Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized for You
we will pick new questions that match your level based on your Timer History
Track Your Progress
every week, we’ll send you an estimated GMAT score based on your performance
Practice Pays
we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
Join the live F2F session with the Admission Directors from Rotman School of Management and Ivey Business School to find out why Canada is increasingly becoming the go-to destination for several MBA aspirants, and gain critical insights....
A live session in which Greg Guglielmo, Haas MBA & Founder of Avanti Prep, analyses resumes of MBA applicants, and suggests ways of improvement in one on one talk with concerned applicants.
Leadership is one of the most important characteristics schools look for in applicants. This session will help define exactly what leadership is and how you can best showcase it in your essays.
Start by taking a free, full-length practice test—at your convenience. Receive a detailed score analysis to understand your strengths and see where you need to improve.
GMAT tests your ability to think critically by presenting "tricky" arguments that require you to notice flaws or vulnerabilities in the construct. e-GMAT is conducting a free webinar in which you can learn the art to decode difficult CR questions.
Attend a Veritas Prep GMAT Class for Free. With free trial classes you can work with a 99th percentile expert free of charge. Learn valuable strategies and find your new favorite instructor; click for a list of upcoming dates and teachers.
Will must choose a 3-character computer password, consisting of 1 lett
[#permalink]
Show Tags
04 Aug 2016, 10:12
1
Top Contributor
17
00:00
A
B
C
D
E
Difficulty:
95% (hard)
Question Stats:
42% (01:51) correct 58% (01:44) wrong based on 265 sessions
HideShow timer Statistics
Will must choose a 3-character computer password, consisting of 1 letter from the alphabet and 2 distinct digits, in any order.From how many different passwords can Will choose?
Re: Will must choose a 3-character computer password, consisting of 1 lett
[#permalink]
Show Tags
05 Aug 2016, 09:34
5
Top Contributor
5
AbdurRakib wrote:
Will must choose a 3-character computer password, consisting of 1 letter from the alphabet and 2 distinct digits, in any order.From how many different passwords can Will choose?
A. 390 B. 2,340 C. 4,680 D. 7,020 E. 14,040
Take the task of creating a password and break it into stages.
Stage 1: Select the one letter to be used in the code There are 26 letters from which to choose, so we can complete this stage in 26 ways.
Stage 2: Select the two digits to be used in the code Since the order in which we select the two digits does not matter, we can use combinations. We can select 2 digits from 10 women in 10C2 ways (45 ways) So, we can complete stage 2 in 45 ways
NOTE: We now have the 3 characters to be used in the code. At this point, we need to arrange those 3 characters.
Stage 3: Arrange the 3 selected characters. RULE: We can arrange n unique objects in n! ways. So, we can arrange the 3 characters in 3! ways (6 ways) So we can complete stage 3 in 6 ways.
By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus create a password ) in (26)(45)(6) ways (26)(45)(6) = 7020
Will must choose a 3-character computer password, consisting of 1 lett
[#permalink]
Show Tags
Updated on: 05 Aug 2016, 06:33
AbdurRakib wrote:
Will must choose a 3-character computer password, consisting of 1 letter from the alphabet and 2 distinct digits, in any order.From how many different passwords can Will choose?
A. 390 B. 2,340 C. 4,680 D. 7,020 E. 14,040
26C1*10C1*9C1 = 2340.
=> 2340 * 3 ! = 14,040.
Option E is correct answer...but OA is D.
Abdur..can you give us official solution...will correct if I missed anything..
Originally posted by msk0657 on 05 Aug 2016, 06:10.
Last edited by msk0657 on 05 Aug 2016, 06:33, edited 1 time in total.
Re: Will must choose a 3-character computer password, consisting of 1 lett
[#permalink]
Show Tags
05 Aug 2016, 06:24
msk0657 wrote:
AbdurRakib wrote:
Will must choose a 3-character computer password, consisting of 1 letter from the alphabet and 2 distinct digits, in any order.From how many different passwords can Will choose?
A. 390 B. 2,340 C. 4,680 D. 7,020 E. 14,040
26C1*10C1*9C1 = 2340.
=> 2340 * 3 = 7020.
Option D is correct answer.
Why have you not multiplied 2340 with 3!. It is a three character password, so order of the characters does matter. I am not sure but I am getting the OA as E.
