Foundations of GMAT Math 5th Edition - Geometry - Drill Q 31

[Orhan SerkanÖ123]

Drill question 31 in geometry section can be solved in two ways.
One of them is to see isosceles by finding angle C and sum all the lenght of all edges.

However, the other way is to draw a line that touches the edge BC so that there would be a new right triangle. Let say the point P at which the new height intersect BC, and we now have APB right triangle, which has 30-60-90 angles.

From 30-60-90 angle relation, BP= 2√3 and AP=2.
In the right triangle APC, PC=√5

Since BP+PC=BC, BC= 2√3+√5, which is not equal to 4.

Therefore, I think that lengths of edges do not correspond to angles of edges.

Thanks,

[RonPurewal]

hi,
per the forum rules, please post the entire text of the problem as originally presented. (if there are answer choices, please provide those as well.)

[RonPurewal]

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thanks.

[Orhan SerkanÖ123]

I am new in the forum, so sorry for the mistake.

I've added screen shots of the question and the answer.

Question:


Answer:

[RonPurewal]

thanks for the screen shots.

oh dear, this is a big big problem. specifically, the triangle given in this question is ... well ... impossible.

i.e., you can have EITHER the 30º/75º/75º angles OR the given side lengths. but you can't have both.

this is a huge mistake, and i don't see it on the errata page yet (you can google "manhattan gmat guide errata"). so i'll submit it.

[RonPurewal]

----- YOU DON'T NEED TO KNOW ANYTHING IN THIS POST FOR THE EXAM -----

you can use trigonometry (which you don't need for this exam) to show that the given sides are incompatible with the given angles.

if the angles and the "4" are correct, then the bottom side is 2 times (4 cos 75º), which works out to about 2.07. incidentally, this is nowhere close to the labeled value of 3. (i suppose that makes the situation even worse--yikes)

if the angles and the "3" are correct, then the side labeled "4" should actually be 1.5/(cos 75º), which works out to about 5.8.

finally, if the sides are all correct, then the angle marked 75º should actually be arccos(1.5/4), which is about 68º (thus making angle B about 44º).

----- again, YOU DON'T NEED TO KNOW ANYTHING IN THIS POST FOR THE EXAM -----

[RonPurewal]

...and thank you for catching that mistake!

[Orhan SerkanÖ123]

You're welcome. Many thanks for your confirmation

[RonPurewal]

no problem!