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

 It is currently 22 Feb 2019, 10:36

### 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

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

## Events & Promotions

###### Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Free GMAT RC Webinar

February 23, 2019

February 23, 2019

07:00 AM PST

09:00 AM PST

Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT
• ### FREE Quant Workshop by e-GMAT!

February 24, 2019

February 24, 2019

07:00 AM PST

09:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.

# If the least common multiple of positive integers A and B is 160 and A

Author Message
TAGS:

### Hide Tags

Manager
Joined: 15 Feb 2018
Posts: 246
If the least common multiple of positive integers A and B is 160 and A  [#permalink]

### Show Tags

11 Feb 2019, 18:18
3
00:00

Difficulty:

35% (medium)

Question Stats:

67% (01:35) correct 33% (01:32) wrong based on 24 sessions

### HideShow timer Statistics

If the least common multiple of positive integers A and B is 160 and A:B=4:5, what is the greatest common divisor of A and B?

A) 8
B) 9
C) 10
D) 12
E) 15
Manager
Joined: 07 Aug 2017
Posts: 59
Location: India
GPA: 4
WE: Information Technology (Consulting)
Re: If the least common multiple of positive integers A and B is 160 and A  [#permalink]

### Show Tags

11 Feb 2019, 20:47
2
From the ratio we can consider A=4x and B=5x.
GCD(A,B)=x

Property of LCM, GCD says, $$A*B=LCM(A,B)*GCD(A,B)$$
$$20x^2=160*x$$
$$20x=160$$
$$x=8$$
GCD(A,B)=8

Ans - A

----------------------------------------------------------------
Manager
Joined: 15 Feb 2018
Posts: 246
Re: If the least common multiple of positive integers A and B is 160 and A  [#permalink]

### Show Tags

16 Feb 2019, 19:52

4 and 5 are relative prime numbers
A=4G
B=5G

L=4·5·G=160
20G=160, G=8
A
Manager
Joined: 12 Apr 2011
Posts: 80
Location: United Arab Emirates
Concentration: Strategy, Marketing
Schools: CBS '21, Yale '21, INSEAD
GMAT 1: 670 Q50 V31
WE: Marketing (Telecommunications)
Re: If the least common multiple of positive integers A and B is 160 and A  [#permalink]

### Show Tags

17 Feb 2019, 22:24
philipssonicare wrote:
If the least common multiple of positive integers A and B is 160 and A:B=4:5, what is the greatest common divisor of A and B?

A) 8
B) 9
C) 10
D) 12
E) 15

Since LCM is 160, both numbers A & B together must have all the roots of 160.

Roots of 160 are = 5*2*2*2*2*2 = 5 * (2^5)

Now since A/B = 4/5 = (2^2)/5
=> A has 2^2 as additional factors over B
and B has 5 as additional factor A
(2^3) are the remaining roots between A and B which must b common.

=> A can be equal to 2^5
and B can be equal to (2^3)*5

Hence the GCD between the two is (2^3) = 8

Therefore option A is the correct answer.
_________________

Hit Kudos if you like what you see!

Re: If the least common multiple of positive integers A and B is 160 and A   [#permalink] 17 Feb 2019, 22:24
Display posts from previous: Sort by