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If all of the telephone extensions in a certain company must be even [#permalink]
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23 Nov 2015, 12:42
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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, 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
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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, 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
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Re: If all of the telephone extensions in a certain company must be even [#permalink]
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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



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



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



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



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



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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, 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
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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, 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
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