Calculator for a DS solution?

Question

Hi! I'll illustrate my confusion by using a DS question:

Are all angles of triangle ABC smaller than 90 degrees?

(1) 2AB=3BC=4AC

(2) AC2+AB2>BC2

So the first given is sufficient, because if we have the ratio of all of the sides of a triangle, then we can find out all of the angles. However, we would need a calculator to that with a bit of trig right? This question is from the gmatclub tests, and it says 1) is sufficient. I just want to make sure that these DS questions are asking merely if the solution is attainable from the given, with or without a calculator, OR if it is specifically attainable without a calculator? I hope that makes sense. Thanks in advance!

KapTeacherEli · Answer

you've got it. DS questions care only that there is a single solution. Whether that solution is attainable through simple arithmetic or through complex trigonometry is irrelevant. In fact, a few concepts, such as standard deviation, will  never  be calculable by hand when they appear!

dandarth1 · Answer

Thanks!! You are like an angel from the gmat heavens

Archit143 · Answer

HI 
I marked D as the answer for this one.
Because we know that for right angle triangle hypotenuse is AC (say C)
C^2 = a^2 + b^2
but when angle is greater than 90:
C^2>a^2 +b^2

So cant we say that if it is given C^2<a^2+b^2, angles in the triangle are less than 90 deg........

KarishmaB · Answer

How do you know which side is the hypotenuse? Can you say that BC must be the hypotenuse?

Say, think of the triangle 3-4-5. Perhaps AB = 5, BC = 4 and AC = 3
 AC^2+AB^2>BC^2  holds for these values. So ABC could be a right angle triangle and hence all angles will not be less than 90.

Say, if sides are AB = 4.5, BC = 4 and AC = 3
 AC^2+AB^2>BC^2  still holds but all angles in this case will be less than 90.

So statement 2 is not sufficient alone.

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Calculator for a DS solution?

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