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

Redeem

Target Test Prep · GMAT

Choose how you want to prepare

Learn live with an expert or move at your own pace. Every option includes the complete TTP study system.

★★★★★5.0559 reviews
GMATLiveTeach 7 seats left
Chris Peckover
NEXT LIVE COHORT

Oct 13 to Jan 7, 2027

with Chris Peckover

Schedule
Tue, Thu · 8:00 to 10:00 PM ET
Included
40 live hours + 6 months of GMAT OnDemand
  • Live instruction and real-time questions
  • Class recordings and assigned practice
View class & enroll
Limited cohort · enrollment openTarget Test Prep
EALiveTeach 5 seats left
Logan Thompson
EXECUTIVE ASSESSMENT

Sep 6 to Dec 6, 2026

with Logan Thompson

Schedule
Sun · 9:30 AM to 12:30 PM ET
Included
Live EA class + 6 months of EA OnDemand
  • Expert-led weekly online sessions
  • EA Masterclass access between classes
View EA class & enroll
Limited cohort · enrollment openTarget Test Prep
GMATOnDemand Start anytime
SELF-PACED MASTERCLASS

Target Test Prep GMAT OnDemand

Complete access from day one. Study on your schedule.

130-point score guarantee
$0to start then $127/mo
  • Personalized study plan and analytics
  • Thousands of lessons and practice questions
Start free 5-day trial
Read 559 reviewsTarget Test Prep

Compare the format, schedule, and included access before enrolling. Prices and seat counts shown reflect the supplied offer details.

s(n) pls helppp

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 131
Joined: Tue Aug 05, 2008 3:28 pm
Thanked: 2 times
by mariah » Mon Feb 02, 2009 3:34 pm
S(n) is denoted that the number of the factors n has, for example S(120)=5, because 120=2*2*2*3*5. If S(m)=4, S(q)=12, S(mq)=?

oa 16
i see its very easy but i am having problems with such kind of Q., (with functions as well)
S(m) - 2 fac.
S(q)-3 fac
both -5 fact.
and how we get 16 please explain !

damn, i think i must get some sleep!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 158
Joined: Tue Sep 30, 2008 8:47 amFollowed by: 1 member
Thanked: 23 times
GMAT Score:660

by DeepakR » Mon Feb 02, 2009 4:24 pm
S(m)=4 = 2*2 hence m=2 and S(q)=12=2*2*3 hence q=3. Now mq=2*3=6.
S(mq)=S(6)=3*2=2. Is the answer 2 ?

- Deepak
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 138
Joined: Thu Jan 15, 2009 7:52 am
Location: Steamboat Springs, CO
Thanked: 15 times

by gaggleofgirls » Mon Feb 02, 2009 4:37 pm
The question appears to be missing the word "prime" becuase what you are showing are the prime factors of the number (for example with s(120) = 5 becuase the primer number 2*2*2*3*5 = 120.

s(n) will not be unique, so you can't figure out n by kn owing s(n) (for example, s(n)=5 is true for 120, but also for 32 (2*2*2*2*2) and for 48 (2*2*2*2*3) and for 3125 (5*5*5*5*5).

The key thing here is that prime factors are reduced as low as they can go, so when you multiple one number times another (for example 120 * 32), then the number of prime factors in the product will be the number of primer factors of the first number + the number of prime factors of the second number (so, for 120 * 32, there will be 5 + 5 prime factors, which will be 2*2*2*3*5*2*2*2*2*2. Both 120*32 and 2*2*2*3*5*2*2*2*2*2 = 3840).

DeepakR you were mistaking s(n) to be the number n instead of the number of prime factors of n.

So, what the question is asking is if s(m) = 4 (if the number m has 4 prime factors) and s(q) = 12 (the number q has 12 prime factors) then how many prime factors are there in the number m*q, which I have shown will be s(m) + s(q), which for this problem = 4 + 12 = 16.

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

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 2623
Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members
Location: Montreal
Thanked: 1090 times
GMAT Score:780

by Ian Stewart » Tue Feb 03, 2009 5:30 am
Carrie has a nice solution above. I'd add that, if you are asked 'how many prime factors does 120 have?', the question normally should be taken to mean 'how many *distinct* prime factors does 120 have?' The answer to that question is three: the only primes which divide 120 are 2, 3 and 5.

The wording in the original question above is very awkward, and I'm curious to know where the question is from - you would never see such wording on the real test, and if all the questions in your book are phrased like this one, it's time to find a better book. s(n) is measuring what is known, in Number Theory, as the 'length' of n - the number of primes, distinct or not, you would need to multiply together to get n. A number like 16 has only one prime factor - 2 - but it has length four, because we need to multiply four 2's to get 16.

You do not need to know what the 'length' of a number is for the GMAT, but there is one question in GMATPrep (I think, or one of the OGs) about this concept - they explain what the 'length' means in the question itself.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 131
Joined: Tue Aug 05, 2008 3:28 pm
Thanked: 2 times

by mariah » Sat Feb 07, 2009 3:29 pm
oa 16
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1