NEW HERE? LEARN MORE
closeclose
Last visit was: 24 Apr 2024, 05:33 It is currently 24 Apr 2024, 05:33
Decision Tracker
My Rewards
New posts
New comers' posts

Close
GMAT Club Daily Prep
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

Fresh Meat!!!

SORT BY:
Date
Kudos
   1   2   3 
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92901
Own Kudos [?]: 618724 [1]
Given Kudos: 81586
Send PM
CAT Tests Forum Quiz Mode
Re: Fresh Meat!!! [#permalink] New post   18 Sep 2013, 03:34
1
Kudos
Expert Reply
muzammil wrote:
Bunuel wrote:
25*1=25 and 25*13=325;
25*3=75 and 25*11=275;
25*5=125 and 25*9=225.

Answer: C.


Hello, what about 175, 175 ? The question doesn't state they are distinct positive numbers.


The point is that if the two integers are 175 and 175, then their greatest common divisor going to be 175, not 25 as given in the stem.

Does this make sense?
User avatar
Transcendentalist
Manager
Manager
Joined: 24 Nov 2012
Posts: 132
Own Kudos [?]: 1013 [0]
Given Kudos: 73
Concentration: Sustainability, Entrepreneurship
Schools: CBS '17 (M) Kellogg '17 (A)
GMAT 1: 770 Q50 V44
WE:Business Development (Internet and New Media)
Send PM
Re: Fresh Meat!!! [#permalink] New post   30 Sep 2013, 04:14
Bunuel wrote:
3. How many different subsets of the set {0, 1, 2, 3, 4, 5} do not contain 0?

A. 16
B. 27
C. 31
D. 32
E. 64

Consider the set without 0: {1, 2, 3, 4, 5}. Each out of 5 elements of the set {1, 2, 3, 4, 5} has TWO options: either to be included in the subset or not, so total number of subsets of this set is 2^5=32. Now, each such set will be a subset of {0, 1, 2, 3, 4, 5} and won't include 0.

Answer: D.


I would like to request some some help with this question..

Could you please elaborate on the theory behind 2^n?
Isnt the null set considered to be a subset of this set?
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92901
Own Kudos [?]: 618724 [0]
Given Kudos: 81586
Send PM
CAT Tests Forum Quiz Mode
Re: Fresh Meat!!! [#permalink] New post   30 Sep 2013, 05:41
Expert Reply
Transcendentalist wrote:
Bunuel wrote:
3. How many different subsets of the set {0, 1, 2, 3, 4, 5} do not contain 0?

A. 16
B. 27
C. 31
D. 32
E. 64

Consider the set without 0: {1, 2, 3, 4, 5}. Each out of 5 elements of the set {1, 2, 3, 4, 5} has TWO options: either to be included in the subset or not, so total number of subsets of this set is 2^5=32. Now, each such set will be a subset of {0, 1, 2, 3, 4, 5} and won't include 0.

Answer: D.


I would like to request some some help with this question..

Could you please elaborate on the theory behind 2^n?
Isnt the null set considered to be a subset of this set?


Consider simpler set: {a, b, c}. How many subsets does it have? Each of a, b, and c has two choices either to be included in subsets or not. Thus total of 2^38 subsets (including an empty set). The subsets are:

{a, b, c} --> each is included;
{a, b} --> a and b are included;
{a, c};
{b, c};
{a};
{b};
{c};
{} empty set, none is included.

2^3=8 subsets.

Harder question to practice about the same concept: how-many-subordinates-does-marcia-have-57169.html#p692676

Hope it helps.
User avatar
lindt123
Intern
Intern
Joined: 19 Jul 2013
Posts: 14
Own Kudos [?]: 6 [0]
Given Kudos: 9
Location: United States
Concentration: Finance, International Business
GMAT 1: 340 Q27 V12
GPA: 3.33
Send PM
Re: Fresh Meat!!! [#permalink] New post   29 Dec 2013, 15:25
bb wrote:
18! and 18!+1 are consecutive integers. Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1. For example 20 and 21 are consecutive integers, thus only common factor they share is 1.

