M7,Q14 : Retired Discussions [Locked]
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# M7,Q14

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Senior Manager
Joined: 17 May 2010
Posts: 299
GMAT 1: 710 Q47 V40
Followers: 4

Kudos [?]: 48 [0], given: 7

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07 Aug 2011, 12:13
What is the number of integers from 1 to 1000 (inclusive) that are divisible by neither 11 nor by 35?

884
890
892
910
945
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Senior Manager
Joined: 17 May 2010
Posts: 299
GMAT 1: 710 Q47 V40
Followers: 4

Kudos [?]: 48 [0], given: 7

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07 Aug 2011, 12:17
The explanation says

"To count the number of integers from 1 to $$N$$ (inclusive) that are divisible by $$x$$ , find the value of $$\frac{N}{x}$$ "

But MGMAT says

(Last-First)/Increment + 1.

How come these two are different?

Also in the explanation, the 1000/11 figure is rounded down, even though the number is 90.9. Why not round it up?
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Manager
Joined: 26 Oct 2010
Posts: 82
Followers: 0

Kudos [?]: 7 [0], given: 10

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09 Aug 2011, 14:40
Let's try to understand the logic behind the formula by taking a smaller example. How many nos are there between 1 to9 that are divisible by 2 ?
Going over the multiples of 2 - 2,4,6,8 , i.e. 4
9/2 = 4.5 ...rounds down to 4.
If we round it up, we are including 10 as well. That is why it is important to round down for these examples.

As for the formulae that you have listed, I would use the first formula, the second formula seems to be taken out of context.
Re: M7,Q14   [#permalink] 09 Aug 2011, 14:40
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# M7,Q14

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