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# If x is a prime number, what is the value of x?

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If x is a prime number, what is the value of x? [#permalink]  25 Jun 2011, 03:58
00:00

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35% (medium)

Question Stats:

75% (01:44) correct 25% (00:01) wrong based on 12 sessions
If x is a prime number, what is the value of x?

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

Here is my understanding
[Reveal] Spoiler:
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.
[Reveal] Spoiler: OA
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Re: If x is a prime number, what is the value of x? [#permalink]  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: If x is a prime number, what is the value of x? [#permalink]  25 Jun 2011, 04:11
Many thanks fluke for such a good reply.
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Re: If x is a prime number, what is the value of x? [#permalink]  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: If x is a prime number, what is the value of x? [#permalink]  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: If x is a prime number, what is the value of x? [#permalink]  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: Number props DS [#permalink]  09 Aug 2011, 21:04
ruturaj wrote:
If x is a prime number, what is the value of x?

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

From 1, x can be identified. Sufficient.
From 2, x is not 2 but could be any prime > 2. No prime is divisible by n given that 1 < n< x. (statement 2 is not much clear for me. May be its a long brake for me).

So it should be A.
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Re: Number props DS [#permalink]  09 Aug 2011, 23:16
Fistail wrote:
ruturaj wrote:
If x is a prime number, what is the value of x?

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

From 1, x can be identified. Sufficient.
From 2, x is not 2 but could be any prime > 2. No prime is divisible by n given that 1 < n< x. (statement 2 is not much clear for me. May be its a long brake for me).

So it should be A.

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Re: Number props DS [#permalink]  09 Aug 2011, 23:23
ruturaj wrote:

There is 1 prime number btwn 2 and 5 (which is 3).

2 prime numbers btwn 2 and 7 (which is 3 and 5).

so 50 prime numbers btwn 2 and x (just put in 50 prime numbers from 3 onwards and get the 51st prime number to get X)

You don't have to calculate it out because its a DS qtn but you know you can get the answer. So (A) is sufficient.
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Re: Number props DS [#permalink]  10 Aug 2011, 00:41
openbox1 wrote:
ruturaj wrote:

There is 1 prime number btwn 2 and 5 (which is 3).

2 prime numbers btwn 2 and 7 (which is 3 and 5).

so 50 prime numbers btwn 2 and x (just put in 50 prime numbers from 3 onwards and get the 51st prime number to get X)

You don't have to calculate it out because its a DS qtn but you know you can get the answer. So (A) is sufficient.

Yes but there are several prime nos how can we find the one exact value of x?
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Re: Number props DS [#permalink]  10 Aug 2011, 01:42
I thought the same first but i think the word to be noticed in the ques stem is between..."There are a total of 50 prime numbers between 2 and x"..

so, x will be the 51st value.
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Re: Number props DS [#permalink]  10 Aug 2011, 02:26
1) 2, p1, p2 ... p51. Sufficient
2) x is not 2. Not sufficient

A

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Re: Number props DS [#permalink]  10 Aug 2011, 10:05
ruturaj wrote:
Fistail wrote:
ruturaj wrote:
If x is a prime number, what is the value of x?

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

From 1, x can be identified. Sufficient.
From 2, x is not 2 but could be any prime > 2. No prime is divisible by n given that 1 < n< x. (statement 2 is not much clear for me. May be its a long brake for me).

So it should be A.

(1) If there are a total of 50 prime numbers between 2 and x, inclusive, then prime numbers are p1 (which is 2), p2 (=3), p3 (=5), ....... p50 (=x). So x = p50. sufficient.

However the question is what is x? But we do not need to answer what exactly is x. What we need is whether statement 1 is sufficient to answer the question or not. That's sufficient.
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Re: If x is a prime number, what is the value of x? (1) There [#permalink]  25 Nov 2013, 20:06
stm2 is not clear to me. Can anyone provide better explanation. thanks
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Re: If x is a prime number, what is the value of x? (1) There [#permalink]  25 Nov 2013, 20:36
Expert's post
monirjewel wrote:
stm2 is not clear to me. Can anyone provide better explanation. thanks

F.S 2 states that "There is no integer n such that x is divisible by n and 1 < n< x."

In other words, it means that for the integer x,there is no other factor of x which is greater than 1 and less than x.

For example, take x=4. We have n=2, where 4 is divisible by 2, and 1<2<4.

But, for x=5,we have no value of 'n', which will be less than 5 and greater than 1.Thus, statement 2 basically means to say that x is a prime integer, which we already know.Insufficient.

Hope this helps.
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Re: If x is a prime number, what is the value of x? (1) There   [#permalink] 25 Nov 2013, 20:36
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