Now, since we can factor out each 15, 17, 33=3*11, and 39=3*13 out of 18!, then 15, 17, 33 and 39 ARE factors of 18! and are NOT factors of 18!+1. Therefore only 19 could be a factor of 18!+1.

Answer: C


I Find it difficult to understand the explaination..is there any other way to solve this question... :(
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92901
Own Kudos [?]: 618724 [19]
Given Kudos: 81586
Send PM
CAT Tests Forum Quiz Mode
Re: Fresh Meat!!! [#permalink] New post   30 Dec 2013, 01:39
4
Kudos
15
Bookmarks
Expert Reply
lindt123 wrote:
bb wrote:
18! and 18!+1 are consecutive integers. Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1. For example 20 and 21 are consecutive integers, thus only common factor they share is 1.

Now, since we can factor out each 15, 17, 33=3*11, and 39=3*13 out of 18!, then 15, 17, 33 and 39 ARE factors of 18! and are NOT factors of 18!+1. Therefore only 19 could be a factor of 18!+1.

Answer: C


I Find it difficult to understand the explaination..is there any other way to solve this question... :(


Frankly, solution provided is the easiest from my point of view.

We have that each 15, 17, 33, and 39 IS a factor of 18!, thus NOT a factor of 18!+1. Therefore, only 19 can be a factor of 18!+1. Since one of the options must be correct and we know that A, B, D and E are not, then C must be correct.

Does this make sense?

Check similar questions to practice:
if-a-and-b-are-odd-integers-a-b-represents-the-product-of-144714.html
is-x-1-a-factor-of-100740.html
if-x-and-y-are-positive-integers-what-is-the-gcf-of-x-and-y-144190.html
what-is-the-greatest-common-factor-of-positive-integers-a-126637.html
what-is-the-greatest-common-factor-of-x-and-y-109273.html
what-is-the-greatest-common-divisor-of-positive-integers-m-129802.html
x-and-y-are-positive-integers-such-that-x-8y-12-what-is-the-126743.html
gcd-of-a-b-126427.html
if-a-and-b-are-positive-integers-divisible-by-6-is-6-the-100324.html
if-a-and-b-are-positive-itegers-what-is-the-value-of-a-b-135199.html
is-x-1-a-factor-of-100740.html
find-the-number-that-divides-103251.html
if-n-is-the-least-of-3-consecutive-positive-integers-and-128102.html
if-both-x-and-y-are-positive-integers-that-are-divisible-by-119658.html
what-is-the-greatest-common-divisor-of-positive-integers-m-129802.html
for-every-positive-even-integer-n-the-function-h-n-is-defi-82314.html
if-a-b-and-c-are-positive-integers-with-a-b-c-85644.html
x-is-the-product-of-all-even-numbers-from-2-to-50-inclusive-156545.html
for-every-positive-even-integer-n-the-function-h-n-is-126691.html
for-every-positive-even-integer-n-the-function-h-n-149722.html
if-n-is-a-positive-integer-greater-than-1-then-p-n-represe-144553.html
if-x-y-and-z-are-3-different-prime-numbers-which-of-the-153338.html

Hope this helps.
User avatar
NGGMAT
Intern
Intern
Joined: 20 Oct 2013
Posts: 38
Own Kudos [?]: 7 [0]
Given Kudos: 27
Send PM
Re: Fresh Meat!!! [#permalink] New post   17 May 2014, 07:44
Bunuel wrote:
3. How many different subsets of the set {0, 1, 2, 3, 4, 5} do not contain 0?

A. 16
B. 27
C. 31
D. 32
E. 64

Consider the set without 0: {1, 2, 3, 4, 5}. Each out of 5 elements of the set {1, 2, 3, 4, 5} has TWO options: either to be included in the subset or not, so total number of subsets of this set is 2^5=32. Now, each such set will be a subset of {0, 1, 2, 3, 4, 5} and won't include 0.

