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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

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:

How many 4 digit codes can be made, if each code can only contain [#permalink]

Show Tags

04 Oct 2010, 07:00

5

This post received KUDOS

7

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

(N/A)

Question Stats:

42% (02:52) correct
58% (01:37) wrong based on 57 sessions

HideShow timer Statistics

How many 4 digit codes can be made, if each code can only contain prime numbers that are less than 20?

A. 24 B. 102 C. 464 D. 656 E. 5040

Hi all,

As you saw, I have published a bunch of questions in the past hour. Most of these questions are taken from a collection of hard quantitative questions provided by The Princeton Review (a.k.a - Killer Math).

I have posted any question that I have solved incorrectly, either due to careless error or concept error, in order to share them with everyone here.

Thank you all for the help and detailed explanations (especially you - Bunuel).

As you saw, I have published a bunch of questions in the past hour. Most of these questions are taken from a collection of hard quantitative questions provided by The Princeton Review (a.k.a - Killer Math).

I have posted any question that I have solved incorrectly, either due to careless error or concept error, in order to share them with everyone here.

Please consider the following problem that I am not sure I understood:

How many 4 digit codes can be made, if each code can only contain prime numbers that are less than 20?

A. 24 B. 102 C. 464 D. 656 E. 5040

Thank you all for the help and detailed explanations (especially you - Bunuel). It is very helpful.

The question is a little bit ambiguous but I think it means the following:

I guess as it's not mentioned primes can be repeated.

There are: 4 one digit primes (O) less than 20 - 2, 3, 5, 7; 4 two digit primes (T) less than 20 - 11, 13, 17, 19;

Thus 4-digit number could be of the following type:

OOOO, for example: 2|3|5|7 or 2|2|7|7. Each O can take 4 values from {2, 3, 5, 7}, so total ways for this type is \(4^4\);

TT, for example: 11|11 or 19|17. Each T can take 4 values from {11, 13, 17, 19}, so total ways for this type is \(4^2\);

TOO, for example: 11|3|5 or 19|7|2. T can take 4 values from {11, 13, 17, 19} and each O can take 4 values from {2, 3, 5, 7}, so total ways for this type is \(4*4^2=4^3\); OTO, for example: 2|13|5 or 7|19|2. The same as above: \(4^3\); OOT, for example: 2|5|19 or 7|2|17. The same as above: \(4^3\);

Re: How many 4 digit codes can be made, if each code can only contain [#permalink]

Show Tags

04 Oct 2010, 08:45

2

This post received KUDOS

eladshush wrote:

Hi all,

As you saw, I have published a bunch of questions in the past hour. Most of these questions are taken from a collection of hard quantitative questions provided by The Princeton Review (a.k.a - Killer Math).

I have posted any question that I have solved incorrectly, either due to careless error or concept error, in order to share them with everyone here.

Please consider the following problem that I am not sure I understood:

How many 4 digit codes can be made, if each code can only contain prime numbers that are less than 20?

A. 24 B. 102 C. 464 D. 656 E. 5040

Thank you all for the help and detailed explanations (especially you - Bunuel). It is very helpful.

First note all the single digit primes {2,3,5,7} And then all the 2-digit ones {11,13,17,19}

Case 1 Codes formed with 2 two digit primes (2-digit prime) (2-digit prime) No of ways = 4x4 = 16

Case 2 Codes formed with 4 one digit primes (1-digit prime) (1-digit prime) (1-digit prime) (1-digit prime) No of ways = 4x4x4x4 = 256

Case 3 Codes formed with 2 one-digit primes and 1 two-digit prime (1-digit prime) (1-digit prime) (2-digit prime) (1-digit prime) (2-digit prime) (1-digit prime) (2-digit prime) (1-digit prime) (1-digit prime) Each set can be formed in 4x4x4 ways So total = 3x64 = 192

Total number = 192+256+16 = 464

Answer is (c)

PS : Some others also deserve thanks
_________________

Re: How many 4 digit codes can be made, if each code can only contain [#permalink]

Show Tags

05 Oct 2010, 13:33

Bunuel wrote:

eladshush wrote:

Hi all,

As you saw, I have published a bunch of questions in the past hour. Most of these questions are taken from a collection of hard quantitative questions provided by The Princeton Review (a.k.a - Killer Math).

I have posted any question that I have solved incorrectly, either due to careless error or concept error, in order to share them with everyone here.

Please consider the following problem that I am not sure I understood:

How many 4 digit codes can be made, if each code can only contain prime numbers that are less than 20?

A. 24 B. 102 C. 464 D. 656 E. 5040

Thank you all for the help and detailed explanations (especially you - Bunuel). It is very helpful.

The question is a little bit ambiguous but I think it means the following:

I guess as it's not mentioned primes can be repeated.

