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# If n=4p, where p is a prime number greater than 2, how many

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If n=4p, where p is a prime number greater than 2, how many [#permalink]

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16 Jan 2007, 11:31
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If n=4p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n?
A)2
B)3
C)4
D)6
E)8
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16 Jan 2007, 11:33
(C) for me

We have : 2, 4, 2p and 4p
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16 Jan 2007, 11:50
Fig, would you mind explaining please? Thanks
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16 Jan 2007, 12:00
A.
Fig, it says even
cucrose,
you can take help of samples in such questions.

4p could be 4 * 7, 4 *11, 4 *13 ...

any of these will have factors : prime number (p) , 4, 1 and n itself.
for only even numbers : has to be n and 4. so 2.

note p cannot be even and prime unless it is 2. and here we are starting off at 4.

cucrose wrote:
If n=4p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n?
A)2
B)3
C)4
D)6
E)8
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16 Jan 2007, 12:01
cucrose wrote:
Fig, would you mind explaining please? Thanks

No problem, ok

n = 4*p = 2*2*p

We know that p is a prime number superior to 2. Thus, p is a number that could not be an even. We do not count it in the even divisor.

Then, to find how many even divisor n has, we do all combinations of prime factors with at least one 2
2
2*2 = 4
2*p
2*2*p = 4*p
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16 Jan 2007, 12:02
If n=4p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n?
A)2
B)3
C)4
D)6
E)8

Prime number greater than 2 is P = 3, 5, 7... Take the first value of 3
n = 4*3 = 12.
What are the factors of 12 = 1X12 (4p);
2X6 (2p);
3X4

Therefor even divisors are: 2, 4, 2p, 4p. 4. Therefore C.

Let's take another example:

P = 5. n = 4p = 4X5 = 20
What are the Factors of 20? = 1X20 (4p)
2X10 (2p)
5X4

Even divisors of n = 2, 4, 2p, 4p. Therefore answer is C.
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16 Jan 2007, 12:04
Fig: WOW!! Looking at your explanation... I do not know if my explanation is correct or not. Your approach is definitely smarter and shorter!
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16 Jan 2007, 12:15
svas wrote:
A.
Fig, it says even
cucrose,
you can take help of samples in such questions.

4p could be 4 * 7, 4 *11, 4 *13 ...

any of these will have factors : prime number (p) , 4, 1 and n itself.
for only even numbers : has to be n and 4. so 2.

note p cannot be even and prime unless it is 2. and here we are starting off at 4.

cucrose wrote:
If n=4p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n?
A)2
B)3
C)4
D)6
E)8

Do you mean to say 4p could be odd depending on p? If so, 2p and 4p can never be odd as even no. multiplied by any no. result in an even no.
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16 Jan 2007, 12:23
axl_oz wrote:
Fig: WOW!! Looking at your explanation... I do not know if my explanation is correct or not. Your approach is definitely smarter and shorter!

Picking numbers is very fitted in such question as well. Many times, this way could save precious energy for more demanding questions during the exam.... 4 hours, it's very long. If we do not spare too much energy in every single question, the overall result should be greater

The essential is to have our own way in which we feel fine with
16 Jan 2007, 12:23
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