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:

Set S consists of numbers 2, 3, 6, 48, and 164. Number K is [#permalink]

Show Tags

28 Mar 2008, 02:32

14

This post received KUDOS

60

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

95% (hard)

Question Stats:

30% (02:51) correct
70% (01:57) wrong based on 1900 sessions

HideShow timer Statistics

Set S consists of numbers 2, 3, 6, 48, and 164. Number K is computed by multiplying one random number from set S by one of the first 10 non-negative integers, also selected at random. If Z=6^K, what is the probability that 678,463 is not a multiple of Z?

Set S consists of numbers 2, 3, 6, 48, and 164. Number K is computed by multiplying one random number from set S by one of the first 10 non-negative integers, also selected at random. If Z=6^K, what is the probability that 678,463 is not a multiple of Z?

I first looked at 678,463. The number is not a multiple of 2,3,7 or 9.

Then I looked at Z. Z = 6*6*6* ...*6 (k times).

If 678,463 has to be a multiple of Z, it has to be a multiple of 6.

Another case is that the integer we pick is 0. Probability of picking 0 as integer is 1/10. If integer is 0, Z becomes 1 and 678,463 becomes a multiple of Z.

I think the answer is 90%, because the probablity of choosing 0 from 0-9 is 10%. If 0 is chosen than only we have 678463 is multiple of 6^0 (= 1). If any other number is chosen, then 678463 is not multiple of 6 (because 6^k)

Set S consists of numbers 2, 3, 6, 48, and 164. Number K is computed by multiplying one random number from set S by one of the first 10 non-negative integers, also selected at random. If Z=6^K, what is the probability that 678,463 is not a multiple of Z?

a. 10% b. 25% c. 50% d. 90% e. 100%

\(S=\{2,3,6,48,164\}\) and set of first 10 non-negative integers, say \(T=\{0,1,2,3,4,5,6,7,8,9\}\).

\(K=s*t\), where \(s\) and \(t\) are random numbers from respective sets.

678,463 is an odd number.

The only case when \(6^k\) IS a factor of 678,463 is when \(k\) equals to 0 (in this case \(6^k=6^0=1\) and 1 is a factor of every integer). Because if \(k>0\), then \(6^k=even\) and even number cannot be a factor of odd number 678,463.

Hence \(6^k\) NOT to be a factor of 678,463 we should pick any number from S and pick any number but 0 from T: \(P=1*\frac{9}{10}=\frac{9}{10}\).

Set S consists of numbers 2, 3, 6, 48, and 164. Number K is computed by multiplying one random number from set S by one of the first 10 non-negative integers, also selected at random. If Z=6^K, what is the probability that 678,463 is not a multiple of Z?

a. 10% b. 25% c. 50% d. 90% e. 100%

\(S=\{2,3,6,48,164\}\) and set of first 10 non-negative integers, say \(T=\{0,1,2,3,4,5,6,7,8,9\}\).

\(K=s*t\), where \(s\) and \(t\) are random numbers from respective sets.

678,463 is an odd number.

The only case when \(6^k\) IS a factor of 678,463 is when \(k\) equals to 0 (in this case \(6^k=6^0=1\) and 1 is a factor of every integer). Because if \(k>0\), then \(6^k=even\) and even number can not be a factor of odd number 678,463.

Hence \(6^k\) NOT to be a factor of 678,463 we should pick any number from S and pick any number but 0 from T: \(P=1*\frac{9}{10}=\frac{9}{10}\).

Answer: D.

Couldn't understand this- Hence 6^k NOT to be a factor of 678,463 we should pick any number from S and pick any number but 0 from T: P=1*\frac{9}{10}=\frac{9}{10}.

I simply calculated probability like this-

45/50

45- when 6^k IS EVEN, 50 total number of outcomes. _________________

Like my post Send me a Kudos It is a Good manner. My Debrief: http://gmatclub.com/forum/how-to-score-750-and-750-i-moved-from-710-to-189016.html

Set S consists of numbers 2, 3, 6, 48, and 164. Number K is computed by multiplying one random number from set S by one of the first 10 non-negative integers, also selected at random. If Z=6^K, what is the probability that 678,463 is not a multiple of Z?

a. 10% b. 25% c. 50% d. 90% e. 100%

\(S=\{2,3,6,48,164\}\) and set of first 10 non-negative integers, say \(T=\{0,1,2,3,4,5,6,7,8,9\}\).

\(K=s*t\), where \(s\) and \(t\) are random numbers from respective sets.

678,463 is an odd number.

The only case when \(6^k\) IS a factor of 678,463 is when \(k\) equals to 0 (in this case \(6^k=6^0=1\) and 1 is a factor of every integer). Because if \(k>0\), then \(6^k=even\) and even number can not be a factor of odd number 678,463.

Hence \(6^k\) NOT to be a factor of 678,463 we should pick any number from S and pick any number but 0 from T: \(P=1*\frac{9}{10}=\frac{9}{10}\).

Answer: D.

Couldn't understand this- Hence 6^k NOT to be a factor of 678,463 we should pick any number from S and pick any number but 0 from T: P=1*\frac{9}{10}=\frac{9}{10}.

I simply calculated probability like this-

45/50

45- when 6^k IS EVEN, 50 total number of outcomes.

