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# A math problem

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Manager
Status: Single
Joined: 05 Jun 2011
Posts: 135
Location: Shanghai China
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A math problem [#permalink]  24 Jul 2011, 02:59
00:00

Difficulty:

5% (low)

Question Stats:

54% (02:30) correct 45% (00:48) wrong based on 11 sessions
If all of the telephone extensions in a certain company must be even numbers, and if each of the extensions uses all four of the digits 1, 2,3,6, what is the greatest number of four-digit extensions that the company can have?

a)4
b)6
c)12
d)16
e)24

pls help
[Reveal] Spoiler: OA
Manager
Joined: 31 May 2011
Posts: 95
Location: India
Concentration: Finance, International Business
GMAT Date: 12-07-2011
GPA: 3.22
WE: Information Technology (Computer Software)
Followers: 1

Kudos [?]: 24 [0], given: 4

Re: A math problem [#permalink]  24 Jul 2011, 05:55
tracyyahoo wrote:
If all of the telephone extensions in a certain company must be even numbers, and if each of the extensions uses all four of the digits 1, 2,3,6, what is the greatest number of four-digit extensions that the company can have?

a)4
b)6
c)12
d)16
e)24

pls help

The number has to be even hence the 4 digit number should end with either 2 or 6. Secondly the question states that all the numbers must be used hence repetitions are not allowed.

Hence: We can have _ _ _ 2 or _ _ _ 6. So now we need to only fill 3 places with digits 1,6,3 or 1,2,3 respectively
Hence 3!*2 = 12.

C
Manager
Status: Single
Joined: 05 Jun 2011
Posts: 135
Location: Shanghai China
Followers: 2

Kudos [?]: 4 [0], given: 0

Re: A math problem [#permalink]  25 Jul 2011, 02:20
Could u explain more details?

uote="Sudhanshuacharya"]
tracyyahoo wrote:
If all of the telephone extensions in a certain company must be even numbers, and if each of the extensions uses all four of the digits 1, 2,3,6, what is the greatest number of four-digit extensions that the company can have?

a)4
b)6
c)12
d)16
e)24

pls help

The number has to be even hence the 4 digit number should end with either 2 or 6. Secondly the question states that all the numbers must be used hence repetitions are not allowed.

Hence: We can have _ _ _ 2 or _ _ _ 6. So now we need to only fill 3 places with digits 1,6,3 or 1,2,3 respectively
Hence 3!*2 = 12.

C[/quote]

Posted from my mobile device
Manager
Joined: 24 Aug 2008
Posts: 233
Location: India
WE 1: 3.75 IT
WE 2: 1.0 IT
Followers: 2

Kudos [?]: 26 [0], given: 5

Re: A math problem [#permalink]  25 Jul 2011, 03:08
If all of the telephone extensions in a certain company must be even numbers, and if each of the extensions uses all four of the digits 1, 2,3,6, what is the greatest number of four-digit extensions that the company can have?

a)4
b)6
c)12
d)16
e)24

The number for the telephone extension has to be even and 4 digit. Hence the 4 digit number should end with either 2 or 6.
Also, the question states that all the numbers must be used because we are talking about greatest number of four-digit extensions.

So, we can have _ _ _ 2 or _ _ _ 6 as four digit even extensions.
if the last number is 2 i.e. _ _ _ 2, the blanks can be filled by number 1, 6, 3 and they can be arranged in 3! ways.
In the same manner if the last number is 6 i.e. _ _ _ 6, the blanks can be filled by number 1, 2, 3 and they can be arranged in 3! ways.

Greatest number of four-digit extensions = 3!*2 = 12.
_________________

Cheers,
Varun

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Re: A math problem   [#permalink] 25 Jul 2011, 03:08
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# A math problem

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