Answer: D.


Dear Bunnel

I didnt understand this.

y didnt we take the set {1,2,3,4,5} into consideration and solve like the above qs? where did we get 2^5 from?
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92901
Own Kudos [?]: 618724 [0]
Given Kudos: 81586
Send PM
CAT Tests Forum Quiz Mode
Re: Fresh Meat!!! [#permalink] New post   17 May 2014, 07:51
Expert Reply
NGGMAT wrote:
Bunuel wrote:
3. How many different subsets of the set {0, 1, 2, 3, 4, 5} do not contain 0?

A. 16
B. 27
C. 31
D. 32
E. 64

Consider the set without 0: {1, 2, 3, 4, 5}. Each out of 5 elements of the set {1, 2, 3, 4, 5} has TWO options: either to be included in the subset or not, so total number of subsets of this set is 2^5=32. Now, each such set will be a subset of {0, 1, 2, 3, 4, 5} and won't include 0.

Answer: D.


Dear Bunnel

I didnt understand this.

y didnt we take the set {1,2,3,4,5} into consideration and solve like the above qs? where did we get 2^5 from?


What do you mean by the red part?

As for 2^5: the number of subsets of n-element set is 2^n, thus the number of subsets of 5-element set {1, 2, 3, 4, 5} is 2^5 (note that this includes an empty set as well as the original set {1, 2, 3, 4, 5}). Now, all subsets of {1, 2, 3, 4, 5} are the subsets of {0, 1, 2, 3, 4, 5} and does not include 0.

Does this make sense?
User avatar
NGGMAT
Intern
Intern
Joined: 20 Oct 2013
Posts: 38
Own Kudos [?]: 7 [0]
Given Kudos: 27
Send PM
Re: Fresh Meat!!! [#permalink] New post   17 May 2014, 08:20
Bunuel wrote:
NGGMAT wrote:
Bunuel wrote:
3. How many different subsets of the set {0, 1, 2, 3, 4, 5} do not contain 0?

A. 16
B. 27
C. 31
D. 32
E. 64

Consider the set without 0: {1, 2, 3, 4, 5}. Each out of 5 elements of the set {1, 2, 3, 4, 5} has TWO options: either to be included in the subset or not, so total number of subsets of this set is 2^5=32. Now, each such set will be a subset of {0, 1, 2, 3, 4, 5} and won't include 0.

Answer: D.


Dear Bunnel

I didnt understand this.

y didnt we take the set {1,2,3,4,5} into consideration and solve like the above qs? where did we get 2^5 from?


What do you mean by the red part?

As for 2^5: the number of subsets of n-element set is 2^n, thus the number of subsets of 5-element set {1, 2, 3, 4, 5} is 2^5 (note that this includes an empty set as well as the original set {1, 2, 3, 4, 5}). Now, all subsets of {1, 2, 3, 4, 5} are the subsets of {0, 1, 2, 3, 4, 5} and does not include 0.

Does this make sense?


By red part i meant that y we havent solved it like we did the below qs:

2. Set S contains 7 different letters. How many subsets of set S, including an empty set, contain at most 3 letters?

A. 29
B. 56
C. 57
D. 63
E. 64

1 empty set;
C^1_7=7 sets with one element;
C^2_7=21 sets with two elements;
C^3_7=35 sets with three element.

Total 1+7+21+35=64 sets

y did 2^n come into qs 3 and not qs 2?
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92901
Own Kudos [?]: 618724 [0]
Given Kudos: 81586
Send PM
CAT Tests Forum Quiz Mode
Re: Fresh Meat!!! [#permalink] New post   17 May 2014, 08:39
Expert Reply
NGGMAT wrote:
Bunuel wrote:
NGGMAT wrote:
Dear Bunnel

I didnt understand this.

y didnt we take the set {1,2,3,4,5} into consideration and solve like the above qs? where did we get 2^5 from?


