Is quadrilateral ABCD a parallelogram?

Question

(1) Area of triangle ABC is equal to area of triangle ACD
(2) AD=DC

BrushMyQuant · Answer

In order to prove that a quadrilateral is a parallelogram at least one of the following should be true:--
1. Two pairs of opposite sides are equal or parallel
2. One pair of opposite side is equal and parallel
3. Both the pairs of opposites angles are equal
4. Diagonals bisect each other

Considering the problem
STAT1 : Area of Triangle ABC = Area of Triangle ACD
From this we just know that there is a diagonal AC and on it's two sides there are two triangles which have same area. IF we would have given that the base of these two triangles are equal and parallel then we could prove that the quadrilateral is a parallelogram. But not we can't.

STAT2: It just tells us that two adjacent are equal. Which is of no use to us.

Combining these two also doesn't give us any concrete information to prove that the figure is a parallelogram.

So, INSUFFICIENT
Hence, Answer will be E

Hope it helps!

DangerPenguin · Answer

We just need to find out if ABCD has 2 sets of parallel sides since we know that it is a quadrilateral.

statement 1: not sufficient
This is true for a square, which is a parallelogram, and also a trapezoid, which is not a parallelogram.

statement 2: not sufficient
No info on if ABCD has 2 sets of parallel sides

Together, ABCD must be either a square or a rhombus, both of which are paralellograms.

Answer C!

Bunuel · Answer

Notice that the correct answer is E, not C. Try again.

testcracker · Answer

hi Still the quadrilateral can be a isosceles trapezoid so the answer is E thanks

siddharth19 · Answer

hi , from st(2) , if adjacent sides are equal , can't we say its not a parallelogram , as in a parallelogram oppo. sides are equal

Veljkoc94 · Answer

Just draw two triangles merged into a figure like boomerang and there are 2 triangles with same area and AD=DC sides... and a parallelogram. Thus, answer is E, its too obvious that C is a trap answer.

GDT · Answer

Hi  VeritasKarishma

Can you pls explain this question

Thanks in advance!

KarishmaB · Answer

For DS geometry problems, I like to draw a diagram to see if I am forced to make it a particular way. For this question, even if I take info from both statements, I need not get a parallelogram. If area of two triangles is the same, it just means that base*height is the same. So I assume base as 6 and height as 4 of one triangle and see whether I need to make it into a parallelogram if the base and height of the other triangle is 2 and 12. Screenshot 2020-05-07 at 15.30.50.png I see that I can adjust AB (which I assume to be 12) to give height of 2. In this case, the quad is not a parallelogram. So the given info is not sufficient. Answer (E)

ayush19 · Answer

Hi,

isn't statement 2 in itself sufficient to answer the prompt? Since it says that AD=DC (adjacent sides are equal), which is not true for a parallelogram.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Is quadrilateral ABCD a parallelogram?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards