NEW HERE? LEARN MORE
closeclose
Last visit was: 01 May 2024, 10:31 It is currently 01 May 2024, 10:31
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

Around the World in 80 Questions (Day 5): What is the number of

SORT BY:
Date
Kudos
 1   2   3   4   5   
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92984
Own Kudos [?]: 620507 [13]
Given Kudos: 81711
Send PM
CAT Tests Forum Quiz Mode
Around the World in 80 Questions (Day 5): What is the number of [#permalink] New post   21 Jul 2023, 08:00
1
Kudos
12
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

35% (medium)

Question Stats:

68% (01:31) correct 32% (02:05) wrong based on 280 sessions
Hide Show timer Statistics
What is the number of positive factors of 900 that are multiples of 5?

A. 27
B. 21
C. 18
D. 15
E. 9



 


This question was provided by GMAT Club
for the Around the World in 80 Questions

Win over $20,000 in prizes: Courses, Tests & more

 



Experience a GMAT Club Test Questions
Yes, you've landed on a GMAT Club Tests question
Craving more? Unlock our full suite of GMAT Club Tests here
Want to experience more? Get a taste of our tests with our free trial today
Rise to the challenge with GMAT Club Tests. Happy practicing!
GMAT Club Tests Check Our Products Try Free Tests
ShowHide Answer
Official Answer
C
User avatar
B
thakurrani81
Intern
Intern
Joined: 09 Dec 2020
Posts: 15
Own Kudos [?]: 14 [1]
Given Kudos: 15
Location: India
Concentration: Strategy, Marketing
Schools: INSEAD Jan'21 Intake IMD
GMAT 1: 640 Q47 V31
GPA: 4
WE:Corporate Finance (Computer Software)
Send PM
Re: Around the World in 80 Questions (Day 5): What is the number of [#permalink] New post   21 Jul 2023, 08:14
1
Kudos
900=2^2*3^2*5^2

if a number is prime factorized as K = P1^a*P2^b.....pn^z , then #(factors) = (a+1)(b+1)....(z+1) , the logic behind this is we are considering each power of every prime factor from 0 to power. but in case where the factor needs to be a multiple of 5 , we can not take 0 as power of 5 because that will mean the factor is not multiple of 5. therefore in this case

#(factors) = (2+1)(2+1)(2)----> last 2 is the powers of 5 we are considering which are 1 and 2.
answer = 18
User avatar
L
Kinshook
GMAT Club Legend
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5346
Own Kudos [?]: 3977 [1]
Given Kudos: 160
Location: India
Schools: HBS '22 CBS '22 Wharton '22
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Send PM
Reviews Badge
Re: Around the World in 80 Questions (Day 5): What is the number of [#permalink] New post   21 Jul 2023, 08:25
1
Kudos
Asked: What is the number of positive factors of 900 that are multiples of 5?

900 = 2^2 * 3^2 * 5^2

Positive factors of 900 that are multiples of 5 are terms in the expansion = (5 + 5^2)(1 + 2 + 2^2)(1+3+3^2)
Number of positive factors of 900 that are multiples of 5 = 2*3*3 = 18

IMO C
User avatar
B
Sushma1215
Intern
Intern
Joined: 12 Mar 2023
Posts: 9
Own Kudos [?]: 7 [0]
Given Kudos: 15
Send PM
Re: Around the World in 80 Questions (Day 5): What is the number of [#permalink] New post   21 Jul 2023, 08:28
positive factors of 900 that are multiples of 5 are - 5,10, 15, 20, 25, 30, 45, 50, 60, 75, 90, 100, 150, 180, 300, 450, 900 -> 17
User avatar
G
limuengaoey
Manager
Manager
Joined: 09 Jun 2021
Posts: 111
Own Kudos [?]: 72 [0]
Given Kudos: 240
Location: Thailand
GMAT 1: 680 Q49 V34
GPA: 3.59
Send PM
Re: Around the World in 80 Questions (Day 5): What is the number of [#permalink] New post   21 Jul 2023, 08:28
900 = 2^2*3^2*5^2
(2+1)(2+1)(2+1) = 27 hence A
User avatar
S
kamalsharmam21
Manager
Manager
Joined: 22 Mar 2023
Posts: 95
Own Kudos [?]: 32 [1]
Given Kudos: 23
Location: India
Schools: IIMA '25
Send PM
Re: Around the World in 80 Questions (Day 5): What is the number of [#permalink] New post   21 Jul 2023, 08:32
1
Kudos
I dis it long way

