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

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Director
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If x is a positive integer, is the number of its divisors [#permalink] New post 11 Sep 2007, 00:39
00:00
A
B
C
D
E

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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
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 [#permalink] New post 11 Sep 2007, 01:44
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.
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 [#permalink] New post 11 Sep 2007, 05:48
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
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 [#permalink] New post 11 Sep 2007, 07:51
I aslo would chose E since there are many numbers which would satify the equation

Ans: E
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 [#permalink] New post 12 Sep 2007, 04:58
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
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 [#permalink] New post 13 Sep 2007, 00:22
E is incorrect!! Anyone with a correct answer??
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 [#permalink] New post 13 Sep 2007, 07:19
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..
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Re: DS: x is a positive integer [#permalink] New post 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.
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 [#permalink] New post 13 Sep 2007, 09:46
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.
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Re: DS: x is a positive integer [#permalink] New post 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?
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 [#permalink] New post 17 Sep 2007, 22:54
As per OA, no one has it right as of yet. Any more tries??
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 [#permalink] New post 23 Nov 2007, 12:46
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
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Re: DS: x is a positive integer [#permalink] New post 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.
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Re: DS: x is a positive integer [#permalink] New post 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
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