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# How many integers divisible by 3 are there between 10! and

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CEO
Joined: 29 Mar 2007
Posts: 2593
Followers: 16

Kudos [?]: 183 [0], given: 0

How many integers divisible by 3 are there between 10! and [#permalink]  16 Oct 2007, 09:41
00:00

Difficulty:

(N/A)

Question Stats:

100% (01:21) correct 0% (00:00) wrong based on 3 sessions
How many integers divisible by 3 are there between 10! and 10! +20 inclusive?

6
7
8
9
10
Manager
Joined: 02 Aug 2007
Posts: 146
Followers: 1

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

Here's how I would approach this one:
(10! + 20) - 10! = 20 total integers

Since 10! doesn't include the integer 0, there are 20 integers possible. So 20 / 3 = 6 2/3 or 6 integers.

A. 6
CEO
Joined: 29 Mar 2007
Posts: 2593
Followers: 16

Kudos [?]: 183 [0], given: 0

yuefei wrote:
Here's how I would approach this one:
(10! + 20) - 10! = 20 total integers

Since 10! doesn't include the integer 0, there are 20 integers possible. So 20 / 3 = 6 2/3 or 6 integers.

A. 6

I said 6 too. This is a challenges problem, but I think the answer 7 is incorrect.

it says between 10! and 10! +20, so im guessin its a mistake.
Manager
Joined: 02 Oct 2007
Posts: 112
Followers: 1

Kudos [?]: 1 [0], given: 0

B - 7

10! is divisible by 3 - The way I look Factorials is that any number included will also be divisible by the product. 10,9,8,7,6,5,4,3,2,1 are all divisors of 10!

There are 6 numbers between 10! and 10!+20 that are divisible by 3.

Hence 7
CEO
Joined: 29 Mar 2007
Posts: 2593
Followers: 16

Kudos [?]: 183 [0], given: 0

JDMBA wrote:
B - 7

10! is divisible by 3 - The way I look Factorials is that any number included will also be divisible by the product. 10,9,8,7,6,5,4,3,2,1 are all divisors of 10!

There are 6 numbers between 10! and 10!+20 that are divisible by 3.

Hence 7

Im just not getting this problem.

I know 10! is divisible by 3. U can just add up the digits of 10! and see that its divisible by 3. But...

it says the numbers between 10! and 10! +20, why are we including 10!??????

Last edited by GMATBLACKBELT on 16 Oct 2007, 10:14, edited 1 time in total.
CEO
Joined: 29 Mar 2007
Posts: 2593
Followers: 16

Kudos [?]: 183 [0], given: 0

OlgaN wrote:
GMATBLACKBELT wrote:
yuefei wrote:
The question says "Inclusive"

Bah

Look, it is very simple. Try this: how many numbers from 1 to 100 inclusive? Not 100-1=99 NO NO NO It is 100-99+1=100. What is 1 here? It is the fist number in your question : 10!. You must count it if it is divisible by 3.

Do not be upset. I have known this only yesterday. My tutor explained it to me.

Thx, I get it, I just hate that I missed the "inclusive" part.

Like a problem the other day i did from MGMAT.

http://www.gmatclub.com/forum/t53866

For some reason my brain was saying .9^2 is already multplied by itself, you dont have to do .9^2*.9^2. I hate it when I get like this, my mind refuses to look at the obvious =(
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