Trapezoid-Quadrilateral

[dell2]

Please explain both statements. thanks.

[MBA.Aspirant]

Is the answer to this E?

To calculate the area of the trapezoid we need the 2 bases and a height. We only have one base given.

Statement 1 tells you that angle A = 120 degrees and that's it. The trapezoid isn't isosceles (it isn't shown/given that AC=BD) so you can't assume angle A and B are equal or that A and C are supplementary.

Statement 2 tells you the perimeter = 36, i.e. sum of sides BD and DC = 36 - ( 6+8) = 22. This doesn't give us the 2nd base or the height.

So we can't calculate the area with the info. given.

[dell2]

OA D

[MBA.Aspirant]

Sorry I just noticed that the angles are equal. Angle A =B and C=D. This means that this is an isosceles trapezoid, and that AC=BD=8.

Using the info. in statement 2 you can get the 2nd base. 36 - (8+6+8) = 14

but I don't know how to get the height or how to prove using statement 1. So I'll leave that to the experts.

[Frankenstein]

Hi,
Trust me this is not a GMAT question. It is really a waste of time doing from such sources.
By marking equal angles with similar notations , he means to say that angle A = angle B and C=D
But, don't worry such weird notations will not given in GMAT.
From(1): Drop a perpendicular(AE) from A to CD. As angle A = 120, C = 180-120 =60
sine 60 = AE/8. So, AE = 4(sqrt3)
Similarly CE = 4
So, CD = AB + 2(CE) = 6+4+4 = 14
Area is (1/2)*(4sqrt3)(6+14)
Sufficient
From(2): perimeter is AB+BC+CD+DA = 36
Drop a perpendicular(AE) from A to CD.
CD = AB + 2(CE) = 6+2x
So, 6+8+(6+2x)+8 = 36 =>2x = 8 =>x=4
From this we can calculate AE from right triangle ACE as sqrt(8^2 - 4^2)
So, area is (1/2)(AE)(CD)
Sufficient

Hence, D

P.S: I have solved this only because I don't want to be harsh. Please start doing from authentic sources. Don't use any CAT(Indian MBA test) materials to prepare for GMAT

[MBA.Aspirant]

Hi,
Trust me this is not a GMAT question. It is really a waste of time doing from such sources.
By marking equal angles with similar notations , he means to say that angle A = angle B and C=D
But, don't worry such weird notations will not given in GMAT.
From(1): Drop a perpendicular(AE) from A to CD. As angle A = 120, C = 180-120 =60
sine 60 = AE/8. So, AE = 4(sqrt3)
Similarly CE = 4
So, CD = AB + 2(CE) = 6+4+4 = 14
Area is (1/2)*(4sqrt3)(6+14)
Sufficient
From(2): perimeter is AB+BC+CD+DA = 36
Drop a perpendicular(AE) from A to CD.
CD = AB + 2(CE) = 6+2x
So, 6+8+(6+2x)+8 = 36 =>2x = 8 =>x=4
From this we can calculate AE from right triangle ACE as sqrt(8^2 - 4^2)
So, area is (1/2)(AE)(CD)
Sufficient

Hence, D

P.S: I have solved this only because I don't want to be harsh. Please start doing from authentic sources. Don't use any CAT(Indian MBA test) materials to prepare for GMAT

Cool. I was about to drop the perpendicular and calculate with the 30:60:90.
Just one thing: in the 2nd statement, you can easily get CD cause the perimeter is given, and we know that AC=BD=8 since this is an isosceles trapezoid.
So after you get the height it becomes: 6+ 14/2 * 4 root 3

[Frankenstein]

Just one thing: in the 2nd statement, you can easily get CD cause the perimeter is given, and we know that AC=BD=8 since this is an isosceles trapezoid.
So after you get the height it becomes: 6+ 14/2 * 4 root 3

True. But to calculate height, I need to again give drop perpendicular(in order to calculate height from that right triangle) and mark the base of right triangle as (14-6)/2 right? So, I have used that notation earlier itself. So, that I don't to write this at the end.

