IMO [spoiler](C)[/spoiler]

If x and y are positive integers, what is the values of xy?

(1) The greatest common factor of x and y is 10.

x -> 2,5...?
y -> 2,5...?
Not sufficient

(2) The least common multiple of x and y is 180.

180-> 2,2,3,3,5
Not sufficient

(3) Statement 1 and 2

x -> 2,5 = 10
y -> 2,2,3,3,5 = 180

x -> 2,3,3,5 = 90
y -> 2,2,5 = 20

The (3,3) must correspond to only one number or else the GCF would be 2*3*5 instead of 2*5.
The only variation you can make is to change one 2 from x to y.

In both cases 10*180 = 90*20 = 1,800

The correct answer is [spoiler](C)[/spoiler]
https://www.manhattangmat.com/forums/if- ... t1609.html

The easy way to do this is:

GCF and LCM tip #1: (GCF of M and N)*(LCM of M and N) = M*N
GCF and LCM tip #2: GCF of M and N cannot be larger than the difference between M and N
GCF and LCM tip #3: Consecutive multiples of N have a GCF of N

ccassel wrote:Hi,

Can anyone explain their method for finding the solution to this problem?

If x and y are positive integers, what is the values of xy?

(1) The greatest common factor of x and y is 10.
(2) The least common multiple of x and y is 180.

Cheers,

hi, remember the following formula...!!!

product of two numbers=lcm of two numbers * hcf of two numbers;

in statement 1) HCF is given and in statement 2) LCM is given,

therefore to find the product,we need to combine the information given in the two statements.!!!!

hence C

great posts.

thanks,