Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 60460

If all of the telephone extensions in a certain company must be even
[#permalink]
Show Tags
23 Nov 2015, 12:42
Question Stats:
73% (01:24) correct 27% (01:30) wrong based on 264 sessions
HideShow timer Statistics
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 fourdigit extensions that the company can have? (A) 4 (B) 6 (C) 12 (D) 16 (E) 24
Official Answer and Stats are available only to registered users. Register/ Login.
_________________



GMAT Club Legend
Joined: 12 Sep 2015
Posts: 4214
Location: Canada

Re: If all of the telephone extensions in a certain company must be even
[#permalink]
Show Tags
23 Nov 2015, 12:57
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 fourdigit 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
_________________
Test confidently with gmatprepnow.com



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9032
Location: United States (CA)

Re: If all of the telephone extensions in a certain company must be even
[#permalink]
Show Tags
06 Mar 2018, 08:03
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 fourdigit 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
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



Manager
Joined: 27 Mar 2017
Posts: 108

Re: If all of the telephone extensions in a certain company must be even
[#permalink]
Show Tags
22 Nov 2019, 03:49
Half even and half odd numbers = 4!/2 = 12 (C)



GMAT Club Legend
Joined: 12 Sep 2015
Posts: 4214
Location: Canada

Re: If all of the telephone extensions in a certain company must be even
[#permalink]
Show Tags
23 Nov 2015, 12:51
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 fourdigit 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 4digit 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/gmatcounting/video/775Cheers, Brent
_________________
Test confidently with gmatprepnow.com



Intern
Joined: 02 Feb 2014
Posts: 4

Re: If all of the telephone extensions in a certain company must be even
[#permalink]
Show Tags
25 Nov 2015, 00:44
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



Manager
Joined: 04 May 2014
Posts: 147
Location: India
WE: Sales (Mutual Funds and Brokerage)

Re: If all of the telephone extensions in a certain company must be even
[#permalink]
Show Tags
23 Jun 2016, 18:22
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 fourdigit 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 4digit 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/gmatcounting/video/775Cheers, Brent



Intern
Joined: 05 May 2016
Posts: 35

Re: If all of the telephone extensions in a certain company must be even
[#permalink]
Show Tags
11 Jul 2016, 10:13
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 fourdigit 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 4digit 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/gmatcounting/video/775Cheers, 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!



Intern
Joined: 08 Jun 2016
Posts: 13

If all of the telephone extensions in a certain company must be even
[#permalink]
Show Tags
11 Jul 2016, 17:57
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, ThreeminusOne possibilities for the hundreds digit, ThreeminusTwo Possibilities for the tens digit and Two (2) is the units digit.
Therefore: 3*(31)*(32)*1 = 6
Option 2 (###6):
Three (1, 2, 3) possibilities for thousands digit, ThreeminusOne possibilities for the hundreds digit, ThreeminusTwo Possibilities for the tens digit and Six (6) is the units digit.
Therefore: 3*(31)*(32)*1 = 6
Add options together: 6 + 6 = 12 (C)



Intern
Joined: 25 Feb 2018
Posts: 5

Re: If all of the telephone extensions in a certain company must be even
[#permalink]
Show Tags
02 Mar 2018, 00:23
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



Director
Affiliations: IIT Dhanbad
Joined: 13 Mar 2017
Posts: 727
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)

Re: If all of the telephone extensions in a certain company must be even
[#permalink]
Show Tags
06 Apr 2018, 02:19
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 fourdigit 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




Re: If all of the telephone extensions in a certain company must be even
[#permalink]
06 Apr 2018, 02:19






