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 [m]N[/m] (inclusive) that are divisible by [m]x[/m] , find the value of [m]\frac{N}{x}[/m] . Use only the integer part of the resulting number. Based on the formula, the number of integers divisible by 11 is [m]\frac{1000}{11} = 90.9 = 90[/m] (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 [m]\frac{1000}{35} = 28.57 = 28[/m] .
Subtract the number of integers that are divisible by both 11 and 35, so that they are not counted twice.
Therefore, [m]\frac{1000}{11} + \frac{1000}{35} - \frac{1000}{11*35} = 90 + 28 - 2 = 116[/m] .
[m]1000-116 = 884[/m] .
The correct answer is A.
 
 
 
My answer was right. Wanted to keep this here to understand why they've used 1000/ 11*35. What I did was calculate 33*11 and 33*11*2 and saw that both are under 1000 and then counted 2. I should know this other method too.

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