## Friday, November 26, 2010

### CP #20

What is the number of integers from 1 to 1000 (inclusive) that are divisible by neither 11 nor by 35?
(C) 2008 GMAT Club - [t]m07#14[/t]
• 884
• 890
• 892
• 910
• 945
To count the number of integers from 1 to $N$ (inclusive) that are divisible by $x$ , find the value of $\frac{N}{x}$ . Use only the integer part of the resulting number. Based on the formula, the number of integers divisible by 11 is $\frac{1000}{11} = 90.9 = 90$ (even though the result could be rounded off to 91, use 90). In the same way, the number of the integers divisible by 35 is $\frac{1000}{35} = 28.57 = 28$ .
Subtract the number of integers that are divisible by both 11 and 35, so that they are not counted twice.
Therefore, $\frac{1000}{11} + \frac{1000}{35} - \frac{1000}{11*35} = 90 + 28 - 2 = 116$ .
$1000-116 = 884$ .