One more thing, if the angles were not given as equal, we can still get the answer by using both statements, which means the answer will be C in that case and not E.

[MBA.Aspirant]

The way I was gonna do it is drop a perpendicular from C to the extension of AB, having AC as the hypotenues. so we get CE for example = 4 root 3 and it's the height, and we already got the 2 bases.

Now that you illustrated that you can drop a perpendicular from the inside and add the base of the triangle you form twice + base 1, you can easily get the 2nd base. As a matter of fact you won't need to use the statements at all

[Frankenstein]

Hi,
I am not sure if you have understood my point of saying C would be the answer if we didn't know about angles being equal. I was referring to your first post.

Is the answer to this E?

To calculate the area of the trapezoid we need the 2 bases and a height. We only have one base given.

Statement 1 tells you that angle A = 120 degrees and that's it. The trapezoid isn't isosceles (it isn't shown/given that AC=BD) so you can't assume angle A and B are equal or that A and C are supplementary.

Statement 2 tells you the perimeter = 36, i.e. sum of sides BD and DC = 36 - ( 6+8) = 22. This doesn't give us the 2nd base or the height.

So we can't calculate the area with the info. given.

For the above quote the answer would be C, not E.

As a matter of fact you won't need to use the statements at all

Can you explain what you mean by this quote.

[GMATGuruNY]

Please explain both statements. thanks.

The formula for the area of trapezoid is (b1 + b2)/2 * h.
In the given trapezoid, b1 = AB and b2 = CD.

Draw the perpendiculars:

Because angle CAB=angle ABD, angle ACD=angle BDC, and the two perpendiculars are equal, the two triangles in the figure above are congruent (all corresponding angles are equal, as are all corresponding sides).
Thus, if we know the value of one angle in one of the triangles, we can determine the values of x and h, allowing us to calculate the area.
If we know the value of x, we can determine the value of h, allowing us to calculate the area.

Statement 1: angle CAB = 120.
Thus, the angles in the triangles must be 30-60-90:

Sufficient.

Statement 2: p=36.
Thus, x=4:

Sufficient.

The correct answer is D.

[MBA.Aspirant]

Statement 1: angle CAB = 120.
Thus, the angles in the triangles must be 30-60-90:

^ That's what I missed. To prove the tri is 30:60:90

[dell2]

Thanks Everyone

Frankenstein: What are the authentic sources for preparing gmat ? OG's & MGMAT ?
This question is from the book given to me by my institute.Sorry

[dell2]

Just Curious How did you find out that question is from INDIAN CAT EXAM ? (its not written in the book also)

[Frankenstein]

Frankenstein: What are the authentic sources for preparing gmat ? OG's & MGMAT ?
This question is from the book given to me by my institute.Sorry

By authentic sources, I mean OG,GMATPrep,MGMAT,Knewton,Veritas,Kaplan,PR..so on. I am not convinced with the material of local institutes. They consider GMAT as just another MBA entrance test and do not follow the norms. It is as if the more mysterious a question is framed, the tougher the question. GMAT never does that.GMAT Questions are always crystal clear. You will hardly see an ambiguous question. Do you know how many questions are incorrect in the real CAT(Indian MBA) test. I could see at least 3 incorrect questions out of 20 Quant questions in each of the tests of last two years. There is no way such things can be normalized as they claim. It is easy to say when you are the one who makes the rules. You can be assured that you won't see bad questions on GMAT. The reason I claim the above sources are authentic is because they do a lot of revision of questions and strive to make them error-free and as close to real questions as possible. Even after all this, if you see any dubious question, they will soon revise it make amends and upload the errata and you can always discuss dubious questions with the experts here.

Just Curious How did you find out that question is from INDIAN CAT EXAM ? (its not written in the book also)

I did not mean to say this is from one of the previous CAT papers. I meant to suggest you not to prepare from CAT material offered by local institutes for your GMAT prep.

[dell2]

Thanks Frankenstein Will Keep That in mind Thx AGAIN.