IanElliott wrote:
If x is an integer, is x even?
1.) x^2-y^2 = 0
2.) x^2+y^2 = 98
First of all, this strikes me as a little harder than 600-level, so I would estimate 700-level. I would be interested to hear other experts' estimations.
Statement #1This tells us
x^2 = y^2
x = +/-y
So, x and y have the same absolute value, could be same signed or opposite signed, and could be anything. We have no idea whether x is even or odd. This statement, alone and by itself, is
insufficient.
Statement #2We know x is an integer, but y doesn't have to be an integer. Remember, never make restrictions for things that aren't there -- that's a huge trap on all GMAT math. We know x is an integer, but y can be absolutely anything from the continuous infinity of the number line. For example
x = 1 y = sqrt(97)
x = 2 y = sqrt(94)
x = 3 y = sqrt(89)
x = 4 y = sqrt(82)
etc. etc.
So, x could be even or odd. This statement, alone and by itself, is
insufficient.
Combined statements Now, we know that both x & y must be integers, either equal, or positive/negative versions of each other.
Since, from statement #1, we know x^2 = y^2, we can sub this into statement #2:
x^2 + y^2 = 98
x^2 + x^2 = 98
2(x^2) = 98
x^2 = 49
x = +/-7
So, x could be positive or negative 7, but either one is an odd integer, and therefore we can give a clear "no" to the prompt question. Since we are able to give a definitive answer to the prompt question, that means the combined statement are
sufficient.
Answer =
CDoes this make sense?
Mike
_________________
Mike McGarry
Magoosh Test PrepEducation is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)