Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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

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.

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 is a prime number, what is the value of x? [#permalink]

Show Tags

16 Jul 2013, 02:33

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\(\to\)Insufficient.

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]

Show Tags

21 Aug 2013, 11:52

1

This post received KUDOS

(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]

Show Tags

21 Oct 2014, 08:12

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Re: If x is a prime number, what is the value of x? [#permalink]

Show Tags

17 Feb 2015, 10:59

Statement 1: Try x=2, works. Potentially the right answer, but x= another prime might also satisfy the equation. Move on.

Statement 2: X is a prime that is not even. Not sufficient.

1 & 2 together: Since both statements can't contradict each other, it means that x=2 can't be the answer. Both statements don't narrow x down to one value. Answer is E

Statement 1: Try x=2, works. Potentially the right answer, but x= another prime might also satisfy the equation. Move on.

Statement 2: X is a prime that is not even. Not sufficient.

1 & 2 together: Since both statements can't contradict each other, it means that x=2 can't be the answer. Both statements don't narrow x down to one value. Answer is E

Let me mention it here...

YOU NEVER ASSUME THAT STATEMENT IS NOT SUFFICIENT BASED ON HUNCH LIKE YOU DID IN STATEMENT 1. Also x=2 doesn't work

You must be able to prove that it's not sufficient in order to improve accuracy therefore the first statement should be considered in the following manner

Statement 1: 2x + 2 is the cube of a positive integer

2x+2 = 2(x+1) for this to be a perfect cube (x+1) must be even i.e. x must be odd

at x=3, 2x+2 = 8 One possibility another Even perfect cube is 64 64 = 2(x+1) => x=31

there are two or more possibilities of x= 3, 31 etc. Inconsistent Values therefore, NOT SUFFICIENT

Statement 2: Average of X consecutive integers is even

True for all Odd values of x therefore NOT SUFFICIENT

Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772 Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html

Re: If x is a prime number, what is the value of x? [#permalink]

Show Tags

11 Mar 2016, 11:13

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

well rather than hitting and trying with multiple prime numbers we can opt for a simpler process. first sort out the cube roots and see if any equation is satisfying it with prime number.

2^3=8 2(x+1)=8 yes prime 3 next 3^3= 27 No primes satify this equation next 4^3=64 any prime satisfying it ? YES 31

DONE STOP PROCEEDING Statement 1 is Not sufficient

Statement 2: well any odd number will satify this statement and we can have multiple answers such as 3 and 31 which are primes.

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

Show Tags

13 Jan 2017, 00:49

Great Question. We are told that x is a prime number and asked about its value.

Statement 1-> 2x+2=t^3 for any positive integer t. Lets use some test cases => 2x+2=1 x=1/2=> Not allowed 2x+2=8 x=3=> Allowed 2x+2=27 x=25/2=> Not allowed 2x+2=64 x=31=>Allowed

Hence 3 and 31 are both acceptable values => Not sufficient.

Statement 2-> Remember for set of consecutive integers is an AP series. Mean can be of the form p if x is odd (p is an integer ) Mean can be of the form p.5 if x is even (p is an integer) RULE->Sum of n consecutive integers is always divisible by n for n being odd and never divisible by n for n being even. Hence this statement tells us that x is odd. But their are ∞ odd primes => Not sufficient. Combing them x=3 and x=31 are both acceptable values. Hence not sufficient .