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

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

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New post 23 Nov 2015, 11:42
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C
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Question Stats:

74% (01:26) correct 26% (01:36) wrong based on 242 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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Re: If all of the telephone extensions in a certain company must be even  [#permalink]

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New post 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)

Answer: D

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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New post 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
Answer: C

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

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New post 24 Nov 2015, 23:44
My answer: C

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

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New post 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)

Answer: D

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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New post 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)

Answer: D

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

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

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New post 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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New post 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.

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

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New post 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 &nbs [#permalink] 06 Apr 2018, 01:19
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