If x and y are prime numbers, is y(x-3) odd?
GMAT Premier 2011
Pages: 457 and 458
For the data sufficiency problem "If x and y are prime numbers, is y(x-3) odd?" on page 457, explained answer on page 458 is D (Each statement alone is sufficient.)
2 statements are:
1. x > 10
2. y < 3
However, I feel that answer should be A (only 1 is sufficient).
Statement 2 is not sufficient, because:
1. If we pick y = 2 and x = 2, equation yields 2(-1) = -2 => Even number2. If we pick y = 1 and x = 2, equation yields 1(-1) = -1 => Odd number
Thus depending on what we pick, the result can be even or odd...hence we cannot conclusively say if y(x-3) will be odd or not based on statement 2.
May you please advise if I am not approaching this correctly?
Thank you for your help in advance!
Note that we are told that both x and y are prime numbers
, also note that 1 is not a prime number
Now, 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.
For more check Number Theory chapter of Math Book: math-number-theory-88376.html
Hope it helps.
I have a question, Can we disregard -ve numbers here for part 2. (y<3) ?