NEW HERE? LEARN MORE
closeclose
Last visit was: 27 Apr 2024, 02:14 It is currently 27 Apr 2024, 02:14
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

The least common multiple and the highest common factor of two positiv

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92951
Own Kudos [?]: 619315 [10]
Given Kudos: 81611
Send PM
CAT Tests Forum Quiz Mode
The least common multiple and the highest common factor of two positiv [#permalink] New post   09 Aug 2021, 07:15
10
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

25% (medium)

Question Stats:

79% (02:11) correct 21% (02:33) wrong based on 78 sessions
Hide Show timer Statistics
The least common multiple and the highest common factor of two positive integers x and y are 105 and 3, respectively. If x + y = 36, the what is the value of 1/x + 1/y ?

(A) 1
(B) 4/35
(C) 1/6
(D) 12/315
(E) 1/315
ShowHide Answer
Official Answer
B
avatar
B
iridescent995
Intern
Intern
Joined: 27 Jun 2021
Posts: 35
Own Kudos [?]: 10 [0]
Given Kudos: 89
Send PM
Re: The least common multiple and the highest common factor of two positiv [#permalink] New post   09 Aug 2021, 07:38
x*y = 3*105
x+y = 36

1/(1/x + 1/y) = 3*105/36

1/x+1/y = 4/35
avatar
B
shivxlon
Intern
Intern
Joined: 02 Dec 2018
Posts: 3
Own Kudos [?]: 4 [1]
Given Kudos: 15
Location: India
Concentration: Finance, Strategy
Send PM
The least common multiple and the highest common factor of two positiv [#permalink] New post   Updated on: 09 Aug 2021, 10:25
1
Bookmarks
Quote:
The least common multiple and the highest common factor of two positive integers x and y are 3 and 105, respectively. If x + y = 36, the what is the value of 1/x + 1/y ?

(A) 1
(B) 4/35
(C) 1/6
(D) 12/315
(E) 1/315


HCF(X,Y) = 3
LCM(X,Y) = 105
also, X+Y = 36

since, we know that X*Y = LCM*HCF, therefore X*Y=3*105

thus 1/x+1/y = (x+y)/x*y = 36/(3*105) = 4/35 (B)

Originally posted by shivxlon on 09 Aug 2021, 08:12.
Last edited by shivxlon on 09 Aug 2021, 10:25, edited 1 time in total.
User avatar
P
sj296
Senior Manager
Senior Manager
Joined: 09 Jul 2014
Posts: 371
Own Kudos [?]: 351 [0]
Given Kudos: 346
Location: India
Concentration: General Management, Finance
Schools: ISB '24
Send PM
Re: The least common multiple and the highest common factor of two positiv [#permalink] New post   09 Aug 2021, 09:50
Bunuel wrote:
The least common multiple and the highest common factor of two positive integers x and y are 3 and 105, respectively. If x + y = 36, the what is the value of 1/x + 1/y ?

(A) 1
(B) 4/35
(C) 1/6
(D) 12/315
(E) 1/315



Hey @Bunnel, the lcm of two positive integers is always greater than HCF, right? so, in this question HCF should be 3 and LCM should be 105.

However, it wouldn't change the answer.
User avatar
L
IanStewart
GMAT Tutor
Joined: 24 Jun 2008
Posts: 4128
Own Kudos [?]: 9247 [0]
Given Kudos: 91
 Q51  V47
Send PM
Re: The least common multiple and the highest common factor of two positiv [#permalink] New post   09 Aug 2021, 10:06
Expert Reply
sj296 wrote:
Hey @Bunnel, the lcm of two positive integers is always greater than HCF, right?


That will be true almost always, but technically, that's not quite right -- the HCF and LCM can also be equal, when your numbers are all the same. The LCM of 25 and 25 is equal to 25, and the HCF of 25 and 25 is also equal to 25, for example. You're very right that there's an error in the question though! :)
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92951
Own Kudos [?]: 619315 [0]
Given Kudos: 81611
Send PM
CAT Tests Forum Quiz Mode
Re: The least common multiple and the highest common factor of two positiv [#permalink] New post   09 Aug 2021, 10:12
Expert Reply
sj296 wrote:
Bunuel wrote:
The least common multiple and the highest common factor of two positive integers x and y are 3 and 105, respectively. If x + y = 36, the what is the value of 1/x + 1/y ?

(A) 1
(B) 4/35
(C) 1/6
(D) 12/315
(E) 1/315



Hey @Bunnel, the lcm of two positive integers is always greater than HCF, right? so, in this question HCF should be 3 and LCM should be 105.

However, it wouldn't change the answer.


Yes, you are right. Edited. Thank you.
User avatar
L
MathRevolution
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10161
Own Kudos [?]: 16608 [1]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
Re: The least common multiple and the highest common factor of two positiv [#permalink] New post   10 Aug 2021, 07:21
1
Kudos
Expert Reply
Product of two numbers (x and y) = LCM (x,y) * HCF (x,y)

=> xy = 105 * 3

=> \(\frac{1}{x} + \frac{1}{y} = \frac{x + y }{ xy} = \frac{36 }{ (105 * 3)} = \frac{12}{105} = \frac{4}{35}\)

Answer B
User avatar
D
BrushMyQuant
Tutor
Joined: 05 Apr 2011
Status:Tutor - BrushMyQuant
Posts: 1778
Own Kudos [?]: 2094 [0]
Given Kudos: 100
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE:Information Technology (Computer Software)
Send PM
Re: The least common multiple and the highest common factor of two positiv [#permalink] New post   04 Aug 2022, 01:32
Expert Reply
Top Contributor
Theory

    ➡ Product of two numbers = Product of their LCM and HCF

The least common multiple and the highest common factor of two positive integers x and y are 105 and 3

LCM = 105, HCF = 3
Product of the numbers = x*y = LCM * HCF = 105 * 3 = 315 ....(1)

If x + y = 36, the what is the value of 1/x + 1/y

x + y = 36
Divide both the sides by xy we get

\(\frac{x + y}{xy}\) = \(\frac{36}{xy}\)
=> \(\frac{x}{xy}\) + \(\frac{y}{xy}\) = \(\frac{36}{315}\) (as xy = 315 from (1) )
=> \(\frac{1}{y}\) + \(\frac{1}{x}\) = \(\frac{4}{35}\)

So, Answer will be B.
Hope it helps!

Watch the following video to Learn the Basics of LCM and GCD

User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32703
Own Kudos [?]: 822 [0]
Given Kudos: 0
Send PM
Re: The least common multiple and the highest common factor of two positiv [#permalink] New post   29 Mar 2024, 07:46
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: The least common multiple and the highest common factor of two positiv [#permalink]
29 Mar 2024, 07:46
Moderators:
Bunuel
Math Expert
92950 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