If x and y are distinct prime numbers, each greater than 2,

Bunuel,

Does that mean that me never count 1 as a factor?

No. 1 is a factor of every positive integer. Also 1 is a perfect square (1=1^2) and it has 1 (so odd) factor - itself.

Hi All,

Roman Numeral questions on the GMAT often come with a "design shortcut", meaning that you probably WON'T have to think about all 3 Roman Numerals (IF you pay attention to how the answer choices are designed).

Here, we're told that X and Y are DISTINCT (meaning "different") PRIME numbers that are each greater than 2. We're asked which of the following Roman Numerals MUST be true (which really means "which of these is ALWAYS TRUE no matter how many different examples you can come up with). It's often easier to try to prove that something is NOT true, so that should be our goal here - try to come up with a way to disprove a Roman Numeral so that we can ELIMINATE it.

TESTing VALUES will work perfectly here.

I. (X+Y) is divisible by 4

3+5 = 8 which is divisible by 4
3+7 = 10 which is NOT divisible by 4
Roman Numeral 1 is NOT always true, so we can ELIMINATE IT.

**NOTE: Look at the answers. Since Roman Numeral 1 has been eliminated, we can....
1) Eliminate answers A, C and E.
2) Notice that the two remaining answers both have Roman Numeral II in them, so that Roman Numeral MUST be TRUE. As such, we don't even have to deal with it!!!!!

III. (X+Y) has an even number of factors

3+5 = 8 which has 4 factors
3+7 = 10 which has 4 factors
3+11 = 14 which has 4 factors
3+13 = 16 which has 5 factors
Roman Numeral 3 is NOT always true, so we can ELIMINATE IT.
Eliminate Answer D.

Final Answer:

GMAT assassins aren't born, they're made,
Rich

Are there any other primes so that there sum yields a perfect square ?
what about x-y being a perfect square ?
is it possible too?
just curious as i got this question wrong ..
Did not think of 13 and 3

2 + 7 = 9 = 3^2
3 + 13 = 16 = 4^2
2 + 23 = 25 = 5^2
5 + 31 = 36 = 6^2
2 + 47 = 49 = 7^2
3 + 61 = 64 = 8^2
...

3 - 2 = 1 = 1^2
7 - 3 = 4 = 2^2
11 - 2 = 9 = 3^2
19 - 3 = 16 = 4^2
...

Since x and y are prime numbers greater than two, they are both odd prime numbers. Let’s analyze each answer choice:

I. x+y is divisible by 4

This is not true. If x = 11 and y = 7, then x + y = 18, which is not divisible by 4.

II. x*y has an even number of factors

The only numbers that have an odd number of factors are perfect squares. Since x and y are distinct primes, x*y can’t be a perfect square, and thus it must have an even number of factors. This statement is true.

III. x+y has an even number of factors

This is not true. If x = 3 and y = 13, then x + y = 16, which is a perfect square. Recall that in Roman numeral II, we’ve mentioned that a perfect square has an odd number of factors.

Answer: B

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