_________________
Re: Will must choose a 3-character computer password, consisting of 1 lett
[#permalink]
Show Tags
05 Aug 2016, 06:29
abhimahna wrote:
msk0657 wrote:
AbdurRakib wrote:
Will must choose a 3-character computer password, consisting of 1 letter from the alphabet and 2 distinct digits, in any order.From how many different passwords can Will choose?
A. 390 B. 2,340 C. 4,680 D. 7,020 E. 14,040
26C1*10C1*9C1 = 2340.
=> 2340 * 3 = 7020.
Option D is correct answer.
Why have you not multiplied 2340 with 3!. It is a three character password, so order of the characters does matter. I am not sure but I am getting the OA as E.
Yes... you are correct I missed 3! ...then it'll be E... I'll update..
Re: Will must choose a 3-character computer password, consisting of 1 lett
[#permalink]
Show Tags
05 Aug 2016, 08:37
msk0657 wrote:
abhimahna wrote:
msk0657 wrote:
26C1*10C1*9C1 = 2340.
=> 2340 * 3 = 7020.
Option D is correct answer.
Why have you not multiplied 2340 with 3!. It is a three character password, so order of the characters does matter. I am not sure but I am getting the OA as E.
Yes... you are correct I missed 3! ...then it'll be E... I'll update..
Thanks , but my concern is why the overall answer marked as D here?
Can someone please explain where I am going wrong?
_________________
Re: Will must choose a 3-character computer password, consisting of 1 lett
[#permalink]
Show Tags
05 Aug 2016, 09:49
1
GMATPrepNow wrote:
AbdurRakib wrote:
Will must choose a 3-character computer password, consisting of 1 letter from the alphabet and 2 distinct digits, in any order.From how many different passwords can Will choose?
A. 390 B. 2,340 C. 4,680 D. 7,020 E. 14,040
Take the task of creating a password and break it into stages.
Stage 1: Select the one letter to be used in the code There are 26 letters from which to choose, so we can complete this stage in 26 ways.
Stage 2: Select the two digits to be used in the code Since the order in which we select the two digits does not matter, we can use combinations. We can select 2 digits from 10 women in 10C2 ways (45 ways) So, we can complete stage 2 in 45 ways
NOTE: We now have the 3 characters to be used in the code. At this point, we need to arrange those 3 characters.
Stage 3: Arrange the 3 selected characters. RULE: We can arrange n unique objects in n! ways. So, we can arrange the 3 characters in 3! ways (6 ways) So we can complete stage 3 in 6 ways.
By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus create a password ) in (26)(45)(6) ways (26)(45)(6) = 7020
Can you please explain the 2nd scenario? Why can't we take 10c1 * 9c1 for selecting the two digits? I think I am missing something here. Please elaborate.
_________________
Will must choose a 3-character computer password, consisting of 1 lett
[#permalink]
Show Tags
Updated on: 26 Jan 2020, 06:28
2
Top Contributor
abhimahna wrote:
GMATPrepNow wrote:
AbdurRakib wrote:
Will must choose a 3-character computer password, consisting of 1 letter from the alphabet and 2 distinct digits, in any order.From how many different passwords can Will choose?
A. 390 B. 2,340 C. 4,680 D. 7,020 E. 14,040
Take the task of creating a password and break it into stages.
Stage 1: Select the one letter to be used in the code There are 26 letters from which to choose, so we can complete this stage in 26 ways.
Stage 2: Select the two digits to be used in the code Since the order in which we select the two digits does not matter, we can use combinations. We can select 2 digits from 10 women in 10C2 ways (45 ways) So, we can complete stage 2 in 45 ways
NOTE: We now have the 3 characters to be used in the code. At this point, we need to arrange those 3 characters.
Stage 3: Arrange the 3 selected characters. RULE: We can arrange n unique objects in n! ways. So, we can arrange the 3 characters in 3! ways (6 ways) So we can complete stage 3 in 6 ways.
By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus create a password ) in (26)(45)(6) ways (26)(45)(6) = 7020
Can you please explain the 2nd scenario? Why can't we take 10c1 * 9c1 for selecting the two digits? I think I am missing something here. Please elaborate.
