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If x is a prime number what is the value of x? a) There are

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If x is a prime number what is the value of x? a) There are [#permalink] New post 25 Jun 2011, 03:58
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If x is a prime number what is the value of x?

a) There are a total of 50 prime numbers between 2 and x inclusive.
b) There is no integer n such that x is divisible by n and 1<n<x.

Here is my understanding

Statement 1--> Sufficient as we can find the value of x i.e the highest prime number.
Statement 2--> I am struggling to understand this statement in the book. Can someone in this forum please be kind enough to let me understand the concept behind this statement if possible with an example? Correct answer is this statement alone is insufficient.
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Re: Chapter 10 Number Properties - MGMAT [#permalink] New post 25 Jun 2011, 04:07
gsaxena26 wrote:
If x is a prime number what is the value of x?

a) There are a total of 50 prime numbers between 2 and x inclusive.
b) There is no integer n such that x is divisible by n and 1<n<x.

Here is my understanding

Statement 1--> Sufficient as we can find the value of x i.e the highest prime number.
Statement 2--> I am struggling to understand this statement in the book. Can someone in this forum please be kind enough to let me understand the concept behind this statement if possible with an example? Correct answer is this statement alone is insufficient.


1) x is the 50th prime number. Sufficient.
2) x is some prime number. Not Sufficient.

1<n<5
n can be 2, 3, 4; none of which is a factor of x i.e. 5.

1<n<13
n can be 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12; none of which is a factor of x i.e. 13.
x can be any prime number.
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Re: Chapter 10 Number Properties - MGMAT [#permalink] New post 25 Jun 2011, 04:11
Many thanks fluke for such a good reply. :P
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Re: Chapter 10 Number Properties - MGMAT [#permalink] New post 25 Jun 2011, 08:06
So Fluke,

Quote:
There is no integer n such that x is divisible by n and 1<n<x.


^ is just a way of saying that x is a prime number?
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Re: Chapter 10 Number Properties - MGMAT [#permalink] New post 25 Jun 2011, 08:19
Yes. Also, there are only two factors of x which are x an x+1 which means that x is a prime number. If a number has only two factors then its a prime number which is the number itself and 1.
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Re: Chapter 10 Number Properties - MGMAT [#permalink] New post 25 Jun 2011, 08:27
386390 wrote:
So Fluke,

Quote:
There is no integer n such that x is divisible by n and 1<n<x.


^ is just a way of saying that x is a prime number?


Yes, provided x is an integer, which it is.
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Re: Chapter 10 Number Properties - MGMAT   [#permalink] 25 Jun 2011, 08:27
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