MathRevolution 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

First integer divisible by \(2\) on the list is \(50\) and last is \(100\).

Divide them by \(2\): \(25\) and \(50\) respectively. So, there are \(50-25+1=26\) integers that are divisible by \(2\).

First integer divisible by 3 on the list is 51 and last is 99.

Divide them by \(3\): \(17\) and \(33\) respectively. So, there are \(33-17+1=17\) integers that are divisible by \(3\).

Pay attention that some integers are divisible by both \(2\) and \(3\). So, they are divisible by \(6\). We have to exclude this overlap.

Thus, first integer divisible by 6 on the list is 54 and last is 96.

Divide them by \(6\): \(9\) and \(16\) respectively. So, there are \(16-9+1=8\) integers that are divisible by \(6\).

\(26-8=18\) integers are divisible by \(2\), but not by \(3\).

\(17-8=9\) integers are divisible by \(3\), but not by \(2\).

\(8\) integers are divisible by both \(2\) and \(3\).

Thus, overall \(18+9+8=35\) integers are divisible by \(2\) or \(3\).

It took about two minutes to solve the question.

Answer: A
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Kindest Regards!

Tulkin.