You are treating stage 2 as though the order in which we select the 2 digits matters, when the order does not matter (we arrange the letters in stage 3). So, in your solution, selecting digit 5 first and then selecting 7 second is treated as an outcome that's DIFFERENT from selecting digit 7 first and then selecting 5 second , when both of these outcomes are IDENTICAL.
Cheers, Brent
_________________
If you enjoy my solutions, you'll love my GMAT prep course.
Re: Will must choose a 3-character computer password, consisting of 1 lett
[#permalink]
Show Tags
05 Aug 2016, 10:23
GMATPrepNow wrote:
abhimahna wrote:
GMATPrepNow wrote:
Take the task of creating a password and break it into stages.
Stage 1: Select the one letter to be used in the code There are 26 letters from which to choose, so we can complete this stage in 26 ways.
Stage 2: Select the two digits to be used in the code Since the order in which we select the two digits does not matter, we can use combinations. We can select 2 digits from 10 women in 10C2 ways (45 ways) So, we can complete stage 2 in 45 ways
NOTE: We now have the 3 characters to be used in the code. At this point, we need to arrange those 3 characters.
Stage 3: Arrange the 3 selected characters. RULE: We can arrange n unique objects in n! ways. So, we can arrange the 3 characters in 3! ways (6 ways) So we can complete stage 3 in 6 ways.
By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus create a password ) in (26)(45)(6) ways (26)(45)(6) = 7020
Can you please explain the 2nd scenario? Why can't we take 10c1 * 9c1 for selecting the two digits? I think I am missing something here. Please elaborate.
You are treating stage 2 as though the order in which we select the 2 digits matters, when the order does not matter (we arrange the letters in stage 3). So, in your solution, selecting digit 5 first and then selecting 7 second is treated as an outcome that's DIFFERENT from selecting digit 7 first and then selecting 5 second , when both of these outcomes are IDENTICAL.
This video might help:
Cheers, Brent
Sounds Cool, Thanks Brent.
May be I am too tired now that I didn't recognize such a simple thing. But your answer made me realize my mistake. Thanks
_________________
Re: Will must choose a 3-character computer password, consisting of 1 lett
[#permalink]
Show Tags
24 Jul 2017, 17:35
GMATPrepNow wrote:
AbdurRakib wrote:
Will must choose a 3-character computer password, consisting of 1 letter from the alphabet and 2 distinct digits, in any order.From how many different passwords can Will choose?
A. 390 B. 2,340 C. 4,680 D. 7,020 E. 14,040
Take the task of creating a password and break it into stages.
Stage 1: Select the one letter to be used in the code There are 26 letters from which to choose, so we can complete this stage in 26 ways.
Stage 2: Select the two digits to be used in the code Since the order in which we select the two digits does not matter, we can use combinations. We can select 2 digits from 10 women in 10C2 ways (45 ways) So, we can complete stage 2 in 45 ways
NOTE: We now have the 3 characters to be used in the code. At this point, we need to arrange those 3 characters.
Stage 3: Arrange the 3 selected characters. RULE: We can arrange n unique objects in n! ways. So, we can arrange the 3 characters in 3! ways (6 ways) So we can complete stage 3 in 6 ways.
By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus create a password ) in (26)(45)(6) ways (26)(45)(6) = 7020
Re: Will must choose a 3-character computer password, consisting of 1 lett
[#permalink]
Show Tags
24 Jul 2017, 18:13
Top Contributor
septwibowo wrote:
GMATPrepNow wrote:
AbdurRakib wrote:
Will must choose a 3-character computer password, consisting of 1 letter from the alphabet and 2 distinct digits, in any order.From how many different passwords can Will choose?
A. 390 B. 2,340 C. 4,680 D. 7,020 E. 14,040
Take the task of creating a password and break it into stages.
Stage 1: Select the one letter to be used in the code There are 26 letters from which to choose, so we can complete this stage in 26 ways.
Stage 2: Select the two digits to be used in the code Since the order in which we select the two digits does not matter, we can use combinations. We can select 2 digits from 10 women in 10C2 ways (45 ways) So, we can complete stage 2 in 45 ways
NOTE: We now have the 3 characters to be used in the code. At this point, we need to arrange those 3 characters.
Stage 3: Arrange the 3 selected characters. RULE: We can arrange n unique objects in n! ways. So, we can arrange the 3 characters in 3! ways (6 ways) So we can complete stage 3 in 6 ways.
