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If all of the telephone extensions in a certain company must [#permalink]
22 Jan 2005, 13:03

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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, and 6, what is the greatest number of four-digit extensions that the company can have?

Re: If all of the telephone extensions in a certain company must [#permalink]
23 Jan 2005, 16:27

Why is it not 48? (I know it's not an option)
Like 4*3*2*2?

Rationale:

We are combining 4 digit extensions which must be even numbers. ABCD i.e., D but be either 2 or 6 from the given digits 1, 2, 3, 6.
Now we are left with the first 3 spaces which can be filled with any of these 4 given digits 1, 2, 3 or 6 which implies 4*3*2.
I stand corrected though.

Re: PS telephones numbers [#permalink]
09 Jun 2005, 01:47

mandy wrote:

:) .hello Does anyone knows how to approach this one thanks PS 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, and 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 four digits available are 1,2,3 and 6
as the extensions can only be even numbers, the last digit has to be either 2 or 6
If it is 2...it leaves 1,3 and 6 for the first three digits...these can be arranged in 3! ways
If the last digit is 6...it leaves 1,2 and 3 for the first three digits...these can be arranged in 3! ways

Re: PS telephones numbers [#permalink]
09 Jun 2005, 08:24

mandy wrote:

:) .hello Does anyone knows how to approach this one thanks PS 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, and 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

4!/2 ,

The total no. extensions possible is 4!.
Of which, equal no. extns can be odd and even.
Hence the ones which are even is 4!/2.

[quote="surbab"]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, and 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

Please explain the answer.[/quote]

(C)

Let's see... the conditions are that:
- 4-digits telephone numbers
- the only digits we can consider are 1,2,3,6
- the telephone extensions must be even numbers, so they will finish in 2 or 6
- ALL the digits (1,2,3,6) should be used in the same telephone number

total # of even numbers = total # with final digit 2 + total # with final digit 6
= 3*2*1 (the 4th digit is nr. 2) + 3*2*1 (the 4th digit is nr. 6)
=12

The easiest way to solve this problem is to think the telephone number digit by digit.
e.g.
4th digit: it must be even, so lets assume that it finishes in 2 -> 1
1st digit: we have 3 options (1 or 3 or 6) -> 3
2nd digit: we have 2 options (1,3 or 1,6 or 3,6) -> 2
3rd digit: we have only 1 nr left (1 or 3 or 6) -> 1
When you multiply all the numbers calculated per digit you get the number of possibilities: 1*3*2*1 = 6

For the extension to be even the last digit should be 2 or 6.
Number of combinations with 2 be the last digit = 6
Number of combinations with 6 be the last digit = 6
Total possible cases = 12

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, and 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

Please explain the answer.

All possibilities for the combination of 4 digits is 4!=4x3x2x1= 24. Since we only need even numbers an we do have 2 even and 2 odd numbers it is 50% or 12!

Re: telephone extensions [#permalink]
09 Jun 2009, 15:04

1

This post received KUDOS

The answer is C.

You are on the right track..the total number of permutations is 4! = 24

However there is a restriction that all extensions should be even i.e. the last digit of each extension should be an even number i.e. the last digit should be either 2 or 6. As there are 2 even digits and two odd digits. Half of the permutations should be even and the remaining odd.

Re: telephone extensions [#permalink]
09 Jun 2009, 15:29

one more way.... let digit4 = 6, the 3! is the way to arrange rest 3 digit, so total 6 ways let digit4 = 2, the 3! is the way to arrange rest 3 digit, so total 6 ways

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.

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.

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

If you like my post, give me KUDOS!!

gmatclubot

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