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 350,000 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:

An infinite sequence of positive integers is called a [#permalink]
16 Feb 2012, 15:11

1

This post received KUDOS

6

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

95% (hard)

Question Stats:

40% (02:16) correct
60% (01:43) wrong based on 289 sessions

An infinite sequence of positive integers is called a perfect sequence. If each term in the sequence is a perfect number, that is, if each term can be expressed as the sum of its divisors, excluding itself. For example, 6 is a perfect number, as its divisors, 1, 2, and 3, sum to 6. Is the infinite sequence S a perfect sequence?

(1) Exactly one term in S is a prime number. (2) In sequence S, each term after the first in S has exactly 3 divisors.

Re: An infinite sequence of positive integers is called a [#permalink]
16 Feb 2012, 20:39

4

This post received KUDOS

Expert's post

3

This post was BOOKMARKED

An infinite sequence of positive integers is called a perfect sequence. If each term in the sequence is a perfect number, that is, if each term can be expressed as the sum of its divisors, excluding itself. For example, 6 is a perfect number, as its divisors, 1, 2, and 3, sum to 6. Is the infinite sequence S a perfect sequence?

(1) Exactly one term in S is a prime number --> primes have exactly two divisors 1 and itself, hence no prime is a perfect number, which means that S is not a perfect sequence. Sufficient.

(2) In sequence S, each term after the first in S has exactly 3 divisors --> a number to have exactly 3 divisors must be square of a prime, for example 3^2=9 has 3 divisors: 1, 3, and 9 (1, p, and p^2). No, such number is a perfect number: 1+3 cannot equal to 9, (1+p cannot equal to p^2 for integer p), which means that S is not a perfect sequence. Sufficient.

Re: Infinite Sequence S [#permalink]
16 Feb 2012, 20:40

1

This post received KUDOS

(D) it is.

Using statement (1), if one term in the sequence is a prime number, that number can never have the sum of the divisors (except the number itself) add up to the number itself. Therefore that number is not a perfect number. Therefore the sequence containing this number is not a perfect sequence. Sufficient.

Using statement (2), if each term after the first has exactly three divisors, none of the numbers with these three divisors can be a perfect number. This is because one of the divisors will be the number itself, which will get excluded. The other two divisors will be 1 and another factor. This means the number must be = the factor + 1, which is not possible. Therefore this sequence is not a perfect sequence. Sufficient.

An infinite sequence of positive integers [#permalink]
06 Sep 2012, 13:23

An infinite sequence of positive integers is called a perfect sequence if each term in the sequence is a perfect number, that is, if each term can be expressed as the sum of its divisors, excluding itself. For example, 6 is a perfect number, as its divisors, 1, 2, and 3, sum to 6. Is the infinite sequence S a perfect sequence?

(1) Exactly one term in S is a prime number. (2) In sequence S, each term after the first in S has exactly 3 divisors.

The OA is D. I put down A as my answer. For statement 2 I get that a positive integer with 3 divisors will be the square of a prime number (4, 9, 25, 49, etc.). This statement though says that each term AFTER THE FIRST has 3 divisors. So the first term could be a perfect number or not. Maybe I'm missing something here. Any help on this will be helpful.

Re: An infinite sequence of positive integers [#permalink]
06 Sep 2012, 15:52

Expert's post

Arbitrageur wrote:

An infinite sequence of positive integers is called a perfect sequence if each term in the sequence is a perfect number, that is, if each term can be expressed as the sum of its divisors, excluding itself. For example, 6 is a perfect number, as its divisors, 1, 2, and 3, sum to 6. Is the infinite sequence S a perfect sequence?

(1) Exactly one term in S is a prime number. (2) In sequence S, each term after the first in S has exactly 3 divisors.

The OA is D. I put down A as my answer. For statement 2 I get that a positive integer with 3 divisors will be the square of a prime number (4, 9, 25, 49, etc.). This statement though says that each term AFTER THE FIRST has 3 divisors. So the first term could be a perfect number or not. Maybe I'm missing something here. Any help on this will be helpful.

