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Interesting Q x^2 y^4 divisible by 9?

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Source: — Data Sufficiency |
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by Frankenstein » Wed Jun 01, 2011 11:56 am
Hi,
Is x^2 y^4 an integer divisible by 9? => xy^2 an integer divisible by 3?
From(1): x is an integer divisible by 3. We know nothing about y
Insufficient
From(2): xy is an integer divisible by 9
if x=81 and y=1/9, then xy is divisible by 9 but xy^2 = 1. Not divisible by 3
if x=27 and y=1/3, then xy is divisible by 9 but xy^2 = 3. Divisible by 3
Insufficient
Both(1) and (2)
if x=81 and y=1/9, then xy is divisible by 9 but xy^2 = 1. Not divisible by 3
if x=27 and y=1/3, then xy is divisible by 9 but xy^2 = 3. Divisible by 3
Insufficient

Hence, E
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by SoCan » Wed Jun 01, 2011 12:00 pm
Frankenstein wrote:Hi,
Is x^2 y^4 an integer divisible by 9? => xy^2 an integer divisible by 3?
From(1): x is an integer divisible by 3. We know nothing about y
Insufficient
From(2): xy is an integer divisible by 9
if x=81 and y=1/9, then xy is divisible by 9 but xy^2 = 1. Not divisible by 3
if x=27 and y=1/3, then xy is divisible by 9 but xy^2 = 3. Divisible by 3
Insufficient
Both(1) and (2)
if x=81 and y=1/9, then xy is divisible by 9 but xy^2 = 1. Not divisible by 3
if x=27 and y=1/3, then xy is divisible by 9 but xy^2 = 3. Divisible by 3
Insufficient

Hence, E
The key point of this is not to assume both x and y are integers. Very easy mistake to make. If you assume they are, you'll get D.
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