MGMAT CAT 5 question 30 DS is x prime? 3x + 5 < x +11

[AnuGhai]

If 3x + 5 < x + 11, is x prime?

(1) the sum of x and y is even

(2) xy is odd

Just checking to see of the question stem should have a "y" in it...somewhere. Both answer choices give us a y, and the y does not appear in the stem...or is that just a trick in the question?

[StaceyKoprince]

The question as written in the database is:

If x and y are positive integers and 3x + 5 < x + 11, is x a prime number?

(1) The sum of x and y is even.

(2) The product of x and y is odd.

Can you go check your test again? If it indeed is not showing all of the text of the question, please send an email to techsupport@manhattangmat.com and let them know about the problem. Please also ask them to forward to me and Chris. Thanks!

[AnuGhai]

If x and y are positive integers and 3x + 5 < x + 11, is x a prime number?

Sorry, the full text is as Stacey posted. I just didn't understand the answer given.

[StaceyKoprince]

x, y = + int.
3x + 5 < x + 11
is x prime?

First, simplify the info provided in the problem.
3x + 5 < x + 11
2x < 6
x < 3

So x is less than 3 and x is also a positive integer. The only two positive integers less than 3 are 1 and 2. 1 is not prime; 2 is prime. Can I tell which one x is? The explanation rephrases as "is x 2?" which is basically the same type of yes/no question. If I can answer that question yes, I know x is prime. If I can answer that question no, I know x is not prime (because if x is not 2, it must be 1).

(1) the sum of x and y is even.
even + even = even, eg, if x=2 and y=4, the sum is even and x is prime
odd + odd = even, eg, if x=1 and y=3, the sum is even and x is not prime
Both x and y could be either even or odd, so this statement is not sufficient.

(2) x*y=odd.
only odd*odd = odd. Anything * even = even. So both x and y must be odd. If x is odd, it must be 1, not 2. So x is not a prime number, and that's a definitive answer to the question. (Remember that definitive "no" is just as sufficient as a definitive "yes." The only not-sufficient answer to a yes/no question is maybe or sometimes yes/sometimes no.)