BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

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

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members
Location: Las Vegas, USA
Thanked: 19 times
by Max@Math Revolution » Thu Dec 13, 2018 4:57 am

Timer

00:00

Answers

A

B

C

D

E

Stats

Difficulty—

[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
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 1449
Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members
Thanked: 59 times

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

by fskilnik@GMATH » Thu Dec 13, 2018 7:40 am
Max@Math Revolution 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
Very nice problem, Max. Congrats!
$$\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$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members
Location: Las Vegas, USA
Thanked: 19 times

by Max@Math Revolution » Sun Dec 16, 2018 5:25 pm
=>

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
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8154
Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members
Location: Los Angeles, CA
Thanked: 43 times

by Scott@TargetTestPrep » Thu Mar 14, 2019 6:03 am
Max@Math Revolution 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
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1