Number Properties: Divisibility & Primes

[miproyecto]

This is a problem from Manhattan Number Properties Book, pg. 117:

What is the value of integer x?
1. x has exactly 2 factors
2. When x is divided by 2, the remainder is 0.

My answer was E, but according to the book, C is right.

I chose E, since from Statement 1 and 2 I can only infer that the answer could be integer 2 or -2, but I do not know how it can be concluded that the answer is only prime number 2.

What am I missing here?

[apoorva.srivastva]

This is a problem from Manhattan Number Properties Book, pg. 117:


1. x has exactly 2 factors

St. 1 says that x is a prime number anf prime numbers are non negative!!

so C is the correct answer as x=2 from st1 and st2 combined

[miproyecto]

Sorry to inquire again, but how many factors does -2 then have?

[apoorva.srivastva]

but y do u need factors of (-2) ...st1 says that x has just two factors and prime numbers are the ones who have exactly two factors i.e integer "1" and "the number itself"

from st1 ..x can be any prime number 2,3,5,7,91 etc.

from st.2 we get that x mod 2 =0

from st1 and st2

2 is the only prime number that satisfies both statements

HTH

[apoorva.srivastva]

and (-2) as per my understanding can have 4 factors..... -1,1,-2,2

i am not too sure though!!

[Ian Stewart]

It's a badly worded question. If this were a real GMAT question, it would say "What is the value of positive integer x?", and Statement 1 would say "x has exactly two positive factors." You won't need to worry about the factors of -2 on a real GMAT question (though -2 does have four factors, -2, -1, 1 and 2), nor will you need to worry about the negative factors of 2 (2 has two negative factors, -1 and -2).

If the word 'positive' is left out, the question in the original post doesn't make sense, mathematically. The only numbers with precisely two factors are 1 and -1 (both have the factors 1 and -1) if we permit negative factors. This contradicts Statement 2. Some prep books claim that 'factor' means 'positive divisor', which simply isn't true in mathematics, but at least on the GMAT, it doesn't matter, since you will never see a question dealing with negative factors.

[miproyecto]

Hi Ian,

In the Manhattan Book, they do omit the word positive. For that reason I was not fully sure the answer was C. But thank you for the explanation, it did help.