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# X is a positive integer. Is x prime? a) x<5929 b) x is

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Director
Joined: 28 Oct 2003
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X is a positive integer. Is x prime? a) x<5929 b) x is [#permalink]  01 Dec 2003, 06:45
X is a positive integer. Is x prime?

a) x<5929
b) x is not divisible by any number <80
Director
Joined: 13 Nov 2003
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anyway,
is X 5927? this is not divisible by numbers<80 ...there could be many, but this is what I came onto.

77^2 = 5929

I guess, C.
Manager
Joined: 26 Aug 2003
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I'd say E.

(1) x can be many numbers. Either prime or non prime. No suff.
(2) What if x is divisible by any prime greater than 80 (i.e. 83, 89, etc.)? Not suff.
(combined) x can be any number equal to or greater than 166 (=83*2) and be divisible by at least one prime. Otherwise it can be one of many primes itself. Not clear so not suff.
Director
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I wrote the question myself.

wonder_gmat-- given conditions 1 and 2, can you come up with prime and nonprime possibilities for x? Think more about condition 2...
Manager
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stoolfi wrote:
I wrote the question myself.

wonder_gmat-- given conditions 1 and 2, can you come up with prime and nonprime possibilities for x? Think more about condition 2...

Hmm... I understood the question in two different ways. And if E is not the answer then I'll have to say C.

Good question, stoolfi!
CEO
Joined: 15 Aug 2003
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wonder_gmat wrote:
stoolfi wrote:
I wrote the question myself.

wonder_gmat-- given conditions 1 and 2, can you come up with prime and nonprime possibilities for x? Think more about condition 2...

Hmm... I understood the question in two different ways. And if E is not the answer then I'll have to say C.

Good question, stoolfi!

Primes are #'s divisible by 1 and itself

B say the X is not divisible by any number < 80.

So X cant be prime as X would not divisible by 1.

here is where i am lost....is there any integer which is not divisible

by 1?

thanks
praetorian

Last edited by Praetorian on 01 Dec 2003, 12:28, edited 1 time in total.
Senior Manager
Joined: 23 Sep 2003
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Yep. C.

83 is the next prime after 80. 83^2 >5969 so (1) and (2) are sufficient to answer the question.
Director
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Praetorian-- You are right about 1 being a factor. That was negligent of me.

The reasoning behind the question: Of course neither of the two statements was in and of itself sufficient.

Together, however, we know that the number isn't divisible by any number less than eighty, and that the number is less than eighty squared.
So if a number greater than eighty is a factor, it's complement must be less than eighty. But we are told that no numbers less than eighty are factors.

So the answer (excepting my flub that Praetorian caught) is C.
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