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

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\(\to\)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

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

Show Tags

17 Feb 2015, 11:14

Expert's post

Sammyh21 wrote:

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

READ:http://gmatclub.com/forum/620-to-760-getting-reborn-161230.html Classroom Centre Address: GMATinsight 107, 1st Floor, Krishna Mall, Sector-12 (Main market), Dwarka, New Delhi-110075 ______________________________________________________ Please press the if you appreciate this post !!

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. _________________

MBA Admission Calculator Officially Launched After 2 years of effort and over 1,000 hours of work, I have finally launched my MBA Admission Calculator . The calculator uses the...

Final decisions are in: Berkeley: Denied with interview Tepper: Waitlisted with interview Rotman: Admitted with scholarship (withdrawn) Random French School: Admitted to MSc in Management with scholarship (...

The London Business School Admits Weekend officially kicked off on Saturday morning with registrations and breakfast. We received a carry bag, name tags, schedules and an MBA2018 tee at...

I may have spoken to over 50+ Said applicants over the course of my year, through various channels. I’ve been assigned as mentor to two incoming students. A...