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# How many different three-digit multiples of 5 can be

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Director
Joined: 11 Jun 2007
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How many different three-digit multiples of 5 can be [#permalink]

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28 Oct 2007, 13:19
00:00

Difficulty:

15% (low)

Question Stats:

77% (00:47) correct 23% (00:50) wrong based on 179 sessions

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How many different three-digit multiples of 5 can be composed of digits 2, 3, 4, and 5 if none of the digits is repeated?

A. 3
B. 6
C. 10
D. 12
E. 18
[Reveal] Spoiler: OA

Last edited by Bunuel on 17 Dec 2013, 01:58, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.

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Director
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28 Oct 2007, 13:31
never mind i think i got it.

since we can only use 2,3,4, and 5. units digit must be 5

so for possible combinations of xy5

it would be 235, 325, 245, 425, 345, 435

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CEO
Joined: 21 Jan 2007
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19 Nov 2007, 09:37
GMAT TIGER wrote:
beckee529 wrote:
How many different three-digit multiples of 5 can be composed of digits 2, 3, 4, and 5 if none of the digits is repeated?

3
6
10
12
18

= 3c2 x 2 = 6

can you explain your method. i solved it differently

XYZ, where Z must be 5. therefore 1 variation of digit in Z.
Y can be any of the 3 possible choices.
X can be any of the 2 possible choices.

2+3+1= 6

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Intern
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Re: How many different three-digit multiples of 5 can be [#permalink]

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16 Dec 2013, 20:52
I don't get why the combination is multiplied by two? i solved by writing out the different possibilities

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Veritas Prep GMAT Instructor
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Re: How many different three-digit multiples of 5 can be [#permalink]

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16 Dec 2013, 21:46
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legitpro wrote:
I don't get why the combination is multiplied by two? i solved by writing out the different possibilities

Available: 2, 3, 4, 5

You need to make 3 digit numbers which are multiples of 5.
___ ___ ___

For the number to be a multiple of 5, it must end with either 0 or 5. We only have 5 available so the number must end with 5.

___ ___ 5

Now you select 2 numbers out of the leftover 3 numbers (2, 3 and 4) in 3C2 ways and arrange them in the 2 places in 2! ways which gives you 3C2*2! = 6

or you can say that you can select a number for the hundreds place in 3 ways and select a number for the tens place in 2 ways (since numbers cannot be repeated). So you can make the number in 3*2 = 6 ways
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Re: How many different three-digit multiples of 5 can be [#permalink]

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26 Jul 2015, 13:10
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: How many different three-digit multiples of 5 can be   [#permalink] 26 Jul 2015, 13:10
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