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(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.

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.

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?

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.