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07 Jun 2008, 12:48
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Not sure if this was discussed earlier...
n is a positive number. Is n divisible by 3?
1. (n^2)/36 is an integer
2. (144/n^2) is an integer
n is a positive number. Is n divisible by 3?
1. (n^2)/36 is an integer
2. (144/n^2) is an integer
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07 Jun 2008, 13:03
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1.\(\frac{n^2}{36}= (\frac{n}{6})^2=(\frac{1}{2})^2(\frac{n}{3})^2\) - sufficient.
2. \(\frac{144}{n^2}=(\frac{12}{n})^2\) --> n can be 2 or 3- insufficient.
1.\(\frac{n^2}{36}= (\frac{n}{6})^2=(\frac{1}{2})^2(\frac{n}{3})^2\) - sufficient.
2. \(\frac{144}{n^2}=(\frac{12}{n})^2\) --> n can be 2 or 3- insufficient.
07 Jun 2008, 13:16
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walker
Nice shortcut Walker.
I have another line of reasoning...
Alternatively, say 36 and 144 satisfy the first condition, so n = 6 or 12.or 36.and other multiples of 36 which are perfect squares(may or may not be but for the purposes of discussion lets say, there are...and in any event, they will be multiples of 6, hence always a multiple of 3.) I guess 1 is sufficient in any event
2 is satisfied by 36, 144 ( n = 6, 12)and both are divisible by 3....isn't this sufficient also?
Thanks for clarifying this.
