with my own eyes, I would say that answer is A
algebraically, well...
statement 1 says that x > y but still <90°
the shape of the sinus curve under such conditions shows that sin(x) > sin(y)
we also know that sin=opposed side/hypotenuse (for a rectangular triangle at least) i.e. opposed side = sinus * hypothenuse
we then have opposed side = sin(x)*QP
and opposed side = sin(y)*SR
in our case, opposed side from angle x is equal to opposed side from angle y
therefore sin(x)*QP = sin(y)*SR
i.e. QP/SR = sin(y) / sin(x) < 1
i.e. QP<SR
statement 2 says that x+y>90, but you just dont know if x>y or y>x therefore it is insufficient to conclude
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Source: Beat The GMAT — Data Sufficiency |
here's a way of thinking about it if you don't know trigonometry.
statement (1)
since angle X is bigger than angle Y, it follows that segment PQ is steeper (i.e., has a greater slope) than segment RS.
imagine drawing perpendiculars (which in this diagram would be vertical lines) down from P and S, and considering the right triangles thereby formed.
the vertical legs of those right triangles would have the same length, because they're drawn between the same parallel lines.
the horizontal leg of the triangle with hypotenuse PQ would be shorter, though, because the slope (= rise/run) is greater. since "rise" is identical, as just mentioned, the fact that (rise/run) is greater means that "run" must be smaller.
because the vertical legs have the same length and the horizontal leg of the left-hand triangle is shorter, it follows that the left-hand hypotenuse (i.e., PQ) is shorter.
sufficient.
(2)
this statement is symmetric in x and y, meaning that you can switch x and y without consequence.
consider two cases in which this happens: say, x = 40 and y = 60, and then x = 60 and y = 40.
in the latter case, the reasoning is the same as for statement (1); in the former case, it's the opposite, and PQ is now longer.
insufficient.
answer = a
statement (1)
since angle X is bigger than angle Y, it follows that segment PQ is steeper (i.e., has a greater slope) than segment RS.
imagine drawing perpendiculars (which in this diagram would be vertical lines) down from P and S, and considering the right triangles thereby formed.
the vertical legs of those right triangles would have the same length, because they're drawn between the same parallel lines.
the horizontal leg of the triangle with hypotenuse PQ would be shorter, though, because the slope (= rise/run) is greater. since "rise" is identical, as just mentioned, the fact that (rise/run) is greater means that "run" must be smaller.
because the vertical legs have the same length and the horizontal leg of the left-hand triangle is shorter, it follows that the left-hand hypotenuse (i.e., PQ) is shorter.
sufficient.
(2)
this statement is symmetric in x and y, meaning that you can switch x and y without consequence.
consider two cases in which this happens: say, x = 40 and y = 60, and then x = 60 and y = 40.
in the latter case, the reasoning is the same as for statement (1); in the former case, it's the opposite, and PQ is now longer.
insufficient.
answer = a
Ron has been teaching various standardized tests for 20 years.
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Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi
--
Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.
Yves Saint-Laurent
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Learn more about ron
Ron,
Is it then safe to say that if the slope of a side is greater than another side, then the side with the greater slope is longer?
Is it then safe to say that if the slope of a side is greater than another side, then the side with the greater slope is longer?
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I'm sure Ron meant- say x=40 and y=50 (not 60), and then, say x = 50 and y = 40 (since x+y = 90). The analysis is perfect otherwise. For statement 1), you could imagine the line segments PQ and SR to be ladders, and make it a real-world problem: of course, if y is smaller than x, then SR should be longer than PQ.lunarpower wrote: (2)
consider two cases in which this happens: say, x = 40 and y = 60, and then x = 60 and y = 40.
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