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# If x is a prime number, what is the value of x? (1) 2x + 2

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Director
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If x is a prime number, what is the value of x? (1) 2x + 2 [#permalink]  05 Feb 2006, 22:05
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If x is a prime number, what is the value of x?

(1) 2x + 2 is the cube of a positive integer.

(2) The average of any x consecutive integers is an integer
Manager
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2*31+2 =64 =4^3

But I am not sure if there are other cases...
VP
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My guess is A.

1) 2x+2 is cube of an +ve integer. Only 3 satisfies this condition.

I think sufficient.

2) Avg of x consecutive int is an integer.

x = 3, 5, 7 ...... odd primes INSUFF.
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celiaXDN wrote:
2*31+2 =64 =4^3

But I am not sure if there are other cases...

Good stuff Celia.

So it is E then

Somehow, my world of primes stops after 2,3,5,7,11, 13...
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razrulz wrote:
celiaXDN wrote:
2*31+2 =64 =4^3

But I am not sure if there are other cases...

2*3+2 = 8 ==> 2^3

That is right!

I only wish I wouldn't overlook it when I am taking the test.
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Cubes: 1,8,27,64

(1) -> not sufficient. x can be 3, 31, etc

(2) -> not sufficient. Any odd prime number will do.

Using (1) and (2), x can be 3 or 31 etc....

Ans E
Senior Manager
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E.

Stat1 is not sufficient,, x could be 3, 31 ...

Stat 2 is not sufficient either

combined together we have more than one vlaue ofr x

So E it is
Director
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OA is E !
I also missed to check for 31 and selected A
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I know I'm a little late , but also wanted to add that 5 is another one that works:

2^5 + 2 = 27 = 3^3, and of course 5 is odd.
Senior Manager
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E. Cannot go behind all prime numbers solving a condition. Already found two nos 3 and 31 matching A.
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Re: DS-Prime Number [#permalink]  21 Mar 2006, 06:40
cool_jonny009 wrote:
If x is a prime number, what is the value of x?

(1) 2x + 2 is the cube of a positive integer.

(2) The average of any x consecutive integers is an integer

This is an interesting question. I'll just add my approach for fun.

(1) 2x+2 = 2(x+1) is cube of a positive integer, meaning x+1 is multiples of 4 and cube of other integers. (meaning x is odd too.)
x=4k^3-1
So if k=1, x=3; k=2, x=31; ...etc.

(2) It says x is odd. If x is odd then the average of any x consecutive integers is always an integer.

Combined (2) does not add any new info to (1).

That's why I'd choose E.
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Senior Manager
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HongHu,

what did you mean by,

(1) 2x+2 = 2(x+1) is cube of a positive integer, meaning x+1 is multiples of 4 and cube of other integers. (meaning x is odd too.)

Must've missed something elementary here.
Manager
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yes, i would chose E also.

But i must say i spent too much time on this question
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macca wrote:
HongHu,

what did you mean by,

(1) 2x+2 = 2(x+1) is cube of a positive integer, meaning x+1 is multiples of 4 and cube of other integers. (meaning x is odd too.)

Must've missed something elementary here.

If order for 2(x+1) to be the cube of a positive integer, then it can be 8, 64, 216..... Then (x+1) has to be 4, 8, 108 etc.. all are multiples of 4.
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