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Another number properties question

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Another number properties question

by yasik19 » Mon Jan 12, 2009 9:29 am
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 nubers.

I put B, the answer is E. Why?

What perfect square will have 4 different prime #s? I figured none, so it's a definite no, so B.

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Re: Another number properties question

by logitech » Mon Jan 12, 2009 9:58 am
If k is a positive integer, is k the square of an integer?

(1) k is divisible by 4.


4 yes

8 no

(2) k is divisible by exactly four different prime nubers.

(2x3x5x7)^2 = k square is an integer

2x3x5x7 is not an integer

together 2x2x3x5x7 = NO i

2x2x3x3x5x5x7x7 = YES
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by yasik19 » Mon Jan 12, 2009 10:54 am
Thank you.

I guess I saw the word "exactly" and thought it means "ONLY" four prime numbers, as in four numbers in total.
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Re: Another number properties question

by malhotneha » Wed Jan 14, 2009 11:55 am
logitech wrote:If k is a positive integer, is k the square of an integer?

(1) k is divisible by 4.


4 yes

8 no

(2) k is divisible by exactly four different prime nubers.

(2x3x5x7)^2 = k square is an integer

2x3x5x7 is not an integer

together 2x2x3x5x7 = NO i

2x2x3x3x5x5x7x7 = YES
Hi there,
I can't understand the explanation for Statement 2. Could you please explain further?
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by logitech » Wed Jan 14, 2009 12:19 pm
where exactly didn't you understand ?
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Re: Another number properties question

by malhotneha » Wed Jan 14, 2009 12:43 pm
The question is:
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.

We know that Statement 1 is insufficient (for reasons already explained above in the thread).
Now statement 2 states that k is divisible by exactly four different prime numbers.
Prime numbers: 2, 3, 5, 7...
so, that means that (2*3*5*7)^2 = k...now I didn't get i:
2x3x5x7 is not an integer (why????)

together 2x2x3x5x7 = NO i

2x2x3x3x5x5x7x7 = YES

Sorry, I may be asking something very silly here...its just that I am unable to get this one. Thanks in advance.
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Re: Another number properties question

by logitech » Wed Jan 14, 2009 12:46 pm
malhotneha wrote:The question is:
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.

We know that Statement 1 is insufficient (for reasons already explained above in the thread).
Now statement 2 states that k is divisible by exactly four different prime numbers.
Prime numbers: 2, 3, 5, 7...
so, that means that (2*3*5*7)^2 = k...now I didn't get i:
2x3x5x7 is not an integer (why????)

together 2x2x3x5x7 = NO i

2x2x3x3x5x5x7x7 = YES

Sorry, I may be asking something very silly here...its just that I am unable to get this one. Thanks in advance.
There is nothing such a silly question.

Question is : is k the square of an integer?

together 2x2x3x5x7 = NO i

2x2x3x3x5x5x7x7 = YES
You can not get the square root of the first example ( NO )

but you can do it for the second example ( YES )
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by malhotneha » Wed Jan 14, 2009 2:13 pm
Thanks! :D
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Re: Another number properties question

by coffee5251 » Fri Jan 16, 2009 6:51 am
logitech wrote:
2x3x5x7 is not an integer

together 2x2x3x5x7 = NO i

2x2x3x3x5x5x7x7 = YES
Can you explain this? What do you mean by "2x3x5x7 is not an integer"?

Also, if it says "k is divisible by exactly 4 prime numbers" does that mean they don't have to be distinct? (i.e. 2x2x3x3x5x5x7x7 is divisible by 8 prime numbers (each prime twice)) ??
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Re: Another number properties question

by coffee5251 » Fri Jan 16, 2009 6:54 am
logitech wrote:
2x3x5x7 is not an integer

together 2x2x3x5x7 = NO i

2x2x3x3x5x5x7x7 = YES
Can you explain this? What do you mean by "2x3x5x7 is not an integer"?

Also, if it says "k is divisible by exactly 4 prime numbers" does that mean they don't have to be distinct? (i.e. 2x2x3x3x5x5x7x7 is divisible by 8 prime numbers (each prime twice)) ??
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Re: Another number properties question

by Brent@GMATPrepNow » Fri Jan 16, 2009 7:26 am
coffee5251 wrote:
logitech wrote:
2x3x5x7 is not an integer

together 2x2x3x5x7 = NO i

2x2x3x3x5x5x7x7 = YES
Can you explain this? What do you mean by "2x3x5x7 is not an integer"?

Also, if it says "k is divisible by exactly 4 prime numbers" does that mean they don't have to be distinct? (i.e. 2x2x3x3x5x5x7x7 is divisible by 8 prime numbers (each prime twice)) ??
With regard to "2x3x5x7 is not an integer," Logitech meant to say "2x3x5x7 is not the square of an integer." In other words, we can't rearrange 2x3x5x7 to be the product of two equivalent values. Conversely, 2x2x3x3 can be written as (2x3)(2x3) which means it is a square (aka 6^2 or six squared).

For the part about "k is divisible by exactly 4 prime numbers," the original question reads, "k is divisible by exactly four different prime numbers," so this rules out the possibility of counting a prime number more than once.

I hope that helps.
Brent Hanneson - Creator of GMATPrepNow.com
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by logitech » Fri Jan 16, 2009 10:21 am
Brent , thanks for making it clear.
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