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Re: Is x and y are positive integers, what is the value of xy? [#permalink]

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26 Apr 2008, 11:50

another thing..with these type of question where we have the GCD and LCM..usually we can tell something like an XY but we cant really tell what X is or what y is...

hi, For (ii) The least common multiple of x and y is 180 isn't x*y = 5400?

my rational...

if 180 is the Lowest Common Multiple, meaning that both x and y have 3, 3, 5, 2, 2 at least appeared twice for x y.

So if

x = 2, ?, 3, 5 y = 2, ?, 3, 5 ------------- x & y's LCM which is 180 = 2* 3* 5* ?* ?*

So after pulling 5 & 3 & 2, we still need one 2 and one 3 to fulfil the 3, 3, 5, 2, 2 = (180) requirement. Having said that, the ? in each x & y should be 2 and 3.

So multiple all 8 digits, it should x*y = 2* 2* 3* 5* 2* 3*3* 5* = 5400?

Re: Is x and y are positive integers, what is the value of xy? [#permalink]

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01 Aug 2011, 09:38

1

This post received KUDOS

GCF * LCM = X*Yit's a general rule 10*180 = 1800 so the the answer is C and u need less than 10 seconds _________________

How can i lose my faith in life's fairness when i know that the dreams of those who sleep on the feathers are not more beautiful than the dreams of those who sleep on the ground? - Jubran Khaleel Jubran

Re: Is x and y are positive integers, what is the value of xy? [#permalink]

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01 Aug 2011, 10:04

Always; if we multiply two positive integers then the multiplication is same as the multiplication of their lcm and gcf. In this case lcm = 180 and gcf = 10 hence xy = (lcm)(gcf) = 180.10 = 1800
_________________

Re: Is x and y are positive integers, what is the value of xy? [#permalink]

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02 Aug 2011, 10:44

manishgeorge wrote:

Could some body help me to understand this a little better.

here is where I am getting stuck

GCF = 10, There for X = 10A nd Y = 10B where A and B are separate constants

for example 20 and 30, here the GDF is 10 and a = 2 and b = 3

sice we dont have a and b from this equation. this is insufficient

statement 2:

LCM is 180 so X*N1 = 180 and Y * N2 = 180

since we do not know the values of N1 and N2 this statement is not sufficient.

even if we combine, we dont have information to solve.

I see come body explaining the answer are LCM*GCD. Could you please tell me how you arrived at that equation

it's a general rule and can always applied . if u want the details about how we arrived at that equation just let me know
_________________

How can i lose my faith in life's fairness when i know that the dreams of those who sleep on the feathers are not more beautiful than the dreams of those who sleep on the ground? - Jubran Khaleel Jubran

Concentration: General Management, Entrepreneurship

GPA: 3.8

WE: Engineering (Energy and Utilities)

Re: Is x and y are positive integers, what is the value of xy? [#permalink]

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19 Sep 2017, 22:46

quiet888 wrote:

Is x and y are positive integers, what is the value of xy?

(i) The greatest common factor of x and y is 10 (ii) The least common multiple of x and y is 180

We can solve this questions using 2 approach. Shorter approach (1 min)

Statement 1: GCF = 10 , (x,y) = (10,20), (10, 30), (20,30), (30,50)...... and so many numbers which are co-prime after division by 10. NOT SUFFICIENT

Statement 2: LCM = 180 , (x,y)= (2,180), (10, 180), (90, 4).... and others NOT SUFFICIENT

Combined : GCF * LCM = x*y .. Its a formula.. SUFFICIENT

Longer approach (Time taking: 2 min ) Statement 1: GCF = 10 , (x,y) = (10,20), (10, 30), (20,30), (30,50)...... and so many numbers which are co-prime after division by 10. NOT SUFFICIENT

Statement 2: LCM = 180 , (x,y)= (2,180), (10, 180), (90, 4).... and others NOT SUFFICIENT

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