Factors of 900

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450 and 900

From this the no of multiple aof 5 are counted i.e 18

Posted from my mobile device
User avatar
S
KanikaJain
Manager
Manager
Joined: 06 Jan 2021
Posts: 52
Own Kudos [?]: 29 [1]
Given Kudos: 6
GMAT 1: 610 Q50 V23
GPA: 4
Send PM
Re: Around the World in 80 Questions (Day 5): What is the number of [#permalink] New post   21 Jul 2023, 08:38
1
Kudos
900 = 3*3*2*2*5*5

thus 3*3*2 = 18
thus 18
User avatar
P
nivivacious
Senior Manager
Senior Manager
Joined: 10 Mar 2015
Posts: 343
Own Kudos [?]: 232 [1]
Given Kudos: 175
Location: India
Concentration: Strategy, Marketing
GPA: 3.5
WE:Advertising (Advertising and PR)
Send PM
GMAT ToolKit User
Re: Around the World in 80 Questions (Day 5): What is the number of [#permalink] New post   21 Jul 2023, 08:40
1
Kudos
Bunuel wrote:
What is the number of positive factors of 900 that are multiples of 5?

A. 27
B. 21
C. 18
D. 15
E. 9



 


This question was provided by GMAT Club
for the Around the World in 80 Questions

Win over $20,000 in prizes: Courses, Tests & more

 



Factors of 900: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, and 900
Counting multiples: 18
Hence C
User avatar
L
Archit3110
GMAT Club Legend
GMAT Club Legend
Joined: 18 Aug 2017
Status:You learn more from failure than from success.
Posts: 8023
Own Kudos [?]: 4104 [1]
Given Kudos: 242
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
Send PM
GMAT ToolKit User
Re: Around the World in 80 Questions (Day 5): What is the number of [#permalink] New post   21 Jul 2023, 08:42
1
Kudos
900 prime factors are
2^2 * 3^2 * 5^2
total factors are 27
multiples of 5 ;
2^2*5^2 ; 9
3^2*5^2 ; 9
5^2 ; 3
total 21 factors are multiples of 5
option B


Bunuel wrote:
What is the number of positive factors of 900 that are multiples of 5?

A. 27
B. 21
C. 18
D. 15
E. 9



 


This question was provided by GMAT Club
for the Around the World in 80 Questions

Win over $20,000 in prizes: Courses, Tests & more

 

User avatar
B
Muskaan09
Intern
Intern
Joined: 13 Jun 2023
Posts: 39
Own Kudos [?]: 21 [1]
Given Kudos: 4
Location: India
Send PM
Re: Around the World in 80 Questions (Day 5): What is the number of [#permalink] New post   21 Jul 2023, 08:49
1
Kudos
The answer is 18.

Don’t really have a method for this, just knew the obvious ones and others were multiples of those 5,10,15,20,25,30,45,50,60,75,90,100,150,180,225,300,450,900.

Posted from my mobile device
User avatar
G
Nabneet
Manager
Manager
Joined: 27 Dec 2022
Posts: 115
Own Kudos [?]: 79 [2]
Given Kudos: 40
Location: India
GMAT 1: 550 Q47 V20
WE:Other (Other)
Send PM
Re: Around the World in 80 Questions (Day 5): What is the number of [#permalink] New post   Updated on: 22 Jul 2023, 08:17
2
Kudos
Bunuel wrote:
What is the number of positive factors of 900 that are multiples of 5?

A. 27
B. 21
C. 18
D. 15
E. 9



 


This question was provided by GMAT Club
for the Around the World in 80 Questions

Win over $20,000 in prizes: Courses, Tests & more

 



\(900 = 2^2 * 3^2 * 5^2\)

Total no. of factors of 900 = (2+1)*(2+1)*(2+1)= 3*3*3 =27

No. of factors not multiple 5 = 2, 3, 2^2, 2^2 *3, 2^2 * 3^2 , 3^2 * 2, 3^2 =1,2,3,4,6,9,12,18,36

