Largest possible number that could be divided into x and 2,1

Expert replies

leonswati: Senior | Next Rank: 100 Posts; Posts: 94; Joined: Sun Aug 29, 2010 3:40 amFollowed by: 1 member; Thanked: 3 times

by leonswati » Sun Sep 18, 2011 6:07 pm

Three is the largest number that can be divided evenly into 27 and the positive integer x, while 10 is the largest number that can be divided evenly into both 100 and x. Which of the following is the largest possible number that could be divided into x and 2,100?
30
70
210
300
700

I have no Idea how to approach this... Need help....

Like this post

Source: Beat The GMAT — Problem Solving | Sun Sep 18, 2011 6:07 pm

Juggernaut_86: Senior | Next Rank: 100 Posts; Posts: 33; Joined: Mon Feb 15, 2010 3:40 pm

by Juggernaut_86 » Sun Sep 18, 2011 7:30 pm

Hi,

Is the answer C - 210?

Thanks!

Like this post

knight247: Legendary Member; Posts: 504; Joined: Tue Apr 19, 2011 1:40 pmFollowed by: 11 members; Thanked: 114 times

by knight247 » Sun Sep 18, 2011 11:25 pm

Hi,

This is a GCD Problem. You may want to brush up on ur GCD and LCM finding skills as this explanation would require it.

If we prime factorise 27 and x we have
27=3^2
x=unknown
GCD=3
Meaning x has a MAXIMUM of one 3 in its prime factorisation. Not more.

Similarly,
100=2^2*5^2
x=3*unknown
GCD=2*5
Meaning x has a MAXIMUM of one 2 and one 5 in its prime factorisation. Not more.

So combining both we have x=2*3*5*unknown
We now have to find the GCD of 2100 and x

2100=(2^2)*(3)*(5^2)*(7)
x=2*3*5*unknown
GCD=2*3*5=30

Hence A

Like this post

excavator: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Mon Sep 19, 2011 12:30 am

by excavator » Mon Sep 19, 2011 1:01 am

Hi,

I agree with knight247

I would suggest another method for the same.
Since x is evenly divisible by 3 and 10.
Hence the largest value for x would be 30
Now the GCD..i.e the largest divisor of both for 1200 and 30 would be 30
So its A

Like this post

leonswati: Senior | Next Rank: 100 Posts; Posts: 94; Joined: Sun Aug 29, 2010 3:40 amFollowed by: 1 member; Thanked: 3 times

by leonswati » Mon Sep 19, 2011 5:33 am

Hey Knight,

The IMO to this is c that is 210.... Can u think of as to why is it 210....? thanks...

Like this post

leonswati: Senior | Next Rank: 100 Posts; Posts: 94; Joined: Sun Aug 29, 2010 3:40 amFollowed by: 1 member; Thanked: 3 times

by leonswati » Mon Sep 19, 2011 5:35 am

Juggernaut_86...

can u plz explain how did u get 210

Like this post

knight247: Legendary Member; Posts: 504; Joined: Tue Apr 19, 2011 1:40 pmFollowed by: 11 members; Thanked: 114 times

by knight247 » Mon Sep 19, 2011 5:52 am

Yes you are right. The OA is C

Check the following link

https://www.beatthegmat.com/number-system-t90932.html

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review