First of all the total number of outcomes will be 10 * 6 = 60 (10 from 0 to 9 and 6 from Set S) 6^k will be even for all the numbers of K but 0. Therefore number of cases when 6^k will be even will be 9*6 = 54 i.e. (9 from 1 to 9 excluding 0 and 6 from Set S). Since K can take any value from 1 to any multiple of 1.

Therefore 54/60 is the probability i.e. 9/10 = 90%.

Regarding what Bunuel has posted "Hence \(6^k\) NOT to be a factor of 678,463 we should pick any number from S and pick any number but 0 from T: \(P=1*\frac{9}{10}=\frac{9}{10}\)."

He means Probability to pick any number from S will be 6/6 i.e. 1 and probability to pick any number from T but 0 will be 9/10. Since K is multiplication of these probabilities it will be 1*9/10 = 90%

Re: Set S consists of numbers 2, 3, 6, 48, and 164. Number K is [#permalink]

Show Tags

07 Apr 2014, 00:02

1

This post received KUDOS

Z=6^K, so Z is even or Z = 1 (K=0) if K is not equal to zero than Z is even and 678,463 is not a multiple of Z if K is equal to zero than z is equal to 1 and 678,463 is a multiple of Z (Z=1) the propability that K is equal to zero is 1/10 =10% (K=a*b where a is one random number from set S whose numbers are all not equal to zero, and b is one of the first 10 non-negative integers) So the propability that 678,463 is not a multiple of Z is 100% - 10% = 90%

Re: Set S consists of numbers 2, 3, 6, 48, and 164. Number K is [#permalink]

Show Tags

13 May 2014, 06:10

Bahh..mistook non negative for non zero integers.. Quite easy...I checked zero too..but it was not in my set anyways..not a 700 I think _________________

Appreciate the efforts...KUDOS for all Don't let an extra chromosome get you down..

Re: Set S consists of numbers 2, 3, 6, 48, and 164. Number K is [#permalink]

Show Tags

20 May 2015, 19:36

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Re: Set S consists of numbers 2, 3, 6, 48, and 164. Number K is [#permalink]

Show Tags

10 Jun 2015, 23:35

sondenso wrote:

Set S consists of numbers 2, 3, 6, 48, and 164. Number K is computed by multiplying one random number from set S by one of the first 10 non-negative integers, also selected at random. If Z=6^K, what is the probability that 678,463 is not a multiple of Z?

A. 10% B. 25% C. 50% D. 90% E. 100%

z is a multiple of 6 and 678,463 is not a multiple of 6. therefore, the answer is E

Set S consists of numbers 2, 3, 6, 48, and 164. Number K is computed by multiplying one random number from set S by one of the first 10 non-negative integers, also selected at random. If Z=6^K, what is the probability that 678,463 is not a multiple of Z?

A. 10% B. 25% C. 50% D. 90% E. 100%

z is a multiple of 6 and 678,463 is not a multiple of 6. therefore, the answer is E

The question is asking the probability of \(\frac{678463}{6^k}\) not being an integer. For a number to be divisible by any positive multiple of \(6\), it should at least be divisible by both \(2\) and \(3\).

Since \(678463\) is not an even number, it is not divisible by \(2\). So for every positive multiple of \(6\), \(\frac{678463}{6^k}\) is not an integer.

However the question talks of \(k\) as one of the first ten non-negative numbers which also includes 0. If \(k = 0\) , then \(6^k = 6^ 0 = 1\). In that case \(678463\) will be a multiple of \(6^0\) i.e.\(1\).

Hence the probability of \(678463\) not being a multiple of \(6^k\) is only possible when \(k = 0\) AND any random number being picked from set S.

Probability calculation Probability of any random number being picked from set S = \(1\)

Probability of \(k\) not being \(0\) = \(\frac{9}{10}\) ( as there are total of \(10\) ways to pick up \(k\) and \(9\) ways for \(k\) not being \(0\))

Since it's an AND event , we will multiply the probabilities of both the events.

Hence total probability = \(1 * \frac{9}{10} = 90\)%.

Re: Set S consists of numbers 2, 3, 6, 48, and 164. Number K is [#permalink]

Show Tags

18 Aug 2015, 23:16

sondenso wrote:

Set S consists of numbers 2, 3, 6, 48, and 164. Number K is computed by multiplying one random number from set S by one of the first 10 non-negative integers, also selected at random. If Z=6^K, what is the probability that 678,463 is not a multiple of Z?

A. 10% B. 25% C. 50% D. 90% E. 100%

z is a multiple of 6 except when k=0 and z=1 the probability of selecting zero from set S is 10% therefore, the probability of the number 678,463 is a multiple of z is 10% because the number is not divisible by 6. Hence, the probability of the number not a multiple of z is 100-10=90%

gmatclubot

Re: Set S consists of numbers 2, 3, 6, 48, and 164. Number K is
[#permalink]
18 Aug 2015, 23:16

This is the kickoff for my 2016-2017 application season. After a summer of introspect and debate I have decided to relaunch my b-school application journey. Why would anyone want...

Check out this awesome article about Anderson on Poets Quants, http://poetsandquants.com/2015/01/02/uclas-anderson-school-morphs-into-a-friendly-tech-hub/ . Anderson is a great place! Sorry for the lack of updates recently. I...

According to the Nebula Award categories, a novel must be over 40,000 words. In the past year I have written assignments for 22 classes totaling just under 65...