first, since AB and DE are parallel angle x = angle z
so we know the two triangles are isosceles and also that they are similar since they share the same angles...
we can get one equation for refrence...
2x + y = 180

we need one more equation in terms of x and y to solve this

Statement 1)
AB = BC + 5

that gives infinite values for AB, BC and AC
also in does not add anything uselful in calculating the angles...
insufficient

Statement 2)
AB + BC = 10

that gives infinite values for AB, BC and AC
also in does not add anything uselful in calculating the angles...
insufficient

together
we can find the exact values of AB, BC, and AC...
still it doesnt prove that the triangle is right angle triangle or a equilateral one...
actually it doesnt add any info, other than for the fact that the triangle is isosceles, which we already know...
insufficient...
I would pick E

Hi Neeraj,
I thought that the measure of AB means the length of line segment AB.

But, is it that measure of AB is angle ACB (the angle opposite to the segment AB)?

ptm_30 wrote:Hi Neeraj,
I thought that the measure of AB means the length of line segment AB.

But, is it that measure of AB is angle ACB (the angle opposite to the segment AB)?

oh no not at all...
ur first thought is right...
AB means the length of line segment AB...
if they ever mention angle... they will always clear the ambiguity...
and certainly never would u find i a gmat question refering AB to the angle opposite segments AB...

Hope this helps...

HI! neerajkumar

I marked C first , I thought it as a simple one two variables , two equation Done,

But when i read your explanation i realized why they have said in the question that AB and DE are parallel to each other.

I would like to ask you one thing.

If we solve both the equation it gives the values of AB = 7.5 and BC = 2.5 and by the value of BC we can determine the value of AC as well because same angles in the triangle also have the same length of side opposite to it,
So AC = 2.5

Now three sides are 7.5 2.5 2.5

Which is not possible in a triangle B/c sum of two sides should always be greater than the IIIrd side.

Is this also a correct logic to discard both the equation and mark the answer as E.

goyalsau wrote:HI! neerajkumar

I marked C first , I thought it as a simple one two variables , two equation Done,

But when i read your explanation i realized why they have said in the question that AB and DE are parallel to each other.

I would like to ask you one thing.

If we solve both the equation it gives the values of AB = 7.5 and BC = 2.5 and by the value of BC we can determine the value of AC as well because same angles in the triangle also have the same length of side opposite to it,
So AC = 2.5

Now three sides are 7.5 2.5 2.5

Which is not possible in a triangle B/c sum of two sides should always be greater than the IIIrd side.

Is this also a correct logic to discard both the equation and mark the answer as E.

yup that is correct...
ur logic is right... with the values deduced... it is not possible to form a triangle...
but overall concept for this problem should be...
that since we cannot deduce anything abt the angles... the statements are insufficient...
as they could have well made the sides in accordance to the triangle prop...
but still with the given statements it would not have been possible to calculate the angles..

Hope i am making my point...

yup that is correct...
ur logic is right... with the values deduced... it is not possible to form a triangle...
but overall concept for this problem should be...
that since we cannot deduce anything abt the angles... the statements are insufficient...
as they could have well made the sides in accordance to the triangle prop...
but still with the given statements it would not have been possible to calculate the angles..

Hope i am making my point...

Hey Neeraj ,
Thanks for the quick reply, I want to know why you are putting the stress on Angles
As the problem wants us to define the measure of AB,

Hi there,

Let me show you a problem (I created) from my e-course, I guess you will like it because it "explores" the same kind of issue discussed here!

To motivate you, I´ll give the first material of my e-course (for free) to the person that solves correctly AND explains CLEARLY the problem below, ok? Please post the solutions here!!

(I´ll "judge" the clearness of the first 3 right answers that are posted. The winner is the right solution, from the 3, that makes me feel that it would be the best one to be explained to my own students...)

Good luck and regards,
Fábio.

fskilnik wrote:Hi there,

Let me show you a problem (I created) from my e-course, I guess you will like it because it "explores" the same kind of issue discussed here!

To motivate you, I´ll give the first material of my e-course (for free) to the person that solves correctly AND explains CLEARLY the problem below, ok? Please post the solutions here!!

(I´ll "judge" the clearness of the first 3 right answers that are posted. The winner is the right solution, from the 3, that makes me feel that it would be the best one to be explained to my own students...)

Good luck and regards,
Fábio.

since all the angle shown in triangle ACD are equal they are all equal to 60

With triangle ACD equilateral.. all sides will be the same measure... which will be 2 cms...
also angle CAE = 60 since its equal to other shown...

so we can deduce angle EAB = 60 ... (prop of straight line... )

now consider two triangles
triangle AEB and triangle DCB
these two triangles are similar... (angle B is common, angle D and angle EAB = 60... )

since they are similar...
their sides will be in proportion...

so AE/DC = AB/(DA +AB)

=> AE/2 = 6/(2+6)
=> AE/2 = 6/8
so AE=3/2

Pick D

I would like to add one thing over here only because you said that you have to explain it to your students.
Otherwise Neeraj Explanation was awesome,


For Two angles to be similar there must be 3 properties of triangles that must be same,

Angle B is common and Angle D is 60 and Angle EAB is also 60,
That means whatever the angle must be for Angle DCB and AEB
It must be same
So from AAA property of triangle, i . e. ( Angle , Angle, Angle )
Traingles are similar

Rest is the same,

Hello guys,

Sorry for the delay...

neerajkumar1_1 : EXCELLENT, really.

goyalsau: thank you for the addition, just one detail:

For Two angles to be similar there must be 3 properties of triangles that must be same

Ok, but this is necessary but not enough... (for instance: two respectively proport. sides and a common angle is not enough, the angle must be the one between the sides)

Anyway, I guess it is nice to give you BOTH the material, correct?

Please register on my website (www.GMATH.net) and as soon as your temporary password is changed I´ll be able to put the "Express Class #1" at your disposal, ok? If you have any difficulties, please write to me on the email given here.

Best Regards and thank you both for answering the problem!
Fábio.

ptm_30 wrote:In the figure, lines AB and DE are parallel.
What is the measure of AB ?
(1) AB - BC = 5
(2) AB + BC = 10




E

how come E? i still dont understand... do yo have its OE?