How many integers between 50 and 100, inclusive, are divisi

Max@Math Revolution wrote:[GMAT math practice question]

How many integers between 50 and 100, inclusive, are divisible by 2 or 3?

A. 35
B. 37
C. 42
D. 47
E. 52

For this problem, we must recall that to calculate the number of integers in a range of values that are divisible by a certain number n, we use the formula: (largest multiple - smallest multiple)/n + 1. For example, to calculate the number of integers between 10 and 29 that are divisible by 3, we see that 27 is the largest multiple of 3 in that range of numbers, and 12 is the smallest multiple of 3. Thus, we have (27 - 12)/3 + 1 = 15/3 + 1 = 6.

The number of integers from 50 to 100, inclusive, that are divisible by 2 is:

(100 - 50)/2 + 1 = 26

The number of integers from 50 to 100, inclusive, that are divisible by 3 is:

(99 - 51)/3 + 1 = 17

Now we need to subtract the overlap, that is, we have to subtract the number of multiples of 6 because multiples of 6 were counted as both multiples of 2 and multiples of 3.

The number of integers from 50 to 100, inclusive, that are divisible by 6 is:

(96 - 54)/6 + 1 = 8

Thus, the number integers between 50 and 100, inclusive, that are divisible by 2 or 3 is 26 + 17 - 8 = 35.

Answer: A