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# If n and p are different positive prime numbers, which of

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Manager
Joined: 14 Dec 2005
Posts: 74
If n and p are different positive prime numbers, which of [#permalink]

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26 Feb 2006, 10:39
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

If n and p are different positive prime numbers, which of the integers ,
and np has (have) exactly 4 positive divisors?
(A) n4 only
(B) p3 only
(C) np only
(D) n4 and np
(E) p3 and np
Intern
Joined: 08 Jan 2006
Posts: 27

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26 Feb 2006, 11:42
Avis wrote:
If n and p are different positive prime numbers, which of the integers ,
and np has (have) exactly 4 positive divisors?
(A) n4 only
(B) p3 only
(C) np only
(D) n4 and np
(E) p3 and np

E?

Here's why:
lets take two prime numbers: n=2 and p=11.
np=22 has 1, 2, 11, and 22 as the only divisors.
n4=8 has 1, 2, 4 and 8 as the only divisors
p3=33 has 1, 3, 11, 33 as the only divisors

So looks like all have exactly 4. But lets take another prime number combination. n=3 and p=5
np=15 has 1, 3, 5 and 15 as the only divisors
n4=12 has 1, 2, 3, 4, 6 and 12 as the divisors (Notice > 4 divisors)
p3=15 has 1, 3, 5 and 15 as the only divisors

So n4 cannot always have exactly 4 divisors.
Manager
Joined: 08 Feb 2006
Posts: 126

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26 Feb 2006, 12:25
I pick C.

If n= 5 and p=3, then n4= 20 which would mean 1, 20, 4, 5, 10, 2 and p3 = 9 which is 1,3 and 9.

So np = 15 still has 1,3, 5 , 15 as its divisors. Np only has 4 positive divisors
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5043
Location: Singapore

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26 Feb 2006, 18:45
A)n4 will have divisors --> 1,2,n,n4 --> Could be 4, but if n = 2, then will be 3
B)same as A
C)np --> 1,n,p,np
D)n4 and np --> 1,n,p,n4,np --> could be as much as 5
E)p3 and np --> 1,3,n,p,p3,np --> could be as many as 6

I go with C
Manager
Joined: 05 Oct 2005
Posts: 200

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01 Mar 2006, 08:23

i try to use numbers , long approach

Anyone has a shortcut ?

Thanks
_________________

when there is a will there is a way

best regards

Manager
Joined: 20 Feb 2006
Posts: 213

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10 Mar 2006, 21:48
Guys, I really did not understand the question. Does np indicate n*p and n4 indicate n*4?
If np = n*p, it is straight C. Otherwise, no choice is correct.
Senior Manager
Joined: 22 Nov 2005
Posts: 474

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11 Mar 2006, 21:39
Nice and tricky question Avis.

Four factors of NP are 1, n, p, Np.

Manager
Joined: 13 Mar 2006
Posts: 73

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23 Jun 2006, 20:54
ONE question.

If n4 means n*4, I think n4 also has 4 factors, which is 1, n, 2n, and 4n.

Am I misdirected?
_________________

GMAT by 8th JUL

VP
Joined: 15 Jun 2006
Posts: 1124
Schools: Chicago Booth

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23 Jun 2006, 23:07
foolbox wrote:
ONE question.

If n4 means n*4, I think n4 also has 4 factors, which is 1, n, 2n, and 4n.

Am I misdirected?

You should also consider 2 and 4, so there are six factors, but the Q ask specifically for four.
Director
Joined: 06 May 2006
Posts: 791

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24 Jun 2006, 09:56
Yup. C is the answer... explanation as discussed above.
_________________

Uh uh. I know what you're thinking. "Is the answer A, B, C, D or E?" Well to tell you the truth in all this excitement I kinda lost track myself. But you've gotta ask yourself one question: "Do I feel lucky?" Well, do ya, punk?

24 Jun 2006, 09:56
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