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 →

Question on Perfect Square 5

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Legendary Member
Posts: 698
Joined: Tue Jul 21, 2015 12:12 amFollowed by: 26 members
Location: Noida, India
Thanked: 32 times
GMAT Score:740
by richachampion » Mon Oct 17, 2016 3:07 am
The number N is not a perfect square. There are 8 factors of N between 1 and N^0.5
How many total factors does N have ?
A) 16
B) 18
C) 19
D) 20
E) 22
R I C H A,
My GMAT Journey: 470 → 720 → 740
Target Score: 760+
[email protected]
1. Press thanks if you like my solution.
2. Contact me if you are not improving. (No Free Lunch!)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
Legendary Member
Posts: 698
Joined: Tue Jul 21, 2015 12:12 amFollowed by: 26 members
Location: Noida, India
Thanked: 32 times
GMAT Score:740

by richachampion » Mon Oct 17, 2016 3:08 am
OA: B
R I C H A,
My GMAT Journey: 470 → 720 → 740
Target Score: 760+
[email protected]
1. Press thanks if you like my solution.
2. Contact me if you are not improving. (No Free Lunch!)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

by Brent@GMATPrepNow » Mon Oct 17, 2016 6:47 am
I have added "INTEGER" to the question to make it more GMAT-like.
richachampion wrote:The INTEGER N is not a perfect square. There are 8 factors of N between 1 and N^0.5 How many total factors does N have ?

A) 16
B) 18
C) 19
D) 20
E) 22
Note: N^(0.5) = √N

If integer K is not a perfect square then HALF of the positive factors of K will be LESS THAN √K and HALF of the positive factors of K will be GREATER THAN √K.

Example: the factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
The square root of 24 equals 4.something. So, as we can see, 4 of the factors are less than 4.something, and 4 of the factors are greater than 4.something

In this question, we're told that N is not a perfect square and there are 8 factors BETWEEN 1 and √N. So, we are not including 1 as a factor. Since 1 is a factor of all integers, we can conclude that there are 9 factors LESS THAN √N, which means that are 9 factors GREATER THAN √N.

So, the total number of factors = 9 + 9 = 18
Answer: A

RELATED VIDEOS
- Introduction to exponents: https://www.gmatprepnow.com/module/gmat ... video/1021
- Squares of integers: https://www.gmatprepnow.com/module/gmat ... /video/829
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 698
Joined: Tue Jul 21, 2015 12:12 amFollowed by: 26 members
Location: Noida, India
Thanked: 32 times
GMAT Score:740

by richachampion » Mon Oct 17, 2016 10:40 am
Brent@GMATPrepNow wrote:I have added "INTEGER" to the question to make it more GMAT-like.
Thanks for the amendment sir and thanks for making it in a structured and correct format.
R I C H A,
My GMAT Journey: 470 → 720 → 740
Target Score: 760+
[email protected]
1. Press thanks if you like my solution.
2. Contact me if you are not improving. (No Free Lunch!)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members
Location: East Bay all the way
Thanked: 625 times
GMAT Score:780

by Matt@VeritasPrep » Fri Oct 28, 2016 12:35 am
Another way of thinking about this: if N is not a perfect square, its factors can be broken into pairs whose product is N. For instance, suppose N = 30. Then we have

30 = 1 * 30
30 = 2 * 15
30 = 3 * 10
30 = 5 * 6

We've got THREE factors between 1 and √30, so we've got 3 pairs of factors, plus 1 and 30 itself.

From there, we can generalize. If N is a positive integer that is not a perfect square, and N has x factors between 1 and √N, then N has 2*x + 1 + 1 factors: the x pairs, the number 1, and x itself.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1