I got the following DS question (Angle Angler):

In the rectangular coordinate system, lines m and n cross at the origin. Is line m perpendicular to line n?

(1) m has a slope of -1 and n passes through the point (-a, -a).

(2) If the slope of m is x and the slope of n is y, then -xy = 1.

--------------------

I believe that the right answer is B (statement 2 is sufficient, statement is not), but the answer in the system is D (each statement alone is sufficient). It seems that (1) is insufficient since it isn't stated that a is not zero. If a is zero, then we have no new information on the slope of n.

-Nadav

Hmmm, I think you are on to something.

If a is positive (the likely assumption--dangerous): (-a,-a) is in Quadrant III and n has slope of 1.
If a is negative (also possible since not specified): (-a,-a) is in Quadrant I and n has slope of 1.
But you are right that if a = 0, then (-a,-a) is the origin, and is thus not new information.

We'll pass that along to the editors for review. Thanks again.

_________________
Emily Sledge
Instructor
ManhattanGMAT

How about approaching it in this manner.

given the line n passes through (-a, -a ) and the origin ( 0,0 )
slope of a line passing through 2 points is given by (y2-y1)/ (x2-x1)

there fore ( 0-(-a) ) / 0-(-a)) = 1
slope of m =-1 and slope of n = 1 there for we can say that the lines are perpendicular...

hence answr choice D

would this be ok?

Since you assumed a is not zero. You can't calculate the slope of the line passing between two points, when the two points are the same point :)

Well, since 0 is not a negative or a positive number, "a" can't be a negative number. I think this is what the GMAT people would be thinking to get the answer to be "d". Can a staff member yay or nay this logic?

A.) In the first statement, it says that N passes through (-A,-A) to get through the origin (0,0), if we calculate the slope of line N using these 2 points, we get: (-a-0)/(-a-0), thus, a slope of 1.
Remember, the slope of a perpendicular bisector is the negative reciprocal of the slope of the line it bisects. Thus, if the slope of N is 1, and the slope of M is -1, then M is the perpendicular bisector of N.

B.)If the slope of m is x and the slope of n is y, then -xy = 1.
When reciprocals of any two numbers are multipled together, the answer is always one. In this case, say the slope 'x' is 5. The slope of the perpendicular bisector 'y'will then be (-1/5). When these two slopes are muliplied together, we get
-1....But the condition says,
-xy=1, tPlugging in x adn y we get, -5*(-1/5)=1....BTW this will work for any real number (In this case, the slope is 1) since statements 'a and b' never contradict each other.
Proving again that M is the perpendicular bisector of N.
Hope this helps.

Please see Emily's response above. The question should really say that a is nonzero and we will try to get this updated. The usage of -a in statement 1 does not tell you definitively that a is non-zero. We we know that the line passes through 0,0. IF we also knew that a = 0, then the line would pass through (a,a) AND (-a, -a). That's because We are allowed to multiply 0 by negative 1. We just get the product 0.