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Re: if x prime, value of x [#permalink]
23 Dec 2009, 10:04

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Expert's post

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xcusemeplz2009 wrote:

IMO E is correct s1) x = 2 , 31, 107 will give a perfect cube and all are prime so insuff s2) x can be any prime no. so insuff togather also no. single value hence E

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

(1) 2x + 2 is the cube of a positive integer --> 2x+2=n^3 --> n even.

(2) The average of any x consecutive integers is an integer. This statement is basically tells us that x is odd, as only the average of odd consecutive numbers are an integer (the average of even number of consecutive integers is a fraction: integer/2). Hence x can be any prime but 2. Not sufficient.

(1)+(2) x can be odd primes, for example 31 or 107, hence insufficient.

Re: if x prime, value of x [#permalink]
23 Dec 2009, 10:17

2

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Got E with a similar approach. Only tip is for statement 1, instead of prime numbers which satisfy 2*x+2 is a perfect cube, find perfect cubes which when subtracted by 2 and divided by 2 yields a prime number. _________________

Re: if x prime, value of x [#permalink]
23 Dec 2009, 09:27

1

This post received KUDOS

IMO E is correct s1) x = 2 , 31, 107 will give a perfect cube and all are prime so insuff s2) x can be any prime no. so insuff togather also no. single value hence E _________________

GMAT is not a game for losers , and the moment u decide to appear for it u are no more a loser........ITS A BRAIN GAME

Re: If x is a prime number, what is the value of x? [#permalink]
21 Aug 2013, 10:52

1

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(1) INSUFFICIENT: Start by listing the cubes of some positive integers: 1, 8, 27, 64, 125. If we set each of these equal to 2x + 2, we see that we can find more than one value for x which is prime. For example x = 3 yields 2x + 2 = 8 and x = 31 yields 2x + 2 = 64. With at least two possible values for x, the statement is insufficient.

(2) INSUFFICIENT: In a set of consecutive integers, the mean is always equal to the median. When there are an odd number of members in a consecutive set, the mean/median will be a member of the set and thus an integer (e.g. 5,6,7,8,9; mean/median = 7). In contrast when there are an even number of members in the set, the mean/median will NOT be a member of the set and thus NOT an integer (e.g. 5,6,7,8; mean/median = 6.5). Statement (2) tells us that we are dealing with an integer mean; therefore x, the number of members in the set, must be odd. This is not sufficient to give us a specific value for the prime number x.

(1) AND (2) INSUFFICIENT: The two x values that we came up with for statement (1) also satisfy the conditions of statement (2).

Re: If x is a prime number, what is the value of x? [#permalink]
16 Jul 2013, 01:33

Expert's post

msunny wrote:

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

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

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

From F.S 1, we know that 2(x+1) = t^3, where t is a positive integer. Two conditions are to be met:

1.x should be a prime number. 2.(x+1) should at-least be equal to 2^2, or have it as a factor.

Now, for x+1 = 2^2, we get x = 4-1 = 3. So , we get x = 3(prime)

Again, to make 2(x+1) as a perfect cube, the next value of (x+1) should be 2^2*2^3 \to x+1 = 32 \to x = 31(prime). Thus x = 31.

Two values of x\toInsufficient.

From F.S 2, for a set of consecutive integers, the mean is always the middle term, which is unique and an integer. Thus, for any x, which is odd, the mean of the given series would be a unique integer. Thus, x = odd. Clearly Insufficient.

Both the statements taken together, x can be 3 or x can be 31. Insufficient.

Re: If x is a prime number, what is the value of x? [#permalink]
21 Oct 2014, 07:12

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