No of factors multiple of 5 = 27-9 =18

Answer: C

Originally posted by Nabneet on 21 Jul 2023, 08:51.
Last edited by Nabneet on 22 Jul 2023, 08:17, edited 2 times in total.
User avatar
S
1111fate
Manager
Manager
Joined: 19 Oct 2021
Posts: 82
Own Kudos [?]: 35 [0]
Given Kudos: 513
Location: India
Send PM
CAT Tests
Re: Around the World in 80 Questions (Day 5): What is the number of [#permalink] New post   21 Jul 2023, 08:55
the Answer is A
You can prime factorize 900 to get 3 (square) x 2( square) x5 ( square)
hence- (2+1)x(2+1) x(2+1)= 3x3x3=27
Hence the answer is 27
User avatar
G
kratos0906
Manager
Manager
Joined: 19 Apr 2022
Posts: 109
Own Kudos [?]: 76 [1]
Given Kudos: 2
GMAT 1: 700 Q50 V34
GMAT 2: 750 Q49 V42
Send PM
Re: Around the World in 80 Questions (Day 5): What is the number of [#permalink] New post   21 Jul 2023, 08:59
1
Kudos
My Answer: C

900=2^2 * 3^2 * 5^2

Now, for factors to be multiple of 5, power of 2 and can be 0 or 1 or 2 and power of 5 can be 1 or 2.

So, Total factors which are multiple of 5= 3*3*2 = 18
User avatar
S
Avneeshyadav01
Manager
Manager
Joined: 16 Jan 2023
Posts: 63
Own Kudos [?]: 36 [1]
Given Kudos: 44
Location: India
Schools: ISB '25 IIMA '25 IIMB '25 IIMC '25
GMAT 1: 680 Q49 V33
Send PM
Forum Quiz Mode
Re: Around the World in 80 Questions (Day 5): What is the number of [#permalink] New post   21 Jul 2023, 09:02
1
Kudos
Quote:
What is the number of positive factors of 900 that are multiples of 5?

A. 27
B. 21
C. 18
D. 15
E. 9


If N = x^a*y^b, then # positive factors of N = (a+1)(b+1)

900= 2^2*3^2*5^2 = 5(2^2*3^2*5). Now prime factorization inside the bracket will give No. of =ve factors that are multiple of 5. So # factots = 3*3*2 = 18.

OA: C
User avatar
B
Aman0076565
Intern
Intern
Joined: 30 Dec 2021
Posts: 20
Own Kudos [?]: 9 [0]
Given Kudos: 264
Location: India
Schools: Rotman '25 Schulich Sep'23 intake
Send PM
Forum Quiz Mode
Re: Around the World in 80 Questions (Day 5): What is the number of [#permalink] New post   21 Jul 2023, 09:03
Quote:
What is the number of positive factors of 900 that are multiples of 5?

A. 27
B. 21
C. 18
D. 15
E. 9


900 = \(2^2\)*\(3^2\)*\(5^2\)

Total numbers of factors: (2+1)*(2+1)*(2+1) = 27

Total numbers of factors without multiple of 5 = (2+1)*(2+1) = 9
User avatar
S
NiranjanaV
Manager
Manager
Joined: 20 Apr 2022
Posts: 95
Own Kudos [?]: 75 [1]
Given Kudos: 125
Location: India
Schools: Ross '26 (A$$) Darden '26 (D) Tepper '26 (D) Tuck '26 (D) Kellogg '26 (I)
GMAT 1: 730 Q48 V42
GPA: 3.23
Send PM
Re: Around the World in 80 Questions (Day 5): What is the number of [#permalink] New post   21 Jul 2023, 09:07
1
Kudos
900 = 2*2*5*5*3*3

