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

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

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....

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

Is the answer C - 210?

Thanks!
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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
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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
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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...
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by leonswati » Mon Sep 19, 2011 5:35 am
Juggernaut_86...

can u plz explain how did u get 210
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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
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