Hi Arbitraguer,

The question asks if S is a perfect sequence, meaning that every term must be perfect. (1) tells us the first term is not perfect; (2) tells us that no term after the first can be perfect. Therefore, each of (1) and (2) answers "NO" to the question of whether the entire sequence is perfect. Both are sufficient! _________________

Re: An infinite sequence of positive integers [#permalink]
06 Sep 2012, 21:12

Expert's post

Arbitrageur wrote:

An infinite sequence of positive integers is called a perfect sequence if each term in the sequence is a perfect number, that is, if each term can be expressed as the sum of its divisors, excluding itself. For example, 6 is a perfect number, as its divisors, 1, 2, and 3, sum to 6. Is the infinite sequence S a perfect sequence?

(1) Exactly one term in S is a prime number. (2) In sequence S, each term after the first in S has exactly 3 divisors.

The OA is D. I put down A as my answer. For statement 2 I get that a positive integer with 3 divisors will be the square of a prime number (4, 9, 25, 49, etc.). This statement though says that each term AFTER THE FIRST has 3 divisors. So the first term could be a perfect number or not. Maybe I'm missing something here. Any help on this will be helpful.

In the sequence S, if there is even one term which is not a perfect number, the sequence is not a perfect sequence. You need every term of the sequence to be a perfect number for the sequence to be a perfect sequence. Statement 2 tells you that after the first term, every term is 'non-perfect'. We don't care whether the first term is perfect or not. Since we know that the sequence has non-perfect numbers, the sequence is not perfect. Hence, statement 2 is also sufficient.

Test makers like to add little twists like these "after the first term" to mess with your mind! I am sure you would have had no problems if the second statement were "...each term has exactly 3 divisors" _________________

Re: An infinite sequence of positive integers is called a [#permalink]
04 Jun 2013, 22:04

enigma123 wrote:

An infinite sequence of positive integers is called a perfect sequence. If each term in the sequence is a perfect number, that is, if each term can be expressed as the sum of its divisors, excluding itself. For example, 6 is a perfect number, as its divisors, 1, 2, and 3, sum to 6. Is the infinite sequence S a perfect sequence?

(1) Exactly one term in S is a prime number. (2) In sequence S, each term after the first in S has exactly 3 divisors.

question can be written in a better way:

An infinite sequence of positive integers is called a perfect sequence, if each term in the sequence is a perfect number, that is, if each term can be expressed as the sum of its divisors, excluding itself. For example, 6 is a perfect number, as its divisors, 1, 2, and 3, sum to 6. Is the infinite sequence S a perfect sequence?

Re: An infinite sequence of positive integers is called a [#permalink]
05 Jun 2013, 02:40

1

This post received KUDOS

An infinite sequence of positive integers is called a perfect sequence. If each term in the sequence is a perfect number, that is, if each term can be expressed as the sum of its divisors, excluding itself. For example, 6 is a perfect number, as its divisors, 1, 2, and 3, sum to 6. Is the infinite sequence S a perfect sequence?

(1) Exactly one term in S is a prime number. (2) In sequence S, each term after the first in S has exactly 3 divisors

1 st.) This statement sufficient by itself, because any the feature of the prime number is that it has only two divisors, 1 and the number itself. But according to the definition of the perfect numbers the sum of the divisors (excl. the number itself) should be equal to the number itself - which is not possible with prime numbers. So the sequence is not perfect. Sufficient.

2 st.) lets take some numbers that have exactly 3 divisors: 4 (1, 2, 4) - the sum of the 1+2 is 3, which is not perfect number. next number is 9 (1, 3, 9) the sum of 1+3=4 again not perfect since it does not equal to 9. Next number is 25 (1, 5, 25) the same conclusion. Here is the pattern, only squares of the prime numbers could have exactly 3 divisors, that means in this sequence we have not perfect numbers - sufficient.

So each statement sufficient on its own - D. _________________

If you found my post useful and/or interesting - you are welcome to give kudos!

Re: An infinite sequence of positive integers is called a [#permalink]
22 Sep 2014, 17:50

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. _________________

safe.txmblr Can business make a difference in the great problems that we face? My own view is nuanced. I think business potentially has a significant role to play...

Still 7 months to go to be at Lausanne. But, as Lausanne has a vacancy rate of 0.1% for rental properties, I booked my rental apartment yesterday for...