By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus create a password ) in (26)(45)(6) ways (26)(45)(6) = 7020
Re: Will must choose a 3-character computer password, consisting of 1 lett
[#permalink]
Show Tags
26 Jul 2017, 15:35
1
AbdurRakib wrote:
Will must choose a 3-character computer password, consisting of 1 letter from the alphabet and 2 distinct digits, in any order.From how many different passwords can Will choose?
A. 390 B. 2,340 C. 4,680 D. 7,020 E. 14,040
Since there are 26 letters and 10 digits, the number of 3-character passwords that can be created is 26 x 10 x 9 = 2,340, if the password is in the form of LDD where L means letter and D means digit. However, the password can be also in the form of DLD and DDL, each of which also can be created in 2,340 ways. Thus, the total number of passwords is 2,340 x 3 = 7,020.
Re: Will must choose a 3-character computer password, consisting of 1 lett
[#permalink]
Show Tags
27 Jul 2017, 17:13
1
ScottTargetTestPrep wrote:
AbdurRakib wrote:
Will must choose a 3-character computer password, consisting of 1 letter from the alphabet and 2 distinct digits, in any order.From how many different passwords can Will choose?
A. 390 B. 2,340 C. 4,680 D. 7,020 E. 14,040
Since there are 26 letters and 10 digits, the number of 3-character passwords that can be created is 26 x 10 x 9 = 2,340, if the password is in the form of LDD where L means letter and D means digit. However, the password can be also in the form of DLD and DDL, each of which also can be created in 2,340 ways. Thus, the total number of passwords is 2,340 x 3 = 7,020.
Answer: D
Order of the Digits don't matter?
or is because we took 9x10, we are already accounting for the order.
Re: Will must choose a 3-character computer password, consisting of 1 lett
[#permalink]
Show Tags
25 Aug 2018, 03:49
GMATPrepNow wrote:
AbdurRakib wrote:
Will must choose a 3-character computer password, consisting of 1 letter from the alphabet and 2 distinct digits, in any order.From how many different passwords can Will choose?
A. 390 B. 2,340 C. 4,680 D. 7,020 E. 14,040
Take the task of creating a password and break it into stages.
Stage 1: Select the one letter to be used in the code There are 26 letters from which to choose, so we can complete this stage in 26 ways.
Stage 2: Select the two digits to be used in the code Since the order in which we select the two digits does not matter, we can use combinations. We can select 2 digits from 10 women in 10C2 ways (45 ways) So, we can complete stage 2 in 45 ways
NOTE: We now have the 3 characters to be used in the code. At this point, we need to arrange those 3 characters.
Stage 3: Arrange the 3 selected characters. RULE: We can arrange n unique objects in n! ways. So, we can arrange the 3 characters in 3! ways (6 ways) So we can complete stage 3 in 6 ways.
By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus create a password ) in (26)(45)(6) ways (26)(45)(6) = 7020
Sorry, I don't understand why the two digits to be used is 10C2, if the first digit can be selected in 10 ways and the second d one in 10 ways then should it not be 10x10? what am I missing?
Re: Will must choose a 3-character computer password, consisting of 1 lett
[#permalink]
Show Tags
25 Aug 2018, 05:31
1
Top Contributor
jackjones wrote:
Sorry, I don't understand why the two digits to be used is 10C2, if the first digit can be selected in 10 ways and the second d one in 10 ways then should it not be 10x10? what am I missing?
There are various ways to answer this question. In my solution, I first chose the 3 characters (disregarding the order) and THEN I arranged the 3 characters I had chosen.
Does that help?
Cheers, Brent
_________________
If you enjoy my solutions, you'll love my GMAT prep course.
Re: Will must choose a 3-character computer password, consisting of 1 lett
[#permalink]
Show Tags
05 Nov 2019, 11:45
1
Hi All,
We're told that Will must choose a 3-character computer password, consisting of 1 letter from the alphabet and 2 distinct digits, in any order. We're asked for the total number of different passwords that Will can choose. Depending on how comfortable you are with the 'math' involved, you can perform the calculations in a couple of different ways. Here's how you can break the prompt down into smaller pieces (which you might find easier than trying to do one gigantic calculation).