What do you mean by the red part?

As for 2^5: the number of subsets of n-element set is 2^n, thus the number of subsets of 5-element set {1, 2, 3, 4, 5} is 2^5 (note that this includes an empty set as well as the original set {1, 2, 3, 4, 5}). Now, all subsets of {1, 2, 3, 4, 5} are the subsets of {0, 1, 2, 3, 4, 5} and does not include 0.

Does this make sense?


By red part i meant that y we havent solved it like we did the below qs:

2. Set S contains 7 different letters. How many subsets of set S, including an empty set, contain at most 3 letters?

A. 29
B. 56
C. 57
D. 63
E. 64

1 empty set;
C^1_7=7 sets with one element;
C^2_7=21 sets with two elements;
C^3_7=35 sets with three element.

Total 1+7+21+35=64 sets

y did 2^n come into qs 3 and not qs 2?


We could use 2^n for the second question too:

{The number of subsets with 0, 1, 2, or 3 terms} = {The total # of subsets} - {Subsets with 4, 5, 6, or 7 elements} = \(2^7 - (C^4_7+C^5_7+C^6_7+C^7_7)=128-(35+21+7+1)=64\).

But as you can see this approach is longer than the one used in my solution for that question.
avatar
logophobic
Intern
Intern
Joined: 03 Sep 2014
Posts: 5
Own Kudos [?]: 9 [0]
Given Kudos: 10
Send PM
Re: Fresh Meat!!! [#permalink] New post   Updated on: 09 Sep 2014, 07:46
Bunuel wrote:
3. How many different subsets of the set {0, 1, 2, 3, 4, 5} do not contain 0?

A. 16
B. 27
C. 31
D. 32
E. 64

Consider the set without 0: {1, 2, 3, 4, 5}. Each out of 5 elements of the set {1, 2, 3, 4, 5} has TWO options: either to be included in the subset or not, so total number of subsets of this set is 2^5=32. Now, each such set will be a subset of {0, 1, 2, 3, 4, 5} and won't include 0.

Answer: D.


I used a choose method and got 31. With the binary method you used, there is a set which contains no numbers. This increases the number to 32. But the question doesn't say there can be a subset with no numbers because 0 is also not included... but I like the binary method & may use it on these kinds of problems & just subtract 1 if that is necessary so THANK YOU. :-D Thank you

Originally posted by logophobic on 09 Sep 2014, 07:35.
Last edited by logophobic on 09 Sep 2014, 07:46, edited 3 times in total.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92901
Own Kudos [?]: 618724 [1]
Given Kudos: 81586
Send PM
CAT Tests Forum Quiz Mode
Re: Fresh Meat!!! [#permalink] New post   09 Sep 2014, 07:38
1
Kudos
Expert Reply
logophobic wrote:
Bunuel wrote:
3. How many different subsets of the set {0, 1, 2, 3, 4, 5} do not contain 0?

A. 16
B. 27
C. 31
D. 32
E. 64

Consider the set without 0: {1, 2, 3, 4, 5}. Each out of 5 elements of the set {1, 2, 3, 4, 5} has TWO options: either to be included in the subset or not, so total number of subsets of this set is 2^5=32. Now, each such set will be a subset of {0, 1, 2, 3, 4, 5} and won't include 0.

Answer: D.


I used a choose method and got 31. With the binary method you used, there is a set which contains no numbers. This increases the number to 32. But the question doesn't say there can be a subset with no numbers because 0 is also not included...


Empty set is a subset of all non-empty sets.
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32645
Own Kudos [?]: 821 [0]
Given Kudos: 0
Send PM
Re: Fresh Meat!!! [#permalink] New post   12 Aug 2023, 06:15
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 Club Bot
gmatclubot
Re: Fresh Meat!!! [#permalink]
12 Aug 2023, 06:15
   1   2   3 
Moderators:
Bunuel
Math Expert
92901 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions