see that there must be 33 numbers in our original list.
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