Integers

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manelgirona: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Thu Oct 15, 2009 11:35 am

by manelgirona » Sun Mar 07, 2010 9:56 am

If the least common multiple between two positive integers is 120 and their ratio is 3:4, what is their greatest common divisor?

a) 5
b) 10
c) 12
d) 15
e) 20

Need your help!

OA: B

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Source: Beat The GMAT — Problem Solving | Sun Mar 07, 2010 9:56 am

thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members; Thanked: 137 times

by thephoenix » Sun Mar 07, 2010 10:11 am

manelgirona wrote:If the least common multiple between two positive integers is 120 and their ratio is 3:4, what is their greatest common divisor?

a) 5
b) 10
c) 12
d) 15
e) 20

Need your help!

OA: B

formulae product of two number=product of their lcm and hcf

let hcf is n
let no's are x and y

so x*y=120*n

now x/y=3/4------>x=3y/4
--->3y^2/4=120n--->y^2=120n*4/3---->y^2=160n--->y^2=4*4*10*n
for y to be a perfect square n has to be 10{bcoz y is an int}

hence hcf is 10

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