There are: 4 one digit primes (O) less than 20 - 2, 3, 5, 7; 4 two digit primes (T) less than 20 - 11, 13, 17, 19;

Thus 4-digit number could be of the following type:

OOOO, for example: 2|3|5|7 or 2|2|7|7. Each O can take 4 values from {2, 3, 5, 7}, so total ways for this type is \(4^4\);

TT, for example: 11|11 or 19|17. Each T can take 4 values from {11, 13, 17, 19}, so total ways for this type is \(4^2\);

TOO, for example: 11|3|5 or 19|7|2. T can take 4 values from {11, 13, 17, 19} and each O can take 4 values from {2, 3, 5, 7}, so total ways for this type is \(4*4^2=4^3\); OTO, for example: 2|13|5 or 7|19|2. The same as above: \(4^3\); OOT, for example: 2|5|19 or 7|2|17. The same as above: \(4^3\);

Total: \(4^4+4^2+3*4^3=464\).

Answer: C.

Hi Bunuel,

why can't i write TOO,OTO,OOT AS

(4^3)*3! , taking the T as one entity ans assuming that 3 things can be arranged in 3! ways???

(4^3)*3! , taking the T as one entity ans assuming that 3 things can be arranged in 3! ways???

Just one thing: TOO can be arranged in 3!/2! ways and not in 3! (# of permutations of 3 letters out which 2 O's are identical is 3!/2!), so it would be \(4^3*\frac{3!}{2!}=4^3*3\).

Re: How many 4 digit codes can be made, if each code can only contain [#permalink]

Show Tags

05 Oct 2010, 13:53

Bunuel wrote:

utin wrote:

Hi Bunuel,

why can't i write TOO,OTO,OOT AS

(4^3)*3! , taking the T as one entity ans assuming that 3 things can be arranged in 3! ways???

Just one thing: TOO can be arranged in 3!/2! ways and not in 3! (# of permutations of 3 letters out which 2 O's are identical is 3!/2!), so it would be \(4^3*\frac{3!}{2!}=4^3*3\).

Hope it's clear.

I though about the same but but when i see that TOO as three things to be arranged in 3! ways then i also thought that OO ARE TWO DIGITS AND THEY ARE TWO DIFFERENT PRIME NOS SO WHY DIVIDE BY 2!

this might clear my entire probability confusion i hope...

(4^3)*3! , taking the T as one entity ans assuming that 3 things can be arranged in 3! ways???

Just one thing: TOO can be arranged in 3!/2! ways and not in 3! (# of permutations of 3 letters out which 2 O's are identical is 3!/2!), so it would be \(4^3*\frac{3!}{2!}=4^3*3\).

Hope it's clear.

I though about the same but but when i see that TOO as three things to be arranged in 3! ways then i also thought that OO ARE TWO DIGITS AND THEY ARE TWO DIFFERENT PRIME NOS SO WHY DIVIDE BY 2!

this might clear my entire probability confusion i hope...

First of all two 1-digit primes can be the same, but it's not important here.

We are counting # of ways 4-digit number can be formed with two 1-digit primes and one 2-digit prime: {1-digit}{1-digit}{2-digit} {1-digit}{2-digit}{1-digit} {2-digit}{1-digit}{1-digit}

Concentration: General Management, Entrepreneurship

GPA: 3.8

WE: Engineering (Energy and Utilities)

Re: How many 4 digit codes can be made, if each code can only contain [#permalink]

Show Tags

03 Oct 2017, 00:09

1

This post received KUDOS

eladshush wrote:

How many 4 digit codes can be made, if each code can only contain prime numbers that are less than 20?

A. 24 B. 102 C. 464 D. 656 E. 5040

Hi all,

As you saw, I have published a bunch of questions in the past hour. Most of these questions are taken from a collection of hard quantitative questions provided by The Princeton Review (a.k.a - Killer Math).

I have posted any question that I have solved incorrectly, either due to careless error or concept error, in order to share them with everyone here.

Thank you all for the help and detailed explanations (especially you - Bunuel).

It is very helpful.

Though the question is little bit confusing, but conceptually this question is a real gem. More details should have been provided about the restrictions on selection of digits.

So, there are 4 one digit prime numbers to be used they are {2,3,5,7}. Lets call the single digits as O & there are 4 2-digit prime numbers to be used they are {11, 13, 15, 17}. And double digits as T.

Now there are 3 ways of selecting digits.

Case 1: All one digit prime numbers OOOO No. of codes = 4^4 (since repetition of digit is allowed = 256

Case 2: 2 Two digit prime numbers TT No. of codes = 4*4 = 16

Case 3 : one two digit prime number & 2 one digit prime number : OOT, OTO, TOO No. of codes = 4*4*4 + 4*4*4 + 4*4*4 = 3*4^3 = 192