# factors that are multiples of 5 = 5+5+4+4 = 18 [C]
5, 5*2, 5*2*2, 5*3, 5*3*3 (#5)
25, 25*2, 25*2*2, 25*3, 25*3*3 (#5)
5*2*3, 5*2*2*3, 5*2*3*3, 5*2*2*3*3 (#4)
25*2*3, 25*2*2*3, 25*2*3*3, 25*2*2*3*3 (#4)
User avatar
D
$!vakumar.m
Director
Director
Joined: 06 Dec 2021
Posts: 641
Own Kudos [?]: 520 [2]
Given Kudos: 737
Location: India
Concentration: Technology, International Business
GPA: 4
WE:Human Resources (Telecommunications)
Send PM
GMAT ToolKit User
Re: Around the World in 80 Questions (Day 5): What is the number of [#permalink] New post   21 Jul 2023, 09:10
2
Kudos
Let’s find the prime factorization of 900.
900 = 2^2 * 3^2 * 5^2. The number of positive factors of 900 is (2 + 1)(2 + 1)(2 + 1) = 27.
Now, a positive factor of 900 that is a multiple of 5 must have at least one factor of 5.
So, the number of positive factors of 900 that are not multiples of 5 is (2 + 1)(2 + 1)(0 + 1) = 9.
Therefore, the number of positive factors of 900 that are multiples of 5 is 27 - 9 = 18.
Answer C
User avatar
G
RahulJain293
Manager
Manager
Joined: 24 Apr 2022
Posts: 190
Own Kudos [?]: 81 [1]
Given Kudos: 83
Location: India
Concentration: General Management, Nonprofit
GMAT Focus 1:
575 Q80 V79 DI76
Send PM
Re: Around the World in 80 Questions (Day 5): What is the number of [#permalink] New post   21 Jul 2023, 09:12
1
Kudos
IMO C

What is the number of positive factors of 900 that are multiples of 5?

A. 27
B. 21
C. 18
D. 15
E. 9

Solu

900 has 2.2.3.3.5.5 factors

For a number to be a multiple of 5, it needs to have a power of 5 in it.

Here 2.2 and 3.3 have powers of 2 each and hence will have (2+1) 3 factors each.

Hence, 3*3 would be possible pairs of 2 and 3 which is 9 possible pairs and each would pair with 5 and 5 (with power 2) hence 9+9 = 18 such numbers.
User avatar
G
SS.56
Manager
Manager
Joined: 18 Jul 2022
Posts: 87
Own Kudos [?]: 50 [1]
Given Kudos: 1059
Location: Nepal
Schools: IIMA PGPX'23
GMAT 1: 570 Q45 V24
GMAT 2: 620 Q46 V30
Send PM
Re: Around the World in 80 Questions (Day 5): What is the number of [#permalink] New post   21 Jul 2023, 09:29
1
Kudos
Bunuel wrote:
What is the number of positive factors of 900 that are multiples of 5?

A. 27
B. 21
C. 18
D. 15
E. 9



 


This question was provided by GMAT Club
for the Around the World in 80 Questions

Win over $20,000 in prizes: Courses, Tests & more

 



I don't how to deal with this question as 2 mins problem. Anyways, got the answer as 18 where I had to find out all the factors of 900.(Obviously, took more than 2 mins)

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900

We can count with the digits 0 and 5 in the last. There are 18 total.

Answer-B

Waiting for the explanation to reveal.
User avatar
G
vishal_gupta
Manager
Manager
Joined: 11 May 2023
Posts: 154
Own Kudos [?]: 111 [1]
Given Kudos: 41
Location: India
Concentration: General Management, Strategy
Schools: Stanford '26 Wharton '26 Yale '26 Columbia CBS'26 HBS '26 Booth '26 HEC Sep'24 Intake IE Sep'24 intake INSEAD Aug'24 intake LBS '26 Ivey '25 IIMA '25 IIMB '25 IIMC '25 Kellogg '26 Judge '25 Oxford Said'25 Sloan '26 Tuck '26 Stern '26
GPA: 76%
WE:Engineering (Energy and Utilities)
Send PM
Forum Quiz Mode
Re: Around the World in 80 Questions (Day 5): What is the number of [#permalink] New post   21 Jul 2023, 09:40
1
Kudos
Bunuel wrote:
What is the number of positive factors of 900 that are multiples of 5?

A. 27
B. 21
C. 18
D. 15
E. 9



 


This question was provided by GMAT Club
for the Around the World in 80 Questions

Win over $20,000 in prizes: Courses, Tests & more

 



900= 2^2 * 3^2 * 5^2

Total factors of 900 = (2+1)*(2+1)*(2+1) = 27

Factors which are not a multiple of 5 will be when power of 5 is zero.
So, the number would be a factor of 2^2 * 3^2 * 5^0
In that case no. of factors = (2+1)*(2+1)*(0+1) = 9.

Hence total no. of factors that are multiple of 5 = 27-9 = 18.

C is correct choice.
GMAT Club Bot
gmatclubot
Re: Around the World in 80 Questions (Day 5): What is the number of [#permalink]
21 Jul 2023, 09:40
 1   2   3   4   5   
Moderators:
Bunuel
Math Expert
92984 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions