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by sankruth » Sat Jan 12, 2008 10:13 am
k is a positive number. Is k a prime number?

1. No integer between 2 and SqRoot(k) inclusive, divides k evenly.
2. No integer between 2 and k/2 inclusive, divides k evenly, and k is greater than 5.

Explanations please!
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Source: — Data Sufficiency |
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by StarDust845 » Sat Jan 12, 2008 5:00 pm
Is the answer A?

Calista.
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by rchadha7 » Sat Jan 12, 2008 6:57 pm
i think its D, whats the OA ?

just tried few nos. with condition 1 and everything is ok.

5,7,9,11,13,15,17,..... all non-prime are divided evenly by nos. less than sqrt k.

2. k/2 is greater than sqrt k for all k >2, thats why D

am i correct ?
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by simplyjat » Sat Jan 12, 2008 9:21 pm
Both the statements alone are sufficient to answer the question.

During my computer programming classes I was told about these laws. If you want to find whether a number is prime or not, the optimal solution is to look till sqrt of that number.

The reasoning goes like this...
1. for 2 to n/2, if the number is indivisible, n/2 to n is 2 * ( 2 to n/2), thus we can ignore the second half as we have already tested 2...
2. for 2 to n/3, if the number is indivisible, n/3 to n is 3 * ( 2 to n/3), thus we can ignore the later as we have already tested 3...
And so on till be reach a number sqrt (n)....

I don't fully agree with the reasoning but it simply works :)
simplyjat
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by sankruth » Sun Jan 13, 2008 1:17 am
Thanks for the explanations!

D is the correct answer.
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