GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 19 Oct 2019, 13:48

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.

Close

Request Expert Reply

Confirm Cancel

How many subsets of {1,2,3,4,5,6,7,8} contain at least one prime numbe

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 8017
GMAT 1: 760 Q51 V42
GPA: 3.82
How many subsets of {1,2,3,4,5,6,7,8} contain at least one prime numbe  [#permalink]

Show Tags

New post 13 Dec 2018, 06:12
11
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

55% (02:06) correct 45% (02:25) wrong based on 56 sessions

HideShow timer Statistics

[Math Revolution GMAT math practice question]

How many subsets of \({1,2,3,4,5,6,7,8}\) contain at least one prime number?

\(A. 60\)
\(B. 120\)
\(C. 150\)
\(D. 180\)
\(E. 240\)

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Manager
Manager
avatar
G
Joined: 14 Jun 2018
Posts: 217
Re: How many subsets of {1,2,3,4,5,6,7,8} contain at least one prime numbe  [#permalink]

Show Tags

New post 13 Dec 2018, 07:29
1
1
Total subsets = 2^8
Out of all the nos , 4 are prime and 4 are non prime.
Subsets without any prime = 2^4
Subsets with at least one prime = 256-16 = 240
GMATH Teacher
User avatar
P
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: How many subsets of {1,2,3,4,5,6,7,8} contain at least one prime numbe  [#permalink]

Show Tags

New post 13 Dec 2018, 08:55
MathRevolution wrote:
[Math Revolution GMAT math practice question]

How many subsets of \({1,2,3,4,5,6,7,8}\) contain at least one prime number?

\(A. 60\)
\(B. 120\)
\(C. 150\)
\(D. 180\)
\(E. 240\)

(This solution is similar to pandeyashwin´s above, but I guess it makes the reasoning a bit more explicit!)

\(\left. \matrix{
\matrix{
{\underline {\,\,\,1\,\,\,} } \cr
{{\rm{yes/no}}} \cr

} \,\,\,\,\matrix{
{\underline {\,\,\,2\,\,\,} } \cr
{{\rm{yes/no}}} \cr

} \,\,\, \ldots \,\,\,\,\matrix{
{\underline {\,\,\,7\,\,\,} } \cr
{{\rm{yes/no}}} \cr

} \,\,\,\,\matrix{
{\underline {\,\,\,8\,\,\,} } \cr
{{\rm{yes/no}}} \cr

} \,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{2^8}\,\,{\rm{subsets}} \hfill \cr
\matrix{
{\underline {\,\,\,1\,\,\,} } \cr
{{\rm{yes/no}}} \cr

} \,\,\,\,\matrix{
{\underline {\,\,\,4\,\,\,} } \cr
{{\rm{yes/no}}} \cr

} \,\,\,\,\matrix{
{\underline {\,\,\,6\,\,\,} } \cr
{{\rm{yes/no}}} \cr

} \,\,\,\,\matrix{
{\underline {\,\,\,8\,\,\,} } \cr
{{\rm{yes/no}}} \cr

} \,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{2^4}\,\,{\rm{subsets}}\,\,{\rm{with}}\,\,{\rm{no}}\,{\rm{ - }}\,{\rm{primes}}\,\,\,\, \hfill \cr} \right\}\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,? = {2^8} - {2^4} = {2^4}\left( {{2^4} - 1} \right) = 240\)


Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Senior Manager
Senior Manager
avatar
P
Joined: 27 Dec 2016
Posts: 309
CAT Tests
Re: How many subsets of {1,2,3,4,5,6,7,8} contain at least one prime numbe  [#permalink]

Show Tags

New post 13 Dec 2018, 19:23
Could someone please explain how we are calculating 2^8 as the total subsets?
Intern
Intern
avatar
Joined: 02 Dec 2018
Posts: 3
How many subsets of {1,2,3,4,5,6,7,8} contain at least one prime numbe  [#permalink]

Show Tags

New post 14 Dec 2018, 01:57
1
csaluja wrote:
Could someone please explain how we are calculating 2^8 as the total subsets?


Take a set A containing only 1 element in it; A={a}
Total subsets possible=2; the set itself and the null set

Take another set B with two elements in it
B={a, s}
Total subsets={a},{s},{a,s} and {}
Therefore, 4=(2^2) subsets possible

You can check it for any other small no. So, we can say that total subsets for a set containing n elements is (2^n)

Posted from my mobile device
Intern
Intern
avatar
Joined: 02 Dec 2018
Posts: 3
Re: How many subsets of {1,2,3,4,5,6,7,8} contain at least one prime numbe  [#permalink]

Show Tags

New post 14 Dec 2018, 02:00
1
csaluja wrote:
Could someone please explain how we are calculating 2^8 as the total subsets?


