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# See attachment. OA will be provided later

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Manager
Joined: 23 Jun 2008
Posts: 140
See attachment. OA will be provided later [#permalink]

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11 Aug 2008, 14:26
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See attachment. OA will be provided later.
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DS2_081108.doc [68 KiB]

SVP
Joined: 30 Apr 2008
Posts: 1855
Location: Oklahoma City
Schools: Hard Knocks

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11 Aug 2008, 20:19
balboa wrote:
If k is a positive integer, is k the square of an integer?

1) k is divisible by 4.
2) k is divisible by exactly four different prime numbers.

Another way to phrase this is: Is $$sqrt{k}$$ an integer?

#1) Insufficient. What are numbers divisible by 4? 4, 8, 12, 16, 20. The question is a yes/no question, so in order to answer the question, the answer must be ALWAYS yes or ALWAYS no.

Since k could be any factor of 4, the possibilities are not always going to be a square of an integer, and there are some instances where k will be a square so it's sometimes yes K is a square of an integer (like when k is 4, 16, 36, 64, etc) but the answer can also be No, k is NOT a square of an integer (like when k = 8, 12, 20, 24, etc).

#2) First figure out what this is telling us. What number are divisible by exactly 4 different prime numbers? This could be 2*3*5*7 = 210. This is not a perfect square. It seems like the statement may be sufficient and the answer is No, when k is divisible by exactly 4 different prime numbers, k will never be the square of an integer, but all we have to do is find 1 instance where k does equal a perfect squre and the statement is insufficient.

Lets think of some perfect squres. 4, 9, 16, 25, 36, 49, 64, 81, 100.
4 = nope 2*2 (only 1 prime, not 4 different prime numbers)
9 = 3*3 (only 1 prime number, not 4 different prime numbers)

16 = 2*2*2*2. Ok, here is where we might be able to say yes. Does the term "different" mean that no prime number can be repeated, or just that there will be 4 terms, and terms may be the same as in this instance.

Can someone say what they think the question means?

#2)
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Joined: 07 Nov 2007
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11 Aug 2008, 20:36
balboa wrote:
See attachment. OA will be provided later.

Question: Is K square of the integer ?( k is positive integer)
1) k is divisable by 4

k = 4 m (m= any postive integer .. 1,2,3,..)

when m=1 k = 4 = 2^2 (k is square of integer (i.e square of 2))
when m=2 k=8 ( here k is not square of integer)

Not suffcient

2) k is divisable by exactly 4 different prime numbers.

k= p1*p2*p3*p4
prime numbes are divisable by 1 and the number itself.
k= 2 *3*5*7 = not square of integer
k never be square of any integer

Suffcieint.

B.
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Re: Gmat Prep: DS   [#permalink] 11 Aug 2008, 20:36
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