x is a prime

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 am; Location: India; Thanked: 267 times; Followed by:80 members; GMAT Score:760

x is a prime

by sanju09 » Fri Mar 04, 2011 1:27 am

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

(1) 2 x + 2 is the cube of a positive integer.

(2) The average of any x consecutive integers is an integer.

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Fri Mar 04, 2011 1:51 am

sanju09 wrote:If x is a prime number, what is the value of x?

(1) 2 x + 2 is the cube of a positive integer.
(2) The average of any x consecutive integers is an integer.

Just remember, we cannot uniquely describe a single prime with some generalized property. Any number of generalized property will be satisfied by more than one prime. Hence, answer to this question is definitely E.

In case you have doubt, you may check as follows,

Statement 1: (2x + 2) is the cube of a positive integer.
Possible values of x are : 3, 31, 107 etc

Not sufficient

Statement 2: The average of any x consecutive integers is an integer.
Any odd value of x is a possible value, i.e. all the primes except 2 is a possible value of x.

Not sufficient

1 & 2 Together: Same values are possible as of statement 1.

Not sufficient

The correct answer is E.

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pesfunk: Master | Next Rank: 500 Posts; Posts: 286; Joined: Tue Sep 21, 2010 5:36 pm; Location: Kolkata, India; Thanked: 11 times; Followed by:5 members

by pesfunk » Fri Mar 04, 2011 8:29 am

Hi anurag, from your point one, you have illustrated numbers like 3, 31, 107...etc.
On a real test day, how do we get this ?....

Anurag@Gurome wrote:
sanju09 wrote:If x is a prime number, what is the value of x?

(1) 2 x + 2 is the cube of a positive integer.
(2) The average of any x consecutive integers is an integer.
Just remember, we cannot uniquely describe a single prime with some generalized property. Any number of generalized property will be satisfied by more than one prime. Hence, answer to this question is definitely E.

In case you have doubt, you may check as follows,

Statement 1: (2x + 2) is the cube of a positive integer.
Possible values of x are : 3, 31, 107 etc

Not sufficient

Statement 2: The average of any x consecutive integers is an integer.
Any odd value of x is a possible value, i.e. all the primes except 2 is a possible value of x.

Not sufficient

1 & 2 Together: Same values are possible as of statement 1.

Not sufficient

The correct answer is E.

Quote

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Fri Mar 04, 2011 8:39 am

pesfunk wrote:Hi anurag, from your point one, you have illustrated numbers like 3, 31, 107...etc.
On a real test day, how do we get this ?

(2x + 2) = Cube of some positive integer n

Hence, n = 2(x + 2) = Multiple of 2
=> n = Cube of some even integer.

If, n = 2Â³ = 8 => x = 3
If, n = 4Â³ = 64 => x = 31
If, n = 6Â³ = 216 => x = 107

Note that this doesn't mean cube of all even integers can expressed as (2x + 2), where x is a prime. For example, n = 8Â³ = 512 = (2*255 + 2). But 255 is not prime.

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