I couldn't think of a more scientific method, but here's how I see it:
First look at what we've got and break it down into prime factors:
6 = 2*3
9 = 3*3
1. tells you that the least common multiple of x and 6 is 30.
30 = 2*3*5. We're lucky, since you can't make too many numbers out of just 2, 3 and 5, with the restriction that 5 MUST be one of x's divisors (there must be a reason for the 5 in 30 - it can't just pop out of nowhere). You can easily tell that there are only 4 possibilities for x:
a. x = 5, case when the lcm of x, 6 and 9 will be 90
b. x = 10, case when the lcm of x, 6 and 9 will be 90
c. x = 15, case when the lcm of x, 6 and 9 will be 90
d. x = 30, case when the lcm of x, 6 and 9 will be 90.
Since you get 90 all over, 1 is sufficient.
2. 45 = 3*3*5. Again, there aren't a lot of possibilities, even fewer in this case:
a. x = 15, with lcm 90
b. x = 45, with lcm 90.
Answer's 90 all over, meaning that 2 is sufficient as well.
BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course
Redeem
Featured Course
Target Test Prep GMAT OnDemand
Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.
- 715+ score guarantee — highest in the industry (99th percentile)
- 52 chapters · 1,500+ lessons · 4,000+ practice questions
- 400 hours of video · 1,500+ instructor-led HD smartboard lessons
- 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
- 24/7 live support + weekly Zoom office hours with GMAT instructors
- TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
- 1,200+ flashcards + AI-powered study assistant & daily calendar
- OnDemand, LiveTeach & GMAT Bootcamp formats available
- Also: GRE, SAT Math & Executive Assessment courses
- MBA Admissions Consulting now available
- 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
- 200,000+ students served
- 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★
5.0
(559 reviews)
130-pt guarantee
$0 to start
then $127/mo
can someone explain this one also?
Source: Beat The GMAT — Problem Solving |
according to 1 - x has to be 5 since LCM is 30 so that is suff
according to 2 - X has to be 5 since LCM is 45 so that is suff
now since we know that x is 5, we can find the LCM of x, 6, 9 to be 90 since x is 5.
I hope I explained correctly. it takes some time to undestand this quesiton, but I am starting to learn.......
Thank you
ST
according to 2 - X has to be 5 since LCM is 45 so that is suff
now since we know that x is 5, we can find the LCM of x, 6, 9 to be 90 since x is 5.
I hope I explained correctly. it takes some time to undestand this quesiton, but I am starting to learn.......
Thank you
ST
Stmt 1 : LCM of x and 6 is 30.
lcm of x,6,9 will be the LCM of 30,9
Stmt1 is sufficient.
similarly
Stmt2 is sufficient.
Thanks
raama
lcm of x,6,9 will be the LCM of 30,9
Stmt1 is sufficient.
similarly
Stmt2 is sufficient.
Thanks
raama
Raama's soln is the simplest and elegent.krisraam wrote:Stmt 1 : LCM of x and 6 is 30.
lcm of x,6,9 will be the LCM of 30,9
Stmt1 is sufficient.
similarly
Stmt2 is sufficient.
Thanks
raama
His soln is based on the following property of LCM:
LCM(a, b, c) = LCM(a, LCM(b,c) ) = LCM( LCM(a,b) , c )
This is your major takeaway.
