hatemnag wrote:
Hi experts
I can not prove that yes or no for statement 2
Actually, I solved by tuition not by evidence.
Please help.
paidlukkha wrote:
going by the logic that GMAT answers specially in DS dont contradict with statements
in this case, can I say that since S1 was suff to answer, 100% S2 will be suff - we will have definite yes or no & since they don't contradict it is a def NO?
Dear
hatemnag &
paidlukkha,
I'm happy to respond.
I don't know whether you saw the solution by the brilliant
VeritasPrepKarishma, but I'm happy to talk about this problem as well.
First of all, think about the prompt:
Lines k and l intersect in the coordinate plane at point (3, –2). Is the largest angle formed at the intersection between these two lines greater than 90°?If two lines intersect at, say, 85°, then the other angle, the larger angle between the lines is 95°. The only way the largest angle would not be greater than 90° is if the lines are perpendicular. Essentially, this question is equivalent to "
are the two lines not perpendicular?" In a DS sense, that's equivalent to the question "
are the two lines perpendicular?" That's the question we are trying to answer.
S1:Lines k and l have positive y-axis intercepts.Both negative sloped lines, obviously not perpendicular. Sufficient.
S2: The distance between the y-axis intercepts of lines k and l is 5. The rule for DS is that we have to ignore entirely the information in S1 and evaluate whether this statement by itself, is sufficient
Call the point (3, –2) the point A, and let B & C be, respectively, the upper and lower y-intercept. We know BC has a length of 5. IF BC is way up or way down the y-axis, at +100 or -100, then the angle at A will be acute, much less than 90°. So we know it's possible for the angle to be less than 90°.
How big can we make the angle at A? The biggest would be when the midpoint of BC is as close to A as possible. This would be when the midpoint of BC is at -2, so that B is at (0, 0.5) and C is at (0, -4.5)
Attachment:
triangle ABC in x-y plane.pdf [12.53 KiB]
Downloaded 77 times
The distance from A to the y-axis is, of course 3. If from the midpoint (0, -2) the segment BC went up 3 and down 3, for a total length of six, then we would have a 45-45-90 triangle, giving us a right angle at A. Instead, the segment BC has a length of only 5, so even in this optimal triangle, the angle at A is less than 90°
Thus, the angle at A is never a right angle, and S2 is perpendicular.
Does all 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)