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by adi_800 » Sat Aug 21, 2010 1:58 am
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
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by kvcpk » Sat Aug 21, 2010 4:12 am
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!!
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don't be afraid of failure and don't abandon it.
People who work sincerely are the happiest."
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by gmatmachoman » Sat Aug 21, 2010 5:32 am
praveen, how many minutes u took to plug in those numbers..

I took near abt 3.5 minutes...Just wanted to cross check!
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by kvcpk » Sat Aug 21, 2010 5:55 am
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!!
"Once you start working on something,
don't be afraid of failure and don't abandon it.
People who work sincerely are the happiest."
Chanakya quotes (Indian politician, strategist and writer, 350 BC-275BC)
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