Number properties

[GodwinG921]

If x > 1, what is the value of integer x? - Source Number properties guide MGMAT

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

I Quote this is the response given in the MGMAT guide. - Statement (1) tells us that there are x unique factors of x. In order for this to be true, EVERY integer between 1and x, inclusive, must be a factor of x. Testing numbers, we can see that this property holds for 1 and for 2, but not for 3 or for 4. In fact, this property does not hold for any higher integer, because no integer x above 2 is divisible by x-I. Therefore, x = 1 or 2. However, the original problem stem told us that x > 1, so x must equal 2. SUFFICIENT..

Statement (2) tells us that x plus any prime number larger than x is odd. Since x > 1, x must equal at least 2, so this includes only prime numbers larger than 2. Therefore, the prime number is odd, and x is even. However, this does not tell us which even number x could be. INSUFFICIENT. The correct answer is (A): Statement (1) is sufficient to answer the question, but Statement (2) is insufficient.

But i cant understand why 3 cannot be a probable answer. Since 3 is also a prime number with unique factors.

[RonPurewal]

3 only has two unique factors (1 and 3).

if x = 3 then statement 1 becomes "There are 3 unique factors of 3", which is a false statement.

[tim]

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