Author 
Message 
TAGS:

Hide Tags

SVP
Joined: 04 May 2006
Posts: 1894
Schools: CBS, Kellogg

Set S consists of numbers 2, 3, 6, 48, and 164. Number K is [#permalink]
Show Tags
28 Mar 2008, 02:32
16
This post received KUDOS
75
This post was BOOKMARKED
Question Stats:
29% (02:49) correct
71% (01:57) wrong based on 2110 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 nonnegative 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%
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
GMAT Club Premium Membership  big benefits and savings
Last edited by Bunuel on 07 Jul 2013, 06:11, edited 1 time in total.
Edited the question and added the OA.



Intern
Joined: 04 May 2004
Posts: 47
Location: India

Re: Probability [#permalink]
Show Tags
28 Mar 2008, 05:26
18
This post received KUDOS
8
This post was BOOKMARKED
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 nonnegative 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. Hence answer is D 90%. What is the answer?
_________________
http://twitter.com/Saurabh



Intern
Joined: 14 Jul 2004
Posts: 11

Re: Probability [#permalink]
Show Tags
28 Mar 2008, 06:53
I think the answer is 90%, because the probablity of choosing 0 from 09 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)



Intern
Joined: 16 Jul 2010
Posts: 11

Re: Probability [#permalink]
Show Tags
04 Aug 2010, 11:20
Are the exact numbers in the set irrelevant to finding the answer? Would any positive integers have worked in lieu of 2, 3, 6, 48, and 164?



VP
Joined: 17 Feb 2010
Posts: 1492

Re: Probability [#permalink]
Show Tags
23 Aug 2010, 13:34
I was not able to understand the solution here.
Bunuel, do you mind explaining the approach to such problems?



Math Expert
Joined: 02 Sep 2009
Posts: 39597

Set S consists of numbers 2, 3, 6, 48, and 164. Number K is [#permalink]
Show Tags
23 Aug 2010, 14:51
14
This post received KUDOS
Expert's post
32
This post was BOOKMARKED
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 nonnegative 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 nonnegative 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: \(P=1*\frac{9}{10}=\frac{9}{10}\). Answer: D.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



VP
Joined: 17 Feb 2010
Posts: 1492

Re: Probability [#permalink]
Show Tags
23 Aug 2010, 20:35
1
This post received KUDOS
Bunuel, I agree that 463 is an odd number but 678 is not odd but an even number. What am I missing here...



Math Expert
Joined: 02 Sep 2009
Posts: 39597

Re: Probability [#permalink]
Show Tags
24 Aug 2010, 05:01



Math Expert
Joined: 02 Sep 2009
Posts: 39597

Re: Set S consists of numbers 2, 3, 6, 48, and 164. Number K is [#permalink]
Show Tags
07 Jul 2013, 06:13



Director
Status: Verbal Forum Moderator
Joined: 17 Apr 2013
Posts: 613
Location: India
GMAT 1: 710 Q50 V36 GMAT 2: 750 Q51 V41 GMAT 3: 790 Q51 V49
GPA: 3.3

Re: Probability [#permalink]
Show Tags
14 Sep 2013, 17:56
1
This post received KUDOS
Bunuel wrote: 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 nonnegative 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 nonnegative 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/howtoscore750and750imovedfrom710to189016.html



Manager
Joined: 29 Aug 2013
Posts: 77
Location: United States
Concentration: Finance, International Business
GMAT 1: 590 Q41 V29 GMAT 2: 540 Q44 V20
GPA: 3.5
WE: Programming (Computer Software)

Re: Probability [#permalink]
Show Tags
15 Sep 2013, 00:15
2
This post received KUDOS
1
This post was BOOKMARKED
honchos wrote: Bunuel wrote: 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 nonnegative 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 nonnegative 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% Hope it helps. Consider Kudos if it helped.



Intern
Joined: 21 Aug 2013
Posts: 8

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 nonnegative integers) So the propability that 678,463 is not a multiple of Z is 100%  10% = 90%



Senior Manager
Joined: 17 Sep 2013
Posts: 390
Concentration: Strategy, General Management
WE: Analyst (Consulting)

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..



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15919

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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Manager
Joined: 10 Jun 2015
Posts: 128

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 nonnegative 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



eGMAT Representative
Joined: 04 Jan 2015
Posts: 726

Re: Set S consists of numbers 2, 3, 6, 48, and 164. Number K is [#permalink]
Show Tags
11 Jun 2015, 00:09
2
This post received KUDOS
Expert's post
1
This post was BOOKMARKED
matvan wrote: 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 nonnegative 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 Hi matvan, The answer is D i.e. 90%. 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 nonnegative 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 calculationProbability 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 = \(1 * \frac{9}{10} = 90\)%. Hope it's clear Regards Harsh
_________________
 '4 out of Top 5' Instructors on gmatclub  70 point improvement guarantee  www.egmat.com



Manager
Joined: 08 Jun 2015
Posts: 123

Set S consists of numbers 2, 3, 6, 48, and 164. Number K is [#permalink]
Show Tags
25 Jul 2015, 17:45
X to the power of 0 = 1 should help out...



Manager
Joined: 25 Nov 2014
Posts: 141
WE: Engineering (Manufacturing)

Re: Set S consists of numbers 2, 3, 6, 48, and 164. Number K is [#permalink]
Show Tags
08 Aug 2015, 03:04
i misread "nonnegative" to be "negative" and my answer came to be 0%..... big mistake...lol



Intern
Joined: 31 Mar 2015
Posts: 4

Set S consists of numbers 2, 3, 6, 48, and 164. Number K is [#permalink]
Show Tags
18 Aug 2015, 22:42
Why is the probability of choosing a number from set s equal to 1? Won't it be 1/5.
Is it equal to 1 because the question says one random number from set S.
Plz explain. Thanks.



Manager
Joined: 10 Jun 2015
Posts: 128

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 nonnegative 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 10010=90%




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



Go to page
1 2
Next
[ 22 posts ]





Similar topics 
Author 
Replies 
Last post 
Similar Topics:


5


There is a set consisting of 5 numbers{1,2,3,4,5}.

chetan2u 
4 
08 May 2016, 19:49 

12


Set X consists of prime numbers {3, 11, 7, K, 17, 19}. If integer Y

Bunuel 
6 
11 Dec 2016, 16:51 

4


There are two set each with the number 1, 2, 3, 4, 5, 6. If

monirjewel 
5 
13 Jan 2017, 22:28 

1


A set consist of 2n1 element. What is the number of subsets

ksharma12 
2 
29 Dec 2013, 17:31 

44


A set of data consists of the following 5 numbers: 0, 2, 4

GK_Gmat 
20 
23 Sep 2016, 20:29 



