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If z is an integer smaller than integer n but greater than zero, is z

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Bunuel
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If z is an integer smaller than integer n but greater than zero, is z [#permalink] New post   13 May 2021, 20:00
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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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Bunuel
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Re: If z is an integer smaller than integer n but greater than zero, is z [#permalink] New post   22 May 2021, 04:30
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Bunuel 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.

Answer: B.
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Re: If z is an integer smaller than integer n but greater than zero, is z [#permalink] New post   13 May 2021, 20:20
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Statement 1: "n is divisible by every integer equal to or less than 9" essentially means m is 9! if z = any integer less than 9, then the answer is YES. If z = 11, the answer is no. The statement is INSUFFICIENT.

Statement 2: z is not a multiple of a prime number. All integers other than 0 and 1 are multiples of prime numbers (including the prime numbers themselves!). Since the constraint in the question stem is that z is greater than zero, the only possible value for z is 1, and n is definitely divisible by 1. The statement is SUFFICIENT.
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Re: If z is an integer smaller than integer n but greater than zero, is z [#permalink] New post   22 Oct 2022, 11:54
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Re: If z is an integer smaller than integer n but greater than zero, is z [#permalink]
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