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

 It is currently 13 Oct 2019, 23:33

### 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

# How many integers less than 100 have exactly 4 odd factors b

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

### Hide Tags

Senior Manager
Joined: 13 Oct 2016
Posts: 359
GPA: 3.98
How many integers less than 100 have exactly 4 odd factors b  [#permalink]

### Show Tags

31 Oct 2016, 03:43
1
In order to achieve requested 4 factors the number should be in the form p^3 or p*q (giving 3+1 and 2+2 total number of factors), where p, and q are odd prime factors.
In first case we have only one match - 3^3 = 27
Second case we’ll calculate in ascending order to evade double counting:
3*5=15
3*7=21
3*11=33
….
3*31=93
____________
5*7=35
5*11=55

5*19=95
____________
7*11=77
7*13=91
Total 16

Total number of integers = 16+1=17

Answer D.
Current Student
Joined: 12 Aug 2015
Posts: 2574
Schools: Boston U '20 (M)
GRE 1: Q169 V154
How many integers less than 100 have exactly 4 odd factors b  [#permalink]

### Show Tags

16 Jan 2017, 05:44
Great Question.
Here is what i did on this one ->
Number can be of the form -> Prime^3 or Prime*prime
Where no prime is 2.

Hence the numbers will be ->
3^3
3*5
3*7
3*11
3*13
3*17
3*19
3*23
3*29
3*31
5*7
5*11
5*13
5*17
5*19
7*11
7*13
THAT'S IT.
Clearly there are 17 such possibilities.
Hence D.

_________________
Manager
Joined: 22 May 2015
Posts: 126
Re: How many integers less than 100 have exactly 4 odd factors b  [#permalink]

### Show Tags

16 Jan 2017, 09:45
The question is easy to solve if we know this rule , no of odd factors for a number X = a^p * b^q where a and b are prime numbers is (p+1)*(q+1)

So possible ways to have 4 odd factors are X = a*b or a^3.
Listing the prime numbers 3,5,7,11,13,17,19,23,29,31
for 3 - 9 combinations+1 combination ( 3^3)
for 5 - 5 combinations
for 7 - 2 combinations
=>17
_________________
Consistency is the Key
Intern
Joined: 10 Dec 2016
Posts: 21
Re: How many integers less than 100 have exactly 4 odd factors b  [#permalink]

### Show Tags

06 Feb 2019, 07:22
Hi Bunuel ,

Can we consider negative integers in this case?
Re: How many integers less than 100 have exactly 4 odd factors b   [#permalink] 06 Feb 2019, 07:22

Go to page   Previous    1   2   [ 24 posts ]

Display posts from previous: Sort by

# How many integers less than 100 have exactly 4 odd factors b

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

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