NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 11:24 It is currently 26 Apr 2024, 11:24
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

If a, b and c are integers, is ab a multiple of 18?

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92948
Own Kudos [?]: 619219 [3]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
If a, b and c are integers, is ab a multiple of 18? [#permalink] New post   22 Mar 2021, 01:30
3
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

65% (hard)

Question Stats:

55% (01:55) correct 45% (01:50) wrong based on 71 sessions
Hide Show timer Statistics
If a, b and c are integers, is ab a multiple of 18?

(1) 2a = 3b
(2) 2b = 3c
ShowHide Answer
Official Answer
C
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92948
Own Kudos [?]: 619219 [0]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
If a, b and c are integers, is ab a multiple of 18? [#permalink] New post   23 Mar 2021, 01:15
Expert Reply
Bunuel wrote:
If a, b and c are integers, is ab a multiple of 18?

(1) 2a = 3b
(2) 2b = 3c


If a, b and c are integers, is (a·b) a multiple of 18?

Notice that we are told that all variables are integers.

(1) 2a = 3b --> a/b = 3/2. a is a multiple of 3 and b is a multiple of 2. ab must be a multiple of 6 but may or may not be a multiple of 18 (for example consider (a,b) = (3,2) and (a,b) = 9,6). Not sufficient.

(2) 2b = 3c --> b/c = 3/2. b is a multiple of 3. Not sufficient.

(1)+(2) b is a multiple of both 2 and 3, so it must be a multiple of 6 and since a is a multiple of 3, then ab must be a multiple of 6*3 = 18. Sufficient.

Answer: C.

Hope it's clear.
General Discussion
avatar
D
TarunKumar1234
VP
VP
Joined: 14 Jul 2020
Posts: 1139
Own Kudos [?]: 1292 [1]
Given Kudos: 351
Location: India
Send PM
Re: If a, b and c are integers, is ab a multiple of 18? [#permalink] New post   22 Mar 2021, 11:50
1
Kudos
If a, b and c are integers, is ab a multiple of 18?

Stat1: 2a = 3b
a = 3, 6, 9..... and b = 2,4,6,..... Now, ab can or can't be divisible by 18. Not sufficient

Stat2: 2b = 3c
b= 3, 6, 9.... and c = 2,4,6,..... But, we don't have any idea of a. Not sufficient

Combining both, a = 3, 6, 9..... and, b= 6, 12, 18....Now, ab will be divisible by 18. Sufficient

So, I think C. :)
User avatar
P
twobagels
Manager
Manager
Joined: 12 Jul 2020
Posts: 137
Own Kudos [?]: 451 [1]
Given Kudos: 2892
Location: United States (CA)
WE:Science (Other)
Send PM
Re: If a, b and c are integers, is ab a multiple of 18? [#permalink] New post   22 Mar 2021, 16:25
1
Kudos
From statement 1
b is mult of 2
a is mult of 3

insufficient: a*b could be 6 or 18 or other numbers

From statement 2
c is mult of 2
b is mult of 3

insufficient: we don't know anything about a

Combined: statements 1 and 2 give us that b is a multiple of both 2 and 3 (ie mult of 6) and a is a multiple of 3: a*b is minimum a multiple of 18
User avatar
B
jonNNNNNy
Intern
Intern
Joined: 09 Jan 2022
Posts: 11
Own Kudos [?]: 0 [0]
Given Kudos: 11
Send PM
Re: If a, b and c are integers, is ab a multiple of 18? [#permalink] New post   06 Dec 2022, 12:13
what about zero? C because b=0 a=0 hence no we can answer ! answer c
User avatar
Shashi128
Intern
Intern
Joined: 29 Nov 2022
Posts: 2
Own Kudos [?]: 1 [0]
Given Kudos: 0
Location: India
Send PM
Re: If a, b and c are integers, is ab a multiple of 18? [#permalink] New post   06 Dec 2022, 20:24
Taking first statement 2a=3b , a = 3/2 b so b must be multiple of 2 say 2m .a=3m, ab=6m^2 so it depends on value of m to decide if ab is multiple of 18 or not . A is not the answer . Similarly 2b=3c b=3/2c c must be multiple of 2 say c=2p ab = 6p condition can't be determined . B is not the answer .
Now taking both sentence together a= 3/2b let b=2n ,a will be 3n.second statement gives 4n=3c ,c=4/3n as c is integerer so n must be multiple of 3 , n= 3t .a now becomes 6t and b 9t clearly ab is 54t^2 so it is multiple of 18

Posted from my mobile device
GMAT Club Bot
gmatclubot
Re: If a, b and c are integers, is ab a multiple of 18? [#permalink]
06 Dec 2022, 20:24
Moderator:
Bunuel
Math Expert
92947 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