Number Properties Chapter 2

[pamela]

In page 31 of the number properties strategy guide, I am having a hard time understanding the data sufficiency problem.

"If x >1, what is the value of integer x"?
1. There are x unique factors of x
2. The sum of x and any prime number larger than x is odd.

My thought process in analyzing statement 1 is:
if x were 1, there's only one unique factor (one)
if x were 2, there are only two unique factors (one and two)
Since we have more than one possibility, statement one would
be insufficient.

In the explanation, it says statement one is sufficient, with reasoning "because no integer x above 2 is divisible by x-1".

Unfortunately this explanation leaves me even more confused. Could you please shed some light?

Thanks for any help you can offer.
Best regards.

[phanideepak6]

"If x >1, what is the value of integer x"?
1. There are x unique factors of x
2. The sum of x and any prime number larger than x is odd.

Here the question is that any number x has x unique factors so consider 4 lets list down the factors 1,2,4 according. Going by the question the number should have 4 factors.

is 3 a factor of 4? No

Let us take one more example

9 the factors of 9 are 1,3,9 here also check if the number has 9 factors. it doesn't it can be proved that 9/(9-1) != 0

The only number X which has X factors is 2. The factors of 2 are 1,2 2/(2-1) = 0

I hope this helps.

I hope this helps.

[jnelson0612]

Hi Pamela! Notice that the problem says "x>1", so x is 1 is not an option. Thus, your only option is x=2. Nice thinking to get that far. Hope this helps! :-)

[pamela]

Thanks to you both.

[jnelson0612]

:-)

[edadams1]

Hi,

I also had trouble with this DS problem. Unfortunately the explanations that were provided still are not very clear to me. Would someone be willing to try and solve this problem from start to finish so I can see the entire thought process straight through?

Thanks

[jnelson0612]

Hi,

I also had trouble with this DS problem. Unfortunately the explanations that were provided still are not very clear to me. Would someone be willing to try and solve this problem from start to finish so I can see the entire thought process straight through?

Thanks

Sure. Let's look at the problem again:

"If x >1, what is the value of integer x?
1. There are x unique factors of x
2. The sum of x and any prime number larger than x is odd."

Okay, so we know that x is an integer that is 2 or greater. What is x?

Let's start with statement 2: x + a prime number larger than x is odd. I would think, hmm, almost all prime numbers are odd themselves. Let me make a list of prime numbers: 2, 3, 5, 7, 11, 13, etc. Let's come up with some values:
x could be 2. Any prime number larger than 2 is odd, so 2 +odd = odd. 2 works as a value of x.
x could be 4. An prime number larger than 4 is odd, so 4 + odd = odd. 4 works as a value of x.

Statement 2 does not tell me what x is; x could be 2 or 4, or really any even number that is 2 or greater. Cross off BD.

Let's go to statement 1: 1. There are x unique factors of x.
Let's test some values:
2--There ARE 2 unique factors of 2, 1 and 2. This works.
3--There ARE NOT 3 unique factors of 3. There are only two, 1 and 3. This doesn't work.
4--There ARE NOT 4 unique factors of 4. There are three, 1, 2, and 4.
5--There ARE NOT 5 unique factors of 5.
6--There ARE NOT 6 unique factors of 6.

See where this is heading? 1 and 2 are the only numbers that have the same number of factors as the number itself. We know that x is greater than 1, so x must be 2. The answer is A.

[venky1711]

I think Statement 2 is also sufficient
Statement 2 says:The sum of x and any prime no. larger than X is odd,
1)Statement 2 is possible only when one of the no. is 2. otherwise the sum of prime no.s is always even.
2)Therefore either X or the prime no. should be 2 and since Prime no. > X and X>1, X has to be 2 .
So i think Statement 2 is also sufficient.Am i correct ?Am i missing something here

[jnelson0612]

venky, be very, very careful with interpreting the statements. Please see my comments below in blue:

I think Statement 2 is also sufficient
Statement 2 says:The sum of x and any prime no. larger than X is odd,
1)Statement 2 is possible only when one of the no. is 2. otherwise the sum of prime no.s is always even.
Be careful! You are adding x and a prime number larger than x and that sum is odd.

x could be 2. 2 plus any larger prime number (they are all odd) is odd.
x could be 4. 4 plus any prime number larger than 4 (again, every prime number above 4 is odd) will yield an odd sum.

x could be 2 or 4; we cannot conclude what x is. insufficient.
Please note that the statement never says that x must be prime, just that we are adding x to a prime number larger than x.

2)Therefore either X or the prime no. should be 2 and since Prime no. > X and X>1, X has to be 2 .
So i think Statement 2 is also sufficient.Am i correct ?Am i missing something here