Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 23 Apr 2014, 19:33

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If x is a positive integer, is the number of its divisors

Author Message
TAGS:
Director
Joined: 09 Aug 2006
Posts: 770
Followers: 1

Kudos [?]: 32 [0], given: 0

If x is a positive integer, is the number of its divisors [#permalink]  11 Sep 2007, 00:39
00:00

Difficulty:

5% (low)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
If x is a positive integer, is the number of its divisors smaller than 2*sqrt(x)-1?

1) x is not a square of an integer
2) x is prime

I have no idea how to even begin on this one. Any suggestions? Thanks.
Manager
Joined: 20 Jun 2007
Posts: 158
Followers: 1

Kudos [?]: 10 [0], given: 0

Not a strength of mine, properties of numbers.

(I) Not a square of an integer could mean a number like 99 or like 2. For these two numbers I think we get different answers, so Insufficient
(II) A square of a prime number has only two divisors - itself and 1. So let's look at a couple of options:

23: No of divisors = 2
2*sqrt(x)-1 = c 9
So the number of divisors is smaller than 2*sqrt(x)-1

2: No of divisors = 2
2*sqrt(x)-1 = c 1.8
So the number of divisors is greater than 2*sqrt(x)-1
So (II) is insufficient

I don't think (I) and (II) combined can help, so the answer should be E.
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5098
Location: Singapore
Followers: 15

Kudos [?]: 120 [0], given: 0

St1:
x can be 2,5,8 etc...
If x = 2, # of divisors > 2*sqrt(x)-1
If x= 7, # of divisors <2> 2*sqrt(x)-1
If x = 11, # of divisors < 2*sqrt(x)-1
Insufficient.

Using both,
All primes are not the square of an integer.
We're back to solving st2. Nothing else extra known. Insufficient.

Ans E
Senior Manager
Joined: 27 Aug 2007
Posts: 257
Followers: 1

Kudos [?]: 8 [0], given: 0

I aslo would chose E since there are many numbers which would satify the equation

Ans: E
Manager
Joined: 29 Aug 2007
Posts: 112
Followers: 1

Kudos [?]: 0 [0], given: 0

A - X is not a perfect square, so X could be 2 , 8, 11 etc .which have various values

B - Clearly says X is prime.. Which means it can only have 2 divisors, the number and itself

2 * Sqrt( prime) - 1

checking for values

for number 2

2 * Sqrt( 2) - 1 <2> 2

So could be any value.. Answer E
Director
Joined: 09 Aug 2006
Posts: 770
Followers: 1

Kudos [?]: 32 [0], given: 0

E is incorrect!! Anyone with a correct answer??
Current Student
Joined: 28 Dec 2004
Posts: 3411
Location: New York City
Schools: Wharton'11 HBS'12
Followers: 13

Kudos [?]: 148 [0], given: 2

I get E...too

lets take X. we are told its not a square

ok..so then for any number X whose primes are say A^n B^m its number of factors will be (n+1)(m+1)

take any non-sqaure number you will find that its number of factors are less than 2*sqrt(x)-1

so if x=2 sqrt(2)=1.41 which means 2*1.41=2.82-1=1.82 but 2 has 2 factors 1 and 2 itself..

if x=11, sqrt(11) aprox=3.3 therefore 2*3.3=6.6-1 5.6 which is greater than 2..

insuff
2) x is a prime number..i just tried 2 examples above...

It has to be E..
Current Student
Joined: 28 Dec 2004
Posts: 3411
Location: New York City
Schools: Wharton'11 HBS'12
Followers: 13

Kudos [?]: 148 [0], given: 2

Re: DS: x is a positive integer [#permalink]  13 Sep 2007, 07:23
I would say statement 2 should either read...

X is not a prime or X is a prime greater than 2...

in that case..the answer would be C..

GK_Gmat wrote:
If x is a positive integer, is the number of its divisors smaller than 2*sqrt(x)-1?

1) x is not a square of an integer
2) x is prime

I have no idea how to even begin on this one. Any suggestions? Thanks.
Manager
Joined: 14 Jan 2007
Posts: 171
Followers: 2

Kudos [?]: 7 [0], given: 0

only 2 is the number which has number of factors(2) greater than 2sqrt(2)-1
and 2 is prime and not a square. it gives answer no to the question asked.
Intern
Joined: 13 Sep 2007
Posts: 2
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: DS: x is a positive integer [#permalink]  13 Sep 2007, 11:48
GK_Gmat wrote:
If x is a positive integer, is the number of its divisors smaller than 2*sqrt(x)-1?

1) x is not a square of an integer
2) x is prime

I have no idea how to even begin on this one. Any suggestions? Thanks.

option 1 & 2 gives probable values of x as 2, 3, 5, 7.. elementary..
also, all have only 2 divisors (prime #s)

the formula 2*sqrt(x)-1 gives value ~ 2.8 for x=2 (smallest prime satisfying 1 & 2)

i.e we have a definite answer to the question posed (in this case, yes; as 2 < 2.8)

similarly, for all other primes the same holds true.. hence we have a definite and same ans (yes) for all possible values of x

hence ans C. (both are needed)

p.s.
1. only prime which wud have given a diff answ would be 1; but statement 1 tells us that 1 is not a possiblity.
2. This was my first ever post on here..did i do ok?
Director
Joined: 09 Aug 2006
Posts: 770
Followers: 1

Kudos [?]: 32 [0], given: 0

As per OA, no one has it right as of yet. Any more tries??
CEO
Joined: 21 Jan 2007
Posts: 2775
Location: New York City
Followers: 6

Kudos [?]: 171 [0], given: 4

GK_Gmat wrote:
As per OA, no one has it right as of yet. Any more tries??

search for this question. seems like OA is wrong. should be E
Intern
Joined: 10 Jan 2008
Posts: 40
Followers: 0

Kudos [?]: 3 [0], given: 0

Re: DS: x is a positive integer [#permalink]  08 Apr 2008, 15:27
GK_Gmat wrote:
If x is a positive integer, is the number of its divisors smaller than 2*sqrt(x)-1?

1) x is not a square of an integer
2) x is prime

I have no idea how to even begin on this one. Any suggestions? Thanks.

I vote D,
but I agree that the question is wrong.

1) and 2) both tell us that x >= 2. If x = 2, you get 2 * sqrt(2)-1 = 2 * 1.4 -1 = 1.8
The divisors for 2 are: 1, 2, -1, and -2 (some questions specify positive divisors, but this one doesn't). So the answer would be no in this case.

The problem is that the answer seems to be no for all integers, and the two statements seem to be pointless.
Manager
Joined: 25 Mar 2008
Posts: 107
Followers: 1

Kudos [?]: 10 [0], given: 0

Re: DS: x is a positive integer [#permalink]  09 Apr 2008, 11:21
i wil go with E after a tiring journey
Re: DS: x is a positive integer   [#permalink] 09 Apr 2008, 11:21
Similar topics Replies Last post
Similar
Topics:
X is the number of distinct positive divisors of X. What is 13 07 Nov 2005, 15:25
x is the number of distinct positive divisors of X/ What is 13 03 Nov 2007, 14:11
If X is a positive integer, what is the largest divisor of 2 16 Nov 2007, 12:11
x is the number of distinct positive divisors of x . What is 6 28 Feb 2008, 08:23
If is a positive integer, is the number of its divisors 2 08 Sep 2008, 09:01
Display posts from previous: Sort by

# If x is a positive integer, is the number of its divisors

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.