Based on the the 'restrictions' in the prompt, we can use 1 letter of the English alphabet and 2 DISTINCT digits IN ANY ORDER to make a code. Thus, the code could be one of 3 options:
The first option = (Letter)(Digit)(Different Digit) = (26)(10)(9) = 2340 The second option = (Digit)(Letter)(Different Digit) = (10)(26)(9) = 2340 The third option = (Digit)(Different Digit)(Letter) = (10)(9)(26) = 2340
You might recognize that each calculation involves the product of the same 3 numbers, so you don't have to do that calculation each time - just do it once and then multiply that result by 3....
Will must choose a 3-character computer password, consisting of 1 lett
[#permalink]
Show Tags
26 Jan 2020, 04:37
EMPOWERgmatRichC wrote:
Hi All,
We're told that Will must choose a 3-character computer password, consisting of 1 letter from the alphabet and 2 distinct digits, in any order. We're asked for the total number of different passwords that Will can choose. Depending on how comfortable you are with the 'math' involved, you can perform the calculations in a couple of different ways. Here's how you can break the prompt down into smaller pieces (which you might find easier than trying to do one gigantic calculation).
Based on the the 'restrictions' in the prompt, we can use 1 letter of the English alphabet and 2 DISTINCT digits IN ANY ORDER to make a code. Thus, the code could be one of 3 options:
The first option = (Letter)(Digit)(Different Digit) = (26)(10)(9) = 2340 The second option = (Digit)(Letter)(Different Digit) = (10)(26)(9) = 2340 The third option = (Digit)(Different Digit)(Letter) = (10)(9)(26) = 2340
You might recognize that each calculation involves the product of the same 3 numbers, so you don't have to do that calculation each time - just do it once and then multiply that result by 3....
Re: Will must choose a 3-character computer password, consisting of 1 lett
[#permalink]
Show Tags
26 Jan 2020, 06:32
Top Contributor
altairahmad wrote:
EMPOWERgmatRichC wrote:
Hi All,
We're told that Will must choose a 3-character computer password, consisting of 1 letter from the alphabet and 2 distinct digits, in any order. We're asked for the total number of different passwords that Will can choose. Depending on how comfortable you are with the 'math' involved, you can perform the calculations in a couple of different ways. Here's how you can break the prompt down into smaller pieces (which you might find easier than trying to do one gigantic calculation).
Based on the the 'restrictions' in the prompt, we can use 1 letter of the English alphabet and 2 DISTINCT digits IN ANY ORDER to make a code. Thus, the code could be one of 3 options:
The first option = (Letter)(Digit)(Different Digit) = (26)(10)(9) = 2340 The second option = (Digit)(Letter)(Different Digit) = (10)(26)(9) = 2340 The third option = (Digit)(Different Digit)(Letter) = (10)(9)(26) = 2340
You might recognize that each calculation involves the product of the same 3 numbers, so you don't have to do that calculation each time - just do it once and then multiply that result by 3....
Why didn't we multiply 2340 with 3! ? Afterall, A31 is different from A13. Isn't it ? In LDD both Ds are distinct and its basically LD1D2 situation ?
Good question. In my approach (at https://gmatclub.com/forum/will-must-ch ... l#p1719321), I first chose two digits and one letter, and then rearrange this collection of three characters in 3! ways. If we use this approach, then we must recognize that the order in which we select our two digits does not matter, which means we can select two distinct digits in 10C2 ways (45 ways).
In Rich's approach shown above, we are not following the same approach that I did. Instead we are treating each case differently. As such we don't need to multiply by 3!
Cheers, Brent
_________________
If you enjoy my solutions, you'll love my GMAT prep course.
Re: Will must choose a 3-character computer password, consisting of 1 lett
[#permalink]
Show Tags
26 Jan 2020, 06:57
possible arrangements ; 26 for alphabet and 10*9 for digits total ways ; 3 26*10*9*3 ; 7020 IMO D
AbdurRakib wrote:
Will must choose a 3-character computer password, consisting of 1 letter from the alphabet and 2 distinct digits, in any order.From how many different passwords can Will choose?
A. 390 B. 2,340 C. 4,680 D. 7,020 E. 14,040
gmatclubot
Re: Will must choose a 3-character computer password, consisting of 1 lett
[#permalink]
26 Jan 2020, 06:57