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If x is an integer greater than zero but less than integer n, is x is

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Bunuel
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If x is an integer greater than zero but less than integer n, is x is [#permalink] New post   29 Apr 2019, 06:18
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If x is an integer greater than zero but less than integer n, is x is a factor of n?

(1) n is divisible by all integers less than 10.
(2) x is not a multiple of a prime number.


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Archit3110
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Re: If x is an integer greater than zero but less than integer n, is x is [#permalink] New post   30 Apr 2019, 08:54
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arorni ; nyashka

given x is an integer >0 but <n so range of x lies 0<x<n also given x & n are integers .. need to determine whether x is a factor of n.
#1
n is divisible by all integers less than 10
possible when n=9! so we can have many values of x cannot be determined , insufficeint

#2
x is not a multiple of a prime number ; or we can say that x is not divisible by any prime no..

The only positive number that isn't divisible by any prime number is 1, any positive integer greater than 1 is either prime or can be broken down into prime numbers eg
x=6;2*3 ; 8; 2*4 so on...
A multiple of a number is integer is when a number is multiplied by another no. for eg ; 2 =2*1 ; 4=2*2 so here 2,4 are multiples of 2
we are given info that x is not a multiple of a prime number only possible integer in that case is 1

hope this helps... :)
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Re: If x is an integer greater than zero but less than integer n, is x is [#permalink] New post   29 Apr 2019, 09:34
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Bunuel wrote:
If x is an integer greater than zero but less than integer n, is x is a factor of n?

(1) n is divisible by all integers less than 10.
(2) x is not a multiple of a prime number.



x>0 but n>x
is x factor of n?
#1
n is divisible by all integers less than 10.
value of n = 9! , but x is not sure what it may be
insufficient
#2
x can be 1 only
sufficient
IMO b
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nyashka
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Re: If x is an integer greater than zero but less than integer n, is x is [#permalink] New post   30 Apr 2019, 06:43
Archit3110 wrote:
Bunuel wrote:
If x is an integer greater than zero but less than integer n, is x is a factor of n?

(1) n is divisible by all integers less than 10.
(2) x is not a multiple of a prime number.



x>0 but n>x
is x factor of n?
#1
n is divisible by all integers less than 10.
value of n = 9! , but x is not sure what it may be
insufficient
#2
x can be 1 only
sufficient
IMO b



could you please explain the second?
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arorni
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Re: If x is an integer greater than zero but less than integer n, is x is [#permalink] New post   30 Apr 2019, 08:34
nyashka wrote:
Archit3110 wrote:
Bunuel wrote:
If x is an integer greater than zero but less than integer n, is x is a factor of n?

(1) n is divisible by all integers less than 10.
(2) x is not a multiple of a prime number.



x>0 but n>x
is x factor of n?
#1
n is divisible by all integers less than 10.
value of n = 9! , but x is not sure what it may be
insufficient
#2
x can be 1 only
sufficient
IMO b



could you please explain the second?


Can you please explain? As, 1 can also be multiple of prime number.
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Re: If x is an integer greater than zero but less than integer n, is x is [#permalink] New post   01 May 2019, 06:39
Archit3110 wrote:
arorni ; nyashka

given x is an integer >0 but <n so range of x lies 0<x<n also given x & n are integers .. need to determine whether x is a factor of n.
#1
n is divisible by all integers less than 10
possible when n=9! so we can have many values of x cannot be determined , insufficeint

#2
x is not a multiple of a prime number ; or we can say that x is not divisible by any prime no..

The only positive number that isn't divisible by any prime number is 1, any positive integer greater than 1 is either prime or can be broken down into prime numbers eg
x=6;2*3 ; 8; 2*4 so on...
A multiple of a number is integer is when a number is multiplied by another no. for eg ; 2 =2*1 ; 4=2*2 so here 2,4 are multiples of 2
we are given info that x is not a multiple of a prime number only possible integer in that case is 1

hope this helps... :)


Thanks Archit3110..
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Re: If x is an integer greater than zero but less than integer n, is x is [#permalink] New post   01 May 2019, 07:41
Archit3110

Statement 2 says x is not a multiple of a prime number

That can mean that x is a prime number.

That means x can be 2,3,5,7,11 etc.

X cannot be only 1.
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Re: If x is an integer greater than zero but less than integer n, is x is [#permalink] New post   01 May 2019, 11:59
sahibr wrote:
Archit3110

Statement 2 says x is not a multiple of a prime number

That can mean that x is a prime number.

That means x can be 2,3,5,7,11 etc.

X cannot be only 1.


sahibr
can you tell a number apart from 1 which is not a mutiple of prime no...
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Re: If x is an integer greater than zero but less than integer n, is x is [#permalink] New post   01 May 2019, 12:53
Archit3110

Any prime number in itself, standing alone is not a multiple of a prime number.

2,3,5,7 etc are not multiples of a prime number.

If the logic is that 2x1 becomes 2 again and hence is a multiple of a prime number then the same logic can be applied to 1 as well.

1 is a multiple of itself.
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Re: If x is an integer greater than zero but less than integer n, is x is [#permalink] New post   01 May 2019, 13:10
sahibr wrote:
Archit3110

Any prime number in itself, standing alone is not a multiple of a prime number.

2,3,5,7 etc are not multiples of a prime number.

If the logic is that 2x1 becomes 2 again and hence is a multiple of a prime number then the same logic can be applied to 1 as well.

1 is a multiple of itself.


You are right but 1 is neither prime nor composite so as per statement (2), x can be 1

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Re: If x is an integer greater than zero but less than integer n, is x is [#permalink]
01 May 2019, 13:10
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