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605-655 (Medium)|   Geometry|      
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siddharthvaid
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In the quadrilateral ABCD, side AD is parallel to side BC. Updated on: 07 Sep 2013, 09:19
Originally posted by siddharthvaid on 25 Aug 2011, 13:42.
Last edited by Bunuel on 07 Sep 2013, 09:19, edited 2 times in total.
Renamed the topic, edited the question, added the OA and moved to DS forum.
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

45% (medium)

Question Stats:

56% (01:17) correct 44% (01:12) wrong based on 546 sessions

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In the quadrilateral ABCD, side AD is parallel to side BC. Is ABCD a parallelogram?

(1) AB = CD
(2) AD = BC
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B
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ConnectTheDots
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In the quadrilateral ABCD, side AD is parallel to side BC. 07 Sep 2013, 05:41
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B is sufficient. Please refer the diagram.
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Parallelogram.jpg
Parallelogram.jpg [ 22.64 KiB | Viewed 52052 times ]

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shilpiruchi
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In the quadrilateral ABCD, side AD is parallel to side BC. 25 Aug 2011, 14:21
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siddharthvaid
Q) In Quadrilateral ABCD, side AD is parallel to side BC. Is ABCD a parallelogram?

a) AB=CD
b) AD=BC

Data sufficiency?
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Are you sure your ans is correct?

I think B (Statement B alone) should be correct as it always gives an ans Yes while statement A gives sometimes yes sometimes no.

cauz-

If one pair of opposite sides of a quadrilateral is congruent and parallel, then the quadrilateral is a parallelogram.
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In the quadrilateral ABCD, side AD is parallel to side BC. 07 Sep 2013, 05:30
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I've found the same answer in Kaplan CAT 5. My answer is E, but the OA is B. I don't understand. What is the difference between answer A and B (there isn't any picture, so for example i can name the same side as AB or BC). am i wrong?
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lucasITA
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In the quadrilateral ABCD, side AD is parallel to side BC. 07 Sep 2013, 06:01
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ConnectTheDots
B is sufficient. Please refer the diagram.
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but is a correct hypothesis that vertex A is the upper vertex on the left?!
can't i chose vertex A as the lower vertex on the left? :?: :?:
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bleajor
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In the quadrilateral ABCD, side AD is parallel to side BC. 04 Feb 2015, 07:24
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In the quadrilateral ABCD, side AD is parallel to side BC. Is ABCD a parallelogram?

(1) AB = CD
(2) AD = BC
-------------------------

If AD = BC & AD is parallel to side BC >> I think ABCD could be a square or a parallelogram .

So, I pick E.

--------------------------
Anyone can explain why B is OA.
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In the quadrilateral ABCD, side AD is parallel to side BC. 04 Feb 2015, 09:11
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bleajor
In the quadrilateral ABCD, side AD is parallel to side BC. Is ABCD a parallelogram?

(1) AB = CD
(2) AD = BC
-------------------------

If AD = BC & AD is parallel to side BC >> I think ABCD could be a square or a parallelogram .

So, I pick E.

--------------------------
Anyone can explain why B is OA.
Show more

A square is a special type of a parallelogram, so if a figure is a square, then it's also a parallelogram (but not vise-versa).

Check Polygons chapter of our math book.

Hope it helps.
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In the quadrilateral ABCD, side AD is parallel to side BC. 11 Aug 2015, 14:00
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siddharthvaid
In the quadrilateral ABCD, side AD is parallel to side BC. Is ABCD a parallelogram?

(1) AB = CD
(2) AD = BC
Show more

Is there a systematic approach for such questions? Do you directly start drawing if the question says AD is parallel to BC and then go on from there with Statement 1, Statement 2 etc?
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In the quadrilateral ABCD, side AD is parallel to side BC. 11 Aug 2015, 14:06
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reto
siddharthvaid
In the quadrilateral ABCD, side AD is parallel to side BC. Is ABCD a parallelogram?

(1) AB = CD
(2) AD = BC

Is there a systematic approach for such questions? Do you directly start drawing if the question says AD is parallel to BC and then go on from there with Statement 1, Statement 2 etc?
Show more

You should remember that for a quadrilateral to be a parallelogram , you need to have either 1 pair of equal and parallel sides ((the equal and parallel sides should refer to the SAME pair) or have 2 pairs of parallel sides (they indirectly mean the same thing).

Once you realise this, you see clearly that statement 1 with AD||BC , does not help us in any way.

Statement 2 with AD||BC does give us a "yes" answer on the basis that any quadrilateral with 1 pair of equal and parallel sides (the equal and parallel sides should refer to the SAME pair). This statement is thus sufficient.
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In the quadrilateral ABCD, side AD is parallel to side BC. 03 Nov 2016, 10:23
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SW4
In the quadrilateral ABCD, side AD is parallel to side BC. Is ABCD a parallelogram?

(1) AB = CD
(2) AD = BC
Show more

Statement 1:

Can be trapezoid or parallelogram

Insufficient

Statement 1:

Must be a parallelogram

Sufficient

B


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In the quadrilateral ABCD, side AD is parallel to side BC. 03 Nov 2016, 11:54
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One of the properties of a parallelogram is one set of parallel lines that are equal. B
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In the quadrilateral ABCD, side AD is parallel to side BC. 22 Jul 2023, 14:49
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