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Sqaure of an integer

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Sqaure of an integer

by sakurle » Mon Sep 14, 2009 8:14 pm
If k is a positivee integer, is k the square of an integer?

1. k is divisible by 4
2. k is divisible by exactly 4 different prime numbers
Last edited by sakurle on Tue Sep 15, 2009 9:04 am, edited 1 time in total.
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imo 2

by xcusemeplz2009 » Mon Sep 14, 2009 9:59 pm
i think with 2 we can know that k is not a square of an integer
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by PussInBoots » Mon Sep 14, 2009 11:21 pm
1. 8 vs 16
2. k = p1 * p2 * p3 * ... * pK

p1, p2, .., pK are prime numbers in prime factorization
"exactly different prime numbers" -> p1 through pK are different (to my understanding)

hence k cannot be square of integer. Square of integers must have even numver of each prime number in its prime factorization
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by PussInBoots » Mon Sep 14, 2009 11:21 pm
B is the answer
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by viju9162 » Tue Sep 15, 2009 12:54 am
A cnt answer the question.. But in "B", i didnt understand ..

Does K should be divisible by all different prime numbers?
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Re: Sqaure of an integer

by Ian Stewart » Tue Sep 15, 2009 2:43 am
viju9162 wrote: Does K should be divisible by all different prime numbers?
There is an infinite number of primes, so it isn't possible for a number to be divisible by all primes. I think the second statement -
sakurle wrote: 2. k is divisible by exactly different prime numbers
which is meaningless as written, is supposed to read "k is divisible by exactly four different prime numbers". This statement is not sufficient; our number might be equal to 2*3*5*7, which is not the square of an integer, or it might be equal to (2^2)(3^2)(5^2)(7^2), which is the square of an integer (it's the square of 2*3*5*7).
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by Onigbogi Tosin » Tue Sep 15, 2009 6:45 am
obviously, 1 Is not sufficient. Since both 8 and 16 are divisible by 4 but 8 is not a square of an integer whereas 16 is.

From statement 2 we can deduce that K/2, K/3, K/5, K/7,..., If K = 14, 2 and 7 divide K, If K = 15, 3 and 5 divide k, if k = 21 3 and 7 divide k, If k is 30, 2, 3 and 5 divide K. We can go on and on. But it's worth noting here that K = 14, 15, 21, 30 are all not square of an integer.Hence, we can say No with statement 2. Therefore, Statement 2 is sufficient (B)
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by sakurle » Tue Sep 15, 2009 8:31 am
This is GMAT Prep question. I was also going with B. However the OA is E. Also as Ian mentioned there was a typo which I have fixed.

Thanks Ian, I understand your explanation. My reasoning was that 4 different prime numbers means 2x3x5x7 I did not think that they can appear twice.
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