Last visit was: 22 Nov 2024, 12:19 It is currently 22 Nov 2024, 12:19
Decision Tracker
My Rewards
New comers' posts
New posts
Unanswered

Close

GRE Prep 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 GRE 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
PREVIOUS TOPIC
NEXT TOPIC

The integer K is positive, but less than 400. If 21K is a multiple of

Tags :
Find Similar Topics  About  Add a Tag

Show Tags
Hide Tags

User avatar
D
GeminiHeat
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Own Kudos [?]: 3621 [3]
Given Kudos: 1053
GPA: 3.39
Send PM
The integer K is positive, but less than 400. If 21K is a multiple of [#permalink] New post   23 May 2021, 23:50
2
Expert Reply
1
Bookmarks
00:00

Question Stats:

45% (01:33) correct 55% (01:38) wrong based on 20 sessions

Hide Show timer Statistics

The integer K is positive, but less than 400. If 21K is a multiple of 180, how many unique prime factors does K have?

A. 1

B. 2

C. 3

D. 4

E. 5
ShowHide Answer
Official Answer
C
avatar
niruparai
Intern
Intern
Joined: 09 Feb 2021
Posts: 3
Own Kudos [?]: 0 [0]
Given Kudos: 15
Send PM
Re: The integer K is positive, but less than 400. If 21K is a multiple of [#permalink] New post   24 May 2021, 00:37
c.
avatar
S
void
Senior Manager
Senior Manager
Joined: 03 Dec 2020
Posts: 440
Own Kudos [?]: 61 [0]
Given Kudos: 68
Send PM
Re: The integer K is positive, but less than 400. If 21K is a multiple of [#permalink] New post   24 May 2021, 07:48
is it option d?
User avatar
D
rx10
Retired Moderator
Joined: 02 Dec 2020
Posts: 1831
Own Kudos [?]: 2146 [1]
Given Kudos: 140
GRE 1: Q168 V157

GRE 2: Q167 V161
Send PM
Re: The integer K is positive, but less than 400. If 21K is a multiple of [#permalink] New post   24 May 2021, 08:03
1
21K is a multiple of 180

\(3 * 7 * K = 3 * 3 * 4 * 5 * x\)

\(7 * K = 60 * x\)

Hence \(K\) will be \(60\) and \(x\) will be \(7\)

Factors of \(60 = 1 , 2 , 3 , 4 , 5 , 6 , 10 , 12 , 15 , 20 , 30 , 60\)

Unique prime factors = \(2 , 3 , 5\)

Answer C
User avatar
G
BrushMyQuant
Moderator
Moderator
Joined: 02 Jan 2020
Status:GRE Quant Tutor
Posts: 1111
Own Kudos [?]: 964 [0]
Given Kudos: 9
Location: India
Concentration: General Management
Schools: XLRI Jamshedpur, India - Class of 2014
GMAT 1: 700 Q51 V31
GPA: 2.8
WE:Engineering (Computer Software)
Send PM
Re: The integer K is positive, but less than 400. If 21K is a multiple of [#permalink] New post   28 Apr 2023, 11:27
↧↧↧ Weekly Video Solution to the Problem Series ↧↧↧




Given that The integer K is positive, but less than 400 and 21K is a multiple of 180. And we need to find how many unique prime factors does K have?

21K is a multiple of 180
=> 21K is divisible by 180
21K = 3*7*K and 180 = 3*60

So, for 21K to be divisible by 60
K should be divisible by 60

=> K is a multiple of 60 (=2^2 * 3 * 5)
Unique prime factors of K = 3

So, Answer will be C
Hope it helps!

Watch the following video to learn the basics of Factors and Multiples

Prep Club for GRE Bot
gmatclubot
Re: The integer K is positive, but less than 400. If 21K is a multiple of [#permalink]
28 Apr 2023, 11:27
Moderators:
adewale223
GRE Instructor
84 posts
bronaugust
GRE Forum Moderator
37 posts
BrushMyQuant
Moderator
1111 posts
VibhuAnurag
GRE Instructor
234 posts

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

Main navigation

Partners

GRE Resources

www.ets.org/gre | About | Terms and Conditions and Privacy Policy | Prep Club for GRE Rules | Contact