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# if z is an integer smaller than integer n but greater than

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Senior Manager
Joined: 18 Sep 2009
Posts: 266
if z is an integer smaller than integer n but greater than  [#permalink]

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22 Oct 2010, 06:58
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Difficulty:

75% (hard)

Question Stats:

48% (01:54) correct 52% (01:54) wrong based on 78 sessions

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if z is an integer smaller than integer n but greater than zero, is z a factor of n?
(1) n is divisible by all the positive integers less than or equal to 9.
(2) z is not a multiple of a prime number.
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Joined: 02 Sep 2009
Posts: 54371

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22 Oct 2010, 07:09
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TomB wrote:
if z is an integer smaller than integer n but greater than zero, is z a factor of n?
(1) n is divisible by all the positive integers less than or equal to 9.
(2) z is not a multiple of a prime number.

Given: $$0<(z=integer)<(n=integer)$$. Question: is $$z$$ a factor of $$n$$?

(1) n is divisible by all the positive integers less than or equal to 9 --> if $$z=1$$ and $$n=9!$$ (note that $$n$$ could be less than 9!) then the answer would be YES but if $$z=11$$ and $$n=9!$$ then the answer would be NO. Not sufficient.

(2) z is not a multiple of a prime number --> $$z=1$$ (the only positive integer which is not a multiple of any prime is 1) and 1 is a factor of every integer including $$n$$. Sufficient.

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Re: if z is an integer smaller than integer n but greater than  [#permalink]

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04 Aug 2017, 01:19
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Re: if z is an integer smaller than integer n but greater than   [#permalink] 04 Aug 2017, 01:19
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