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# If all of the telephone extensions in a certain company must be even

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Joined: 02 Sep 2009
Posts: 52905
If all of the telephone extensions in a certain company must be even  [#permalink]

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23 Nov 2015, 11:42
00:00

Difficulty:

25% (medium)

Question Stats:

73% (01:26) correct 27% (01:35) wrong based on 252 sessions

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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?

(A) 4
(B) 6
(C) 12
(D) 16
(E) 24

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Joined: 11 Sep 2015
Posts: 3429
Re: If all of the telephone extensions in a certain company must be even  [#permalink]

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23 Nov 2015, 11:51
Bunuel 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, 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

Take the task of arranging the 4 digits and break it into stages.

We’ll begin with the most restrictive stage.

Stage 1: Select the digit in the units position
Since the 4-digit extension must be EVEN, the unit digit must be either 2 or 6
So, we can complete stage 1 in 2 ways

Stage 2: Select the tens digit
There are 3 remaining digits from which to choose, so we can complete this stage in 3 ways.

Stage 3: Select the hundreds digit
There are 2 digits remaining, so we can complete this stage in 2 ways.

Stage 4: Select the thousands digit
There 1 digit remaining, so we can complete this stage in 1 way.

By the Fundamental Counting Principle (FCP), we can complete all 4 stages (and thus create an even extension) in (2)(3)(2)(1) ways (= 12 ways)

NOTE: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. For more information about the FCP, watch our free video: http://www.gmatprepnow.com/module/gmat-counting/video/775

Cheers,
Brent
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Re: If all of the telephone extensions in a certain company must be even  [#permalink]

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23 Nov 2015, 11:57
1
Bunuel 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, 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

NOTE: Always SCAN the answer choices before performing any calculations.
Here, we notice that the answer choices are pretty small, so if we don't come up a full solution, we should consider LISTING AND COUNTING

We get the following extensions:
1236
1326
1362
1632
2136
2316
3126
3162
3216
3612
6132
6312
TOTAL = 12

For more on the benefits of Listing and Counting, see our free video - http://www.gmatprepnow.com/module/gmat- ... /video/773

Cheers,
Brent
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Joined: 02 Feb 2014
Posts: 4
Re: If all of the telephone extensions in a certain company must be even  [#permalink]

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24 Nov 2015, 23:44

Extension : abcd
Since all 4 nos. need to be in the extension, numbers cannot be repeated
d( can be either 2 or 6..) so 2 ways
c: 3 ways
b: 2 ways
a: 1 way

=2*2*3
=12
Manager
Joined: 03 May 2014
Posts: 158
Location: India
WE: Sales (Mutual Funds and Brokerage)
Re: If all of the telephone extensions in a certain company must be even  [#permalink]

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23 Jun 2016, 17:22
correct answer choice is C and not D.

GMATPrepNow wrote:
Bunuel 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, 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

Take the task of arranging the 4 digits and break it into stages.

We’ll begin with the most restrictive stage.

Stage 1: Select the digit in the units position
Since the 4-digit extension must be EVEN, the unit digit must be either 2 or 6
So, we can complete stage 1 in 2 ways

Stage 2: Select the tens digit
There are 3 remaining digits from which to choose, so we can complete this stage in 3 ways.

Stage 3: Select the hundreds digit
There are 2 digits remaining, so we can complete this stage in 2 ways.

Stage 4: Select the thousands digit
There 1 digit remaining, so we can complete this stage in 1 way.

By the Fundamental Counting Principle (FCP), we can complete all 4 stages (and thus create an even extension) in (2)(3)(2)(1) ways (= 12 ways)

NOTE: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. For more information about the FCP, watch our free video: http://www.gmatprepnow.com/module/gmat-counting/video/775

Cheers,
Brent
Intern
Joined: 05 May 2016
Posts: 36
Re: If all of the telephone extensions in a certain company must be even  [#permalink]

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11 Jul 2016, 09:13
gps5441 wrote:
correct answer choice is C and not D.

GMATPrepNow wrote:
Bunuel 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, 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

Take the task of arranging the 4 digits and break it into stages.

We’ll begin with the most restrictive stage.

Stage 1: Select the digit in the units position
Since the 4-digit extension must be EVEN, the unit digit must be either 2 or 6
So, we can complete stage 1 in 2 ways

Stage 2: Select the tens digit
There are 3 remaining digits from which to choose, so we can complete this stage in 3 ways.

Stage 3: Select the hundreds digit
There are 2 digits remaining, so we can complete this stage in 2 ways.

Stage 4: Select the thousands digit
There 1 digit remaining, so we can complete this stage in 1 way.

By the Fundamental Counting Principle (FCP), we can complete all 4 stages (and thus create an even extension) in (2)(3)(2)(1) ways (= 12 ways)

NOTE: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. For more information about the FCP, watch our free video: http://www.gmatprepnow.com/module/gmat-counting/video/775

Cheers,
Brent

Quote:
I got this answer in two steps.
Since the extension has to be an EVEN number, Unit's place can take ONLY two digits (either 2 or 6).
That leaves us with 3 numbers only.
So,

3! *2 = 12

Bunuel sir:
Please correct me if I am wrong.
Thanks again!

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Joined: 08 Jun 2016
Posts: 13
If all of the telephone extensions in a certain company must be even  [#permalink]

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11 Jul 2016, 16:57
There are two options for even telephone extensions: 2 or 6 is the units digit.

Option 1 (###2):

Three (1, 3, 6) possibilities for thousands digit, Three-minus-One possibilities for the hundreds digit, Three-minus-Two Possibilities for the tens digit and Two (2) is the units digit.

Therefore: 3*(3-1)*(3-2)*1 = 6

Option 2 (###6):

Three (1, 2, 3) possibilities for thousands digit, Three-minus-One possibilities for the hundreds digit, Three-minus-Two Possibilities for the tens digit and Six (6) is the units digit.

Therefore: 3*(3-1)*(3-2)*1 = 6

Add options together: 6 + 6 = 12 (C)
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Joined: 25 Feb 2018
Posts: 6
Re: If all of the telephone extensions in a certain company must be even  [#permalink]

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01 Mar 2018, 23:23
Extension : abcd
Since all 4 nos. need to be in the extension, numbers cannot be repeated
d( can be either 2 or 6..) so 2 ways
c: 3 ways
b: 2 ways
a: 1 way
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Re: If all of the telephone extensions in a certain company must be even  [#permalink]

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06 Mar 2018, 07:03
1
Bunuel 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, 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

If we let 6 be the last digit, then we have 3! = 6 options for the other 3 digits. If we let 2 be the last digit, we have 6 options also. Therefore, we have a total of 12 options.

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Re: If all of the telephone extensions in a certain company must be even  [#permalink]

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06 Apr 2018, 01:19
Bunuel 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, 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

X X X X
(Remaining 3 numbers) (Remaining 2 numbers) (Remaining 1 number) (2 or 6)
3 ways 2 ways 1 way 2 ways

Total Number of ways = 3*2*1*2 = 12 ways
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Re: If all of the telephone extensions in a certain company must be even   [#permalink] 06 Apr 2018, 01:19
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