Data Sufficiency example problem, NP pg 31 - confused

[ryan.fogelgren]

If x>1, what is the value of integer x?

(1) There are unique factors of x.
(2) The sum of x and any prime number larger than x is odd.

I can see why statement 2 is insufficient but do not understand how statement 1 is sufficient. The explanation is confusing.

Any help is appreciated!

[leovavassori]

Hello there,

Lets starts from the basic:

The question gives you the information that x>1 AND an integer. It then asks you what is the value of x - hence the correct statement will provide only ONE value for x.

(1) There are x unique factors of x.

So x has x unique factors. Unique should hint you that the factors do not repeat - meaning x is a small number. Then is just a case of trying:

x>1 AND an integer, so you best start with 2:

- Are there 2 unique factors of 2?

Yes 2 has 2 factors - 1 and itself. You should now check to see whether there could be any other values that satisfy the criteria.


- Are there 3 unique factors of 3?

No! 3 has only 1 and itself as a factor. That will be the same for ever other number you might try after that. Only the number 1 would fit the statement but since the question asks for a integer larger than 1, the number 2 is the only solution.

Hopes this helps,

Leo

[tim]

well, it's not true that every integer larger than 3 has only 1 and itself as factors, but the point is that none of them will have enough factors regardless, and the only integer larger than 1 that will work is 2..