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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Sat Nov 30, 2013 7:05 am
[email protected] wrote:Just want to know what is mean when we write 10!+20, I man how do u simply this?

Thanks
10! + 20 = (10)(9)(8)..(3)(2)(1) + 20

The GMAT would never require you to actually evaluate this (too many tedious calculations)

Cheers,
Brent
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by [email protected] » Sat Nov 30, 2013 7:09 am
Thanks Brent, the question is how many numbers between 10! and 10!+20 are divisible by 3.



Brent@GMATPrepNow wrote:
[email protected] wrote:Just want to know what is mean when we write 10!+20, I man how do u simply this?

Thanks
10! + 20 = (10)(9)(8)..(3)(2)(1) + 20

The GMAT would never require you to actually evaluate this (too many tedious calculations)

Cheers,
Brent
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GMAT/MBA Expert

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by Brent@GMATPrepNow » Sat Nov 30, 2013 7:21 am
[email protected] wrote:How many numbers from 10! to 10!+20 inclusive, are divisible by 3?
NOTE: I reworded the question to avoid ambiguity.

There's a nice rule that says: If M is divisible by k, and N is divisible by k, then (M + N) is divisible by k.

First, since 10! = (10)(9)(8)..(3)(2)(1), we know that 10! is divisible by 3.

So, by the above rule, we know that 10! + 3 is divisible by 3
And 10! + 6 is divisible by 3
10! + 9 is divisible by 3
10! + 12 is divisible by 3
10! + 15 is divisible by 3
10! + 18 is divisible by 3

So, there are 7 integers from 10! to 10! + 20 inclusive that are divisible by 3.

Cheers,
Brent
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