If x and y are prime numbers, is y(x-3) odd?

I have a question, Can we disregard -ve numbers here for part 2. (y<3) ?

Yes, because it is mentioned in the stem that "x and y are prime numbers". Prime numbers are never -ve;

Per GMATClub Math Book:
A Prime number is a natural number with exactly two distinct natural number divisors: 1 and itself.

If x and y are prime numbers, is y(x-3) odd?

(1) x > 10
(2) y < 3

This is from the Kaplan 2013 book, page 562 #11

If x and y are prime numbers, is y(x-3) odd?

In order the product of 2 integers to be odd, both must be odd. So, y(x-3) to be odd, y must be any odd prime and x must be the only even prime 2, so that x-3=even-odd=odd. In all other cases given product will be even.

(1) x > 10 --> x is not 2, so the product is even. Sufficient.

Or: x is a prime number more than 10, so it's odd --> x-3=odd-odd=even --> y(x-3)=y*even=even.

(2) y < 3 --> the only prime less than 3 is 2, so y(x-3)=even*(x-3)=even. Sufficient.

Answer: D.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Thank you.

Ok, i'll follow rules next time, srry new to forum.

anyways i understand now, feel dumb lol

Hi Banuel,

why are we presuming one of x and y to be 2 ?
for statement 1 : x is odd, so x-3 will be odd. y can also be odd, why do we presume it to be 2 ?

pl help.

We are not doing that.

y(x-3) to be odd, y must be any odd prime and x must be the only even prime 2, so that x-3=even-odd=odd.

Also, if x is odd, then x-3=odd-odd=even.

Thanx Bunuel. I suddenly feel stupid. odd-odd=even, how silly of me.

Are there no negative prime numbers? Because if there are negative prime numbers, the answer to this question would be A.

No, only positive integers can be primes. The smallest prime (and the only even prime) is 2. For more check here: math-number-theory-88376.html

Hope it helps.

Take a look at the question is y(x-3) odd?

Now, x,y both primes right? So x-3 will always be even except when x = 2, only even prime

(1) x>10 so x is not 2
Suff

(2) y<3 so 'y' has to be 2 cause is the smallest prime number

Remember negatives can't be prime numbers
1 is of course not prime either

Hence D here

Cheers!
J

Hi All,

This is a great Number Property question; even if you don't immediately recognize the Number Properties involved, you can still discover the patterns (although it might take a little work).

We're told that X and Y are PRIME NUMBERS. We're asked if Y(X-3) is ODD. This is a YES/NO question.

Fact 1: X > 10

Since we know that X is PRIME, this Fact tells us that X must also be ODD. Y can be ANY PRIME number....

IF....
X = 11
then (X-3) = (11-3) = 8
(any prime)(8) will be EVEN, so the answer to the question is NO.

IF....
X = 13
then (X-3) = (13-3) = 10
(any prime)(10) will be EVEN, so the answer to the question is NO.

IF....
X = 17
then (X-3) = (17-3) = 14
(any prime)(14) will be EVEN, so the answer to the question is NO.

This pattern continues on; the answer to the question is ALWAYS NO.
Fact 1 is SUFFICIENT

Fact 2: Y < 3

Since Y is PRIME, we know that Y MUST be 2. X can be ANY PRIME number....

IF....
Y = 2 and X = ANY PRIME
then (X-3) = an integer
(2)(any integer) will be EVEN, so the answer to the question is ALWAYS NO.
Fact 2 is SUFFICIENT

Final Answer:

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

Hi Rich,

So is this question telling me that Prime numbers cannot be -ve numbers??

Is that also true for the GMAT

That's true in all of math, GMAT or otherwise - prime numbers are never negative. The smallest prime is 2.

Hi IanStewart,

Thanks a lot for that clarification....

Hi,
Maybe somebody can explain me, whi we can't take x=3 in the (2)? In this case it would be 2(3-3) = 0 => insufficient
Hence, the answer is A
Why it's not like that?

ZERO.

1. 0 is an integer.

2. 0 is an even integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even.

3. 0 is neither positive nor negative integer (the only one of this kind).

4. 0 is divisible by EVERY integer except 0 itself.

Check for more below threads:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread

Hope it helps.