GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Oct 2019, 07:02

GMAT Club Daily Prep

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

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

If n is a positive integer, is n divisible by at least six positive in

Author Message
TAGS:

Hide Tags

Intern
Joined: 29 Jul 2010
Posts: 2
If n is a positive integer, is n divisible by at least six positive in  [#permalink]

Show Tags

29 Jul 2010, 11:08
1
4
00:00

Difficulty:

15% (low)

Question Stats:

83% (01:06) correct 17% (01:18) wrong based on 83 sessions

HideShow timer Statistics

If n is a positive integer, is n divisible by at least six positive integers?

(1) n is the product of three different prime numbers
(2) n=30
SVP
Status: Three Down.
Joined: 09 Jun 2010
Posts: 1823
Concentration: General Management, Nonprofit
Re: If n is a positive integer, is n divisible by at least six positive in  [#permalink]

Show Tags

29 Jul 2010, 11:42
3
1
It's quite simple. I think the confusion arises when you confuse divisibility by integers with divisibility by prime factors.

Statement 1: n is the product of three prime numbers.

Prime numbers are numbers that are only divisible by 1 and by itself. So, for an example's sake, let's consider the following:

n = a*b*c where a, b and c are three different prime numbers. This implicitly tells us that n = a*b*c*1. This means we know that n is divisible by 4 different positive integers now.

But n is also divisible by the following combinations of numbers:

a*b
b*c
c*a
a*b*c

Add to this the original factors:

a
b
c
1

And you get that n is divisible by at least 8 different positive numbers.

Hence 1 is sufficient.

Statement 2: n = 30

This is even easier. This is a special case of the first statement where a = 2 b =3 and c =5, the first three prime numbers. So the factors are

1
2
3
5
6
15
10
30

So this is also sufficient.

Hope this helps.
Intern
Joined: 29 Jul 2010
Posts: 2
Re: If n is a positive integer, is n divisible by at least six positive in  [#permalink]

Show Tags

29 Jul 2010, 13:37
Thanks a lot!!
I considered 1 as a prime number by mistake. That's why I doubt that statement 1 is sufficient.
You're awesome!
Manager
Joined: 30 May 2010
Posts: 165
Re: If n is a positive integer, is n divisible by at least six positive in  [#permalink]

Show Tags

30 Jul 2010, 13:39
Even if you make the mistake that 1 is prime, Statement 1 would still be sufficient. The question asks is n is divisible by at least six positive integers?

n = a * b * 1

Divisible by: a, b, 1, and ab.

To answer the question, "no" n is not divisible by at least six positive integers (4).

Did you maybe make the mistake of thinking not sufficient means "no" to the question?
Non-Human User
Joined: 09 Sep 2013
Posts: 13392
Re: If n is a positive integer, is n divisible by at least six positive in  [#permalink]

Show Tags

29 Oct 2018, 22:24
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 n is a positive integer, is n divisible by at least six positive in   [#permalink] 29 Oct 2018, 22:24
Display posts from previous: Sort by