adi_800 wrote:The integers y and z are both positive. Is yz a multiple of 500 ?

(1) yz is a multiple of 25 and z is a multiple of 20.

(2) y2 is a multiple of 10 and z2 is a multiple of 5.

OA E

yz is a multiple of 25 and z is a multiple of 20.
let yz=100, z=20
100 is not a multi0le od 500 .. NO
let yz=1000,z=20
1000 is a multiple of 500..YES
INSUFF

(2) y2 is a multiple of 10 and z2 is a multiple of 5.
Let y^2=100, z^2 = 25
implies y=10, z=5
yz=50 is not a multiple of 500..NO
let y^2 = 10000, z^2 = 25
implies y= 100, z=5
yz=500 is a multiple of 500..YES
INSUFF

combining:
Let y=20, z= 20
yz = 400..not a multiple of 500..NO
Let y=200, z=200
yz=40000..Multiple of 500..YES

pick E.

Hope this helps!!

praveen, how many minutes u took to plug in those numbers..

I took near abt 3.5 minutes...Just wanted to cross check!

gmatmachoman wrote:praveen, how many minutes u took to plug in those numbers..

I took near abt 3.5 minutes...Just wanted to cross check!

I took around 3 mins to type it. So should have done it normally with in 2 minutes.

Numbers for disproving A and B are starightforward.
one set of numbers for C makes us think. ohter set should be easy.

In case we do not wan to plugin:

z is multiple of 20 -> z=20a
y^2 is multiple of 10 means y is multiple of 10 -> y=10b
z^2 is multiple of 5 -> z is multiple of 5. -> 20a is already multiple of 5.
now, yz = 200ab is already multiple of 25.

so possible values for for yz=200,400,600...

among these, some are multiples of 500 and some are not.

hence C is INSUFF.

Cheers!!