Take a set A containing only 1 element in it; A={a}
Total subsets possible=2; the set itself and the null set

Take another set B with two elements in it
B={a, s}
Total subsets={a},{s},{a,s} and {}
Therefore, 4=(2^2) subsets possible

You can check it for any other small no. So, we can say that total subsets for a set containing n elements is (2^n)

Posted from my mobile device
GMATH Teacher
User avatar
P
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: How many subsets of {1,2,3,4,5,6,7,8} contain at least one prime numbe  [#permalink]

Show Tags

New post 14 Dec 2018, 12:08
csaluja wrote:
Could someone please explain how we are calculating 2^8 as the total subsets?

Hi csaluja !

Let me add to ShubhamAjmera95 ´s correct explanation:

Each element that belongs to the set X={1,2,..,7,8} wil be present ("yes") or will not be present ("no") in any given subset of the set X.

Therefore there are 2 possibilities for 1 ("yes","no") and for each of them, there are two possibilities for 2 ("yes", "no"), and so on.

The sequential application of the Multiplicative Principle goes:

2 (possibilities for 1, "yes" or "no") x 2 (idem for 2) x ... x 2 (idem for 7) x 2 (idem for 8) gives 2^8, the number of possible subsets of X.

Some explicit examples of the reasoning explained above:

"no" , "no" , "no" , ... , "no" ::: gives the null (void) set, that is, the set with no elements.
"yes" , "no" , "no" , ... , "no" ::: gives {1}
"yes" , "no" , "yes" , "no" , ... , "yes", "no" ::: gives {1, 3, 5, 7}
"yes" , "yes" , "yes" , ... , "yes", "yes" ::: gives X itself

I hope things got clearer.

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Intern
Intern
avatar
Joined: 31 Mar 2017
Posts: 8
Re: How many subsets of {1,2,3,4,5,6,7,8} contain at least one prime numbe  [#permalink]

Show Tags

New post 16 Dec 2018, 16:35
2^8-2^4= 256 - 16 = 240

Posted from my mobile device
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 8017
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: How many subsets of {1,2,3,4,5,6,7,8} contain at least one prime numbe  [#permalink]

Show Tags

New post 16 Dec 2018, 18:39
=>

It is easiest to use complementary counting. That is, count the number of subsets that contain no prime number and subtract it from the total number of subsets.

The number of subsets containing no prime number is the number of subsets of \({ 1, 4, 6, 8 }\). Note that 1 is neither a prime number nor a composite number.

The number of subsets of \({1,2,3,4,5,6,7,8}\) is \(2^8 = 256.\)
The number of subsets of \({1,4,6,8}\) is \(2^4 = 16.\)
Thus, the number of subsets of \({1,2,3,4,5,6,7,8}\) containing at least one prime number is \(256 – 16 = 240.\)

Therefore, the answer is E.
Answer: E
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Target Test Prep Representative
User avatar
D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8109
Location: United States (CA)
Re: How many subsets of {1,2,3,4,5,6,7,8} contain at least one prime numbe  [#permalink]

Show Tags

New post 14 Mar 2019, 07:18
MathRevolution wrote:
[Math Revolution GMAT math practice question]

How many subsets of \({1,2,3,4,5,6,7,8}\) contain at least one prime number?

\(A. 60\)
\(B. 120\)
\(C. 150\)
\(D. 180\)
\(E. 240\)


We can use the formula:

The number of subsets with at least one prime number = Total number of subsets - the number of subsets that have no prime numbers

The total number of subsets of a set with n elements is 2^n. Therefore, there are 2^8 subsets in the given set. Since the prime numbers are 2, 3, 5, and 7, the numbers in the set that are not primes are 1, 4, 6 and 8. The number of subsets these 4 numbers can create is 2^4.

Therefore, the number of subsets with at least one prime number is 2^8 - 2^4 = 256 - 16 = 240.

Answer: E.
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

GMAT Club Bot
Re: How many subsets of {1,2,3,4,5,6,7,8} contain at least one prime numbe   [#permalink] 14 Mar 2019, 07:18
Display posts from previous: Sort by

How many subsets of {1,2,3,4,5,6,7,8} contain at least one prime numbe

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne