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

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Manager
Joined: 23 Jan 2008
Posts: 108
If n=4p, where p is a prime number greater than 2, how many [#permalink]

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23 Jan 2008, 12:07
2
KUDOS
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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

Last edited by blog on 23 Jan 2008, 12:41, edited 1 time in total.
CEO
Joined: 17 Nov 2007
Posts: 3584
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40

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23 Jan 2008, 12:37
D

n=4p=2^2*p

N=(2+1)(1+1)=6
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Manager
Joined: 23 Jan 2008
Posts: 108

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23 Jan 2008, 12:42
walker wrote:
D

n=4p=2^2*p

N=(2+1)(1+1)=6

Quote:
oops m sorry its : where p is a prime no greater than 2 here in the question.
Director
Joined: 01 Jan 2008
Posts: 622

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23 Jan 2008, 12:44
The answer is A. The even divisors are 2*p and 4*p. There are two more divisors 1 and p but they are odd since p > 2
Senior Manager
Joined: 15 Aug 2007
Posts: 252
Schools: Chicago Booth

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23 Jan 2008, 12:47
My pick B (3)

Even divisors - 2, 4, and n (n will be even after multiplying with 4)
Manager
Joined: 23 Jan 2008
Posts: 108

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23 Jan 2008, 12:48
maratikus wrote:
The answer is A. The even divisors are 2*p and 4*p. There are two more divisors 1 and p but they are odd since p > 2

but here ans is C.
CEO
Joined: 17 Nov 2007
Posts: 3584
Concentration: Entrepreneurship, Other
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23 Jan 2008, 12:54
maratikus wrote:
The answer is A. The even divisors are 2*p and 4*p. There are two more divisors 1 and p but they are odd since p > 2

I lose "even"...
I should go to sleep....bye-bye!
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Senior Manager
Joined: 15 Aug 2007
Posts: 252
Schools: Chicago Booth

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23 Jan 2008, 12:59
What am I thinking, of course the anser is C:

2, 4, 2*p, and 4*p.

Last two are even numbers too.
Director
Joined: 01 Jan 2008
Posts: 622

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23 Jan 2008, 13:00
1
KUDOS
that's funny, I totally messed up too - concentration is important.
CEO
Joined: 21 Jan 2007
Posts: 2739
Location: New York City

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01 Feb 2008, 03:59
blog 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

i plugged an easy number.

n=4p
n =4*3
n =12

12 = 2^2 * 3
(2+1)(1+1) = total
3*2=6

total - odd = even
6 - (2)= 4
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Director
Joined: 12 Jul 2007
Posts: 858

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01 Feb 2008, 04:51
1
KUDOS
I agree with BMW here, why not plug in the easiest numbers you can find? What works in one situation will work for the problem.
SVP
Joined: 28 Dec 2005
Posts: 1558

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01 Feb 2008, 07:06
dont overcomplicate things, just pick numbers

n=12,20,28,40...

youll see that each of these numbers have 4 even divisors.
Senior Manager
Joined: 26 Jan 2008
Posts: 263

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01 Feb 2008, 16:16
blog 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

(C)

4*p = 2*2*p

Hence, 4 even divisors:
2, 4, 2*p, 4*p
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SVP
Joined: 29 Aug 2007
Posts: 2473

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01 Feb 2008, 16:37
walker wrote:
D

n=4p=2^2*p

N=(2+1)(1+1)=6

nice formulae to remember.
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Senior Manager
Joined: 20 Dec 2004
Posts: 251

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02 Feb 2008, 12:55
GMAT TIGER wrote:
walker wrote:
D

n=4p=2^2*p

N=(2+1)(1+1)=6

nice formulae to remember.

What is the rule for this formula.. ?
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Manager
Joined: 02 Jan 2008
Posts: 158

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02 Feb 2008, 13:08
2
KUDOS
neelesh wrote:

What is the rule for this formula.. ?

Number of divisors of N = (m+1)(n+1)(p+1)...

Where, $$N = (a^m)(b^n)(c^p)..$$and a,b,c.. are prime numbers

example,

$$24 = 2^3*3^1$$; number of divisors = (3+1)(1+1)=8 (1,24,2,4,6,8,3,12)
CEO
Joined: 17 Nov 2007
Posts: 3584
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40

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02 Feb 2008, 13:08
1
KUDOS
Expert's post
neelesh wrote:
What is the rule for this formula.. ?

for positive integer $$n=p_1^a*p_2^b...p_m^k$$, where $$p_i$$ - are prime numbers
The number of positive factors is:

$$N=(a+1)(b+1)....(k+1)$$
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Manager
Joined: 07 Jan 2008
Posts: 115

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02 Feb 2008, 13:17
what a great formula!!!!
that itself will improve my score
Senior Manager
Joined: 20 Dec 2004
Posts: 251

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02 Feb 2008, 13:46
+1 to both walker and srp.

thx.
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Re: prime number   [#permalink] 02 Feb 2008, 13:46
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